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AN INVESTIGATION OF THEWEAK LINKS IN THE SEISMIC

LOAD PATH OF UNREINFORCEI)MASONRY BUILDINGS

Kevin Thomas DohertyB.E. Hons (Civil) The University of Adelaide

A thesis submitted to the Faculty of Engineering at The University of Adelaide for theDegree of Doctor of Philosophy

Department of Civil and Environmental Engineering,

'n"'ïi;Äi[ff#""'o'

May 2000

Amendments To Thesis'An Investigation of the Weak Links in the Seismic Load Path of Unreinforced

Masonry Buildings'

A1 Replace on Page 53, Figure 4.2.1the text 'Rigid Frame Fixed to LaboratoryStrong Floor'' with 'Stationary Reference Datum'.

A2 Insert the following regression coefficients to the figures indicated

Figure4.4.3 R=0.999Figure 4.4.4 R=0.996Figure4.4.5 R=0.997Figure4.4.6 R=0.998Figure4.4.7 R=0.999Figure 4.4.8R=0.988

The regression coefficient R for the plots indicate a very good correlation of thetest data with a straight line.

A3 Insert the following paragraph as a new second paragraph on page 106:Under the assumption adopted of unreinforced masonry building systems havingstiff shear waìl and diaphragms the restrained translation of floors providing equalinput motions at the base on top of wall specimens is appropriate. This is not thecase however where floor diaphragms are flexible such as those constructed oftimber. Where this is the case the response of the floor diaphragm may govern thewall response with possibly quite different inputs at the base and top of the wall.Here a different dynamic stability problem than that being investigated in thecurrent research project may develop as it is possible that the walls will not crackat mid-height but will rock about their base after a crack forms at the base bed -

joint. Consequently these systems will have a much lower frequency thari thaf ofthe individual wall panel.

A4 Insert the following paragraph as a new third paragraph on page 219:The following points summarise the salient findings of the bending tests:. Confirmation of mid-height cracking and dynamic stability problems. Damping associated with the rocking walls was determined and generally

found to be of the order of 5Vo. Rayleigh Damping was found to bestapproximate the damping by combining both stiffness and mass proportionaldamping components. Increases in damping where found at high and lowfrequencies,

. The force displacement relationship for URM walls cracked at mid height wasassessed via push tests. Here the variation in the force displacementrelationship with wall slenderness, boundary conditions, precompression anddegradation due to rocking cycles where determined. A tri-linear approximationof the force displacement relationship was proposed to best approximate the truerelationship with empirically derived points to define the initial stiffness andplateau for various levels of wall degradation.

. The effective resonant frequency associated with the frequency for maximumdisplacement amplification was determined for URM walls cracked at mid

height for various slenderness, boundary conditions, precompression anddegradation due to rocking cycles.

Both displacement and acceleration responses were recorded for wallssubjected to transient, impulse and free vibration for later comparison withan al ytically derived response.

a

A5 Insert the following paragraph as the final paragraph on page220:Since the current research project has focussed on the one-way bending ofunreinforced masonry walls to now take jnto account the two-way bending actionwhich is often observed in seismic failure modes further research is required.Further as the assumption of the restrained translation of floors providing equalinput motions at the base on top of wall specimens appropriate for unreinforcedmasonry building systems having stiff shear wall and diaphragms has beenadopted fulther research is requiled to take into account flexible floor diaphragmsand shear walls.

A6 Typographical errors:page9,line l4page l6,1ine 6page 43,line 3page 47,line 8

page 49,line l1page 51, titlepage 221, I 0'r' CitationThroughout document

replace'earthquake' with'earthquakes'replace 'Masonry' with 'masonry'replace 'Section 0' with 'Section 2.4'replace 'Chapter 0' with 'Chaprter 4'replace 'f6"' with 'f¿'replace'Connection' with'Connections'replace'P.D.' with'D.P.'replace 'Nigel Priestly' with 'Nigel Pliestley'

A7 Insert the following paragraph as the final paragraph on page 47.Along with variations in local material properties the wide variety of testconfigurations discussed above may also be responsible for the wide scatter ofreported results. In particular in-plane tests are seen to be particularly sensitive tovariation in test configuration. Typically an average shear stress along the frictionplane is used to determine the friction coefficient. Accordingly where three highbrick plisms have been used for in plane testing the average shear stress and thusfrictional coefficient determined may be significantly effected by the endconditions and the moment induced at the friction plane. By adopting wallets withmultiple brick lengths the effect of the end conditions and the variation in normalstresses over the friction plane is reduced.

Insert the following paragraph as the final paragraph on page 54.The results of the in plane tests presented in Figures 4.4.6to 4.4.8 show a

regression coefficient of near unity thus indicating a very good linear correlation.Although in plane tests are always difficult due to the nature of pure shear tests thegood linear correlation indicates the assumption of a uniform shear stress for thederivation of the average friction coefficient is appropriate. In reality, due to theheight of the lead weights a lever arm and thus overturning moment exists so thata triangular stress profile is likely. Here the increase in frictional resistance at theend subject to the increased vertical stress is offset by the decrease at the opposite

end. As a result the average frictional resistance is unaffected and thus thederivation of the average frictional resistance remains appropriate.

Due to the length of the four brick wallets any end effects are also not apparent inthis test series.

A8 Add to Section 3.3.2last paragraph on page 42: Expected differential movementsassociated with tirne dependant behaviour of URM walls including concreteshrinkage or clay masonry expansion are generally in the order of around 3mm permeter run of wall. This is dependant on ¡nany factors as has been brieflydiscussed.

Tests associated with the time dependant movement of URM connectionscontaining DPC have recently been undertaken at the University of Newcastle,New South Wales, Australia. These tests have highlighted that under shrinkagecreep the frictional resistance force appears to be less than under dynamic loading.Consequently, the connections have been observed to slip undel the timedependant forces but are less likely to slip under dynamic loading.

A9 Insert the following paragraph as the final paragraph on page 49:It is widely recognised that vertical accelerations associatecl with seismic loadingmay effectively reduce the gravitational force at the friction interface of DPCconnections. As a result, the frictional resistance and thus the shear resistivecapacity of the connection is also reduced. The SAA Masonry Code takes thisreduction into account in the derivation of the frictional resistance in Equation3.4.1 by the application of the 0.9 factor applied to the gravitiational force. Theshear friction strength of the shear section under earthquake actions is thus definedby

Vt" = 0.9 G,c k,

410 Page 55, last paragraph replace 'Although these four specimen tests were carriedout at only one value of vertical compressive stress (0.164MPa) both in-plane andout-of-plane shaking were examined so that a total of eight tests were undertaken.''With 'Since each of the four standard and centered connection specimen wheretested at only one value of vertical compressive stress (0.164MPa) a total of eighttests were undertaken.'

Page 57, first paragraph replace 'The slip joint tests were performed over a rangeof three normal compression stresses being 0.04, 0.18 and 0.33 MPa conductedonly in the in-plane direction.'With 'The slip joint tests were performed over arange of three normal compression stresses being 0.04, 0.I 8 and 0.33 MPaconducted both in the in-plane and out-of-plane directions.'

All It is noted that the term 'overburden' used throughout the document may be morecommonly referred to as 'Pre-compression'.

Ã12 It is noted that in Section 6.3.1 the Characteristic bond strength should have beencalculated taking into account the specimen size. Also the standard deviation

values reported being based on three tests are relatively meaningless however areprovided as indicative for the quality of masonry.

413 Page 115 second paragraph replace 'The brickwork modulus was then calculatedfor each specimen as the chold modulus between 57o and 33Vo of the ultimatebrickwork compressive strength, f',n.' with 'The brickwork modulus was thencalculated for each specimen as the chord modulus associated with the linearportion of developed stress - strain curve.'

Page 115 last paragraph replace 'Table Ç3.2 presents a summary of the modulustest results ranging from 3,300 MPa to 16,000 MPa for the l lOmm specimens and6,'/00 MPa to 9,800 MPa for the 50mm specimens. While the results variedsignificantly the modulus values were typically found to be relatively high asexpected of modern masonry.' With 'Table 6.3.2 presents a summary of themodulus test results ranging from 4,000 MPa to 10,000 MPa for the l10mmspecimens and 5,000 MPa to 8,000 MPa for the 50mm specimens. It is suspectedthat the large apparent variation in the brickwork modulus is due toinconsistencies in the preparation of the five brick prisms. Here any slighteccentricity of construction causes non uniform loading of he prism so that themodulus calculation in some cases may have been slightly modified. The modulusresults attained however are provided typically the results are quite high as wouldbe expected of modern masonry.'

Replace Table 6.3.2Brickwork Modulus Test Results withTable 6.3.2 Brickwork Modulus Test Results

Specimen No. SpecimenThickness

ModulusE- (MPa)

Ultimate CompressiveLoad (N)

Masonry Compressi.veStrength, f'- (MPa)

l lOmm 330.000 13

2 l1Omm 10,000 332,000 13.1J l1Omm 5.000 336,000 13.34 I .l 0rnrn 4,000 333,000 13.1

5 llOmm 9,000 360,000 t4.26 llOmm 338,000 \3.41 l1Omm 9,000 313,000 t2.48 l10lnm 5,400 245,000 9.1t1 l1Omm 8,000 359,000 14.2t2 l1Omrn I 1,000 397,000 15.113 I lOlnm 397,000 15.1

AVERAGE 11Omm 7,700 339,000 13.4STANDARDDEVIATION

2,500 47,528 1.64

l0 50mm 8,000 307.000 26.114 50mm 5,000 303,000 26.3

AVERAGE 50mm 6.s00 305.000 26.5STANDARDDEVIATION

2,Loo 2,824 0.28

TABLE OF CONTENTS

TABLE OF CONTENTS ................

LIST OF FIGURES

LIST OF TABLES

ABSTRACT v

DECLARATION

ACKNOWLEDGMENT

1. INTRODUCTION.. 1

1.1. Study Objectives and Key Outcomes

l.2.Brief Outline of Report

2. EARTHQUAKES AND UNREINFORCED MASONRY

2. 1. lntroduction..........

2.2. Ausr: alian Seismicity ............

2.3.IJRM Building Stock in Australia

2.4. IJRM Vulnerability in Moderate Seismicity Regions .................2.4.l.Fa1ture Modes of URM Elements (Related to Seismic Load Path)...2.4.2.Review of the Seismic Performance of URM Buildings

ll

vr

xrl

..20

..212.4.3.Common URM Element Failure Modes2.4.4.'Weak Link' URM Failure Modes ........

3. 1. Introduction..........

3.2. General Friction Review3.2.1. Coulomb Friction Behaviour .........,

3.2.1.1. Classically Behaving Materials

.25

.29

2.5.'Capacity' Design for Improved Seismic Response

2.6 Overall Project Aim.....

3. DPC CONNECTIONS IN IJRM CONSTRUCTION..... ......34

3l32

34

3535

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37

TABLE OF CONTENTS

3.2.1.2. Polymers

3.3. LJRM Connection: Previous Research3.3.1. Plain-Masonry Joint Shear3.3.2. Serviceability Requirements ........3.3.3. Positive Anchorage.............3.3.4. Shea¡ Resistance of URM Connection Containing DPC Membrane....

3.4. Australian Code Provision: URM Connections ............

3.5.Implication of the Dynamic Friction Coefficient

3.6. Specific Research Focus

4. DYNAMIC SHEAR CAPACITY TF^STS ON TJRM CONNECTIONCONTAINING DAMP PROOF COTJRSE MEM8RAN8.............

4.1. Introduction...

4.2. Dynarmc Shear Tests..........4.2.1. Instrumentation4.2,2. D amp-Proof Course Membrane and Materials ................4.2.3 . Dynamic Test Methodolo gy....................4.2.4. DPC Connection Tests ................4.2.5. Slip Joint Connection Tests...................

4.3. Results Formulation and Data Analysis.......4.3.l.Data Filtering4 .3 .2. Dynamic Friction Coefficient Representative Calculation4.3.3. Theoretical Check

4.4.Dynamic Test Results .......4.4.l.DPC Connection Dynamic Test Results .........4.4.2. Slip Joint Connection Dynamic Test Results..4.4.3. Comparison of Dynamic with Static and Quasi-Static Test Results .....

4.5. Summary and Conclusion: Implication for Design.

5.2. Fundamentals of Out-of-Plane URM WalI Behaviour.......5. 2. I . Post-cracked Force-Disp lace ment (F-A) Relationship5.2.2. Boundary Condition Impact on Force-Displacement Relationship..5 .2.3 . Un-cracked Force-Displacement Relationship ................

5.2.3.L. Low Applied Overburden Force5.2.3.2. High Applied Overburden Force

5.3. Previous Research: Experimental Studies5.3.1. Static Tests .........5.3.2. Dynamic Tests...

5. STABILITY OF SIMPLY SUPPORTED IJRM lryALLS SUBJECTED TOTRANSIENT OUT.OF-PLANE FORCES. ............69

5.1. Introduction

37

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..............38'......,,.....41....,,,.......43

,...,...44

...,,...48

........50

........50

5758596l62626467

68

..70

.69

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TABLE OF CONTENTS

5.4. Critical Review of Current Analysis Methodologies5.4. 1 . Quasi-Static Analysis Procedures5 .4.2. Dynamic Analysis Procedures ...............

5.5. Specific Research Focus

6.2. General Test Set Up6.2.1. Test Specimens6.2.2.Test Rig.....6.2.3. Instrumentation .....

7. 1. Introduction............

.92

.97

6. OUT-OF.PLANE SHAKE TABLE TESTING OF SIMPLY SUPPORTED IJRMwaLLS .............102

101

102

111rt2lt4tt7tt7119tt912072r124737142143t45149153r53160

6. I . Introduction..........

........... 103

........... 103

...........105,.......... 109

6.3. Material Tests...6.3.1. Bond Wrench .........6.3.2. Modulus of Elasticity......6.3.3. Mortar Compressive Strength ...............

6.4. Out-of-Plane Testing of Simply Supported URM Walls.........6.4.l.Data Filter....6.4.2. U n-cracked Natural Frequency of Vibration

6.4.2.1. Comparison with Simple Elastic Beam Theory............6.4.3. Specimen Lateral Capacity Analysis6.4.4. Harmonic Excitation Tests6.4.5. Static Push Tests6.4.6. Free Vibration Tests .........

6.4.6.1. Non-linear Frequency - Mid-Height Displacement Relationship6.4.6.2. Non-linear Dynamic Force- Mid-Height Displacement Relationship.....6.4.6.3 . Non-linea¡ Damping-Frequency Relationship ................

6.4.7 . Transient Excitation Tests...6.4.7.1. Pulse Tests6.4.7 .2. Real Earthquake Excitation Tests

7. NON.LII\EAR TIME IIISTORY ANALYSIS D8V8LOPMENT.......................163

7 .2.Brief Description of Basic Linear SDOF System ............164

7.3. Negative Stiffness System Modelled as a Basic Linear SDOF System....... .........167

7.4. Rigid Simply Supported Object Rocking Response About Mid-height - DynamicEquation of Motion.. ......... 169

7.5. Semi-rigid URM Loadbea¡ing Wall Dynamic Equation of Motion .....................174

7.6. Modelling of Non-Linear Damping............ ... 180

7.7.Event Based Time-Stepping 4na1ysis................ ............... 183

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TABLE OF CONTENTS

7.8. Comparison of Experimental and Analytical Results ..... 184

8. LTNEARTSED DTSPLACEMENT-BASED (DB) ANALYSTS ...........188

8. I . Linearised DB Analysis Methodology.........

8.2. Proposed Linearised DB Analysis....8.2. I . Derivation of Characteristic SDOF' Substitute Stucture' Stiffness8.2.2. Simply Supported llRM Walls Modelled as a SDOF Oscillaror..

8.2.2.1. Modelled Displacement Capacity8.2.2.2. Modelled Damping Appropriate During Rocking Response

8.3. Effectiveness of the Linearised DB 4na1ysis...............8.3.1. Effective Resonant Frequency of Simply Supported URM Walls8.3.2. Linearised DB Analysis8.3.3. THA for Various Transient Excitation8.3.4. Comparison of Predictive Model Results...............

8.4. Conclusion ..205

9. STTMMARY AND CONCLUSIONS 218

REFERENCES

APPENDIX (A): Band Pass Filter Program FortranTT Code

APPENDIX (B): Representative DPC Connection Test Results

APPENDIX (D): Rigid F-Â - Various Boundary Conditions

APPENDIX (E): Material Test Resulrs

APPENDIX (F): Simply Supported Wall Test Results

APPENDIX (Itr): Non-linea¡ Time History Analysis Experimental Confirmation........339

188

190192194194195

195197199200202

APPENDIX (C): Representative Slip Joint Connecrion Test Results.............................251

221

241

247

25s

261

275

APPENDIX (G): Non-linear Time History Analysis ROV/MANRY - ForhanTT Code3lg

v

LIST OF FIGURES

Figure 1.1.1 Depiction of Damage During the 62 AD Earthquake in Pompeii... 2

Fi gure 2.2.1 Aastralia's Tectonic l-ocation................. 11

Figure 2.3 .1 lnternal Partition'Wall' Cornice' Connection Detail....... 18

Figure 2.3.2 URM Cavity Wall to Roof Truss Connection Detail (Inner L¡adbearing)...18

Figure 2.3.3 LJRM Cavity Wall to Roof Truss Connection Detail (Outer Loadbearing)..19

Figure 2.3.4 tlRM Wall to Inter Story Floor Slab DPC Connection Detail.......................19

Figure 2.3.5 IJRM Wall to Ground Floor Slab DPC Connection Detail............................19

Figure 2.4.1 Seismic [,oad Path for Unreinforced Masonry Building.... .........21

Figure 2.4.2Parapet Failure, Tighes Hill Campus, Newcastle Technical College ............22

Figure 2.4.3 Masonry Damage During 1997 labalpar, India Earthquake .......24

Figure 2.4.4Damage to URM Building, Tangshan, China, 1976........... .........29

Figure 3.1.1 Types of URM Connection Containing DPC Membranes.............................35

Figure 3.2.1Diagrammatic Representation: Frictional Resistance vs Applied Shear.......38

Figure 3.3.1 Shear Failure Hypothesis .41

Figure 3.3.2 Results of Typical Quasi-static on DPC Connection .47

Figure 4.2.1 Schematic URM Connection Containing DPC Dynamic Test Set-up ..........53

Figure 4.2.2Test Specimen Free Body Diagram: DPC Connection during Sliding.........55

Figure 4.2.3 Dynamic Test Set-up for Standa¡d/Centered DPC Connection.....................56

Figure 4.2.4Photograph of Standard DPC Connection Set up - In-plane.........................56

Figure 4.2.5 SchematicDiagram of Dynamic Test Set-up For Slip Joint Connection......57

Figure 4.3.1 Dominant Response Acceleration Frequencies................. ...........58

Figure 4.3.2Parabolic Sided Band Pass Filter - Bandwidth

Figure 4.3.3 Relative Connection Displacements

Figure 4.3.4 Response Acceleration above Slip Interface during Slipping.....

Figure 4.3.5 Hysteresis Behaviour after Slip showing Maximum Shear Resistive Force.60

.59

.60

.60

V1

LIST OF FIGURES

Figure 4.4.1 Graphical Results Summary for Standard DPC Connection Tests.......... ......62

Figure 4.4.2 Grapbical Results Summary for Centered DPC Connection Tests.......... ......63

Figure 4.4.3 Out-of-plane Slip Joint - I Layer of Standard Alcor .. 65

Figure 4.4.4 Out-of-plane Slip Joint Test - 2Layers of Standard Alcor............................65

Figure 4.4.5 Out-of-plane Slip Joint Test - 2Layers of Greased Galvanised Steel..........

Figure 4.4.6Ln-plane Slip Joint Test Results - I Layer of Standard Alcor.Figure 4.4.7 ln-plane Slip Joint Test Results -2Layers of Standa¡d AlcorFigure 4.4.8 In-plane Slip Joint Test Results -2[-ayers of Greased Galvanised Steel

Figure 5.1.1 Out-of-plane \ilall Failure during Loma Prieta Earthquake, 1989................70

Figure 5.2. 1 Real Semi-rigid Non-linear Force-Displacement Relationship

Figure 5 .2.2 P ost-cr acked Frequency-Displace ment Relationship ... ....

Figure 5.2.3Un-cracked F-À for Low Applied Overburden Sftess URM Wall 82

65

66

66

66

74

78

5.2.4Un-cracked F-À for High Applied Overburden Stress URM Wa11................83

5.3.1 Comparison of Yokel Study with Simple Rigid Body Theory......................85

5.3.2 Typical Lateral Failure of Brick V/all .......... .............85

5.3.3 Comparison of West etal1973 Tests with Simple Rigid Body Theory.......87

5.3.4 Top of Parapet Wall Disp. Correlated to Table Velocity and Acceleration..gl5.3.5 Top of Parapet Wall Disp. Conelated to Table Disp........... ........91

5.4.1 Quasi-Static Linear Elastic Design Methodology............... .........94

Fi gure 5 .4.2 Expenmental and An alytical F-AComp ari son

Figure 5.4.3 Compa¡ison of Analysis Predictions....... 99

Figure 6.2.1 Standard Three Hole Extruded Clay Brick (110mm)

Figure 6.2.2 Constuction of URM Wall Panels ...................

Figure 6.2.3Top 'Cornice' Support Connection

Figure 6.2.4 Out-of-plane Test Rig

Figure 6.2.5 Overburden Rig............

Figure 6.2.6Top Vertical Reaction - Overburden Test RigFigure 6.2.7 Out-of-plane Wall Test Instrumentation Locations ...................

Figure 6.3.1 Bond Wrench Apparatus Dimensions (1lOmm Brick)..............

Figure

Figure

Figure

Figure

Figure

Figure

Figure

96

104

105

106

707

107

108

109

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Figure 6.3.2 Bond Wrench Test Set Up

113

113

LIST OF FIGURES

Figure 6.3.3 Five Brick Prism at Ultimate Compressive Load 115

Figure 6.4.1Un-cracked Natural Frequency of Vibration 50mm Non-loadbearing Wall120

Figure 6.4.2 Cunent Available Analysis Comparison - 11Omm Thick WaII.......... .......I22

Figure 6.4.3 Current Available Analysis Comparison - 110mm Thick WaII.......... .......122

Figure 6.4.4Un-cracked Non-loadbearing URM Wall Ha¡monic Excitation Test ........129

Figure 6.4.5 Pre-cracked Non-loadbearing URM Wall Harmonic Excitation Test........ 130

Figure 6.4.6 Un-cracked Non-loadbearing URM Wall Harmonic Excitation Test ........134

Figure 6.4.7 Un-cracked Non-loadbearing URM V/all - First Cracking........................ 135

Figure 6.4.8 Un-cracked Non-loadbearing URM Wall - First Rocking 135

137Figure 6.4.9 Static Push Test

Figure 6.4.10 Comparison of 11Omm Specimen Static Push F-A with Analytical......... 139

Figure 6.4.11Comparison of 50mm Specimen Static Push F-A with Anal¡ical........... 140

Figure 6.4.12 Mid-height Rotation Joint Condition............ ........l4lFigure 6.4.13 Free Vibration Calculation............ ....143Figure 6.4.14 50mm Specimen Frequency vs Average Cycle Mid-Height Disp............144

Figure 6.4.15 110mm Specimen Frequency vs Average Cycle Mid-Height Disp. ........145

Figure 6.4.t6 50mm Wall Dynamic F-A Relationships (Various Overburden)..............147

Figure 6.4.17 110mm Wall Dynamic F-Â Relationship................ ................147

Figure 6.4.18 50mm Wall Compa¡ison of Static and Dynamic F-Â Relationships........ 148

Figure 6.4.19 110mm Wall Comparison of Static and Dynamic F-A Relationship........ 149

Figure 6.4.20 50mm Wall Non-linear ( vs Frequency (Various Overburden)............... 150

Figure 6.4.2150mm Wall Non-linear Cs¡,op/ùI" vs Frequency (Various Overburden) . 151

Figure 6.4.22 Non-loadbearing 11Omm Wall Non-linear ( vs Frequency............... ......I52

Figure 6.4.23 Nonloadbearing 50mm and 110mm'Wall Csr,oe/lVl, vs Frequency ........152

Figure 6.4.24 0.5H2 Normalized Gaussian Displacement Pulse Input....

Fi gure 6.4.25 Correspondin g Acce leration Input.

Figure 6.4.26 Effective Resonant Frequency (By Wall Thickness and Overburden) .... 159

r54154

Figure 7 .2.t Basic Linear SDOF System.............. 165

Figure 7.3.1 Negative Stiffness F-Â Relationship 167

Figure 7.4.1 Non-loadbearing Simply Supported Object at Rocking at Mid-height...... 171

Figure 7.5.1 Tri-tinear 'Semi-rigid' Non-linear F-Â Relationship Approximation........ 175

vlll

LIST OF FIGURES

Figure 7.5.2Tri-ltnear F-A Approximation for Va¡ious V/all Degradation

Figure 7.5.3 Analytical vs Experimental F-A- 11Omm, No Overburden...........

Figure 7.5.4 Analytical vs Experimental F-Â- 50mm, No Overburden...........

Figure 7.5.5 Analytical vs Experimental F-A- 50mm, 0.07MPa Overburden

Figure 7.5.6 Analytical vs Experimental F-Â- 50mm, 0.15MPa Overburden

Figure 7.6.1 Experimental I vs Rayleigh 6 - 50mm \ù/all, No Applied overburden.....

Figure 7 .6.2 lterative Damping 182

Figure 7.7.1 'Pseudo Static' F-A relationship 183

Figure 7.8.1 Comparison of Analytical and Experimental Pulse Test Results ............... 185

Figure 7.8.2 THA and Experimental Peak Pulse Mid-height Disp. Response................ 186

Figure 7.8.3 Comparison of Analytical and Experimental Earthquake Test Results ..... 187

Figure 8.1.1 Linearised DB Analysis for Elastic Perfectly Plastic System..................... 189

Figure 8.2.1 Typical Elastic Displacement Response Spectrum ................... 191

Figure 8.2.2Linearised DB Analysis Characteristic Stiffness, IÇ6

176

178

179

179

779

181

193

251

252

Figure 8.3.1Gaussian Pulse: 3.3m Tall, 110mm Thick, Moderate Degradation THA ... 198

Figure 8.3.2 Relative ElCent¡o Earthquake Elastic Response Specftum (3Vo damping) 200Figure 8.3.3 THA ElCentro Earthquake: 1.5m Tall, Moderate Degradation.......... ........201Figure 8.3.4 ElCentro Earthquake: 3.3m Tall, Moderate Degradation............................ 201

Figure 8.3.5 ElCentro Earthquake: 4.0m Tall, Moderate Degradation............................202

Figure 8.3.6 Comparison of DB Analysis and THA Ultimate Instability Prediction .....203Figure 8.3.7 R*(1) vs THA Ultimate Instability Prediction. ......204Figure 8.3.8 'Quasi-static' Rigid Body vs THA Ultimate Instability Prediction...........205

APPENDICIES

Figure B 1 - Standard DPC Connection One Layer of Standard 41cor...........................247

Figure B 2 - Standard DPC Connection One Layer of Super 41cor......... ....248Figure B 3 - Standard DPC Connection One Layer of Polyflash ................ ....................249

Figure B 4 - Standard DPC Connection One Layer of Dry-Cor (Embossed Potythene) 250

Figure C 1- Slip Joint Two layers of Standard Alcor .......Figure C 2- Slip Joint One layer of Standa¡d 41cor..........

lx

LIST OF FIGURES

Figure C 3- Slip Joint Two layers of Greased Galvanised Steel..........

Figure C 4- Slip Joint One layer of Embossed Polythene (Dry-Cor)

253

254

281

282

282

283

284

285

286

287

288

Figure D 1 - Concrete Slab with DPC Connection Above........ 255

Figure D 2 - Rigid F-Â Relationship- Top Vertical Reaction at læeward Face.............257

Figure D 3 - Timber Top Plate Above............ 258

Figure D 4 - Rigid F-Â Relationship- Top Vertical Reaction at Centerline ................ ...260

Figure E 1 - Bond Vy'rench Calibration Plot 110mm Brick Specimen Bond Wrench....26l

Figure E 2- Bond Wrench Calibration Plot 50mm Brick Specimen Bond'Wrench.......26l

Figure F 1- Static Push Test - Un-cracked, 11Omm, No Overburden .........275

Figure F 2- Static Push Test - Un-cracked, 11Omm, 0.15MPa Overburden ..................275

FigureF3-StaticPushTest-Cracked, 11Omm, 0.l5MPaOverburden ....,276

Figure F 4- Static Push Test - Cracked, 50mm, No Overburden ........... ......276

Figure F 5 - Static Push Test - Un-cracked, 50mm, 0.075MPa Overburden ..................277

Figure F 6- Static Push Test - Cracked, 50mm, 0.075 Overburden .............277

Figure F 7- Static Push Test - Cracked, 11Omm, No Overburden ........... ....278

Figure F 8 - Static Push Test - Un-cracked, 110mm, 0.15MPa Overburden ..................278

Figure F 9 - Static Push Test - UN-cracked, 11Omm, No Overburden........... ................279

Figure F 10- Static Push Test - Cracked, 110mm, No Overburden 279

Figure F 11- Static Push Test - Un-cracked, 1lOmm, No Overburden........................... 280

Figure F 12- Static Push Test (Hysteretic) - Cracked, 110mm, No Overburden ........... 280

Figure F 13- September9S Specimen 13 - Resonant Energy l¡ss Per Cycle

Figure F 14 - Static Push Test - Un-cracked, 11Omm, No Overburden..........

Figure F 15 - Static Push Test - Cracked, 50mm, 0.15MPa Overburden.......

Figure F 16 - Release Test (1) - 50mm, No Overburden...........

Figure F 17 - Release Test (2) - 50mm, No Overburden...........

Figure F 18 - Release Test (3) - 50mm, 0.075MPa Overburden

Figure F 19 - Release Test (4) - 11Omm, No Overburden...........

Figure F 20 - Release Test (5) - 110mm, No Overburden

Figure F 2l - Release Test (6) - 110mm, No Ove¡burden.....................

x

LIST OF FIGURES

Figure F 22 - 0.5H2 Half Sine Displacement Pulse, 50mm, No Overburden ........... ......289Figure F 23- 7.0HzHalf Sine Displacement Pulse, 50mm, No Overburden............. .....29O

Figure F 24 - 2.OHzHalf Sine Displacement Pulse, 50mm, No Overburden ........... ......291Figure F 25 - 0.5H2 Half Sine Displacement Pulse, 50mm, 0.075MPa Overburden .....292Figure F 26- 1.0H2 Half Sine Displacement Pulse, 50mm, 0.075MPa Overburden .....293Figure F 27 - Z.OHz Half Sine Displacement Pulse, 50mm, 0.075MPa Overburden .....294Figure F 28- 3.OHz Half Sine Displacement Pulse, 50mm, 0.075MPa Overburden ....295Figure F 29- 0.5}l2 Half Sine Displacement Pulse, 50mm, 0.l5MPa Overburden ........296Figure F 30- 1.0H2 Half Sine Displacement Pulse, 50mm, 0.15MPa Overburden........297

Figure F 31 - 2.0}J.2 Half Sine Displacement Pulse, 50nim, 0.15MPa Overburden .......298Figure F 32- 2.OHz Half Sine Displacement Pulse, 50mm, 0.15MPa Overburden ........299Figure F 33- 1.0H2 Half Sine Displacement Pulse, 110mm, No Overburden ................ 300

Figure F 34- l.0Hz Half Sine Displacement Pulse, 11Omm, No Overburden ................ 301

Figure F 35- 2.0}{2 Half Sine Displacement Pulse, 11Omm, No Overburden ........... .....302Figure F 36- 1.0H2 Gaussian Displacement Pulse, 11Omm, No Overburden................. 303

FigureF3T-l.O}lzGaussianDisplacementPulse, 110mm,NoOverburden.................304

Figure F 38- 1.0H2 Gaussian Displacement Pulse, 11Omm, No Overburden................. 305

Figure F 39- 1.0H2 Gaussian Displacement Pulse, 11Omm, No Overburden................. 306

Figure F 40- 0.5H2 Gaussian Displacement Pulse, 11Omm, No Overburden........... .....307Figure F 4l- 0.5H2 Gaussian Displacement Pulse, 11Omm, No Overburden................. 308

Figure F 42- 0.5}{2 Gaussian Displacement Pulse, I 10mm, No Overburden................. 309

Figure F 43- Transient Excitation Test - 66VoF,lcenfto, 11Omm, No Overburden........ 310

Figure F 44 - Transient Excitation Test - l00Vo Nahanni, I 10mm, No Overburden...... 31 1

Figure F 45- Transient Excitation Test - 200Vo Nahanni, 1 10mm, No Overburden.......3l2Figure F 46 - Transient Excitation Test - 300Vo Nahanni, 110mm, No Overburden......3l3Figure F 47 - Transient Excitation Test - 400Vo Nahanni, I 10mm, No Overburden...... 3 14

Figure F 48 - Transient Excitation Test - 66VoElCentro, 11Omm, No Overburden...... 315

Figure F 49- Transient Excitation Test - 66Vo Pacoima Dam, 110mm, No Overburden3l6Figure F 50- Transient Excitation Test - 80Vo Pacoima Dam, 1 10mm, No Overburd en3l7FigureF5l -TransientExcitationTest- lÙOVo PacoimaDam, llOmm,NoOverburden

xl

318

LIST OF TABLES

Table 3.3.1 DPC Connection Static Friction Coefficient Summary (Page 1994)..............46

Table 3.3.2 Slip Joint Connection Static Friction Coefficient Summary (Page 1994)......46

Table 4.2.lDPC Membrane Test Specimens

Table 4.4.1 Results Summary for Standard DPC Connection Tests...

Table 4.4.2 Results Summary for Centered DPC Connection Tests ..........

Table 4.4.3 Standard DPC Connection Friction Coefficient Comparison

Table 4.4.4 Slip Joint Connection Friction Coefficient Comparison

Table 6.3.1 Bond \ürench Test Results Summary

Table 6.3.2 Brickwork Modulus Test Results

Table 6.4.1 Experimental Phase Test Program

Table 6.4.2 Analysis of Test Specimen

Table 6.4.3 llOmm'Wall, Non-loadbearing - Harmonic Excitation Test Results.......

Table 6.4.411Omm Wall, 0.15MPa - Harmonic Excitation Test Results.............

Table 6.4.5 Result Summary of Static Push Tests

.54

.62

.63

.67

.67

Table 5.2.1 Rigid Bi-Linear F-A Relationship - Various Boundary Conditions 80

Table 6.2. 1 Out-of-plane'Wall Test Instrumentation Description 110

tt4116

118

124

t3r

Table

Table

Table

Table

Table

Table

6.4.6 Summary of Release Test Results

6.4.7 Summary of Key Pulse Test Results (50mm Walls)........

6.4.8 Summary of Key Pulse Test Results (110mm Walls)........

6 .4.9 Earthquake Excitation Descripti on

ó.4.10 Summary of Key Earthquake Excitation Test Results (50mm Walls)

6.4.71Summary of Key Earthquake Excitation Test Results (110mm Walls

Table 7.5.1 Dehning Displacements of the Tri-linea¡ F-A Approximation

......136

...... 138

......t43

...... 155

......157

...... 161

......162

) ....162

xll

t76

LIST OF TABLES

Table 8.4.1 ElCentro Analysis Comparison: 1.5m Height WallTable 8.4.2 ElCentro Analysis Comparison: 3.3m Height WallTable 8.4.3 ElCentro Analysis Comparison: 4.0m Height WallTable 8.4.4Taft Analysis Comparison: 1.5m Height V/aII........

Table 8.4.5 Taft Analysis Comparison: 3.3m Height V/all........Table 8.4.6 Taft Analysis Comparison: 4.0m Height WaII........

Table 8.4.7 Pacoima Dam Analysis Comparison: 1.5m Height WallTable 8.4.8 Pacoima Dam Analysis Comparison: 3.3m Height V/allTable 8.4.9 Pacoima Dam Analysis Comparison: 4.0m Height Wall .......Table 8.4.10 Nahanni Analysis Comparison: 1.5m Height Wa1I...............

Table 8.4.11 Nahanni Analysis Comparison: 3.3m Height WaII...............

Table 8.4.12 Nahanni Analysis Comparison: 4.0m Height WaII...............

206

207

....208

....209

....210

,...211

....212

....213

....274

....215

216

217

xllt

ABSTRACT

A large proportion of domestic and low rise building stock in Australia is of unreinforced

masonry (URM) construction and has not been designed to resist earthquake loads.

Previous researchers have identifred that under current Australian design conditions the

two predominant weak links in the seismic load path for URM buildings are the shear

connections between the walls and floor or roof and out-of-plane wall flexure.

This report documents the experimental and analytical research undertaken at The

University of Adelaide aimed at providing the fundamental tools required to successfully

avoid the identified brittle 'weak link' failures in the design of new and the assessment ofexisting URM buildings. This was achieved for the DPC connections through an

extensive series of shaking table tests, which provided realistic data on the dynamic

capacity of these connections. For the out-of-plane failure of walls in the upper stories of

URM buildings, an extensive series of shaking table tests was used to develop a botter

understanding of the physical processes governing the collapse behaviour. Following this

realistic anal¡ical models were developed to provide accurate and reliable assessment of

actual wall capacities. Since these were necessarily complex, a further refinement was

undertaken to produce a more simplistic but rational analysis procedure for practical

applications based on the 'Displacement-based' failure criteria.

xlv

DECLARATION

This thesis contains no material which has been accepted for the award of any otherdegree or diploma in any university or other tertiary institution and, to the best of myknowledge and belief, contains no material previously published or written by anotherperson, except where due reference is made in the text.

I give consent to this copy of my thesis, when deposited in the University Library, beingmade available for loan or photocopying.

Kevin Thomas Doherty Dare '2a lS lo-

xv

ACKNOWLEDGMENT

I would firstly like to recognise the contributions made throughout the duration of this

project by Associate Professor Mike Griffith of The University of Adelaide as his

foresight and direction \Mas largely responsible for the conception and success of this

project. I am also indebted to my collaborative researchers, Dr. Nelson Lam and Dr. John

V/ilson of The University of Melbourne for valuable research meetings, ideas and

discussions. I would also like to acknowledge the exceptional technical assistance

provided by the Laboratory staff at the Chapman Structural Testing Laboratory at The

University of Adelaide under the supervision of Mr. Greg Atkins.

Funding for this project was provided through an Australian Research Council grant as

well as a University of Adelaide Postgraduate Scholarship Award for which I am

appreciative.

I would also like to express my sincerest appreciation to my Mother and Father, Joan and

Lindsay Doherty for their guidance and encouragement throughout both my under- and

post-graduate careers. My Father, whom also being a structural engineer has spent many

nights discussing with me issues related to structural and earthquake engineering

providing me with motivation to succeed in my professional endeavors. Finally,I would

like to acknowledge the contribution of my Fiancée Tammie. For her endless tolerance

and support I am eternally indebted. The supports of these exceptional people have

provided me with the inspiration and resolve to undertake this project for which I am

extremely grateful.

XVI

I.. INTRODUCTION

From the time of earliest civilisation, the use of masonry has provided a successful

building technique. Examples of early stone masonry construction can be found dating as

far back as c. 9000 BC in Israel and to the better known pyramids of Egypt constructed

around c. 2800 - 2000 BC. Later, along with the emergent Roman Empire in around 700

BC, the use of masonry became widespread. Notable cities were established and

developed throughout the colony comprising elaborate masonry palaces, churches,

bridges and aqueducts. Over the centuries significant advancements have been made in

the processes of masoffy construction and to this day world cities have substantial

building stock comprised of unreinforced masonry (LJRM).

The main characteristics of masoffy that have enabled it to endure as a building medium

through the ages are both the simplicity of laying stones or bricks on top of one another

and the ready availability of materials and labour. Aesthetically, masoffy is available in

a vast array of colour and texture. Due to the small modular size of bricks and blocks it is

also extremely versatile in application in that it can be used to form a great variety of

shapes and sizes of walls, piers, arches, domes or chimneys. Furthermore masonry's

exceptional fire resistance prompted Charles II to insist that all buildings built after the

1666 Great Fire of t¡ndon be constructed of brick or stone. Durability, sound insulation

and thermal mass are other advantageous characteristics of masonry construction.

In contrast, from its very foundation, the intrinsic drawback of masonry construction has

been its poor seismic performance. While recent earthquakes have heightened modern

awareness of this problem (Benuska 1990, Page 1990, Somers 1994, Pham 1995,

Bruneau 1996, Spence 1999, Alcocer 1999,Pujol 1999) it is also evident that the problem

existed even from the early days of the Roman Empire (Dobbins 1994). One remarkable

example was the city of Pompeii. l,ocated near the Bay of Naples in ltaly, Pompeii,

1

CHAPTER ( I ) - Introduction

having been incorporated as a Roman Colony in 808C, had an estimated population ofbetween 8,000 and 12,000 people. It is believed that the final years of the city wereframed by two natural disasters. The first \ryas a devastating earthquake in 62 AD whichcaused considerable damage to the city's masonry infrastructure requiring large scale

rebuilding. The second, a cataclysmic eruption of Mount Versuvius 17 years later,

desfroyed Pompeii and the neighboring city of Herculaneum. The eruption of 79 AD issignificant here as the resulting ash layer preserved much of the evidence of theearthquake damage that would have otherwise been obscured had Pompeii endured

throughout antiquity. Figure 1.1.1 shows an ancient depiction taken from the house ofLucius Caecilius Iucundus of damage to the Temple of Jupiter and The Arch of Triumphat Pompeii during the 62 AD earthquake.

Figure 1.1.1 Depiction of Damage During the 62 AD Earthquake in pompeü(Kozak Collection, Earthquake Engineering Research Center, University of Califomia, Berkeley)

Unlike modern steel and reinforced concrete construction it is clear that the development

of masonry construction followed a different path. Throughout history, forms ofstructural masonry passed from generation to generation and evolved from trial and erroras opposed to that of specialised research. As a consequence, methods have tended to be

less sophisticated and more empirically based with generally little if any consideration

2

CHAPTER (l) - Intoduction

given to seismic action until comparatively recently. These buildings have thus tended to

be at greater seismic risk than comparable new buildings. This is not only because they

have not been designed for seismic loading requirements but also because they are less

capable of dissipating energy through large inelastic deformations during an earthquake.

Historically this has resulted in an abundance of seismically induced catastrophic

masonry failures often with a high loss of life. For example 50 years ago it was

customary to support floors on stone or masonry corbels. During an earthquake the floor

and walls would vibrate typically eventuating in the floor slipping from the corbel and

collapsing dramatically.

In response to the observed damage to un-engineered or poorly constructed buildings,

public prejudice developed against the use of structural URM. A consequence has been

its disappearance from modern construction in regions of high seismicity with a

respective increase in the popularity of steel and concrete construction. Owing to this

shift in focus comparatively little research has been undertaken on the ultimate dynamic

behaviour of URM construction.

Although the performance of URM buildings when subjected to earthquake excitation

has typically been poor there is also signif,rcant evidence suggesting that these buildings

do not necessarily perform poorly in areas of low to moderate seismicity (Scrivener 1993,

Tomazevic and lùy'eiss 1994, Abrams 1995). This was highlighted in 1989 in Australia by

the Mr5.6 Newcastle eafthquake. Here it was reported (Melchers 1990, Griffith 1991,

Page 1992, Murphy 1993) that while older masonry buildings, typically in poor condition

and not having been designed with any consideration to lateral loading, suffered

significant damage, many other masonry buildings performed well suffering only minor

or no damage at all. These findings have placed an increased pressure on engineers in

regions of low to moderate seismicity to continue taking advantage of the significant

beneficial characteristics of masonry construction by designing and detailing URM

buildings to perform adequately during an earthquake.

3

CHAPTER ( I ) - Introduction

The current URM research focus is therefore twofold. Firstly, there is a need torationalise the design of new URM buildings for regions of low to moderate seismicity.

This involves the identification of weaknesses in masonry construction practices and

correlating these to observed catastrophic failures. Consequent development and

implementation of design guidelines would then prevent future occurrences of similarbrittle failures occurring in newly designed structures.

Secondly, there is a need to assess the seismic vulnerability of the large numbers of URMbuilding stock of unknown quality and condition in cities around the world. These

structures were generally constructed prior to mandatory earthquake design requirements

and due to the sporadic nature of earthquake loading many remain untested against

seismic action. Earthquakes have repeatedly impressed the need to review the seismic

adequacy of existing masonry buildings. As a recent example historically significantstructures in Italy, having stood for hundreds of years, have failed dramatically under

seismic loading. These failures clearly illustrate the potential risk in assuming age-old

structures will last forever and the possible physical and social consequence of inaction.With these constant reminders owners are now recognising that they must reconcile thepotential for structural retrofitting with the level of seismic risk.

The distinction is drawn between the development of analysis and design procedures fornew and existing buildings since for the design of a new building a ceftain degree ofconservatism may impose only a minor economic penalty. In contrast, the same degree

of conservatism for the review of an existing structure may impose substantial economicpenalty and hence cross the line of being economically viable to seismically retrofit.Should the imposed economic penalty be deemed too great historically or socially

significant structures could be lost.

The research challenge therefore lay in establishing a better understanding of the physical

processes governing the collapse behaviour thus permitting the development of realistic,

accurate assessment methodologies for the determination of the dynamic capacity ofURM buildings and their constituent components.

4

CHAPTER ( 1 ) - Introduction

1.1. Study Objectives and Key Outcomes

The specific focus of the current research project was an investigation of the brittle 'weak

links' in the seismic load path for Australian URM buildings under earthquake loading.

As is discussed in more detail in Chapter (2) the 'weak links' are evident through the

review of damage surveillance documentation and have been confirmed through an

analytical study (Klopp 1998) as:

( 1) The limited force capacity of connections between floors and walls, in particular the

friction dependent connections containing damp proof course (DPC) membranes and

(2) the out-of-plane failure of walls in the upper stories of URM buildings.

The primary intention of the cunent project \Mas therefore to provide the fundamental

tools required to successfully avoid the identified brittle 'weak link' failures in the design

of new and the assessment of existing tlRM buildings. This was achieved for the DPC

connections through an extensive series of shaking table tests, which provided realistic

data on the dynamic capacity of these connections. For the out-of-plane failure of walls

in the upper stories of URM buildings, an extensive series of shaking table tests was used

to develop a better understanding of the physical processes governing the collapse

behaviour. Following this realistic analytical models were developed to provide accurate

and reliable assessment of actual wall capacities. Since these were necessarily complex,

a further refinement was undertaken to produce a more simplistic but rational analysis

procedure for practical applications. To encourage the ready introduction and acceptance

into the real design environment, where optimisation of design output is often the driving

force, it was necessary that the simplihed procedure be formulated through easily

understood and familiar concepts while still encompassing the essential ingredients of the

dynamic behaviour.

Since a building's structural capacity is related to its weakest link, by avoiding the

identif,red brittle 'weak link' failure modes the overall effective structural capacity and

thus seismic performance will improve. An additional beneht is that with a better

5

CHAPTER ( I ) - Introduction

understanding of the physical process governing the dynamic collapse behaviour,

designers will more readily be able to adopt the desirable 'Capacity' type design

approach discussed further in Chapter (2). Where this enables more ductile failure modes

to be activated, the structure's effective capacity and energy dissipating characteristics

will be further enhanced.

Although specifically related to Australian construction practices and conditions, it isexpected that these research outcomes are sufficiently general so that they will be easily

extrapolated to other regions of similar seismicity and construction techniques.

1.2. Brief Outline of Report

To set the overall scene a general overview of earthquakes and URM is presented inChapter (2) where the basic aspects of seismicity and URM performance, both

internationally and in Australia are covered. Following this, a brief review of the

development of seismic design criteria and URM construction practices in Australia are

presented as these dictate the standard of the existing URM buitding stock. This includes

the results of a survey performed as part of the current research project to catalogue

typical URM wall connections and levels of applied overburden stress based on

Australian masonry construction. A review of the vulnerability of LJRM failure modes

from reconnaissance documentation is then presented to conñrm the typical weak linkURM failure patterns in areas of moderate intensity shaking.

Chapters (3) and (4) are devoted to the shear capacity of URM connections containing

DPC membranes being, the first of the previously identified weak links. Chapter (3)

commences with a general description of connections containing DPC membranes. Aspecihc literature survey covering previous experimental and related work is then

presented. Chapter (3) concludes with the specific research requirement to be undertaken

within the scope of this project being the experimental dete¡mination of dynamic frictiondata for DPC connections typically used in Australian masonry construction.

6

CHAPTER ( I ) - Introduction

Chapter (4) presents the results of a series of dynamic friction tests for DPC connections.

Here the experimentally determined dynamic friction coefficients ¿re compared with

static test results (Page 1995, Griffith et al 1998) for connections of the same

configuration and concludes with recommendations on the suitability of current codified

friction coefficients.

Chapters (5) to (8) are devoted to the out-of-plane failure of walls in the upper stories of

URM buildings being the second of the weak links to be investigated. This is specifically

related to the dynamic stability of simply supported tlRM walls subjected to transient

out-of-plane forces.

Chapter (5) introduces the physical considerations that must be assessed for out-of-plane

analysis including boundary conditions and dynamic stabilising effects. Following this a

specific literature review is presented which hightights key aspects of previous related

experimental and analytical work. Further to the literature review a critical assessment of

currently available analysis and design methodologies for face-loaded URM walls under

one-way bending action subjected to transient excitations is presented. Here it is found

that the existing methods have serious limitations for the realistic prediction of the

ultimate dynamic wall capacity.

In Chapter (6) the key results of an extensive series of static push and shaking table tests

on simply supported face loaded LJRM walls are presented. Here the results of static,

impulse and free vibration tests are used to examine the non-linear force-displacement (F-

Â), frequency-displacement (fA) and damping characteristics of URM walls. Harmonic

and transient excitations are also used to examine the dynamic response at various

excitation frequency and amplitude content and for later confirmation of the

comprehensive analytical model.

Chapter (7) describes the development of a comprehensive analytical model for the semi-

rigid rocking response of post cracked URM walls subjected to out-of-plane forces. The

computer software ROWMANRY, developed as part of the current research project to

7

CHAPTER (l) - Introduction

the highly non-linear time-history analysis (THA), is also presented. Results ofexperimental work as described in Chapter (6) are then used to calibrate and confirm the

accuracy of the analytical results.

In Chapter (8) a rational simplistic displacement-based (DB) analysis procedure is

presented for the prediction of the ultimate capacity of face loaded URM walls. A briefdescription of the displacement-based design methodology is provided and followed by

key aspects as it is applied to rocking URM walls. In order to confirm the effectiveness

of the linearised DB analysis, comparisons with experimental and comprehensive TFIA

results are presented. Similar comparisons are also made with currently available

ultimate analysis methodologies where it is concluded that the linea¡ised DBmethodology provides the most effective estimate of ultimate wall capacity.

Chapter (9) summarises the results of the study, highlighting key outcomes, design

recommendations and future research requirements.

8

2. EARTHQUAKES AND UNREINFORCEI)

MASONRY

2.1. Introduction

Earthquakes pose a substantial threat to life with an average fatality rate this century of

around 10,000 deaths per year (McCue t992). Damage to unreinforced masonry (uRM)

buildings and elements is a ubiquitous aspect of many earthquakes and as such URM has

a poor seismic performance record throughout the world. It has been reported (Scrivener

1993), however, that the poor overall public perception of URM can generally be

attributed to media reports not mentioning typical causes of the failures such as:

- buildings not designed to any engineering code, let alone an earthquake code;

- poorly constructed of adobe, mud brick or weak clay bricks with weak mortar of

mud or earth or with insufficient cement; and

- un-connected structural elements often with heavy roofs

In many instances the damage level has been enormous with masonry littering streets and

in larger earthquakes the complete collapse of URM buildings. This severe damage has

often been responsible for a non-commensurable loss of life and injury during

earthquake, which is both unacceptable and unnecessary. The spectacular nature of the

damage has therefore tended to obscure the satisfactory performance of many other URM

buildings in earthquakes. This is supported by research (Griffrth 1991, Page 1992,

Schrivener 1993, Tomazevic and \ileiss 1994, Abrarns 1995) indicating that URM

buildings can satisfactorily withstand moderate levels of ground shaking if designed,

detailed and constructed with consideration to seismic loading.

This Chapter provides a general overview of the seismicity, URM construction and

seismic performance in Australia. Aspects which are applicable for Australian conditions

are clarified and vulnerable weak links in URM buildings designed to current practices

9

CHAPTER (2) - Earthquakes and Unreinforced Masonry

are identified. To quantify the performance of IJRM buildings in areas of moderate

seismicity, a summary of observed damage patterns for Australian and relevant

international earthquakes is presented. This section concludes with the specific research

focus to be addressed within the scope of this report.

2.2. A¡ustralian Seismicity

While it is possible for an earthquake to occur at any location their occurrence frequency

is unevenly distributed over the earth. The majority of earthquakes are found to occur

along relatively narrow continuous belts at the convergent boundaries of the major crustal

plates. Here, inter-plate earthquakes contribute more than 90Vo of the earth's release ofseismic energy (Bolt 1996) with the remaining released as interior or intra-plate type

events. Further, approximately 75Vo of the total energy release is believed to occur along

the edges of the Pacific ocean, where the thinner Pacific plate is being forced beneath the

thicker continental crust (BGS 1999). This is demonstrated in active inter-plate regions

such as Japan, California or Papua New Guinea where the major plates interact at

velocities of up to 100 mm/year. As a consequence, it can take only tens to hundreds ofyears for sufficient strain energy to build culminating in the release of a large magnitude

earthquake. In contrast, for an intra-plate region it may take hundreds of thousands ofyears for similar levels of compressive stress and strain energy to develop. Thus, due to

the paucity of records this type of event is far more difficult to forecast.

The long return period of major earthquakes and the absence of interim perceptible

seismic activity in intra-plate regions has led to these areas being referred to as being oflow seismicity or low seismic risk. A common misconception follows that this infers

weak ground motion while the reality is that strong ground motion can still occur but less

frequently. In probabilistic terms there is a much reduced likelihood of intra-plate strong

ground motion occurring at a particular time and place than inter-plate. This aspect

substantially impacts on building code provisions where the design basis event isprescribed in probabilistic terms, rather than on maximum earthquake potential. Thus for

l0

CHAPTER (2) - Earthquakes and Unreinforced Masonry

intra-plate regions the design event magnitude will be smaller than for inter-plate regions

(Somerville et al 1998).

The ea¡liest earthquake reported in Australia was in June 1788 at Port Jackson (Sydney)

where the First Fleet settlers were shaken by a strong local earthquake lasting for not

more than two or three seconds. Since this time small earthquakes have been reported

under most of the major Australian cities (AGSO 1999).

The Australian continent lies whoþ within the Indo-Australian tectonic plate (refer

Figure 2.2.1) and as such is only subjected to intra-plate earthquakes. The closest

Australian city to an active plate boundary is Darwin, which is regularly but lightly

shaken by earthquakes along the subducting Java Trench in the Banda Sea.

Pacific Plate

Convergent plateboundaryInter-Plate RegionDirection of

crustal plaæmovement --+

\\Indo-Ausüalia Plate v

High Seismicity ZonesSeparating major crustalplaæs

Antårctic Plate

Since earthquakes only occur in the earth's outer crust where rocks a¡e cold enough to be

brittle, in Australia, earthquakes typically only occur to a depth of a¡ound 20km (Gibson

i

Figure 2.2.1 Australia's Tectonic Location

Ausüalia

11

CHAPTER (2) - Eanhquakes ønd Unreinforced Masonry

1990). This limitation constrains the vertical fault dimension so that for the release of alarge amount of strain energy the rupture would need to be very long. By practically

limiting the fault length to around 100km the maximum magnitude of earthquake that

could be realistically expected in Australia is around Ms 7.5. This assumption is

supported by studies of prehistoric Australian fault scarps where no scarp longer than

45km has yet been found (Denham 1992). It is therefore not unreasonable to argue that a

maximum credible earthquake of this magnitude be adopted for earthquake risk inAustralia.

Over the relatively short-recorded seismic history in Australia the largest known

earthquake occurred in 1906 off of the Northwest Coast of the continent with an

estimated magnitude of 7.2. On land the 1941 Meeberrie earthquake, which was felt over

most of Western Australia, appears to have been the largest having a magnitude ofapproximately 7 (Denham 1992).

In 1968 a magnitude 6.9 earthquake devastated the Western Australian agricultural

township of Meckering. Here although no people died, 85 dwellings were severely

damaged being predominantly of unreinforced masonry construction. Later, in 1954,

Adelaide was subjected to a damaging magnitude 5.5 earthquake. Here again there were

no fatalities however over 30,000 dwellings sustained damage (hish 1992) costing at the

time in excess of 4 million pounds or $91m in 1995 dollars (AGSO 1999). More

recently, in 1988, a magnitude 6.8 earthquake having a 35km fault length and maximum

surface displacement of 2.0m (AGSO 1999) struck Tennant Creek in the Northern

Territory of Australia. Fortunately due to the remoteness of the area there was only

moderate damage caused.

By far the most devastating and expensive, although not the largest seismic event inAustralia's brief recorded history, was the 1989 Newcastle earthquake. Despite by world

standards being only a moderate magnitude 5.6 the earthquake caused massive damage to

both property and infrastructure with damage estimates of over a billion dollars at the

time of the earthquake (Melchers 1990, Blong 1992). It is also the only earthquake in

t2

CHAPTER (2) - Earthquakes qnd Unreinforced Masonry

recorded Australian history to have been responsible for the loss of life with thirteen

people killed and over one hundred injured. Furthermore, it was only the fortunate

timing of the event that saved many more from being killed or injured (Melchers 1990).

Attributed to the vastness of the Australian continent it has been fortunate that previous

large magnitude Australian earthquakes have occurred far from populated centers causing

only relatively low-level property damage. With an ever-increasing population density

and aging building stock the potential for earthquake disaster in Australia is becoming a

far greater threat to our society so that earthquake hazud must now be fully considered in

risk assessment scenarios. To further place the seismic risk of Australian cities into

perspective it has been reported (Blong 1993) that a design magnitude event, i.e. a 500

year return period earthquake, in Melbourne or Sydney could result in more than 500

deaths and $8 billion dollars worth of damage to domestic construction alone.

2.3. URM Building Stock in Australia

Due to Australia's modest level of seismicity and the many advantageous characteristics

of masonry, the use of URM as a building medium in Australia has been widely

embraced. The majority of Australian URM building stock is of either or

commercial low-rise construction although some taller buildings, up have

been constructed. For housing, masonry is often used as a veneer although with older

homes in the 'Western states cavity wall construction is more prevalent. Single skin

grouted or partially grouted masonry is also popular in the north of Australia (Page

1995). V/ith a large proportion of LJRM building stock comprising single occupancy

housing, multiple occupancy residence (three to four storey 'walk up' flats) and low rise

commercial buildings, URM is prevalent in the inner suburban areas of Australian cities.

In these areas the population densities are often the highest and combined with the

relative older age of the URM building stock the potential seismic vulnerability of these

areas is appreciable.

7

t3

CHAPTER (2) - Earthquakes and Unreinforced Masonry

The historical development and implementation of the Australian Earthquake Loading

Code provides an insight into the current thinking in AustraHa on the seismic

vulnerability of existing URM building stock. As highlighted in Section 2.2, even though

there had been a number of Australian earthquakes greater in magnitude 5.0, the firstAustralian Earthquake Code, AS2l2l, was not published until 1979 as a response to the

1968 Meckering earthquake. Due to the lack of prior Australian strong ground motion

and research, this standard was based largely on requirements in the 1977 Structural

Engineers Association of California (SEAOC) Code and the 1976 Uniform Building

Code (UBC). After its release AS2l2l was seldom used and with the seismic zone map

having most of the country located in 'zone 0', which did not require seismic loading to

be considered, very few buildings were designed for earthquake loading. In fact, only the

South Australian and Commonwealth Governments actually used the code and in some

states with seismic design requirements these were ignored as they were not gazetted by

state authorities. It is possible that the misconception that design for wind also provided

for earthquakes led to this oversight.

With an increased understanding of earthquakes, 452121 was due for revision in 1989

when the Newcastle earthquake struck giving impetus and point to the deliberation. The

revised standard was again adapted from codes developed by Ameerican institutions such

as the Applied Technology Council (ATC), The National Hazatd Reduction Program

(NEHRP) and SEAOC before being incorporated into the Australian Loading Code in1993 as the SAA Earthquake Loading Code, 4S1170.4-1993. This, the current standard,

ensures that for every building constructed in Australia a minimum consideration is given

to seismic loading. The level required varies in sophistication from simple detailing to

comprehensive dynamic analysis depending on structural category and regularity. For

masonry the general detailing provisions are referenced from the respective material

standard being the SAA Masonry Code, 453700-1998. As a consequence of the recent

development of earthquake codes almost all of Australia's existing URM building stock

was constructed in the absence of mandatory earthquake design requirements.

t4

CHAPTER (2) - Earthquakes ønd Unreinforced Masonry

Unlike other popular methods, masonry construction is labour intensive in nature and

consequently quality is particularly sensitive to workmanship. Paradoxically, unlike more

modern construction methods, masonry is often not subjected to a high degree of quality

control due largely to its traditional background. For these reasons finished product

quality has been highly variable and is often not indicative of the designer's assumptions.

For URM buildings having relatively low levels of overburden stress a critical property

of masonry is the bond between brick units and mortar known as the flexural tensile

strength. This is also possibly the most variable and sensitive property to workmanship

with variations of 30Vo to 35Vo found to be not unusual. The factors influencing bond

strength have been well-documented (Taylor-Firth 1990, Van den Boon 1994, DeVitis

1995,Lawrence 1995, Page 1998) and include the suction of the masonry units, the water

retention of the mortar, the morta¡ ingredients, the use of additives and the method of

laying.

A recent study (Nawar 1994) which documented current masonry construction practices

on building sites in Sydney identified large gaps between the designers intent and actual

practices. Here it was found that over 50Vo of the sites inspected had serious omissions

capable of compromising the long-term performance of the masonry. In a second study

(Zsembery 1995) the measurement of flexural bond strength at 19 sites in the Melbourne

area was undertaken where a significant va¡iation in the results was also found.

The 1989 Newcastle earthquake highlighted the vulnerability of non seismicaþ designed

buildings with a significant proportion of the damage attributed to the lack of

consideration to ea¡thquake loading and inadequate standards of URM design, detailing

and construction (Melchers 1990, Page 7992). An additional finding was that the real

masonry quality was much lower than would have been expected (Page 1992). In many

cases damage surveillance reported that in what appeared to be sound outer masomy

skins, problems such as inadequately frlled bed and perpend joints and inadequate tying

or support of one or both of the skins was evident. In older structures poor maintenance

and wall tie corrosion also played a significant role in exacerbating the damage. The

15

CHAPTER (2) - Earthquakes and Unreinforced Masonry

presence of weak lime mortars is also thought to have been responsible for a highproportion of the billion dolla¡s worth of damage during the Newcastle earthquake. Itfollowed that the resistance of the effectively pre-cracked LJRM walls was left to relysolely on stabilising gravity effects.

While deficiencies associated with poor workmanship and maintenance are the

responsibility of the Masonry industry as a whole, their existence and consequent

influence on structural durability and ductility must be recognised. As the Newcastle

situation is not unique in Australia it must be assumed that the same scen¿rio of non-

seismically designed buildings in poorly maintained condition, constructed of poor

quality materials and concentrated in inner suburban areas where population densities are

greatest exist in other Australian cities.

In recognition of the need to strengthen existing buildings with an assessed inadequate

seismic resistance the voluntary code 'strengthening of Existing Buildings forEarthquakes',453826-1998, has recently been released in Australia. This requires the

designer to consider the same philosophical approach as 4S1170.4-1993 by establishing

clear load paths for the transmission of vertical and lateral loads. Many existing masonry

structures would be economically infeasible to upgrade to a capacity able to withstand the

full loads specihed in AS1l7O.4-1993. 453826-1998 therefore specifies lower th¡eshold

values for retrofitting structures based on the buildings use classification being either

33Vo or 66Vo of the full A51170.4-1993 specihed loads. In the absence of realistic

dynamic anaþsis methodologies the rationale here is that with the long return period oflarge magnitude earthquakes, a greater degree of risk is acceptable in existing buildingsthan that allowed in the design and construction of new buildings.

In the ideal situation structural engineers retained to investigate the seismic resistance ofa URM building would have at their disposal tools enabling them to prepare a realistic,

neither unduly conservative nor permissive, statement of the seismic resistive capacity ofboth structural and architectural components. Since the traditional design methodologies

inherently provide conservative assessment of the seismic vulnerability of a URM

t6

CHAPTER (2) - Earthquakes and Unreinforced Masonry

building, adoption of these techniques may lead to the possibility of incorrectly labeling a

seismically adequate building as unsafe. In contrast overestimating the dynamic capacity

of elements to resist damaging cycles of seismic excitation could lead to a false and

dangerous sense of security. In this context, the benefit of developing better tools to

accurately determine the seismic resistance capacity of URM buildings and components

is apparent.

The first stage of the current research project was to survey and catalogue URM

connection details and overburden stress levels typical of Australian masonry

construction. Figures 2.3.1 to 2.3.5 show construction drawings of the most

predominantly used URM connections.

Figure 2.3.1 shows a 'cornice' type connection frequently used for internal non-

loadbearing URM partition walls. Often return walls are not incorporated into the

internal partition walls so that one-way bending predominates. Since the cornice

connection provides only horizontal restraint, the wall acts as a propped cantilever under

face loading.

Figure 2.3.2 and Figure 2.3.3 show conìmon connection details used in cavity wall

construction. V/here both brick leaves are laid on flat, the roof truss is typically

supported on the internal loadbearing leaf using a 'wooden top plate'. Alternatively,

often for economy of material use, the external leaf is laid brick on flat but the internal

leaf is brick on edge. In this case the internal leaf is unsuitable for roof support and the

roof truss is supported on the outer loadbearing leaf. For either case nails or masonry

anchors are used to fix the top plate to the tlRM wall providing a positive connection to

resist horizontal shearing forces. Light gauge steel trusses and wall plates are now also

used as an alternative to timber. To resist wind uplift a galvanised strap is typically

detailed being fixed to the roof truss and hooked around a support bar in the wall

approximately l.2mbelow the top (Figure 2.3.3).

t7

CHAPTER (2) - Earthquøkes and Unreinforced Masonry

Connections sholvn in Figure 2.3.4 andFigure 2.3.5 are often used between concrete slab

and loadbearing masonry elements. As will be discussed in Chapter 3, this type ofconnection is typically detailed to meet serviceability design criteria.

Since, in general, only one wall leaf of cavity wall construction is loadbearing with the

other supporting only its own weight, the loadbearing leaf has a superior lateral strength.

Both URM wall leaves are connected via wall ties. The stiffer loadbearing wall therefore

must carry the combined inertia load from the dynamic response of both of the URM wallleaves. Past earthquakes, in particular the Newcastle earthquake (Page 1992), havedemonstrated that wall ties can corrode thus becoming ineffective or that they may pullout from deteriorated weak lime mortar under lateral loading. This often leads to the

weaker non-loadbearing outer leaf acting as an individual element being extremely

vulnerable to earthquake damage with a peeling off of the outer leaf commonly reported.

Ceiling undertrussed roof

Timber or plastercornice

Figure 2.3.1 Internal Partition Wall 'Cornice' Connection Detail

75 x25mmwoodentop plate

Non-loadbearing Nails or masonry anchors @outer leaf 720 centers (third perpend)

f-oadbearing inner leaf -Brick on flat

Figure 2.3.2 URM Cavity Wall to Roof Truss Connection Detail (Inner Loadbearing)

g

Þ;Ër

18

CHAPTER ( 2 ) - Earthquake s and Unr e info rc e d M as onry

Truss connection -and hoop iron strips

Galv strap for wind uplift Non-loadbearinginternal leaf -Brick on edge

Figure 2.3.3 URM Cavity \üall to Roof Truss Connection Detail (Outcr Loadbearing)

DPC

a ..;f,,,û

Figure 2.3.4 URM Wall to Inter Story Floor Slab DPC Connection Detail

ItDs{;.'

I

DPC

¡;-';. ró'.

l, r.

I

Figure 2.3.5 URM Wall to Ground Floor Slab DPC Connection lÞtail

I-a]at

-r

t9

CHAPTER (2) - Earthquakes anà Unreinforced Møsonry

A second outcome of this survey was the determination of typical levels of overburden

stress in Australia. This involved the analysis of numerous existing two to four story tallLJRM buildings. Structural configurations included cavity and veneer URM consüuction,

concrete slab and timber floor diaphragms and both light gauge galvanised and heavy

tiled roof diaphragms. The conclusion of this survey was that overburden stress typicallyranged from 0.4MPa in the lower stories reducing to less than 0.1MPa in the upper

stories.

2.4. URM Vulnerability in Moderate Seismicity Regions

2.4.1. Failure Modes of LIRM Elements (Related to Seismic Load Path)

While the earthquake ground motion itself does not constitute a direct threat to life safety

the subsequent failure of man made structures does. During an earthquake a building is

subjected to a series of random ground displacements. As the structure reacts to these

displacements inertial forces are induced. The structural response to these inertia forces

is dependent on the natural frequencies and inherent damping of the building, and itscomponents, which themselves are dependent on the structural mass and stiffness.

To assist in illustrating elemental failure modes within a URM building it is pertinent to

describe the path that seismic input energy follows (Priestly 1985, Bruneau 1994, Calvi et

al 1996) as is shown in Figure 2.4.I. When subjected to seismic ground motion, the

foundation transmits seismic energy to the stiffest elements of the LJRM building beirrg

the in-plane sûuctural walls. The response of the shear walls, which itself is dependent

on height, stiffrress and overburden stress excite the floor diaphragm, through the wall tofloor connection, with a motion that has now been filtered by the shear wall. Followingthis the floor diaphragm response excites the out-of-pl¿¡1s vvalls, through the wall to floorconnection, such that its dynamic characteristics directly influence the severity of the out-

of-plane wall excitation. The input excitation at the top of the face-loaded walls need

therefore not necessarily be in phase or even of the same magnitude as the bottom.

20

CHAPTER (2) - Eatthqual<es and Unreinforced Masonry

Floor diaphragm responseamplifies accelerations andtransmits load to out-of-plane

Shakingmotion \ Parapet wall

walls

In-plane shear wallsresponse filærs theground motion andtransmits to floordiaphragms e

Earthquake Excitation atfootings

.<-Out-of-plane wall

Figure 2.4.1 Seismic Load Path for Unreinforced Masonry Building

2.42. Review of the Seismic Performance of URM Buildings

As has been discussed in Section 2.2 the most damaging and therefore relevant

earthquake in Australia's recorded history was the 1989 Newcastle earthquake, Mr 5.6.

The earthquake intensity in outer Newcastle has been assessed at MM6.0Cí.5 (McCue

1990, Melchers 1990) while for inner Newcastle areas the general level of damage was

consistent with an intensity of MM7.0t0.5. Mean soft soil amplification factors of 3+1

are therefore considered indicative for the inner areas of Newcastle.

In reviewing damage patterns in Newcastle (Bubb 1990, Donaldson 1990, toke 1990,

Pederson 1990, Melchers 1990, Jordan et al 1990, Page 1990:1992, Griffith 1991,

Welhelm 1998) it is apparent that timber housing performed best followed by brick

veneer construction and that cavity brick construction was worst affected. It is noted

however that the latter mainly consisted of older buildings, many at least 60 years old,

and with significant structural deterioration. With few exceptions modern buildings

2-

II

III).-ì

2l

CHAPTER (2) - Earthquakes and Unreinforced Masonry

performed better with damage conflned to masonry cladding and infill. The nature of the

damage can be summarised as:

- extensive cracking and deterioration of walls due to in-plane racking

- tilting of walls under transverse forces including sliding at damp proof courses

- partial loss of roof support by sliding from support walls

- cracking of walls in flexure under the action of transverse forces

- loss of end walls under transverse forces due to corroded wall ties

- gable end and parapet failures

LJRM parapet wall failure was the major form of damage in both older and newer

buildings and constituted a signif,rcant safety hazard both during and after the earthquake.

Often the collapse of parapets onto awnings preempted failure of the awnings in turnleading to out-of-plane wall collapse. The most widespread incidence of parapet failurewas at the Tighes Hill Campus of the Newcastle Technical College as shown in Figure

2.4.2.

Figure 2.4.2Panpet Failure, Tighes Hill Campus, Newcastle Technical College(Newcastle Earthqu.ake Study, The Institution of Etrgineers, Ar¡stralia, 1990)

22

CHAPTER (2) - Earthquakcs and Unreinforced Masonry

A study (Murphy & Stewa¡t 1993) of 651 Government buildings damaged during the

earthquake at 300 different locations found that parapets on buildings founded on

alluvium soil appear to have been the most haza¡dous with 55Vo of these incurring

hazardous damage as opposed to l77o on non-alluvium. This then suggested that the

amplified gtound motion on the soft alluvium \ryas substantial enough to cause the parapet

walls to become unstable. In contrast, on non-alluvium soil areas where there was less

ground motion amplification the parapets were less prone to becoming unstable, although

base cracking of parapets was still observed.

The Australian experience of IJRM performing poorly in earthquakes is not unique.

However, care must be taken when reviewing overseas URM research papers as the

lessons learnt from their experience is typically determined from different standards of

URM construction. Often the type of masonry construction and materials being referred

to bear little resemblance to materials and practices used in Australia. For example, after

both the 1997 labalpar, India, Ms 6.0, and 1999 Mexico, Ms 6.7, earthquakes, the

collapse and severe damage to URM housing was reported (Jain et al 1997, Alcocer

1999). The implication for poor URM performance is apparent. \With poor quality

materials such as burnt brick in mud mortar and very weak adobe masonry being the

predominantly used building materials, these bear little resemblance to materials used'in

Australia and as such few lessons can be learnt. Figure 2.4.3 gives an indication of the

typical quality of masonry in the Jabalpar earthquake.

Similar examples can be made of Greek (Fardis 1995) and Italian (Spence et al 1999)

earthquakes where damage to URM buildings often dating as far back as the middle ages

are being reported.

23

CHAPTER (2) - Eørthqualces and Unreinforced Masonry

Figure 2.4.3 lldasonry Darmge During 1997 Jabalpar, India Earthquake(Jain er at 1997)

An analogy can however be drawn between earthquake damage to URM in some US,

New Zealand and Chinese cities where simila¡ LJRM construction types, materials and

seismic design histories to that in Australia exist. For example, like Ausfialia, many ofthese cities comprise old LJRM buildings in inner suburban areas that havg been designed

with Iittle or no consideration for seismic action. Similarly weak lime mortars and poor

maintenance are also commonly found. Recent events in seismically active a¡eas where

ordinances have been place to upgrade vulnerable URM buildings have also enabled

comparisons of reEofitted and un-reftofitted damage to be made.

Selected documented events include: 1933 long Beach, California (Fatemi t999),1935Helena, Montana (James 1999), 1971 San Fernando, California (Iæeds lg72), 1975

Imperial Valley, California and Mexico (Blakie et al 1992), 1983 Colinga, California(Blakie et al1992),1983 Borah Peak, Idaho (Reitherman 1985), 1987 Whittier Narrows,

California (Deppe 1988, Hart 1988, Moore et al 1988), 1989 l¡ma Prieta, California(Benuska 1990, Lizundia et al1994),1994 Northridge, California (Somers 1996), 1855

24

CHAPTER (2) - Earthquakes and Unreinforced Masonry

and 1942 Wairarapa, Central New Zealand (Grapes & Downes 1997, Blakie et al 1992),

1931 Hawke's Bay, East Coast New Zealand (Blakie et all992),1990 Weber, East Coast

New Zealand (Blakie etal7992),Tangshan, China, 1976 (Yuxian1979).

2.43. Common tlRM Element Failure Modes

Blakie et al1992 has presented URM damage data relevant for MM6 to MM8 intensities

as could be expected for regions of moderate seismicity although some examples of high

intensity shaking to MM10 are also included. At MM7 no URM buildings were reported

to collapse as compared with 87o to 45Vo at MM8. Similarly, around 70Vo had only slight

or no damage at MM7, dropping to 20Vo at MM8. Where retrof,rt o¡dinances had been

undertaken URM performance was acceptable with mostly only low level damage. At

MM10 severe damage was reported for URM buildings with as many as 75Vo of multi-

storey brick buildings collapsing. Here current retrofit methods were found to be

insufficient to prevent failures.

The following paragraphs provide a brief description and review of common failure

modes for URM buildings which have been more prevalent during past earthquakes.

Anchorage failures'. Anchorage is an important factor as it enables seismic load to pass

between walls and the floor or roof diaphragm. In many URM buildings diaphragm

joists and beams rest on LJRM walls, sometimes on special corbels although mostþ these

are recessed into the wall. Without effective anchorage face loaded exterior walls behave

as cantilevets over the total building height thus increasing the risk of face loaded wall

failure which may in turn precipitate total collapse. Global structural failure may also

occur by slippage of joists and beams from their supports. Where floor diaphragms are

positively connected to URM walls these anchors may rupture at the connection points

leading to the condition of 'lack of anchorage' as described above.

Anchorage failure has been the most frequent cause of wall and gable collapse in

mode¡ate earthquakes however this has often been ¡elated to deteriorated or poor quality

lime mortar.

25

CHAPTER (2) - Earthquakes an¿ Unreinforced Møsonry

Diaphragm flexibility and strengrå: No instance of complete diaphragm failure wasreported for any moderate intensity earthquake although the flexibility of the floor and

roof diaphragm has been suggested as a possible cause of wall damage. A particular case

is unsecured gable wall ends, which are extremely vulnerable through impact with the

roof structure.

As the floor diaphragm response directly excites the out-of-plane walls it is critical to the

URM building seismic response. In an attempt to mitigate the effect that diaphragmresponse has on the dynamic behaviour of URM buildings, research has been undertaken

in the United States (ABK 1984). Here fourteen different diaphragms were tested toobtain information on their in-plane static and dynamic, linear and non-linear properties.

Eleven of the diaphragms tested were of wood construction and the remaining of steel

decking either filled with concrete or not. Results showed that strong diaphragmsproduced large amplifications of up to 3 to 4 times the input accelerations in the elastic

range essentially behaving as 2Vo damped oscillators. Flexible diaphragms were found to

have highly non-linear flexible behaviou¡ with typical amplifications in the order of 2 to2.25.

Out-of-plane wallfailur¿s: When suff,rcient anchorage exists between the diaphragms and

walls, out-of-plane wall behaviour is as a one storey high panel dynamically excited at

either end. These panels themselves are susceptible to out-of-plane bending failure and

while in-plane failure does not always endanger the gravity load carrying capabilities ofthe structure out-of-plane failure does. As amplihcation of the ground motion increases

with building height, face loaded walls in the upper stories of URM buildings tend to be

at the highest risk of failure. Parapet wall failures are also prone to flexural failure due tothe lack of masonry tensile strength.

In moderate magnitude earthquakes cracking of walls loaded in the out-of-plane directionis common. For MM7 intensity shaking there appear to have been very few instances

where pure simply supported out-of-plane collapse occurred where walls were adequately

supported at the top and bottom. For MM8 intensity areas out-of-plane wall collapse was

26

CHAPTER (2) - Earthquakes and Unreinforced Masonry

a more prevalent cause of URM damage. Although many of these failures would have

been instigated by anchorage problems it is possible that a number resulted from

excessive out-of-plane displacements at the mid-height of the wall spanning between the

diaphragms. At MM10 intensity shaking out-of-plane wall failure was reported as

profuse, In some instances, adequately supported out-of-plane walls have survived even

this intensity shaking. It was also found that buildings with concrete floors had a lower

percentage of damage attributed to increased overburden stress.

Interior partition walls: As generally these walls are only one wythe thick and typically

have no overburden other than their own self weight they have been particularly

vulnerable even in moderate intensity shaking.

Parapet wall failure: Parapet collapse has been reported in all reviewed earthquakes. For

moderate intensity shaking these typically have been responsible for most loss of life.

In-Plane WaIl Failures: As seismic load passes through the structural shear wall, in-plane

failure may occur if the inertial bending or shear forces induced exceeds the wall

capacity. Over the past ten or so years a substantial quantity of experimental and

analytical research into in-plane ultimate behavioral properties of URM walls has been

reported (König et al 1988, Abrams 1992, Tercelj et al 1992, Pdtrsenjad et al t994,

Magenes et al 1995, Jankulovski et al 1995, Gambarotta et al1995, Lafuente et al1995,

Romano et al 1995, Anthoine et al 1995, Zhuge et al 1996). In reviewing this

documentation a wide variety of behaviour, which depends on the wall height to length

ratio, the applied load and the mechanical properties of the materials constituting the

brickwork can be found.

With different combinations of parameters three failure mechanisms have been identified.

These include (1) rocking/flexural mechanism, (2) shear-sliding mechanism and (3) shear

cracking mechanism typified by double diagonal (X) cracking. The first two failure

modes are considered to be favourable as they are capable of significant energy

dissipation without compromising the gravity load carrying capacity thus providing an

27

CHAPTER (2) - Earthquakes and Unreinforced Masonry

effective ductility. In contrast the third failure mechanism is considered to be non-favourable as brittle collapse often results. If a stair stepped crack pattern occurs along

bed and head joints the element may still possess ductile characteristics as shear forces

can still be resisted through friction. [,ow aspect ratios and high axial loads have been

reported to develop diagonal cracking failure, while rocking and sliding were more likelyto occur with low axial loads and high aspect ¡atio walls. Higher mortar strength was

also found to inhibit shear cracking failure mechanisms in favour of rocking and slidingfailure. lncreased axial load was found to increase lateral strength in terms of the

maximum load carrying capacity although the seismic performance lvas also worsened

with the undesirable transition from a favourable to non-favourable failure mechanism.

Whether a URM wall element is controlled by flexural or shear, if suitable details are

provided the lateral force deflection behaviour will include a significant plateau portionmuch like an elastic plastic material provided vertical compressive stress is present.

Both diagonal (X) cracking and horizontal cracking at the top and bottom of piers have

been commonly reported in most areas of moderate intensity shaking but do not appear tohave been responsible for any total building collapse. In contrast, brittle shear failurecaused by the diagonal shear (X) cracking failure mechanism was a serious cause ofcollapse in more intensely shaken regions. For example in the 1976 Tangshan

earthquake, M5 8.0, where shaking intensities reached MM10, hundreds of URMbuildings were reported to have failed due to shear failure in loadbearing URM walls.

Figure 2.4.4 shows a school in Tangshan damaged by the earthquake where in-plane

distress can clearly be seen in the front wall piers and out-of-plane wall failure has

occurred at the top end wall.

28

CHAPTER (2) - Earthquakcs and Unreinforced Møsonry

Figure 2.4.4Darage to IIRM Building, Tangshan' China' 1976

(Steinbrugge Colleclion, Eartþuake Engineering Research Center, University of Califomia Be¡keley)

z.4A.'Weak LinK LIRM Failure Modes

In summarising the data presented in Section 2.4.3, for moderate intensity shaking, the

'weak link' failure mode, which predominates for regular LJRM buildings, is the lack of

anchorage between structural elements, in particular between floor/roof diaphragms and

URM walls. Typically this has been due to a lack of consideration to lateral loading and

in most cases could have been avoided by the provision of positive connections. As will

be discussed funher in Chapter 3, where the diaphragm is relatively rigid the provision of

positive connections may cause serviceability problems and as such friction based

connections are often relied upon. 'Where sufficient anchorage between structural

elements has been provided the dominant 'weak link' failure mode is the out-of-plane

flexure of URM walls including both simply supported and parapet walls. Tytng patapets

back to the main structure has proven to be a successful retrofit method for moderate

intensity shaking.

In regions of moderate intensity shaking there have been many reported instances of

URM buildings that have suffered minimal or no damage at all while other buildings of a

simila¡ nature and in the same shaking intensity region have suffered substantial

29

CHAPTER (2) - Earthquakcs and. Unreinforced Masonry

structural damage. It is therefore clear that provided the 'weak link' failure modes can be

avoided URM can be relied upon to behave adequately during moderate earthquakes.

Clearly for areas where the probability of stronger intensity shaking is deemed

sufficiently high LJRM construction is not appropriate with the logical alternatives being

more ductile methods such as reinforced masonry, reinforced concrete or steel

construction.

Analytical resea¡ch by Klopp 1998 has also identified 'weak link' URM failure modes.

This involved the analysis of eleven existing LJRM buildings in Adelaide using the

response spectrum method and equivalent static force requirements of ASl 170.4-1993.

As a results Klopp reported that the two most likely failure modes for Australian URMconstruction are:

(I ) The limited force capacity of connections betvveen floors and walls. Klopp reported

that the code guidelines for connection force capacities benveen the floors and walls ofLJRM buildings were found to be insufficient being significantly smaller than the

requirement determined by elastic response spectrum analysis to ASI170.4-I993.Despite this Klopp also reported that typical forms of positive connection could generally

easily meet the earthquake shearing forces induced. Of more concern were connections

containing a DPC membrane often found in URM-concrete slab buildings, which rely on

friction to transfer horizontal forces. In comparing the calculated connection shear force

demand under the AS1170.4-1993 design earthquake, friction coefficients of a¡ound 0.3

to 0.4 were required. These values are of about the same magnitude as static frictioncoeff,rcients reported by Page 1994,1995 for connections containing DPC membranes

commonly used in Australian masoffy construction. This suggests that friction mightsufficientþ transfer the shearing forces although this assumes that the full static frictionalresistance can be relied upon. This assumption therefore warrants further investigation.

(2) The out-of-plane bending failure of walls of URM buildings. Klopp found that hveout of the eleven LJRM buildings analysed under the A51770.4-1993 earthquake had

bending stresses greater than the simply supported elastic bending capacity of the wall.

30

CHAPTER (2) - Earthquakes and Unreinforced Masonry

Current design practice in Australia would thus indicate failure. As will be discussed in

Chapter 5, however, the resulting cracked condition may not constitute failure or collapse

as a reserve dynamic capacity may exist. An additional factor was reported that the stress

was more likely to exceed capacity in the upper stories of URM buildings where

excitation amplification is a maximum and beneficial overburden stress is at a minimum.

2.5.'Capacity' Design for Improved Seismic Response

\ühen considering the preservation of life the most important design criterion is the

Ultimate Limit State. In Australia only the Ultimate Limit State is considered. Here

relatively large inelastic deformations must be accommodated without significant loss of

lateral force resistance or the integrity of the structure to support gravity loads. Although

non-repairable residual plastic deformations may occur the principal aim is to ensure that

collapse is avoided.

The 'Capacity' design strategy has been defined (Paulay 1997) as "In structures so

designed for earthquake resistance, distinct elements of the prinnry lateral forceresisting system are chosen and suitably designed and detailed for energy dissipation

under severe imposed deþrmations. All other elements are then to be protected against

actions that could cause failure by providing them with strength greater than that

corresponding to the mnximum feasible strength in the potential plastic regions." In

theory the application of the 'Capacity' design principal leads to a benign and tolerant

inelastic response with a high degree of protection against the collapse of structures

subjected to severe earthquakes.

For framed reinforced concrete structures the 'Capacity' design methodology can be

followed by detailing plastic hinge locations in beam elements ¡ather than in columns.

Thus, at the Ultimate Limit State a ductile inelastic sway mechanism having strong

energy dissipative qualities is formed without the creation of a failure mechanism. In a

similar fashion for a URM building the 'Capacity' design methodology can be followed

31

CHAPTER (2) - Earthquakes and Unreinforced Masonry

by the selection of a suitably ductile mechanism capable of dissipating seismic energy

without damaging other structural elements due to severe deformations.

As has been discussed in Section 2.4.3 with the correct selection of URM in-plane wallgeometry a failure mode capable of inelastic deformation and seismic energy dissipation

suitable for 'Capacity' design is possible. Other less desirable failure modes such as out-

of-plane bending and anchorage failure must then be protected against. Clearly if the

'Capacity' design principals are to be used effectively for URM it is important that

realistic assessment of dynamic capacity of these failure modes is possible.

2.6 Overall Project AimAs a result of this literature suryey the research aim to be addressed within the scope ofthis report has been determined as providing designers with appropriate tools to avoid the

brittle 'weak link' failure modes in the design of new and the assessment of existing

URM buildings being:

( 1 ) The limited force capacity of connections between floors and walls, in particular the

friction dependent connections containing damp proof course (DPC) membranes and

(2) the out-of-planefailure of walls in the upper stories of URM buildings

The first aim was achieved for the DPC connections through an extensive series ofshaking table tests, which provided realistic data on the connections' dynamic capacity.

The second aim was achieved by an extensive series of shaking table tests used todevelop a better understanding of the physical processes governing the collapse

behaviour of face loaded URM walls. From this improved understanding realistic

analytical models were developed to provide an accurate and reliable assessment ofactual capacity. As these were complex, by necessity, a further rehnement was toproduce a simplistic rational analysis procedure for practical applications.

32

CHAPTER (2) - Earthquakes and Unreinforced Masonry

Once these 'weak links' have been avoided with adequate seismic load paths developed,

carefully designed, detailed and constructed, regular URM buildings have repeatedly

shown that they will behave adequately during moderate intensity earthquakes. Further,

this allows the 'capacity' design methodology to be more effectively undertaken resulting

in an increased effective ductility for URM buildings to be realized.

JJ

3. DPC CONNBCTIONS IN URM

CONSTRUCTION

3.L. Introduction

In general, masonry buildings are constructed utilising a vast array of flashings, damp

proof course (DPC) membranes and construction joints aimed at ensuring satisfactory

serviceability performance. As highlighted in Section 2.3 for Australian unreinforced

masonry (tlRM) construction, connections between a concrete slab and masonry wall are

commonly detailed containing DPC membrane.

Typically, DPC membranes used for URM connections are flexible, manufactured from

either embossed polythene or a light gauge aluminium and covered with polythene or

bitumen. Normal practice is either to incorporate the membrane laid directly adjacent to

the slab with a single mortar layer placed between the membrane and brick or to place it

one to two brick courses up from the slab. This configuration is referred to as a standard

DPC connection. Alternatively, the membrane may also be sandwiched between two

mortar layers although not often used in practice as it is labour intensive. This is referred

to as a centered DPC connection. Finally, in some circumstances no mortar is used with

the membrane laid directly between the brick and slab or brick and brick. For these

connections two layers of DPC membrane are often used back to back. This is referred to

as a slip joint connection. Figure 3.1.1 provides a representation of the above three

connection configurations.

In masonry construction, connections containing a DPC membrane are generally detailed

to fulfil the dual serviceability role of providing an impervious barrier to moisture

movement while acting as a plane of separation between structural elements. The latter

role prevents distress of the connected elements by limiting the transfer of forces and

34

CHAPTER (3) - DPC Connections in URM Construction

strains through the connection, caused by differential movements. While these

movements will be discussed further in Section 3.3.2 it is clear that these connections

must be capable of satisfying two conflicting horizontal shear requirements. Firstly, theymust have the ability to allow for long-term relative movements between structural

elements by limiting force transfer. Secondly, they must provide sufficient shear

resistance to give lateral support to the wall under short-term earthquake loading. Withfriction being relied upon for horizontal shear resistance, the frictional properties are

therefore critical to the successful application of these connections.

Standard DPC Connection Centered DPC Connection Slip Joint Connection

BrickMortarDPCSlab \

BrickMortarDPCMort¿¡Slab

BrickDPCSlab Often2

layers DPCÀAÀA

A4

AÀ

À

Figure 3.1.1 Types of URM Connection Containing DpC Membranes

This Chapter reviews previous work and relevant literature associated with bothserviceability requirements and shear-resisting capacity of URM to concrete slab

connections containing DPC membrane material and presents the specific 'weak link'research focus to be further considered within the scope of this project.

3.2. General Friction Review

The shear-resisting behaviour of a URM connection containing a DPC membrane is

characterised by Coulomb (dry) friction, which involves rigid bodies in contact along a

non-lubricated surface.

3.2.1. Coulomb Friction Behaviour

Investigations (Suh & Turner 1975) into surface topography have shown that the surface

of a dry material such as metal, polymer or brickwork is not smooth but made up of many

tiny peaks called 'asperities'. Thus, when two surfaces touch the real contact area is much

35

CHAPTER (3) - DPC Connections in URM Construction

less than is apparent as only the asperities interact and consequently these govern the

frictional behaviour. When a normal stress is applied to the friction plane the real contact

area increases along with interaction between the asperities.

The static friction coefficient, kv.st¿tic, can be defined as the minimal tangential foÍce, F^,

required to initiate tangential motion divided by the normal load acting on the interface,

N, as is represented by Equation 3.2.1. Hencl, kv.stotic is governed by adhesion of the

touching asperities and has been found to be independent of the apparent contact area,

normal load and duration of loading. Once the adhesion force between asperities F. isexceeded slip at the friction interface follows (refer Figure 3.2.1).

(3.2.1)

The plowing of soft surface layers by hard asperities primarily controls the sliding or

dynamic friction between solids. On sliding, the magnitude of force required to sustain

motion drops from F, to the lesser dynamic friction force, Fr. This reduction in resistance

is caused by less interpenetration of the surface asperities when the surfaces move with

respect to one another and is well documented to be generally of the order of 25Vo (Suh &.

Turner 1975). Thus, the dynamic friction coefficient, kv dynamic, is less than the static

friction coefficient, kv.sta¡c.

Both the static and dynamic friction coefficients strongly depend on the nature of the

surfaces in contact. As the exact condition of the surface dictates these coefhcients they

are seldom known within an accuracy of greater than 5Vo as any foreign material present

at the interface, such as corrosion or dirt, will alter the coefficient.

Coulomb friction can be further catagorised by the type of material at the friction plane as

classically (e.g. metals) and non-classically behaving (e.g. polymers) friction. Since DPC

membranes found in Australian URM construction are cornmonly produced in both of

these materials a brief review of both Coulomb friction behaviours will be presented.

kv.statíc='/*

36

CHAPTER (3) - DPC Connections in URM Construction

3.2. I J. Clas sic ally B ehaving Materíals

There are three generally accepted laws of friction for classically behaving materials.

These are (i) Friction is proportional to the normal load, (ii) Friction is independent of the

apparent area of contact and (iii) Friction is independent of sliding speed.

Once sliding for a classically behaving material has commenced the dynamic frictionforce, F¿, remains approximately constant provided there is no material degradation (refer

Figure 3.2.1).

3.2.1.2. Polymers

The frictional behaviour of polymers differs from that of classically behaving materials inthat it does not necessarily obey the classical laws of friction. Since the static frictioncoefficient for polymers is sensitive to the hydrostatic component of stress it becomes

dependent on normal stress. It has been reported (Suh and Turner 1975) that the dynamicfriction coefficient for polymers can reduce substantially with increased normal force.

A second difference is that polymer frictional behaviour is very sensitive to slidingvelocity caused by the large strain rate and temperature dependence of the flow stress ofpolymers. In any frictional scenario, as sliding velocities are increased the mechanical

work done also increases the interfacial temperature. At a critical velocity/temperature a

maximum dynamic friction coefhcient is reached, and thus a maximum dynamicfrictional resistance force, F q (refer Figure 3.2.1).

For some polymers Fp bas been reported (Rosato et al 1991) to be higher than the

original static resistance force, F.. This is attributed to sliding velocity/temperature

increase prior to the maximum coefhcient of dynamic friction being reached. As strain

rate effects dominate the frictional behaviour the shear force for deformation also

increases. After the critical velocity is passed the frictional behaviour is no longer

dominated by strain rate increases but softening of the polymer which reduces the

dynamic friction coefficient. It has been reported (Corneliussen 1986) that the reduction

37

CHAPTER (3) - DPC Connections in URM Construction

of dynamic friction coefficient may be due to a molten film of polymer developing which

acts as a lubricant so that a hydrostatic sliding condition prevails.

EquilibriumStatic

MotionDynamic

F-Frp

Fr

t¡r(l)okof¡ro9søac)úCdÉo'É()tli

Polymer dynanic frictionbehaviour, increase due tostrain effects with maximumdynamic friction coefficient atpolymer critical velociw

Classical DynamicBehaviour

CRJTICAL FRICTIONAL SIIEARRESISTANCE: F. notreached due ûo

vertical disturbance of the planes

Applied Horizontal Shear Force

Figure 3.2.1 Diagrammatic Representation: Frictional Resistance vs Applied Shear

3.3. URM Connection: Previous Research

In the following section a review of previous work carried out by other researchers

relevant to the serviceability and shear resistance of URM connections is presented.

33.1. Plain-Masonry Joint Shear

As URM connections containing DPC are in essence a plain-masoffy joint containing a

thin flexible DPC membrane, thefu shear behaviour is closely related to that of a plain-

masomy joint. The main differences are frrstly that the frictional properties of the DPC-

brick, slab or mortar interface rather than the mortar-brick interface must be considered.

Secondly, the initial shear bond, caused by mechanical interlock of mortar and brick in a

plain-masonry joint, is typically reduced significantly where a DPC membrane is present.

38

CHAPTER ( 3 ) - D PC Conne uions in U RM Construction

Previous investigators have shown that when an increasing normal compressive stress is

applied to brickwork, the horizontal shear strength at a plain-masonry joint increases

linearly with compressive stress up to a limiting compressive stress. The widely accepted

explanation for this is that the strength of the joint is derived from a combination of initialshea¡ bond and Coulomb friction between the brick and the mortat. Consequentþ, the

relationship between ultimate shear strengh, G, and normal compressive stress, o", isoften expressed by a Coulomb type relationship, such as that shown in Equation 3.3.1

where to is the initial shea¡ bond and p is the friction coefficient of the brick-mortar

interface.

Íu=To* FC" (3.3.1)

Hendry and Sinha, 1981 have reported on a series of tests carried out on full-scale and

model shear walls built of wire cut bricks in l:V¿:3lime mortar. It was found that the

shear resistance for this type of brickwork was well represented by the Coulomb type

relationship shown in Equation 3.3.2urp to a normal compressive stress level of 2MPa.

t,=03+0.5o" (3.3.2)

Similar results using different brick and mortar combinations have also been reported

(Stafford Smith & Carter 1971, Riddington &Ghazali 1990, Magenes & Ca\vi 1992,

seisun etal1994, Mullins & o'conner 1995). Although ro (0.1 to 1.19) and ¡r (0.4 to

1.33) have varied signif,rcantly with the type of materials tested, a similar Coulomb type

relationship has been obtained for low levels of normal compressive stress.

While the linear Coulomb relationship has been consistently reported for relatively lowIevels of normal compressive stress the above resea¡ch has also indicated that the rate ofincrease in shear strength reduces at higher normal compressive stresses. Where this is

the case the value of p appears to decrease with increasing normal compressive stress.

The level at which this reduction begins has generally been reported to be a¡ound 2MPa

39

CHAPTER (3) - DPC Connections in URM Construction

although this is dependent on the quality of masonry construction and materials

considered.

Although initially it was proposed that an average value of ¡r could be assumed over all

normal compressive stress ranges this was questioned as it did not realistically model the

true shear behaviour at higher over burden stresses. In recognition of this Riddington

and Ghazzali (1990) proposed a hypothesis for the shear failure of plain

Here, simila¡ to the original findings of Hendry and Sinha (1981) and

postulated that below a normal compressive strsss of around 2MPa,

initiated by joint slip as predicted by a typical Coulomb relationship. Above this the

shear failure mechanism is governed by tensile failure within the mortar and finally at

very high compressive stress the compression failure of the brickwork becomes the

dominant factor. An experimental investigation was also reported (Riddington & Ghazali

1990) confirming the plain-masonry shear failure hypothesis as represented in Figure

3.3.t.

Also shown in Figure 3.1.1, the plain-masomy joint failure hypothesis (Riddington &Ghazah 1990) can be related to URM connections containing DPC membrane. Since for

these connections both the initial shear bond and friction coefficient may be reduced as

compared with a plain-masonry joint, the intersection of the DPC joint slip and mortar

tensile failure lines will occur at a higher normal compressive stress. For the range of

normal compressive stress commonly found in Australian masonry construction, as

described Section 2.3 it is therefore unlikely that a mortar tensile failure mechanism

would dominate under horizontal load but rather a joint slip mechanism (refer Figure

3.3.1).

n lô.'.

the was

1S

.t,1

'.t*rY

, l,t"Q trüd\l ,il

\"Ì tl

\ ''- v

I

\,¿l' \'f 'r.t'

\"

\,r f'u

-l 40

CHAPTER (3) - DPC Connections in URM Construction

Plain-Slip

oçto.ñt

L)kñl(l)

U)()c!E

at:¡

Morar Tensile Failure

Initialshearbond

Brickwork

Approx.2MPa

Overburden SEess, o.

Range of overburden stress associated with typical Australian applicationsJoint slip is the critical failure mode

Figure 3.3.1 She¡r Failure Hypothesis(Riddington & Ghazali 1990)

In a real loading scen¿rio masonry elements are rarely subject to only one type of load

and are generally in a complex state of stress where in-plane and out-of-plane actions

occur simultaneously (Yokel & Fattal 1976). rüith loading such as earthquake or wind,

URM walls can experience cyclic bi-axial stress states being either tension or

compression. Dhanasekar (1985) has reported on a series of half scale brick masonry

panel tests subjected to bi-axial compression-compression and compression-tension.

Here, it was found that morta¡ joints acted as planes of weakness influencing the failure

loads and failure patterns.

3 3 2. Serviceability Requirements

The following section presents a brief summary of previous research associated withserviceability requirements of connections within URM buildings. One such connection

serviceability requirement is the prevention of distress caused by differential movement

of structural elements. Since movement may be caused by differential movements

associated with concrete slab shrinkage, growth/shrinkage of claylconcrete masoffy

units, thermal movements or foundation settlement, each structural element will behave

differently over time. Consequently, each element will induce forces into adjoining

4l

CHAPTER (3) - DPC Connections in URM Construction

elements. Where the induced force is in shear its magnitude is limited by the shear

capacity of the connection joining the structural elements.

It is well documented that concrete, whether it constitutes masonry units or floor slab

undergoes shrinkage and creep with time. In contrast the time dependent behaviour of

clay masonry is not as well documented and is complicated by the composite nature of

the material. It has however been reported (Beard et al 1969) that the time dependent

movement of brickwork is caused by one or a combination of thermal movement,

moisture movement, chemical expansion or deformation under load. Further research

(Beard et al1969, Cole & læwis I974,Wyatt 1976) has reported on studies associated

with the movement of brickwork. In general, findings were that all of the walls expanded

horizontally and vertically with time and the rate of expansion was maximum during the

early life of the wall and decreased with time.^(- T tp J r'Ln !

It is therefore clear that there is a conflict between the time dependent behaviour of

concrete and clay constructed structural elements. As mentioned in Section 3.1, URM

connections containing DPC are typically detailed to fulfil a dual serviceability role, one

of which is that the shear resistive capacity is sufficiently low to allow the differential

movement between structural elements. Research (Beard et al 1969) has been carried out

to determine if this is actually the case as the magnitude of force transmitted by the

differential movement is difficult to ascertain. Here the movement of brickwork above

and below a lead cored bituminous standard DPC connection at the base of an actual

building was measured. It was found that the lack of shear restraint offered allowed the

brickwork above the connection to move.

Although not directly related to seismic loading another important aspect of URM

building serviceability is the movement of footings supporting masonry walls. Research

(Page & Kleenman 1994) has been undertaken to establish parameters influencing wall

behaviour under such actions. Here, provided the walls had sufficient strength to resist

cracking they were found to bridge the movement of the flexible footings. [n practice

42

( t\'

CHAPTER (3) - DPC Connections in URM Construction

masonry walls often do not have sufficient strength to resist cracking and are commonly

observed to crack under deformations permitted by flexible footing movement.

3.33. Positive Anchorage

As highlighted in S lack of anchorage of masonry walls to floor and roofdiaphragms contributed separation and non-uniform vibration of walls in areas ofmoderate intensity shaking. This was less prevalent, however, with concrete slab

diaphragms, which provided a higher normal compressive stress and increased frictionalresistance than in LJRM buildings with flexible timber diaphragms. Conversely,

anchorage through positive connection of concrete slab and URM wall is more likely tocreate a serviceability conflict due to differential movement whereas this is less likelywith the more flexible timber diaphragms.

In order to assess the vulnerabilify of non-anchored timber diaphragms a non-linear

dynamic analysis able to model the friction and impact characteristics of wood joistbearing on a brick wall has been developed (Jones & Cross 1993). Using this model

comparisons were made with the dynamic response of a retrofitted building in Gilroy,California having a well anchored timber floor diaphragm which survived the M. 7.1

[,oma Prieta (1989) earthquake. While entire city blocks were demolished in nearby

Santa C¡uz and another LJRM building, a Town Hall, two blocks south was severely

damaged the Gilroy building sustained very little damage despite roof accelerations of0.799. As a result of the analysis it was found that the structural response remained

elastic provided the diaphragms and wall were connected. If, however, the joist to wallconnections were disconnected the response of the structure moved into the inelastic

range. In the latter case two possible failure mechanisms were identified as (1) collapse

of the wall in out-of-plane bending and (2) when joists moved sufficiently to cause them

to fall from the wall.

Tomazevic et al (1995) have also reported on a series of shaking table tests completed

with V¿ - scale, 2 storey masonry and stone houses having both unconnected timber joists

supporting a concrete slab and connected timber joists also supporting a concrete slab. It

43

CHAPTER (i) - DPC Connections in URM Construction

was found that freely supported wooden floors did not prevent separation of the walls and

severe out-of-plane vibration of the wall was noted. Where horizontal steel ties were

provided separation of the walls was prevented with ultimate collapse caused by shear

failure of the walls in the first story. The input energy needed to cause collapse of the

model building with connected timber joists was over two times greater than the case of

the model without ties. It was concluded that separation of wall can be prevented by

either anchoring wooden floor joists into the wall using steel ties or replacing wooden

floors with reinforced concrete slabs.

Buccino and Vitiello (1995) have reported on an experimental investigation on three

types of anchorage to assess their pull out resistance. The experiments showed that the

shape of the anchorage and quality of the brickwork had a great influence on the

resistance to pull out ofthe anchorage.

ì'- ¡rlì'-L "" l" .''6''"'' .;'' "J' 4 :

3.3.4. Shear Resistance of URM Connection Containing DPC Membrane

Since the frictional resistance properties of connections containing a DPC membrane íue

specific to the particular membrane used overseas research data is not strictly applicable

for Australian URM construction. This being the case a brief review will be presented

for overseas research where applicable with more focus placed on Australian resea¡ch.

As part of a study of the long term differential movement resistance of DPC connections

British researchers (Beard et al1969) first highlighted the need for an understanding of

the frictional resistance of DPC connections. Here it was highlighted that the shear

resistance was significantly less than for a plain-masonry joint. This was confi¡med by a

further experimental study (Hodgkinson & West 1982) which reported on shear tests to

determine the shear resistance of British DPC materials.

Experimental investigations (McGinley & Borchelt 1990:1991) have also been

undertaken to evaluate static friction coefficients for eight connections containing a DPC

membrane commonly found in the United States. Both in-plane and out-of-plane loading

M

CHAPTER (3) - DPC Connections in URM Construction

directions were investigated with both concrete and steel supports. For standard DpCconnections on a concrete slab, static friction coefficients were found to vary from 0.19 to

0.5. Simila¡ results were reported for steel supports however a significant reduction was

noted with the presence of a coating such as galvanising or paint. While it is generally

accepted that rougher slip plane surfaces produce higher coefficients offriction this study

indicated that both the stiffness of the support material on either side of the membrane as

well as the DPC membrane had a significant effect on the friction behaviour. For a given

roughness of DPC material, stiffer membranes produced higher friction coefficients and

are more likely affected by the properties of the supports. In contrast, for a more flexibleDPC the properties of the membrane tended to dominate the frictional behaviour. The in-plane and out-of-plane behaviour was also found to vary significantly which was

attributed to the differing surface texture of the brickwork in either direction.

Static friction tests on a series of three-brick high prisms with up to 0.9MPa normal

compressive stress have also been reported (Suter & Ibrahim 1992) for DPC materials

commonly available in North America. The significance of these tests is that it was hrstrecognised that the location of the DPC membrane within the mortar joint has an effect

on the frictional behaviour. As such, standard DPC, centered DPC and slip jointconnections were tested. Static friction coefficients were found to range from 0.1 for slipjoint connections to 0.6 for the centered DPC connections.

To establish the frictional characteristics of connections containing DPC membranes

directly applicable to Australian masonry construction a comprehensive series of static

tests (Page 1994:1995) has been reported. The membrane t)pes selected were chosen on

the basis of advice from industry to obtain a reasonable representation of common

construction practice in Australia. Here both two and th¡ee-brick long specimens laid inrunning bond with standard DPC, centered DPC and slip joint connection configurations

were tested. Both in-plane and out-of-plane tests were carried out with normal

compressive stress ranging up to l.5MPa. For the range of compressive stress considered

a Coulomb friction relationship was used to describe the shear resistive behaviour. Thus,

tests were performed at various normal compressive sffess and a linear regression of the

45

CHAPTER ( 3 ) - DPC Conne ctions ín URM Construction

data points used to determine the static friction coefficient and initial shear bond strength.

The resulting static friction coefficients are summarised for DPC connections in Table

3.3.1 and slip joint connections in Table 3.3.2.

Table 3.3.1 DPC Connection Static Friction Coefficient Sumnury (Page 1994)

Table 3.3.2 Slip Joint Connection Static Friction Coeffcient Summary (Page 1994)

SLIP JOINT CONNECTION CONFIGERATION Out-of-Plane(k")

1 Layer of Super Alcor 0.572Layers of Super Alcor 0.482Layers of Galvanised Steel with MolydenumDisulphide Grease

0.06

In conclusion Page reported that for all of the DPC materials considered, with the

exception of poþthylene/bitumen coated aluminium (Rencourse), the static friction

coefficient could conservatively be taken as 0.3 for earthquake loading. Also, although

small shear bond strengths were reported these were generally very small (OMPa to

0.12MPa) and as such would be neglected.

Using similar connection details to the static tests reported by Page (1994:1995), quasi-

static (cyclic) shear tests have also been reported (Griffith & Page 1998). These tests

were aimed at studying the cychc performance of the various membranes under repeated

In-plane 0c,) Out-of-Plane (/s")

CONNECTIONCONFIGERATION

COMMERCIALNAME

Centered Standard Centered Standard

Bitumen CoatedAluminium

Standard Alcore 0.41 0.49 0.50 0.47

Bitumen CoatedAluminium

Super Alcore 0.60 0.41 0.57 0.48

Poþthylene/BitumenCoated Aluminium

Rencourse 0.26 0.26 0.31 0.35

Embossed Polythene Supercourse 500 0.68 0.59 0.59 0.56Embossed Pol¡hene SupercourseT5O o.7l 0.58 0.60 0.59

46

CHAPTER (3) - DPC Connections in URM Construction

loading cycles, in particular the potential degradation of the materials. Quasi-static tests

were performed at velocities of between 50 and 2OOmm/minute and at three levels ofnormal compressive stress. A continuous plot of shear force versus shear displacement

recorded which resulted in a series of hysteresis curves (refer Figure 3.3.2). From these

curves the maximum quasi-static shear resistance force was determined for each level ofnormal compressive stress as the plateau of the hysteresis loop. The quasi-static frictioncoefficient was then the quasi-static friction coefficients determined

were found to be slightly larger than thosewill be presented in

determined previously by A second significant finding of this research was

that even after many cycles of shear displacement very little degradation in shear capacity

was observed indicating that tlRM connections containing a DPC membrane would

perform satisfactorily in service under cyclic loading.

0,ôCËô-àØc)tsv)

3 .10

Figure 3.3.2 Results of Typical Quasi-static on DPC Connection(Griffith & Page 1998)

þ()U)

/IDisplacement (mm)

t0

47

CHAPTER (3) - DPC Connections in URM Construction

3.4. Australian Code Provision: UII,M Connections

The 'SAA Earthquake toading Code', 451170.4-1993 requires connections to be

capable of transmitting a horizontal force of lO(aS) kN/m where ¿ is the acceleration

coefficient and S the site factor. To illustrate this requirement, for a firm soil site in

Adelaide, a = O.lE and S = 1.0. Thus, in this case, connections must be capable of

transmitting a force of lkN/m. Research (Klopp 1996) has indicated that this

requirement may be inadequate being as little as 1/13ù of the required shear capacity for

a two-storey URM building when subjected to the design magnitude earthquake. Despite

this, it was also reported that most typical forms of positive connection would still be

suff,rcient.

As discussed in Section 3.3.3, the positive connection of a concrete diaphragm to a

masonry wall may produce a serviceability problem so that URM connections containing

DPC are often used. Klopp (1996) therefore also compared the calculated confection

shear capacity with experimentally determined (Page 1994:1995) static shear resistance

of connection containing DPC membrane. In general he found that the frictional

resistance capacity was adequate.

Consequently, although friction is generally not recommended as a method of

transferring horizontal loads the 4S1170.4-1993 amendment No.l OCTOBER 1994, now

allows friction to be relied upon at connections containing DPC membrane within

loadbearing masonry construction. The shear resistance capacity however must still be

determined in accordance with the 'SAA Masonry Code',453700-1998 as:

48

CHAPTER (3) - DPC Connections in URM Construction

(3.4.r)

= the earthquake induced design shearforce

= the shear bond strength of the shear section

= Qf'^rA¿*

= the shearfriction strength of the shear section under earthquake actions

= 0.9 kuf¿, A¿n

= the capacity reductionfactor

= the characteristic shear strength of masonry

= the bedded area

- friction cofficient

= the design compressive stress on the bed joint for earthquake actions

= Gr/A¿n

= the gravity load

volv.+vr.

where V¿

vo

Vt"

0

l'^,A¿n

k"

fa

Gs

The first term in Equation 3.4.1 represents the basic shear bond strength and the second

the frictional component of the capacity. For a plane containing a DPC membrane the

shear bond strength is usually negligible as the membrane is generally placed directlyonto brick. The shear capacity of the joint is therefore almost solely a function of frictionand thus on the friction coefficient, k, and the design compressive stress at the frictionplane,f¿.

Importantly, it must be recognised that the currently recommended friction coefficients

are based upon static friction coefficients for URM connections containing DPC

membrane. Confirmation was therefore required to determine if these will be indicative

of the dynamic friction coefficient under true dynamic excitation.

49

CHAPTER (3) - DPC Connections in URM Construction

3.5. Implication of the Dynamic Friction Coefficient

In any seismic event it is well recognised that both horizontal and vertical accelerations

occur. For example Glogau (1974) reported that vertical acceleration as large as two

thirds of the horizontal were recorded during the l9ll San Fernando earthquake. It istherefore possible that with vertical disturbances at the slip interface of a connection

containing a DPC membrane that the maximum static peak tangential force, Fr, may not

be reached as the adhesion between the asperities may already be reduced or broken. Ifthis were the case the critical resistance to shear would then be governed by the lower

dynamic friction force, F¡, and thus dynamic coefficient of friction , kv dynamíc.

As can be seen in Figure 3.2.I the frictional behaviour of the polymer up to the static

frictional resistance force is similar to that of a classical behaving material. Although for

polymers it is possible for the dynamic shea¡ resistance to peak at a critical velocity this

value could not be relied upon due to the unpredictability of earthquake excitation. For

the above reasons it would therefore non-conservative to assume a maximum frictional

resistance force of either F^ or it is possible that the critical resistance to shear

would come from the lower force, F¡.(n4I

3.6. Specific Research Focus

While both static and quasi-static testing has provided data on initial shear bond, static

friction coefficients and the potential degradation of the materials, realistic dynamic

testing is required to quantify the influence of dynamic loading on the frictional

resistance of connections containing DPC membranes. The specific focus of the current

research project related to the DPC connection 'weak link' has therefore been the

undertaking of dynamic testing for the provision of information regarding the true

dynamic behaviour of connections containing DPC membranes commonly found in

Australian masonry construction. This experimental testing phase is presented in Chapter

4 where recommendations are made on the applicability of assuming static or quasi-static

friction coefficients for the seismic design of connections containing DPC membranes.

f År,

50

4. DYNAMIC SHEAR CAPACITYTESTS

ON URM CONNBCTION CONTAINING

DAMP PROOF COURSE MEMBRANE

4.1. Introduction

As highlighted in Chapter 3, concern that the shear capacity of connections containing

DPC membrane under true dynamic loading will be less than under static loading have

led to a series of dynamic shear tests being undertaken. The tests described in this

Chapter were therefore aimed at determining values of dynamic friction coefficients for

connections containing DPC membrane commonly used in Australian masonry

construction.

4.2. Dynamic Shear Tests

Dynamic shear tests were conducted on clay brick masonry connections containing a

variety of DPC membrane material on the eafthquake simulator at the Chapman

Structural Testing Laboratory, University of Adelaide. These have included standard

DPC, centered DPC and slip joint connection conhgurations and considered both in-plane

and out-of-plane shaking. The main advantages of dynamic testing, as opposed to quasi-

static testing, are firstly that true inertial loading can be generated in contrast to

displacement-controlled testing. Secondly, a frequency of loading more representative of

the frequencies normally associated with earthquake induced loading can be applied.

Since dynamic tests are generally more expensive than quasi-static tests, these were used

as 'spot checks' to determine to what extent the quasi-statically determined friction

5l

CHAPTER (4)- þnamic Shear Capaciry Tests On URM ConnectionsContaining Proof Course Membrane

coefficients were representative of those which could be expected in seismic events. Acomparison of dynamic and quasi-statically determined friction coefficients is therefore

presented in Section 4.4.

The earthquake simulator at The University of Adelaide consists of a 1400mm x 2000mm

shake table mounted on bearing runners and is connected to a 200kN INSTRON

load/displacement hydraulic actuator, which is rigidly connected to the laboratory strong

floor. The maximum vertical load capacity (on table) of the INSTRON is 66kN and has a

maximum horizontal displacement capacity of +125mm.

4.2.1. Instrumentation

Prior to and during slip, response accelerations of the applied weight, W, above the slip

interface and the reference acceleration at the shaking table were recorded. The

instruments used to measure these horizontal accelerations were Kistler Servo

Accelerometers powered by a servo amplifier.

To determine relative displacements of the test specimen above and below the frictioninterface, absolute displacements at both the table and concrete slab above the connection

were recorded relative to a stationary datum. Table displacements were recorded

internally by the INSTRON controller. A Linea¡ Voltage Potentiometer (POT), mounted

to a rigid frame connected to the laboratory strong floor, was used to record the absolute

response displacement of the unit above the slip interface. The POT used was a Housten

Scientihc model 1850-050 having a maximum displacement capacity of 500mm and was

powered by a lOVolt DC supply.

The 'Microsoft Windows' based data acquisition system 'Visual Designer' was used to

collect the four channels of data from the two accelerometers, displacement POT and

INSTRON. Data was collected at a period interval of 0.008 seconds (l25Hz), which was

found to be sufficient to capture all relevant frequencies of the response. Since 'Visual

Designer' uses a buffer system to temporarily store data prior to saving to disc, care had

to be taken to ensure that the buffer was sufficiently sized to hold data for the full test.

52

CHAPTER (4)- Dynamic Shear Capacity Tests On URM ConnectionsContøining Damp Proof Course Metnbrane

The overall test set up, location of instrumentation and data acquisition is shown

schematically in Figure 4.2.1.

Test specimenRigid frame fixed ûo

laboratory stong floor

Displacement(POT) Accelerometer

INSTRONHydraulic

Accelerometer

INSTRON conhol panel Data acquisition

Figure 4.2.1 Schenratic URM Connection Containing DPC Dynamic Test Set-up

4.22. Damp-Proof Course Membrane and Materials

For the various dynamic connection shear tests undertaken, four different types of DPC

membrane were tested, having been selected to match as closely as possible materials

used in previous quasi-static tests (Griffith & Page 1998). A brief description of each

DPC material tested is given in Table 4.2.1.

It should be noted that both the Polyflash and Dry-Cor membrane were not identical to

the products used in quasi-static tests. Although the membranes were produced from

similar materials they had a different commercial name and the thickness varied slightly.

Despite this it was expected that their frictional behaviour would be similar.

lrrarÂ"*F ^rfu-

Shaking table

ooo ooo

53

CHAPTER (4)- þnamic Shear Capacity Tests On (JRM ConnectionsContaining Damp Proof Course Mernbrane

T able 4.2.1 DFC Membrane Test Specinrens

Bricks used to construct the connections were standard 'Red' 3 hole extruded clay bricks.

These had the nominal dimensions 230x110x76mm. Mortar was bucket batched using a

l:1:6 cement:lime:sand mix where water was added by the tradesman to achieve a

reasonable workability. Including sand absorbed moisture this typically resulted in a

total batch water content of approximately 23Vo. Associated material tests includingmortar compressive strength and masonry modulus will be described later in Chapter 6.

4.23. Dynamic Test Methodology

As shown in Figure 4.2.2 a concrete slab of dimensions 1000 x 1400 x 100mm was used

to support lead ingots above the connection to be tested thus providing a total normal

weight, W, at the friction interface. By varying the number of lead ingots the normal

compressive force at the friction interface, N (=W), could be varied enabling dynamic

shear tests to be carried out at various levels of normal compressive stress.

While an earthquake event comprises a wide range of frequencies, dominant frequencies

of around 2-5Hz arsnot uncommon. For all the dynamic tests reported here inertial loads

were induced across the friction interface by applying a represent ative ZHz sinusoidal

displacement motion to the earthquake platform. The amplitude of the motion was

gradually increased until slipping occurred at the connection. Once slip occurred, the

dynamic inertia force, Fi, was determined as, Fi -'W x a.¡0, where â5¡p wôs the slidingresponse acceleration sustained by the mass above the friction interface. Since the weightwas already in motion it was assumed that initial shear bond was not relevant so that the

entire resistance force was due to friction. Therefore, for horizontal equilibrium,equating the inertia force with the dynamic frictional resistance force, F* the dynamic

CommercialName Description Nominal Thickness

Standard Alcor Bitumen Coated Aluminium 950 pmm

Super Alcor Bitumen Coated Aluminium 1550 ¡rmmPolyflash Polyethylene/ Bitumen Coated Aluminium 650 pmm

Dry-Cor Embossed Polythene Plastic 850 pmm

54

CHAPTER (4)- þnarnic Sheør Capa.ciry Tests On URM Conn¿ctionsContaining Danp Proof Course Membrane

friction coef|lcient, ku¿you-i"could be determined. As indicated in Figure 4.2.2, kv<lræamic

can be seen to be equal to the response sliding acceleration, rkup, in units of g's.

Rkad ingots

V/

Concrete Slab

t

Sþ responseacceleration, 4¡n Fr=Ìüxa'þ

F.=ku¿t*¡xNButW=NFi=Fa .Iip (8's) = k

"¿yo*t

Test connectioncontaining DPCmembrane

F-

2Hz sinusoidaldisplacement motion

Earthquake simulator pladorm

Figure 4.2.2 Test Specimen Free Body Diagram: DPC Connection durirry Sliding

4.2.4. DPC Connection Tests

For both the standard and centered DPC connection test specimens, two rolvs of

brickwork, four bricks long and two courses high were used to support the concrete slab

and lead ingots. The total area of the friction plane was 194,300mm2. For standard DPC

connections the membrane was placed directly on top of the bottom course of bricks and

mortar placed on top of the membrane material. For centered DPC connections the

membrane was sandwiched between two mortar layers located centrally between the top

and bottom course of bricks. The overall layout of a standard DPC test specimen is

shown schematically in Figure 4.2.3.

For both the standard and centered connections the following membrane conf,igurations

were tested dynamically: I layer of Standard Alcor; 1 layer of Super Alcor; I layer of

embossed plastic; attd ,1 layer of Coated Aluminium. Although

these four tests were ca.rried out at oqy one of vertical compressive sffess

both in-plane and out-of-plane shaking

I

Concrete Base

(0.1

55

examined so that a total of eight

CHAPTER (4)- þnamic Shcør Capøcity Tests On URM ConnectionsDanp Proof Course Membrane

tests were undertaken. Figure 4.2.4 shows a photograph of the set up for a standatd

connection containing I layer of Standard Alcor to be tested in the in-plane direction.

Standard DPCconnection

simulator

Figure 4.2.3 Dynam¡c Test Set-up for Standard/Centered DpC Connection

Displacement

Accelerometers

Shakingdirection(h-plane)

Figure 4.2.4 Photograph of Standard DPC Connection Set up - In-plarrc

425. Slip Joint Connection Tests

The slip joint tests were conducted using a similar procedure to that for the DPC

connection tests. The main difference \ryas that the concrete slab plus lead weights were

supported by four bricks which were bedded directly onto the earthquake simulator using

a high strength dental paste. The membrane material was placed between the top of each

brick and the underside of the concrete slab. Slip joint connections containing the

POT

Iæad Ingots

Concrete

Concrete Base

56

CHAPTER (4)- þnanic Shear Capaciry Tests On URM ConnectionsContaining Damp Proof Course Membran¿

following membrane conflgurations were tested dynamically: 1 layer of Standard Alcor;

2 layers of Standard Alcor; 1 layer of embossed plastic; and 2 layers of greased

galvanised steel sheets. The slip joint tests rr¡vere performed over a range of three normal

compression stresses being 9,q4,_Q.J8 an{_0.33 MPa.\

direction. According,.ly, twelve tests' \ryere'bompleted.'\- -,multiple conf,rrmatory tests were also undertaken.

conducted only the in-plane

As for the DPC

Slip Jointmembranebetween brick and slab

Dental paste Earthquake simulator pladormIn-plane shaking direction

Figure 4.2.5 Schemtic Diagram of Dynamic Test Set-up For Slip Joint Connection

Although some polishing of the concrete slab was observed after multiple tests this was

not found to greatly reduce the dynamic friction coefficient.

4.3. Results Formulation and Data Analysis

The basic procedure for the formulation of results, including the calculation of the

dynamic friction coefficients was the same for both DPC and slip joint connections. This

process included:

(1) calibration of raw output data to the required units;

(2) filtering of calibrated data;

(3) determination of the time of first slip;

(4) determination of slip acceleration and corresponding force;

(5) check slip force using displacement amplitude just prior to slip;

(6) plotting of the shear stress versus normal compressive stress; and

(7) determination of the dynamic friction coefficient as the gradient of the shear stress

versus normal compressive stress plot.

ingots

Concrete slab

57

CHAPTER Ø)- Dynanic Shear Capaciry Tests On URM ConnectionsContaining Proof Course Membrane

43.1. Data Filtering

Since a zlfz sinusoidal displacement motion was input to the earthquake platform onlyfrequencies near this were considered to be relevant to the response. Figure 4.3.1 shows a

typical Fast Fourier Transform (FFT) of response acceleration data where the 2Hz

frequency amplitude is clearly dominant. In order to remove irrelevant noise frequencies

from the raw data a Fortran 77 band-pass filter program was specif,rcally developed forthese tests (the code is included in Appendix (A)).

Figure 4.3.1 Dominant Response Acceleration Frequencies

Extensive testing of this filter was undertaken to determine the most suitable band-pass

shape and provide an indication of the accuracy of the filter. It was found that a parabolic

sided band-pass filter gave the best results although the hrst and last second of data was

found to be slightly corrupted and as such were discarded. Although the filter program

allows any band-pass range to be set to best encompass the relevant frequencies full pass

was considered between 1.5 and2.5Hz reducing to zero at 0.5H2 and3.SHzrespectively(refer Figure 4.3.2).

I

J .I^

350

300

250

2N

150

100

50

0

o€e

?clcgq?eqqgeqcqqqqeeqocto{h\oræo\O ÈÈÊÊcl

tr'requency (Fz)

58

CHAPTER (4)- þnatnic Shzør Capøcity Tests On URM ConncctionsContaining Danp Proof Course Membrane

1.2

zrõ? o.a

é o.uF<

4. o.¿I

?, o,0

N or¡so

FREQIIENCY (Hz)o o N

r \I \I \I \/

Figure 4.3.2 Parabolic Sided Band Pass Filter - Bandlvidth

4.3 2. Dynamic Friction Coefficient Represent¿tive Calculation

The following Section provides a representative calculation of the dynamic friction

coefficient. Here a slip joint configuration with two layers of Standa¡d Alcor (refer Table

4.2.1), subjected to in-plane shaking with a normal overburden stress of 0.18MPa

(N=17.8kN) is used to illustrate the result formulation procedure.

Figure 4.3.3 shows the absolute displacement response of both the connection above and

below the slip interface relative to the stationary datum. Prior to 24.5 seconds both the

top and bottom units behave as one as the input table sinusoidal displacement motion is

gradually increased. At 24.5 seconds the connection's shea¡ resistive capacity is

exceeded and slip occurs. From this time on the frictional resistive force is proportional

to the dynamic friction coefficient, ku.¿vou-i". Since this is slightly less than the static

friction coefficient there is a respective decrease in the sinusoidal response displacement

amplitude that the unit above the connection can sustain during sliding. The response

accelerations of the unit above the interface are recorded as is shown in Figure 4.3.4.

Here a maximum of 0.469 is observed. The dynamic friction coeff,rcient is then

determined directly from the slip acceleration as 0.46. From the acceleration response

data, hysteresis behaviour can also be developed as shown in Figure 4.3.5. The

maximum dynamic frictional resistive force can be determined as the top and bottom

plateau of each hysteresis loop as 7.7kN.

59

CHAPTER (4)- þrnmic Shear Capaciry Tests On URM ConnectionsContaining Danp Proof Course Membrane

Absolutc Dlsplacements

- Displacement belotÃ, connection

- Displacemøt above connection

60

40

E 'rnÈËoogcÊ -20Ê

40

-60Tlrne (secs)

Unit above connection moves to one side due ø slightly different frictional behaviou¡ in eiiber shakingdi¡ection. The average of botb directions must th¡efo¡e be considered.

ocmô¡

First slip hls 6çPuI€d at 24.5 s€cs

ôl

oc!{cìdeì

oô!\od

a(sllp) Just Aftor Xìrst Sllp V's TlmeFllûercd ave alnax (after first slip) = kv = 0.469

e6oogg

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

-0.5Tlme (secs)

çqa.¡

æqçN\oac¡

(ìa\oN

Figure 4.3.3 Relative Connection Displacenrcnts

Figure 4.3.4 Response Acceleration above Slip Interface during Slipping

Figure 4.3.5 llysteresis Behavior¡r after Slip showing Maximum Shear Resistive Force

Hystereüc BehavlourFllte¡ed Ff(max) = 7.7 kN = amx N

z.¡a

oo

f¡rÊ

(t)

l07.5

5

2.5

0

-2.5

-5

:7.5

-10Reladve Jolnt Dbplacemcnt (mm)

ne.¡

q)t-N

nN

60

CHAPTER (4)- þnamic Shear Capacity Tests On URM ConnectionsContaining Darnp Proof Course Membrane

4.33. Theoretical Check

To check that recorded accelerations were of the correct order the following calculation

was undertaken for all tests.

The steady-state displacement response of a single degree of freedom system (SDOÐ

subjected to harmonic loading is of the form:

u(t;=Asin(CIt-0)where u(t) = displacement response

A = Displacement amplitude

6 = Angular frequency =2ftf/= Frequency

0 = Phase angle

(4.3.1)

By integrating and double integrating this both the velocity v(t), and acceleration a(t)

response can be determined respectively as:

v(t) = -A sin (ot - e) (4.3.2)

a(t) = -Aõ2 sin (õt - 0) (4.3.3)

The maximum acceleration therefore occurs when sin(õt - e) = I and is given as:

âunx = l-eot l= l-Nzrrn'l Ø3.4)

For the case of a 2Hz sinusoidal response, the maximum acceleration is related to the

amplitude of the displacement response by:

Írnax= l-n4ù'l =157.94 1mm/s2)

For the example in Section 4.3.2, A at slip = 28.5mm implies

ârnx = 157.9 x28.5t(9.81x 103) = 0.46 g

This agrees thereby confirming that the acceleration data (and hence friction coeff,rcients)

were consistent.

6t

/

CHAPTER (4)- þnamic Shear Capacity Tests On'URM ConnectionsContaining Proof Course Membrane

4.4. Dynamic Test Results

4.4.1. DPC Connection Dynamic Test Results

Representative DPC connection test data is presented in Appendix (B) in a similar format

to that described in Section 4.3.2. A summary of results for standard DPC connection is

given below in Table 4.4.1 and presented graphically in Figure 4.4.1. Similarly a

summary of results for centered DPC connections is given in Table 4.4.2 and presented

graphically in Figure 4.4.2.

4.4.1 Results Sumrmry for Standard DPC Connection Tests

Figure 4.4.1 Graphical Results Sumrnary for Standard DPC Connection Tests

1

(/'a\

0/

/^\LI

(

'1 Standard DPC Connection(Ref. Table 4.2.1)

NormalForce(kN)

NormalStress(MPa)

flma*

(g)

FL

(kN)

ShearStress(MPa)

k v.dynamic

1 Layer Standard Alcor 31.9 0.164 0.44 14.0 0.072 0.44

1 Layer Super Alco¡ 31.9 0.164 0.47 15.0 0.077 o.4l1 Layer Polyflash 3r.9 0.764 0.37 1 1.8 0.061 o.37

I Layer Dry-Cor 31.9 0.164 0.36 .511 0.059 0.36

-Linear

(Super Alcore)

Linea¡ (Polyflash)

- - - - - -Linear (Standa¡d Alcore)

Linear (Dry-Cor)=l(

a

-

tfJ

Slope defines dynamiccoeffrcient of friction

clÈÀøoq)L

(t)¡rco)

v)

0.09

0.08

0.07

0.06

0.05

0.ù1

0.03

0.02

0.01

0.00

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Normal Stress(MPa)

62

CHAPTER (4)- Dynnmic Shear Capaciry Tests On URM ConnectionsContaining Damp Proof Course Membrane

Standard DPC Connection(Ref. Table 4.2.1)

NormalForce(kN)

NormalStress(MPa)

ânnx

(e)

Fr

(kN)

ShearStress(MPa)

k v.dFamic

1 Layer Standard Alcor 3t.9 0.164 0.31 9.9 0.05r 0.31

1 Layer Super Alcor 3r.9 0.164 0.35 tt.2 0.057 0.35

1 Layer Polyflash 31.9 0.164 0.38 t2.t 0.062 0.38

1 Layer Dry-Cor 3r.9 0.t64 0.41 13.1 0.067 0.41

Table 4.4.2 Results Sunmnry for Centered DPC Connection Tests

Figure 4.4.2 Graphical Results Sumrmry for Centered DPC Connection Tests

On completion of the dynamic tests the connection was examined to determine at which

interface slip had occurred. For centered DPC connections slip was always observed

between the mortar and DPC membrane and for standard DPC connections slip was

always observed between the brick and DPC membrane.

rüith the exception of embossed polythene (Dry-Cor) and Polyflash membrane, the

dynamic friction coefficient for centered DPC connections \Mere less than for standard

DPC connections. In contrast, other researchers (Page 1994) have reported static friction

coefficients for centered DPC connections usually greater than for standard DPC

îÈ¿6øc)

U)¡r6lO

(t)

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

0.00 0.o2 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

Normal Stress(MPa)

-Linear

(Super Alcore)

Linea¡ (Polyftash)

- - - - - -Linear (Standard Alcore)

Linea¡ (Dry-Cor)a

X

63

CHAPTER (4)- þrumic Shear Capaciry Tests On URM ConnectionsContaining Damp Proof Course Membrane

connections. This difference is attributed to a high dependency on workmanship, as any

irregularity in the mortar bed below the membrane will significantly impact on the

frictional properties of a centered DPC connection. As such, comparison of the frictionalbehaviour of these connections, with other researcher's results, is difficult.

As mentioned in Section 3.3.4 previous resea¡chers have found that for a given roughness

of flashing material, stiffer DPC membranes produce higher coefficients of friction and

are more likely to be affected by the properties of the support. The dynamic test results

imply that the mortar-DPC sliding plane of the centered DPC connection provided less

frictional resistance than the brick-DPC sliding plane of the standard DPC connection.

This indicates that the stiffness of the support mate¡ial on either side of the membrane

had a significant effect on the friction behaviour for the relatively stiffer Alcormembranes. Further the Polyflash and embossed polythene, which were less stiff,frictional properties did not appear to be as greatly effected by the properties of the

supports but were dominated by the behaviour of the DPC membrane.

4.42. Slip Joint Connection Dynamic Test Results

Representative DPC connection test data is presented in Appendix (C) in a similar format

to that described in Section 4.3.2. Results of dynamic stip joint shear tests at various

levels of normal compressive are presented in Figure 4.4.3 to Figure 4.4.5 for out-

of-plane loading and Figure 4.4.8 for in-plane loading. The dynamic\as the gradient of the-lirea¡-regression line. Thefriction coefficient,

embossed plastic (Dry-Cor) slip joint connection shear test was only completed at one

level of normal compressive stress (0.33MPa) where the dynamic friction coefficient was

0.41. Comparison of the in-plane and out-of plane plots indicated that no significant

difference was apparent in the dynamic friction coefficient obtained for the two loading

directions. This is attributed to there being no distinct difference in the roughness of the

brick fo¡ the two directions. Consequently no further distinction will be made with regard

to loading direction.

1IìI

2.4.1

64

CHAPTER (4)- Dynamic Shear Capacity Tests On URM ConnectionsContaining Damp Proof Course Membrane

(dê.àØ.t)c)k€

V)L(Úo)

V)

0.15

0.10

0 .05

0.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35Normal Stress (MPa)

Figure 4.4.3 Out-of-plane Slip Joint - l Layer of Standard Alcor

Figure 4.4.4 Out-of-plane Slip Joint Test - 2 Layers of Standard Alcor

Figure 4.4.5 Out-of-plane Slip Joint Test - 2 Layers of Greased Galvanised Steel

0.20(nÀàØ.t)o)t<

V)li

o(t)

0.

0.

1 5

01

0 .05

0.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35Normal Stress (MPa)

v =0.47x )

e 0.05Àe o.o4ØØg 0.03

(t)E 0.02C)

Ø 0.01

0.000.00 0.0s 0.10 0.15 0.20 o.25 0.30 0.35

Normal Stress (MPa)

65

CHAPTER (41 þnatnic Shear Capacity Tests On URM ConnectionsContaining Damp Proof Course Membrane

0.20(!ô-

ØE 0.10LV)þ 0.0so)u) o.oo

0.00 0.0s 0.10 0.15 0.20 0.25 0.30 0.3sNormal Stress (MPa)

1ù'' Y =o'44x

Figure 4.4.6 In-plane Slip Joint Test Resr¡lts - 1 Layer of Standard Alcor

Figure 4.4.7 In-plane Slip Joint Test Results - 2 Layers of Standard Alcor

Figure 4.4.8 In-plane Slip Joint Test Resr¡lts - 2 Layers of Greased Galvanised Steel

CÚÀl<rÀ.t).t)(l)È

U)¡rclo)

v)

0.

0.

0.

20

I 5

0I

0.05

0.00

0.00 0.05 0.10 . 0.15 0.20 0.25 0.30 0.35Normal Stress (MPa)

C€lJiàØØ6)È

U)L(Éc)

v)

0.04

0.03

0.02

0.01

0.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35Normal Stress (MPa)

Y = 0'lx

a

)

o

66

CHAPTER (4)- þnamíc Shear Capaciry Tests On URM ConnectionsContøining Damp Proof Course Membrane

4.43. Comparison of Dynamic with Static and Quasi-Static Test Results

Table 4.4.3 and Table 4.4.4 respectively present a comparison of friction coefficients for

standard DPC and slip joint connections determined statically and quasi-statically by

previous research and dynamically as part of the current resea¡ch project.

Table 4.4.3 Standard DPC Connection Friction Coefficient Comparison

* Not same commercial product as used in the quasi-static tests

Table 4.4.4 Slip Joint Connection Friction Coeffcient Comparison

* Not same conìmercial product as used in the quasi-static tests

Since by necessity the geometry of the quasi-static and dynamic testing apparatus were

not identical the direct comparison of results is somewhat limited. However, an indicative

comparison of results is still useful. It is of particular interest to note that the value of the

dynamic friction coefficient divided by the quasi-static result (as a percentage). For the

membrane qrpes, which \ilere coflìmon to both sets of tests, the dynamic friction

coefficients were greater than or equal to 80Vo of the quasi-static test value. For all

membranes, except the greased galvanised steel, the dynamic friction factor was also

found to be greater than the 453700-1998 code prescribed design value of 0.30.

Joint Type Friction Coefhcient, ku Dynamic (%)Quasi-StaticStatic

Page/1994)

Quasi-staticGriffith et al

(1998)

Dynamic

1 layer of Standard Alcor 0.460 0.520 0.43 827o

2layer of Standard Alcor 0.470 0.569 0.46 817o

I Layer Dry-Cor (Embossed plastic) 0.304 o.267 0.41* N/A2Layerc of Greased Galvanised Steel 0.074 0.108 0.11* lOOTo

Joint Type Friction Coefficient, k,, Dynamic (7o)

Quasi-StaticStaticPage

(tee4)

Quasi-staticGriffith et al

(1ee8)

Dynamic

Standard Alcor 0.44 N/ASuper Alcor o.527 0.541 0.47 87Vo

Rencourse/Polyflash 0.259 0.3r7 o.37* N/AEmbossed Polythene/Dry-Cor o.397 0.329 0.36* N/A

67

CHAPTER (4)- þnamic Shear Capacity Tests On URM ConnectionsContaining Damp Proof Course Membrane

4.5. Summary and Conclusion: ImplÍcation for Design

The results of dynamic shake table tests on DPC and slip joint connections which are

typically used in unreinforced masonry construction in Australia have been presented.

The main purpose of these tests was to evaluate the connection performance underdynamic loading in order to assess their seismic integrity. Dynamic friction coefficientsdetermined from these tests were then compared with qtrasi-static friction coefficientsdetermined by previous research (Griffith et al 1998) to assess to what extent the quasi-

statically determined friction coefficients represented those which could be expected inseismic events. Here it was found that the dynamic friction coefficients were not more

than 20Vo less than those determined quasi-statically. Further, with the exception ofgreased galvanised sheets no connection had a friction coefficient less than the 453700-1998 code prescribed design value of 0.3. Additionally the observed 'seismic strengthcapacity' of the connections considered were greater than the 'seismic load demand'calculated by Klopp for most of the eleven buildings he analysed.

68

5. STABILITY OF SIMPLY SUPPORTED

URM WALLS SUBJECTED TO

TRANSIENT OUT-OF.PLANE FORCES

5.1. Introduction

(Paulay & Priestþ 1992) have described the response of masonry walls to out-of-plane

seismic excitation as:

" one of the most complex and ill-un-derstood areas of seismic a nalysis"

Traditionally designers have perceived URM as a brittle form of construction, and thus

considered it particularly sensitive to peak ground accelerations. In contrast, recent

research has shown that dynamically loaded IIRM walls may sustain accelerations well

exceeding their elastic capabilities (ABK 1985, Bariola 1990, Lam 1995). This apparent

anomaly points to our lack of understanding of the true collapse behaviour of URM

walls.

The complexity arises from the fact that the response can be highly non-linear as the

behaviour is largely governed by stability mechanisms rather than material failure. Not

surprisingly, when compared with other areas of structural and earthquake engineering,

the current knowledge of the out-of-plane behaviour of masonry walls to seismic loading

is sparse.

Figure 5.1.1 shows a fypical outof-plane wall failure in the upper story of a URM

building during the 1989 Loma Prieta, California earthquake.

69

CHAPTER (5)- Stability of Simply Supported URM WaIIsSubjected to Transient Out-of-Pløne Forces

Figure 5.1.1 Out-of-plane Wall Failure during Lonra Prieta Earthquake, 1989

The following sections review important rispects of the behaviour of URM walls when

subjected to transient out-of-plane forces. Previous experimental and analytical work isdiscussed and followed by a critical review of the current analysis and designmethodologies. This Chapter concludes with both the specific experimental and

analytical resea¡ch focus to be addressed within the scope of this report.

5.2. Fundamentåls of Out-of-Plane URM Walt Behaviour

The lateral strength capacity of a simply supported URM walls s,uþjscted to out-of-plane

loading depends on many variables. Possibly the most fundamental of these is the

manner of spanning of the wall between supports. In the simplest case a verticallyspanning wall is supported only at the top and bottom so that under out-of-plane loading

a vertical one-waj'bending action develops. Since vertical movement at the top support is

not restrained any applied vertical compressive force remains constant regardless of any

elongation of the tension face during loading. This type of wall can be related to eitherloadbearing or non-loadbearing internal LIRM partition walls (without returns) or verylong URM walls where the side boundary conditions do not significantþ impact on the

wall behaviour.

70

CHAPTER (5)- Stability of Simply Supported URM WalkSubjected to Transient Out-of-Plane Forces

When return walls or engaged piers are more closely spaced, the wall's response to out-

of-plane loading becomes more complicated, consisting of combined vertical and

horizontal bending. These walls are therefore referred to as two-way spanning walls and

tend to have an increased lateral force resistance capacity over that of a simila¡ sized but

one-way spanning wall. Further complications arise since brickwork is strongly

anistropic, i.e. behaving differently in orthogonal directions. Depending on the number

and nature of supported edges, various cracking patterns are also possible, thus affecting

the lateral resistive capacity of the wall. Over the past 30 years a number of static testing

programs have been completed on the two-way bending of URM wall panels (Baker

1973, Hendry 7973, West et al1973:1977, Lawrence 1975:1994, DeVerkey et al 1986,

Drysdale et al 1988) resulting in several static analysis techniques. The most recent of

these is the Virtual Work Method (Lawrence 1998) where internal and external work are

equated. Due to the complexity of the problem, however, as yet no static analysis

methodology has been readily evolved into a dynamic analysis procedure.

7 Another category of URM wall commonly found in Australia is the full infill panel whereti

a masonry wall is constructed within a framed construction without gaps. In this case,

under lateral load, elongation of the tension face due to bending can not occur without

inducing a large compressive force from the surrounding frame, which acts as a rigid

abutment. This results in an arching behaviour where the vertical compressive force

increases with mid-height displacement. On further increasing lateral load the vertical

compressive forces become suff,rciently large to crumble the brickwork at vertical

reaction points. This material failure permits further displacement of the wall as its

length is reduced until ultimately instability occurs. However, a lateral strength capacity

typically much greater than one or two-way bending walls is realised. As the wall's

ultimate behaviour is dominated by progressive damage and material failure, a 'quasi-

static' analysis is often used to assess the peak lateral capacity of these walls. Various

researchers have addressed the out-of-plane behaviour of this type of wall resulting in

static arching analysis procedures (Baker 1978, Hendry 1981, Abrams et al 1996). In

Australia many inhll panels are constructed with a gap at the top, filled with mastic or

7l

CHAPTER (5)- Støbiliry of Simply SupportedURM WaltsSubjected to Transient Out-of-Plane Forces

sealant, and a gap at the sides with special connectors to allow for brick expansion. Thistype of wall is therefore a special case of two-way spanning wall.

As a first stage in the development of a method that may also be applicable as acomponent of the more complicated dynamic two-way behaviour, an understanding ofthe physical process underlying one-way dynamic action must first be developed.

Consequently, the fundamental focus of the current research project has been the

experimental and analytical evaluation of the dynamic behaviour of one-way bending

URM walls.

For the one-way bending failure of URM walls there are three key contributingphenomenon; (1) tension cracking of the masonry, (2) compression crushing of the

masomy at the vertical reactions (including mid-height) and (3) ultimate instabitiry of the

wall. Unless the walls have very high compressive axial loading, crushing is rarelysignificant. Since in Australia overburden stresses are generally relatively low, localcrushing at vertical ¡eactions is not a major problem. Hence, cracking and instability ofthe wall typically dominate the ultimate behaviour.

Another distinguishing aspect of URM walls subjected to out-of-plane forces is whether

the loading is a gradual monotonically increasing static load, or a more rapid and

reversible dynamic load. This distinction is drawn as 'dynamic stability' concepts,

discussed further in Section 5.3.2, contribute to the walls lateral force resistive capacity.

When a one-way spanning wall is dynamically loaded in the out-of-plane direction an

inertia load is induced into the masonry wall. Prior to cracking, the wall essentially acts

elastically where deformations are relatively small and hence do not significantly impact

on the distribution of inertia force. The accelerations felt by the wall can therefore be

obtained by averaging the input accelerations at the top and base of the wall. Should the

applied accelerations exceed the elastic capacity of the wall, cracks will form at locations

of maximum moment i.e. the top and base support and near the mid-height of the wall. Ifthe top and base crack occur first the theoretical position of the span crack will be

72

CHAPTER ( 5 )- Stability of S imply Supp orte d URM WøllsSubjected to Transient Out-of-Plarc Forces

determined by the relative value of the induced moment at these locations. These

moments can be related to the eccentricity of the vertical reaction forces and are therefore

dependent on the connections forming the boundary conditions. Typically, the crack

occurs near the mid-height of the wall as the bending moment diagram in this region is

usually reasonably flat, generally only varying by 1l7o from the mid-height to the three

quarter height of the wall (Phipps 1994). Practically, the crack will only appear at a

mortar joint and will therefore depend on the relative weakness of individual mortar

joints in the region ofpeak stress.

As was discussed in Section 2.3, the 1989 Newcastle earthquake highlighted that the

condition of both new and existing LJRM building stock is generally unknown with poor

maintenance and workmanship common place. Further, many existing URM buildings

are already cracked due to low strength mortar, settlement of footings, or temperature and

moisture changes. Past earthquakes and/or accidental damage may also have previously

induced cracking. Despite this many severely cracked masonry buildings are often still

standing after earthquakes and have been able to resist strong aftershocks. Following

these observations it is pertinent to examine the post-cracked seismic resistance of simply

supported tlRM walls.

5.2.1,. Post-cracked Force-Displacernent (F-^) Relationship

Once cracking occurs three joints are formed at the top, mid-height and base of the wall,

such that the portions of the wall above and below the mid-height crack act as free

rocking bodies' __j

The non-linea¡ F-Â relationship of a face loaded IJRM wall results f¡om the complex

interaction of gravity restoring moments, the movement of vertical reactions with mid-

height displacement and P-Â overturning moments. A coÍImon simplification is toapproximate the two free bodies as rigid thus having an infinite material stiffness as

shown in Figure 5.2.1. I-ateral load is initially resisted by gravity restoring moments due

to self-weight and applied overburden loads with the vertical reactions at the three joints

acting at the extreme compressive faces of the wall. This initial rigid resistance is termed

73

CHAPTER (5)- Stability of Sinply Supported URM WøttsSubjected to Transient PI¿ne Forces

the 'rigid threshold resistance' force, R"(l) and is related to wall geometry, overburden

and eccentricity of the vertical reactions and thus the wall boundary conditions.

R"(l)

R*(1

(A)

'Peak Rigid Resistance Threshold' Force

Rigid Infinite Initial Stiffness

Idealised Rigid Bi-linear F-Â Relationship

'Peak Semi-rigid Resistance' Force

(BReal Semi-rigid Non-linear F-Â Relationship

\Rigid IncipientInstabiliryDisplacement

Mid-height Displacement ( A) \rr, ¡o6 ¡¡¡y &rs ubìatyiígid )

(B) (c)OverburdenForce = O

Self weightabove crack='ttrI12

Base reaction=O+W

Figure 5.2.1 Reat Semi-rigid Non-linear X'orceDisplaccnænt Relationship

\

\\\\(

\\

\\

zJ¿

Èqtoof¡i3HE€€oÞ.È

\ \ \

Âc A¡or¡o6¡Y.¡y

74

CHAPTER (5)- Stability of Simply Supported URM WøllsSubjected to Transient Out-of-Plane Forces

When the lateral force exceeds R*(l), a mid-height displacement occurs, permitted by the

rigid rotation at the three joints. P-À effects then reduce the gravity restoring moments as

the resultant of the vertical forces above the mid-height crack moves toward the wall's

back compressive face. With further displacement P-À effects continue to reduce the

lateral resistance of the wall creating a negative stiffness arm, Ç(1), of the bi-linear F-A

relationship (refer Figure 5.2.1). \ilhen the vertical force resultant above the mid-height

crack moves outside of the wall thickness the resistance to overturning is reduced to zero.

The displacement at which this occurs is termed the 'rigid instability displacement',

Ainstabilitfrigid).

For a real URM wall, the brickwork comprising the two free bodies does not have an

infinite stiffness and as such does not behave completely as assumed by the idealised

rigid body theory. Instead the real semi-rigid F-À relationship for the rocking system is

more complicated and non-linear than that of the idealised bi-linear rigid F-A

relationship.

More realistically, in the vertical position prior to lateral load being applied, all vertical

reactions act along the centerline of the wall. Consequently, any applied lateral load will

cause a mid-height displacement to occur. This then forces the vertical reactions at the

joints to move towards the extreme compressive faces of the wall, thus increasing the

gravitational restoring moment lever arm (refer Figure 5.2.1 (A)). The rate at which the

reactions move is proportional to the rate of loading and modulus of the brickwork. On

further displacement the lateral resistance continues to increase due to the movement of

the vertical reactions increasing the gravity restoring moments at a greater rate than the

reduction caused by the P-A effects. At a critical displacement, ^",

when the stabilising

effect of these two opposing actions equalize the peak 'semi-rigid resistance th¡eshold'

force, R*(l), is realised (refer Figure 5.2.1 (B)). The higher the modulus of brickwork

the closer the scenario is to that of the rigid assumption. As a result the closer the critical

displacement will occur to the vertical position and the higher the relative value of 'semi-

rigid resistance threshold' force. Beyond ^c

the non-linear relationship approaches the bi-

linear rigid relationship as the vertical reactions are forced into the extreme compressive

75

CHAPTER (5)- Stability of Simply Supported URM WallsSubjected to Transient Out-of-Plane Forces

zones. The curves do not converge, however, due to the finite compressive stress block

at the vertical reactions (refer gap Figure 5.2.1). The larger the overburden and the lower

the brickwork modulus the larger the gap.

For a static lateral load scenario, beyond the 'threshold resistance', regardless of whether

rigid or semi-rigid behaviour is considered, survival of the rocking wall is dependent on

the removal or reduction of the static load. Here the wall is said to be in 'unstable

equilibrium'. At any displacement, prior to the instability displacement being reached, ifthe load is statically removed the wall unloading F-A relationship will trace back the

loading relationship to the vertical position.

As the wall mid-height is displaced its potential energy (PE) is increased with the raising

of the wall's center of gravity to a maximum at the incipient instability displacement.

Thus, in a dynamic lateral load scenario, survival of a wall beyond the 'threshold limit' isdependent on whether or not the inertia force has sufficient energy to overcome the

increased potential energy (PE) so as to further increase the displacement to incipient

instability. This energy requirement can be related to the kinetic energy (KE) or velocity

of the rocking wall as it passes the static vertical alignment plus any additional input

energy that may occur within the failure half cycle. If insufficient energy is available and

instability does not take place, the PE which is a maximum at the peak half cycle

displacement, is converted back to KE by the gravitational restoring moments. As such,

the wall's F-A relationship will trace back the loading relationship forming a naffo\¡/

hysteresis loop due to energy losses in joint rotation. As the wall again passes the static

vertical alignment the KE is at a maximum (since the velocity is a maximum) and PE is

zeÍo. Again, KE is converted to PE with displacement in the opposite direction. This

exchange ofenergy continues as free vibration until energy losses reduce the total system

energy to zero. At this time the wall has returned to the vertical position. Provided the

three joints have not degraded through impact or joint dislocation on re-loading, the wall

will have a similar F-A relationship and dynamic behaviour.

76

CHAPTER (5)- Snbiliry of Simply Supported URM WølIsSubjected to Trønsient Out-of-Plane Forces

Since the non-linear F-A relationship also largely governs the frequencydisplacement (/-

A) relationship of a rocking wall system, this is also highly non-linear. The non-linearity

can be illustrated by a comparison of secant stiffness at low and high levels of

displacement amplitude. Here the secant stiffness is associated with the effective

average half cycle secant stiffness. At low displacement amplitude ^{-,

the secant

stiffness K¡, is substantially larger than at large displacement amplitude Ân, where the

secant stiffness is Ks (refer Figure 5.2.2). Since the secant stiffness is directly

proportional to the square of the haH cycle natural frequency it can be shown that the

frequency at low displacement amplitude is relatively large and reduces to zero at the

incipient instability displacement. Figure 5.2.2 also shows a schematicf relationship.

The schematic/-A relationship shown in Figure 5.2.2 is somewhat idealised as it is ra¡e

for frequencies nea¡ to the incipient instability displacement to occur so that a lower

frequencies limit, fi.¡t, is often observed. V/hile it is theoretically possible for

frequencies below/¡¡6¡ to occur they are unlikely as the system becomes unstable at these

displacements for reasons described below.

As already discussed the F-A relationship of URM walls are highly non-linear and as a

consequence the responses have no unique natural or resonant frequency. It has however

been shown that URM walls undergo larger displacement amplification at certain forcing

frequencies. This indicates that they have a unique effective resonant frequency being

related to the forcing frequency associated with the largest displacement amplification in

a simila¡ fashion to the natural frequency of an elastic system. For the non-linea¡ rocking

URM wall systems, the maximum displacement amplification will result when the

applied forcing frequency is derived from the average secant stiffness of the half cycle

under consideration. Thus, for the critical case where the maximum half cycle

displacement reaches the incipient instability displacement, Âinsrablity, the associated

effective resonant frequency,,f"n is related to the average incremental secant stiffness,

Ku,,", determined from the vertical to incipient instability displacements (refer Figure

s.2.2).

77

CHAPTER (5)- Stabiliry of Simply Supported URM WallsSubjected to Transient Out-of-Plane Forces

During any transient excitation the wall displacement response increases and the response

frequencies decrease in accordance with the average half cycle secant stiffness. It is rare

for the frequency response to pass through the effective resonant frequency as the

likelihood of instability is increased with the increasing displacement amplification. The

effective resonant frequency thus provides the observed lower frequency limit so that

r _rJetr - Jlimit

The effective resonant frequency therefore also provides the corresponding maximum

expected average cycle mid-height displacement, Âr¡-¡t before collapse (refer Figure

s.2.2).

K¿> KøReal Semi-rigid Non-linea¡ F-ÂRelationship

Average instability cycleincremental secant stiffness

A¡nstabitity

Mid-height Displacement (Á)

f" * lK"f, * {K,rt¡n¡, n lr*"

fi¡75¡aþ¡¡¡¡y

Mid-height Displacement (/)Figure 5.2.2 Post-cracked Frequency-Displacenænt Relatioruhip

\zJlÈdooq.

Ec.)ctEc)

o.o.

N

6(.)

t)-øgf¡.q)2rólLÀøc)ú

Frequencies d¡¡¡ are theoreticallypossible but a¡e unlikely, as morelikely that instability would occurwith displacement amplification

=fefr

fn

_1- Javelm¿,

Ar

78

CHAPTER(5)- Stability of Simply SupportedURM WallsSubjected to Trønsient Out-of-Plane Forces

5.2.2. Boundary Condition Impact on Force-Displacement Relationship

The types of wall support comprising the wall boundary conditions are an important

aspect that must be considered when assessing out-of-plane URM wall behaviour. To

some extent these determine the moment induced into the wall under lateral loading in

relation to the eccentricity of the vertical reaction forces at the joints. Typical

connections used in Australian masonry construction, such as DPC and 'timber top plate'

connections, have been reviewed in Section2.3.

In URM wall construction, connections to concrete footing beams and floor slabs

containing DPC membrane at the top and base wall supports are commonly used to meet

serviceability criteria. Consequently, at large mid-height displacements the vertical

reactions at the top, middle and base supports will all have been forced to the extreme

compressive faces of the wall. Thus, in comparison with other boundary conditions,

which do not force the vertical reactions to the wall edge, this scenario provides the

greatest 'rigid resistance threshold' force, R"(1), due to the larger overburden force lever

arm providing a maximum restoring moment. In Appendix (D) a generic calculation of

the bi-linear F-A relationship is presented for the concrete slab support at the top and

bottom connections. The generic defining terms Re(l), Ke(1) and Ai,'rauiuty (rieid) of the

rigid bi-linear F-A shown in Figure 5.2.2 arc summarised in Table 5.2.1 for these

boundary conditions as rigid loadbearing simply supported: top and base vertical

reactions at the leeward face (LBSSLL).

A second conìmon URM wall support, which is used in single storey URM dwellings, is

the connection of the timber roof truss to the masonry wall via a 'timber top plate' where

the wall base is set on a concrete slab and DPC connection. As the 'timber top plate' and

truss generally provide little rotational support even at large mid-height displacements the

top vertical reaction remains near the centerline of the wall, while the middle and base are

forced to the extreme compressive faces. With a reduced overburden force lever arm,

compared with the concrete slab above case, the 'rigid resistance threshold' force, R.(1),

is also respectively reduced. In Appendix (D) a generic calculation of the bi-linear F-A

relationship is presented for 'timber top plate' above and concrete slab below boundary

79

CHAPTER (5)- Stability of Simply SupportedURM WaltsSubjected to Transient Out-of-Plane Forces

conditions. The generic defining terms Re(l), Ke(l) ând ¡os¡¿6¡ty (rigid) of the rigid bi-

linear F-Â are sunìmarised in Table 5.2.1 for these boundary conditions as rigidloadbearing simply supported: top vertical reaction at the centerline and base vertical

reaction at the leeward face (LBSSCL).

Table 5.2.1 also presents the generic def,rning terms &(1), &(1) and A¡r¡u5i¡¡r.¡g¡¿, for

other wall boundary conditions also relevant to Australian masonry construction

including rigid parapet (P), rigid non-loadbearing simply supported (NLBSSCL) and

rigid loadbearing simply supported at the centerline (LBSSCC). For walls with an applied

overburden stress, oo, the overburden factor, y, is defined as, +, where M is theMs

total wall mass.

Table 5.2.1 Rigid Bi-Linear F-À Relationship - Various Boundary Conditions

[=

Table 5.2.1 shows that for most of the support conditions, with the exception of LBSSCC

and LBSSCL, the mid-height displacement at which static instability occurs is the

thickness of the rigid object (t). For the loadbearing simply supported object with top and

Support Type Support TypeAbbreviation

&(1) K(1) A^øUilitv

Rigid Parapet (P) hgt

-hûb

t

Rigid Non-loadbearing SimplySupporæd:base Reaction at theI-eeward Face

(NLBSSCL) 4.0 hgt

-4.0hob

t

Rigid Loadbearing Simply Supported:Top and Bottom Vertical Reaction atthe Centerline

(LBSSCC) 2.0(1+v)hgt

-4.0 (l + v)hoÞ

0.5t

Rigid Loadbearing Simply Supported:Top Reaction at Centerline and BaseReaction at The læewa¡d Face

(LBSSCL) 4.0 (l+7¿\¡) hgt

-4.0 (l + V)hob

%t(¡"s¡,¡x,(t

(l#/tv\ t(l+v)

Rigid hadbearing Simply Supported:Top and Base Vertical Reactions atthe Leeward Face

(LBSSLL) 4.0(l +v)hgt

-4.0 (l + v)ho

t

80

CHAPTER(5)- Snbiliry of Simply SupportedURM WallsSubjected to Transient Out-of-Plane Forces

bottom vertical reactions at the centerline (LBSSCC) the mid-height displacement at

static instability occurs at half the thickness of the rigid object. For the loadbearing

simply supported object with the top vertical reaction at the centerline and the base

vertical reaction at the leeward face (LBSSCL) the mid-height displacement at which

static instability occurs is dependent on the ratio of self-weight to the applied overburden.

If the applied overburden is much greater than the seH-weight the mid-height instability

displacement approaches 75Vo of the thickness of the rigid object. If the self-weight is

much greater than the applied overburden the mid-height instability displacement

approaches the thickness of the rigid object. Accordingly the static mid-height instability

displacement is always between 3/r t and t.

5.23. Un-cracked Force-Displacement Relationship

In the un-cracked wall behaves essentially elastically where the lateral force

resistance increases linearly with displacement. Here the lateral elastic capacity is

governed by the tensile strength of the brickwork plus any compressive load due to

gravity. Once the elastic capacity has been exceeded, cracking takes place and the wall's

lateral force resistive capacity reverts to that of the cracked wall governed by the semi-

rigid non-linear F-Â relationship, as described in Section 5.2.1. The behaviour at

cracking is therefore dependent on whether or not the wall's elastic capacity is gteater

than the post-cracked 'semi-rigid resistance threshold' force, zu(l).For non-loadbearing

or low apptied overburden force walls the elastic capacity is typically greater than the

&,(1). In contrast, for high-applied overburden force walls the tensile strength of the

brickwork becomes less significant. Accordingly zu(1) is greater than the elastic

capacity. Therefore, to distinguish between the two types of un-cracked behaviour of

URM wall they must be catagorised as either low-applied overburden or high-applied

overburden force.

5.2.3.1. Low Applieil Overburden Force

The first category includes walls where there is no or a low applied overburden force so

that the compressive stresses at the critical mid-height cross section are also low. This

category of wall could be found as non-loadbearing internal partition walls or as

loadbearing walls in low-rise buildings or in the upper stories of multi story buildings.

81

Á\zJ¿

Èd()kÕ

tG!c)(ú

E()ÈÞr

CHAPTER (5)- Stability of Simply Supported URM WailsSubjected to Transient Out-of-Plane Forces

For this category of wall, prior to cracking the lateral strength is almost entirely governed

by the masomy flexural tensile strength, fl1, so that the elastic capacity is greater than the

R*(1) (refer Figure 5.2.3). Thus, once the elastic capacity, &ur,i", has been exceeded the

lateral resistive force reverts back to the lower cracked wall resistance. Therefore, no

additional lateral capacity exists beyond cracking and wall survival is reliant on the

applied force being reduced to the cracked lateral capacity of the wall.

&u",i"

Force ControUDynamic I-oading @xplosive)

Un-cracked Elastic Capacity

Displacement Conrol Loading

zu(l)Real Semi-rigid Non-linear F-ÂRelationship

Mid-heightDisplacement (/) A¡nsøbirity

Figure 5.23 Urrcracked F-A for Low Applied Overburden Stress URM Vl¡all

Where the wall is dynamically loaded, once the elastic capacity has been exceeded the

elastic inertia force is typically sufficient to continue to increase the wall displacement

(refer Figure 5.2.3). As a result this category of wall generally fail explosively under

dynamic loading having no reserve capacity to 'rock'. Consequently, an elastic static

analysis will provide a reasonable estimate of the dynamic capacity of this category ofwall. Should, however, the wall become cracked at any time during its life this type ofelastic static analysis may be highly non-conservative. Alternatively, should high

frequency spikes exist within a dynamic excitation these may have sufficient energy to

Un-cracked Linea¡ ElasticBehaviour

82

CHAPTER(5)- Stability of Simply SupportedURM WallsSubjected to Transient Out-of-Plone Forces

crack a wall prematurely such that the maximum elastic capacity may not be realised and

the elastic static analysis methodology would again be non-conservative.

5.2.3.2. High þplied Overburden Force

The second category of wall is generally found two or more stories below roof level or in

upper concrete slab-URM wall construction. Here, where the applied overburden force is

larger, compressive stresses at the critical mid-height cross section are correspondingly

higher. In this case the benefit provided by the tensile capacity of the briclorork is

outweighed by the additional gravity restoring moment resulting from an increased lever

arm, as vertical reactions move towards the extreme compressive faces of the wall with

increased displacement. Accordingly, cracking of the wall does not alter the wall's

ultimate lateral capacity (refer

Figure 5.2.4). Typically, for a dynamic load scena¡io when the elastic capacity is

exceeded the elastic inertia force will not be sufficient to then exceed the 'semi-rigid

resistance threshold' force. Therefore, this category of wall behaves similarly to a pre-

cracked wall where a reserye capacity due to rocking and 'dynamic stability' concepts

must be considered.

z&Fc)ooI¡rGko)Cd

€6)

o.È

R*(1)

&u",i"

Real Semi-rigid Non-linear F-ÂRelationship

Mid-heightDisplacement(/) Ainsøb¿iry

Figure 5.2.4 Ur¡crackedF-Â for lligh Apptied Overburden Stress URM Wall

Un-cracked Linear Elas[cBehaviour

Force/DynamicConrol loading

DisplacementConrol I-oading

83

CHAPTER (5)- Snbility of Simply Supported UFJttI WallsSubjected to Trqnsient Out-of-Plane Forces

5.3. Previous Research: Experimental Studies

Over the past 30 years or so there have been various experimental studies carried out on

both the static and dynamic out-of-plane behaviour of face loaded URM walls. Since

ea¡lier research was predominantly concerned with the effect of wind loading these

studies mainly considered static loading. More recently, however, the research focus has

been placed on seismic loading so that experimental studies have largely involved

dynamic loading. The following section provides a brief review of previous works

carried out by other researchers relevant to the one-way bending of face loaded LJRM

wall panels.

53.1. Static Tests

In the early L970's the U.S. Building Research Division of the National Bureau ofStandards (now the National Institute of Science and Technology, NIST) undertook an

extensive experimental study (Yokel et al 1971) on the static one-way out-of-plane

bending behaviour of masonry wall panels. In total 192 tests were completed including

both single leaf unreinforced brick and concrete block, cavity wall and reinforced

masonry. For each type of construction, specimens were subjected to a static vertical

compressive load, applied as a point load at the centerline of the top of the wall, followed

by a gradually increasing lateral pressure exerted by an inflated air bag. The boundary

condition at the base wall support was a steel channel with a fiberboard sheet adjacent to

the wall specimen. Boundary conditions were therefore representative of 'timber top

plate' above and concrete slab below.

Specimens with both low and high levels of appted overburden force were tested. Atlow levels it was found that the maximum lateral strength occurred prior to cracking and

that this was related to the tensile strength of the masomy. In contrast, at higher levels ofapplied overburden force additional wall capacity was found after cracking. The reasons

for this have been discussed in Section 5.2.3. For walls with moderate levels ofoverburden force applied, a comparison with simple rigid body theory was found to be

consistent. Above lMPa overburden stress, however, the continuity began to drop away,

as crushing of the brickwork at vertical reactions became apparent (refer Figure 5.3.1).

84

CHAPTER (5)- Snbility of Simply Supported URM WallsSubjected to Trutsient Out-of-Planc Forces

Typical failures for both low and high applied overburden stress are shown in Figure

5.3.2). \ühile the primary objective of this study was the development of appropriate

interaction curves for combined bending and the force-displacement (F-A)

relationships were also published (refer 2

o-05

r.o 2.A 30Overbwden Sress MN/m2

Figure 5.3.1 Comparison of Yokel Sûrdy with Simple Rigid Body Theory(Hødry 1973)

Crushing ofmasonry

o10

(\ËgooÉ.2aÉñoñÈ

Low VerticalCompressiveLoad

High VerticalCompressive Load

Figure 5.3.2 Typical Latcral Failure of Brick l{all

cYokel et al l97l)

5.4.2)

--- Hollow Uocl(s-

Sot-rd Þkrçhs

a--tGil,Þ\

-iffi-]___l+__i_L_-Ì.HJ_- : ;---TÈ

85

CHAPTER (5)- Stability of Simply Supported URM WallsSubjected to Transient Out-of-Plane Forces

l-ater, Yokel and Fattal (1976) performed a similar experimental study to that of Yokel et

al (1971) also at the National Bureau of Standards. The main differences between the

studies where that for the 1976 tests smaller panel were used having steel half round bars

inserted at both top and base boundary conditions. This represented a simply supported

wall at its centerline. Since here the movement of vertical reactions was limited to only

the center joint, the prediction of the F-Â relationship w¿rs greatly simplified.

Experimental F-A relationships were again reported (refer Figure 5.4.2). For this case itwas observed that both the displacement at which instability occurred and the maximum

resistance were reduced in comparison with the Yokel study.

Base and Baker (1973) reported on a series of low overburden force out-of-plane tests.

These were aimed at providing fundamental data and an understanding of the action ofbrickwork under a variety of loading conditions. Here the brickwork specimens were

observed to behave essentially elastically in the un-cracked state. A significant reduction

in bending strength was reported when brickwork beams were tested under simulated

uniform loading as compared with testing under central load over a shorter span. This

was attributed to the increased number of mortar joints within the loading span, thus

increasing the probability of a weak joint.

West et aI (1977) have also performed a series of static out-of-plane tests on wall panels.

Here no applied overburden force was considered so that the cracking load was reported

to be the maximum load the wall could resist. For these tests the top of the wall was

propped against lateral movement and a connection containing a DPC was used at the

base to represent as closely as possible the conditions used in practice. It was reported

that the material used for the DPC and the way in which it was embedded were important

in achieving the full bending strength. \ilhere the shea¡ capacity of the DPC connection

was exceeded the full bending sftength of the wall was not achieved since slip occurred at

the DPC. Further, both vertical and horizontal panels were examined where it was found

that the strength in the two orthogonal directions differed. The overall ratios of strength

in the direction perpendicular to the bed joint to that parallel joint were reported as being

I .2 ro 6.2 with a mean of around 3.

86

CHAPTER (5)- Stability of Simply Supported URM WallsSubjected to Transient Out-of-Plane Forces

West, Hodkinson and Webb (1973) conducted extensive tests on strip walls

demonstrating the relationship between lateral strength and overburden force of storey

height walls of various thickness and materials. Support conditions considered were

similar to those of concrete slab above and below. Experimental results were reported as

being well represented up to a mid-height compressive stress of 1.4 MPa by the simple

relationship (refer Figure 5.3.3)

Pa = 8o/52

where po = ultimate lateral pressure

6c = ovêrburden compressive stress

S = slenderness ration = II/t

ot

0.os

1bl .,2

10 20 30 40 ÀlÍ{

Overbr.¡rden Stress

t?

Figure 5.3.3 Comparison of Wes 3 et al 1973 Tests with Simple Rigid Body Theory(Hendry 1973)

This relationship was based on the rigid body theory with all vertical reactions pushed to

the extreme faces of the wall. Above 1.4 MPa overburden stress, the lateral resistance

was again reported to fall away from the linear relationship owing to compression and

local crushing. At low overburden force, experimental results tended to exceed the

theoretical values because of the tensile strength of the brickwork that is not taken into

MN nr2 bl rn

0.r5oÉ

.go&EoËÈ

+18+

t

/+

12

I

r

x3?5 500

x

+

f,e j"yx ¡t

bs,/

rfs{

6 xo+ (¡tt-r¡¡,a

250

9/tI

x 1:?4:3 Morrero Do Fmdu+ 1:1:6

---- Srmpletheory

x.a

87

CHAPTER (5)- Stability of Simply Supported URM WallsSubjected to Transient Out-of-Plane Forces

account. It was also reported that the lateral strength of a wall with compression is only

slightly affected by brick and mortar strengths.

Anderson (1994) reported on the most recent series of static tests where 90 lateral load

tests on LIRM walls with various support conditions were undertaken. Here the

behaviour of vertically spanning strip walls was reported to be difficult to predict withpost-cracked rigid body theory considered to be a more satisfactory approach for static

limit state design. Eccentricity of the vertical load due to rotation of the base of the wall

was found to induce a stabilising moment. Consequently it was recommended that the

partial fixity moment due to the self-weight acting at an eccentricity of 0.45 of the wall

thickness be applied at the base of the wall. The mean height at which the bed jointfailed was 0.6 of the vertical span above the base. Failure by sliding was reported at the

DPC for some walls with low levels of applied overburden force.

5.32. Dynamic Tests

In the early 1980's a consortium of Californian engineers called the ABK Joint Venture

(ABK 1984) ca¡ried out research into the post-cracking seismic behaviour of URM wall

panels. The aim of the research was to develop standards for the renovation of URMbuildings in Los Angeles, particularly with respect to wall height-to-thickness ratios

(Kariotis et al 1985, Adham et al 1985). The study examined the one-way behaviour ofeight specimens of varying construction and geometry under a range of gravity loads.

Several dynamic motions were applied at the base and top support, simulating the input

motion from the ground or diaphragm anchorage. The base of the wall was allowed to

displace without rotation and the top of the wall was free to rotate and to move in the

vertical direction without restraint.

It was reported (ABK 1984) that a single horizontal crack typically formed near the mid-

height of the test specimen with another forming nea¡ its base. The stability of the fullycracked URM wall, shaken by less than critical ground motion intensities, was

maintained by gravity load moments applied at the cracked surface. \ühen the center ofgravity of the vertical loads, above the cracked surface, lay within the wall thickness

88

CHAPTER (5)- Stability of Simply Supported URM WaIIsSubjected to Trønsient Out-of-Plane Forces

dimension the gravity load moments were found to provide a restoring moment that

closed the crack upon reversal of the earthquake displacement motion. This ability to

displace without collapse resulted in the walls having a significant reserve capacity above

that of the 'semi-rigid threshold' force. The term 'dynamic stability' was used to

distinguish this type of behaviour from that which might be expected from static

calculations. Correspondingly, a major finding of the study was that neither static elastic

nor 'quasi-static' analysis procedures were completely satisfactory to define the dynamic

and highly nonlhnear response of the post-üacked URM walls'

Like the static F-A relationship, the hysteretic behaviour was found to have a declining

branch and on unloading the hysteretic F-A plot traced back along the loading plot.

As a result of this experimental investigation (ABK 1984) key parameters for predicting

the failure of URM walls subjected to face loading were identif,red. These were the waII

slenderness, the ratio of the applied gravity load to the wall self weight and the peak input

velocities at the base and top of the wall. A further important finding was that although

various phase shifts between the top and bottom excitation were examined, input

velocities simultaneous in time were found to be the critical case. That is, an in-phase

excitation at the top and base of the wall was the critical excitation case.

During the study the effect of vertical ground motion was not considered as it was

thought to not have a significant influence on the dynamic stability. This was explained,

as the frequency band of vertical motions in seismic events is generally not in the critical

frequency band of the horizontal ground motions. That is, the effect of high frequency

vertical motions on the restoring moments will not result in a bias of increasing or

reducing the restoring moment. This is due to the significantly lower frequency of

instability excursions as compared to the typical frequency of vertical seismic motions,

especially as the relative excursion of the center part of the wall approaches instability.

Ba¡iola et al (1990) reported on a series of tests where a gradually increasing excitation

was applied to the base of parapet URM walls. Here it was reported that prior to cracking

89

CHAPTER (5)- Stabiliry of Simply SupportedURM WallsSubjected to Transient Out-of-Plane Forces

the natural frequency of the wall correlated well with simple elastic beam theory. In the

cracked state, however, no unique natural frequency was found as it decreased withincreased displacement response. Also, wall slenderness was not found to have a clear

influence on the peak acceleration required to cause instability. For walls of the same

slenderness wall but with different thickness, the thicker wall appeared to be more stable.

Results of another important dynamic experimental study of out-of-plane URM wall

behaviour was recently published by Lam et al (1995). This study focussed on one-way

bending of parapet walls with the objective of comparing various analytical approaches

with the experimental results. The subject of the experiment was a lm tall, I 10mm thick,

clay brick IJRM wall and was subjected to the El Centro ground motion. Free vibration

tests were also used to identify the frequency response and damping characteristics of the

cantilevered wall. The un-cracked elastic natural frequency was found to be between 5

and l0 Hz depending on the amplitude of vibration. Once the wall was cracked the

rocking frequency was found to decrease from about 4Hz at low amplitude displacements

to a lower frequency limit of approximately lHz at larger displacements. Although the

equivalent viscous damping, (, being a measure of energy loss was observed to vary

slightly (2.67o-3.4%o) with displacement it was reported to be fairly consistently around

37o.

Continuing from their earlier tests Lam et al (1998) have also reported on shaking table

tests on parapet walls of different dimensions using harmonic excitations of varying

amplitude and frequencies. Here the peak displacement of the wall was correlated to the

peak shaking table acceleration and velocity. These relationships were found to be highly

dependent on the excitation frequency so that plotting results associated with different

forcing frequencies produced large scatters (refer Figure 5.3.4). In contrast, a good linear

correlation was obtained between the relative displacement of the wall and the absolute

displacement of the shaking table (refer Figure 5.3.5). Typically, the peak relative

displacement at the top of the parapet wall was reported to be twice the peak absolute

displacement of the table irrespective of the frequency and amplitude of the table

motions. Inspection of the test results further showed that the center of gravity of the

90

30âd

c

Ë20.5a

304ãË

Ég

Ízo_!A.þâ

CHAPTER (5)- Støbility of Simply Supported URM WallsSubjected to Transient Out-of-Plane Forces

wall was displaced by a similar amount to the table so that the response was 1800 out of

phase with the table motion. In effect the center of gravity position remained effectively

stationary in space. Lam et al (1998) therefore postulated that for the harmonic forcing

frequencies considered, the 'equal displacement theory' could be adopted. Consequently,

wall instability would be predicted when the base displacement equaled half the thickness

of the parapet wall.

10 10

0 04 ú B 10 1¿

Table Acceleratio n (nr¡ts2)0,0 o-1 o.2

T¡bh Vebciiy(¡n/Ð

(Harmonic tests on 500mm tall cantilever walls)

Figure 5.3.4 Top of Parapet \üall Disp. Correlated to Table Velocity and Acceleration(Lam 1998)

10

Ë

10 15

T¡ble Displ¡nertpnt ( m m)

Figure 5.3.5 Top of Parapet Wall Disp. Correlated to Table Disp.

(Lam 1998)

20 o-3

^30ÉÉ

ãasüÉ0-ä eoA.9a

15

05o

E Etqr¡ry5l5Hr. ElqEry 4 H¡¡ Êtgwy3.25IIrc Êt$EEy2tH¡

aE

ê

¡+t

Iga

qa

o &rqu¿Ft535Hr+ &Êq¡{úy4H¡¡ ftr4ffJ31sH¡c fte{ury2ll¡¡

!o

aE

o

qa

+

É

lo

E¡

tE

o &tçnrn¡5f5IIro Êtçttts¡{I&¡ Êtqury3l5IIzo &tEurcyS-?Iù

ûô

I

IE¡

!

fa

!

E

9l

CHAPTER (5)- Stability of Simply Supported URM WqllsSubjected to Transient Out-of-Plane Forces

It was noted, however, that the frequencies used were much higher than the effective

resonant frequency of the parapet wall tested at large displacements. Consequenily,

should excitation frequencies closer to those of the wall's effective resonant frequency at

large displacements have been used, displacement amplifications greater than unity

would have been more likely and the 'equal displacement theory' would not apply.

5.4. Critical Review of Current Analysis Methodologies

As a result of experimental and analytical studies previously carried out, various analysis

methodologies have been developed over the years to analyse the one-way out-of-plane

seismic capacity of URM walls. The following sections critically review these

methodologies highlighting the advantages and limitations of each method.

5.4.1. Quasi-Static Analysis Procedures

The response of a URM wall to earthquake induced base excitations is a complex

dynamic process. Analysis, however, is often simplified by considering an instantaneous

maximum acceleration occurring at a critical snapshot in time. As such, the peak-input

acceleration associated with either the ground motion (PGA) or building response,

depending on the location of the wall within the structure, is often used to represent the

associated inertia force. Displacements are assumed to be small so prior to failure the

induced inertia force is assumed to be uniformly distributed over the height of the wallrelative to the distribution of mass.

Alternatively, it is possible to estimate the wall's critical natural frequency, either in the

cracked or un-cracked state, thus permitting an estimate of the elastic spectral response

acceleration to be determined from an elastic response spectrum. The main limitation

here is that the natural frequency of a URM wall is not unique, as described in Section

5.2.I. In addition, for the cracked wall case where response displacements are relatively

large, in contrast to the uniformly distributed inertia load assumed above a trapezoidal

distributed inertia load is more likely. This is due to the additional triangular inertia force

induced by the vibration of the wall ove¡ the rectangular inertia force resulting from the

motion of the supports.

92

CHAPTER (5)- Snbiliry of Sirnply SupportedURM WallsSubjected to Trqnsient Out-of-Plnn¿ Forces

Regardless of the method used to determine the 'snapshot acceleration' the dynamic

action is represented by a 'quasi-static' type analysis. Earthquake design codes and

standatds typically specify analysis methods based on this 'quasi-static' analysis

philosophy. The two most common methods are: (a) the stress based linear elastic (LE)

and (b) the rigid body (RB) equilibrium analyses. Both are briefly reviewed in this

section.

As described in Section 5.2.3 previous researchers have found that in the un-cracked state

URM walls behave essentially elastically. It is possible therefore to utilise the well

established linear elastic (LE) anatysis methodology to predict at what equivalent lateral

inertia force cracking stresses within a URM wall will be exceeded. The fundamental

principle is to equate the maximum seismically induced moment at a critical section Mu,

to the moment required for the cracking stresses at the leeward face lv[", to be exceeded.

Resistance to cracking is provided by both the flexural tensile strength of the brickwork

fl¡, and the compressive force at the mid-height of the wall from seH-weight and

overburden. Figure 5.4.1 shows a representation of the LE analysis for the prediction of

the cracking acceleration for a simply supported URM wall. Since elastic deformation

prior to cracking in URM walls is generally relatively small the vertical reactions at the

top and base supports are assumed to act at the centerline of the wall.

The current seismic design methodology in Australia (453700-1998) for the vertical one-

way bending of URM walls subjected to transient out-of-plane forces adopts the stress

based LE analysis of the un-cracked section. Here a 'Capacity Reduction Factor' of 0.6

is also used in design to allow for the variability in the flexural tensile sfrength.

93

f,f,I{TTTTftrIIf,flrIITTTTIIT

CHAPTER (5)- Snbiliry of Simply Supported URM WallsSubjected to Transient Out-of-Plane Forces

ow kN/m

wh2

h2

O+W2It

r"./' ft o

tr"

w+-h Me

6

Predicæd inertia induceddistributed load to cause cracking

f

Predicted cracking acceleration

8

F t.f"w6

wh2

W+Owhere

W = self weightof URM walUm (kN/m)w = wind or earüquake inertia load/mT = specific weight of URM (ld{/m3)f r = flexural tensile strengthO = superimposed load (concrete slab above)

O+ w2a=

t

where w=m.a-^lgt.a

Figure 5.4.1 Quas¡-Static Linear Elastic Design Methodolory

The assumption of an un-cracked wall and elastic stress-strain behaviour is a major

limitation of the linea¡ elastic anaþis methodology. As highlighted by the Newcastle

earthquake much of Australia's older LJRM building stock may have an appreciably

depleted masonry flexural tensile capacity or even be pre-cracked. Also, since the

analysis is dependent on a reliable estimate of the highly va¡iable flexural tensile strength

of the brickwork at the time of loading it is consequently diff,rcult to accurately predict

the cracking capacity. Another major limitation of this method is that the formation offlexural tensile cracks does not necessarily result in failure of the wall as implied. [n fact,

as discussed in Section 5.2.3, for walls with applied overburden force, this is rarely the

case. Instead, after f,rrst cracking a small mid-height displacement causes the wall's

94

CHAPTER (5)- Stability of Simply Supported URM WallsSubjected to Trønsient Out-of-Plane Forces

neutral axis to be forced in the direction of the compression zone at both mid-height and

vertical support reactions. This neutral-axis shift associated with crack propagation can

lead to a "tip-toe" situation in which the wall is supported on its edges.

The post-cracked seismic performance of an URM wall is therefore more realistically

analysed by the rigid body (RB) equilibrium analysis method, which compares the

overturning moment with the restoring moment taken about the rocking edge of the wall.

The overturning moment is obtained in the same manner as for LE analysis using the

quasi-static methodology, whereas the restoring moment is obtained by consideration of

the forces due to self-weight and any overburden acting on the free body above the mid-

height crack. This is identical to the method described in Section 5.2.1 for determining

the 'rigid threshold resistance' force, R.(1). A major limitation of this method is that it

assumes that the brickwork has an inhnite stiffness. In reality, it is semi-rigid and highly

dependent on its constituent materials. Correspondingly, the real 'semi-rigid resistance

threshold' force, zu(1), can be much lower than R"(1) as it occurs at a larger

displacement where P-A effects are more prominent.

To account for the reduced 'resistance threshold' caused by the semi-rigid behaviour of

URM walls, Priestly (1985) and Paulay (1992) proposed a method of determining the real

non-linear F-Â relationship. This method is based on first principles of beam theory, and

assumes a zero tensile strength for the masonry and simply supported wall at the

centerline. The fundamental approach is based on the assumption that the gradient of the

linear elastic stress diagram at the critical mid-height section, and thus the wall curvature,

is related to the mid-height displacement of the wall. As this relationship is derived

through examination of the stress diagram at the cracking displacement the assumed

modulus and boundary conditions are important considerations.

A finite element model ¡amed the Block-Interface Model has also been developed

(Martini IggT) in an attempt to determine the real static post-cracked F-^ relationship.

Here joints are represented by discontinuum elements so that the elastic properties of the

mortar and associated local effects at the block mortar interface are neglected with the

95

CHAPTER (5)- Stability of Simply SupportedURM WallsS ubj e cte d to Transient O ut- of- Plane F or c e s

mortar joint representing a potential line of failure due to cracking (refer Figure 5.4.2).

Here increasing the number of laminations and layers increases the density of the frnite

element mesh and thus allows more accurate refinement however this also increases the

complexity of the model. The finite element Block-Interface approach has the advantage

of being able to be implemented using commercial software.

Figure 5.4.2 shows a comparison of experimentally derived F-A relationships from the

Fattal (1976) and Yokel (1971) studies with those determined analytically by the BlockInterface finite element model (Martini 1997) and the Priestly (1986) method.

+ FàHål ErDuihül-è- Fifile ELld-{" Prisdyl{rtlod

I

Ë

3

Ilo

:JtarzJtr

+ Yolil E.rüiÐdå- FEil. ELþ!t, ¡l LsiEtios, I l¿Ft-è- fEù€ ElÊEÈ! ó l¡niutiry I l¡r¡ô FEile ELñ.!t, ó lÀniDtios, 5 )¡nr

¡ú JÙ

Lòlerôl Dirph!Ê¡d d Biùheût (m) L.ld¡¡DieDl¡.æd ¡t Ei¡l-luùht (m)

Figure 5.4.2 Experimental and Analytical F-AComparison(Martini 1997)

It must be recognized that none of the previously mentioned 'quasi-static' analyses take

into account the time-dependent nature of the response of the wall since only an

instantaneous acceleration occurring at a critical snapshot of the response is considered.

A URM wall will not necessarily become unstable and collapse should the quasi-static

force exceed the resistant capacity of the wall, as the incipient instability displacement

may not be reached. As such, the level of seismic loading to cause failure can greatly

exceed that predicted by the quasi-static analysis methods (ABK 1985, Bariola 1990,

Lam 1995) such that a reserve capacity exists. The quantification of the reserve capacity

is reliant on the frequency and amplitude content of the applied excitation so that more

realistic dynamic modeling approaches should be used to account for the dynamic

behaviour.

96

CHAPTER (5)- Stability of Simply Supported URM WaIIsSubjected to Transient Outof-Plane Forces

5.4.2. Dynamic Analysis Procedures

Although being particularly useful as suitably conservative modern design tools the

'snapshot' quasi-static design methodologies described above may not be appropriate for

the review of existing URM structures. In the design of new structures the application of

conservative design tools will generally have only minor economic consequence.

However, in reviewing existing structures using procedures which do not recognise the

additional lateral strength capacity resulting from 'dynamic stability', a more significant

economic penalty may be incurred. An example is where the decision to demolish,

retrofit or 'leave as is' for a significant monumental IJRM structure may be in the

balance.

In recognition of the problem of assessing the dynamic response by the 'snapshot'

principle an alternative analysis method based on the widely recognised 'Equal Energy'

procedure has been proposed by (Priestly 19S5). The 'Equal Energy' procedure is based

on the observation that 'dynamic stability' concepts can be considered by using an

equivalent elastic capacity derived by equating the real energy required for instability

with that of an elastic system having a stiffness equal to the initial un-cracked stiffness of

the wall. Although based on an observation, this simplification has been shown to

predict reasonable estimates of peak displacement response for simple systems with

relatively short periods (Priestly 1985, Lam 1995). It has been observed however that for

systems with very short periods this procedure can provide very un-conservative

estimates of lateral dynamic capacity and for systems with longer periods a conservative

estimate of lateral dynamic capacity (Priestly 1985, Robertson 1985).

For URM wall dynamic capacity prediction using this method, the potential energy

absorptive capacity of a wall undergoing large displacement is first quantified. This is

achieved by determining the area under the non-linear F-À curve as the wall is pushed

from the vertical non-displaced position to that of the incipient instability displacement.

The procedure to approximate the F-Â curve of a simply supported load-bearing URM

wall pinned at the centerline for the purpose of appþing the equal-energy procedure has

been reported in Section 5.4.1. The maximum kinetic energy (KE) demand is then

97

CHAPTER (5)- Stability of Simply Supported URM WaIIsSubjected to Transient Out-of-Plane Forces

derived from the maximum spectral velocity as obtained from an elastic response

spectrum to compare with the potential energy (PE) capacity. Thus, it is assumed that the

wall would remain un-cracked and behave linearly up to the time when the maximum KEis reached (vertical position) and at commencement of the failure half cycle. At this time

the wall is assumed to crack and begin to rock as the PE is increased to absorb the KE.

The abrupt transition from the linear elastic response (in the un-cracked state) to the non-

linear rocking response (in the cracked state) is a major assumption of the equal energy

procedure. In reality, the dynamic behaviour of the wall at the commencement of the

failure half cycle is not always linearly elastic. It has been demonstrated by dynamic tests

(Lam 1995) that the stiffness and natural period of a URM wall can be highly amplitude

dependent even in the un-cracked state. Thus, the "elastic" natural period of vibration ofthe wall, which governs its spectral velocity (and hence its maximum KE) can not be

predicted with certainty. Further, it is possible that the wall may have already cracked

and be responding in-elastically prior to the commencement of the failure half cycle. Asecond major shortcoming of the 'equal energy' method is that ground excitations are

also assumed to have stopped once the failure rocking half cycle has commenced. As aresult the accumulated effects of multiple pulses on the wall during rocking can not be

accounted for as additional input energy into the system within the failure half cycle is

not considered.

Figure 5.4.3 presents a comparison of the predicted URM wall acceleration capacity

utilising the 'equal energy' method with the previously described quasi-static analyses.

As expected the linear elastic anaþis provides the most conservative prediction ofdynamic lateral capacity for moderate to high overburden stress ranges. For lowoverburden stress, however, the rigid body analysis is more conservative. For alloverburden stress the 'Equal Energy' method provides the least conservative prediction

as an allowance is made for 'dynamic stability'. As the effectiveness of the 'equal

energy' observation is highly dependent on the system's un-cracked natural frequency the

prediction is very sensitive to the selection of elastic modulus. Often a realistic modulus

value can result in an extremely un-conservative lateral strength prediction.

98

CHAPTER (5)- Søbility of Simply Supported URM WallsSubjected to Transient Out-of-Plane Forces

2.5

3'oÊ F'=HÉroEi r'lH$0.

40.0

----lr*LINEAR ELASTICRIGID EODY

'.'.'.'.{r'."'."' EQUAL ENERGY

...._,-._..........1

¡i¡¡.....{.ìr.r!\'þnqf ¡''

0.0u 0.05 0.10 0.15 0.20OVEREURDEN STRESS AT TOP OFI¡TALL

Figure 5.4.3 Comparison of Analysis Predictions

As discussed in Section 5.3.2, Lam (1998) has reported that for harmonic excitations of

varying amplitude and relatively high frequencies the center of gravity of a parapet wall

effectively remained stationary in space. Consequently, based on an 'equal-

displacement' methodology, wall instability could only occur when the table

displacement exceeded the incipient instability displacement, which could be related to

the thickness of the wall. It was also highlighted that for forcing frequencies closer to the

natural frequency of the wall at large displacements that significant displacement

amplification was possible so that instability could occur at table displacements less than

the incipient instability displacement thus invalidating the'equal-displacement'

methodology for practical applications. To overcome this shortfall a dynamic

amplification factor was proposed. \ilhile this method is useful for the dynamic analysis

subjected to ha¡monic excitations it is limited for multiple frequency, transient excitations

where random pulse arival will significantly affect the wall response.

The methods described so far have all used a single parameter (acceleration, velocity, or

displacement) to predict the effect of the excitation on the response of a URM wall. As a

result these methods all have limitations for dynamic analysis although the velocity based

dynamic analysis is satisfactory to analyse the response of single pulse excitation and the

equal displacement method is suitable for stationary periodic excitations. Unfortunately,

general, transient excitations can not be accurately represented by a single parameter so

99

CHAPTER(51 Stability of Simply SupportedURM WallsSubjected to Transient Out-of-Plane Forces

that Time History Analysis (THA) procedures are required to take into account the effect

of the frequency content, duration and pulse arrival details of the excitations.

Although researchers (Housner 1963, Yim et al 1980, Hogan 1989) have reported on

analytical studies where explicit mathematical solutions of rigid rocking motion

equations have been derived these are limited for applications where the system can not

readily be idealised. Further, where transient excitations are considered explicit

mathematical representation is not possible. Consequently, to undertake a THA an

approximate numerical evaluation of the response integral must be used. This requires an

assumption to be made on the motion between consecutive time steps. For example,

acceleration may be assumed to be constant or linearly varying thus allowing the basic

integration equations to be developed (Clough & Penzien 1993).

Lam (19958) has reported on the development of specific THA software for the analysis

of the dynamic response of a parapet walls to transient excitations using the Constant

Average Acceleration Integration technique and a rigid bi-linear F-Â relationship. To

minimise computational time an iterative procedure was not included to model damping

but rather an average mass proportional damping coefficient for the response was

developed based on an estimate of the response frequency. Nevertheless, despite the

approximations made in modelling the F-Â and damping properties, results from this

THA have provided reasonable agreement with experimental results. Similar THAtechniques are also currently being developed for the in-plane rocking analysis of URMwalls (Magenes & Calvi 1996:1997, Abrams 1998).

In 1992 Blakie et al reported that a simplified Displacement-based (DB) analysis, which

compared the displacement demand with capacity, might better predict the seismic

capacity of out-of-plane panels. Although approximate, this method has the potential to

account for the dynamic behaviour and thus the walls reserve capacity. Simitar DB

analysis procedures are currently also being developed for the prediction of in-plane

rocking capacity of URM walls (Magenes & Calvi 1996:1997).

100

t

CHAPTER(5)- Stability of Simply SupportedURM WallsSubjected to Transient Out-of-Plane Forces

5.5. Specific Research Focus

Although most URM walls are designed as two-way spanning elements, as a first stage in

the development of a method that may also be applicable as an analysis component of

dynamic two-way behaviour, an understanding of the physical process underlying one-

way dynamic action must first be developed.

While there has been a substantial research effort undertaken on the static loading

behaviour of one-way spanning wall panels, dynamic action has not been as well

examined. Consequently, simple static analysis procedures have been developed which

are capable of predicting cracking and ultimate loads and have been shown to correlate

well with experimental results. In contrast, the dynamic behaviour is not well

understood.

The few dynamic loading experimental studies that have been previously undertaken

have indicated that URM walls have a significant capacity to displace without becoming

unstable. As a result they are often observed to have the capability of sustaining inertia

forces greater than that predicted by 'quasi-static' methods. This is referred to as the

wall's dynamic 'reserve capacity' to rock. Unfortunately, currently available seismic

predictive models have been unable to account for this large displacement post-cracked

behaviour. Where the 'reserve capacity' to rock is overlooked in analysis a conservative

estimate of seismic capacity is made. Although this may be acceptable for the design of

new buildings, it may impose serious economic penalties in the analysis of existing

structures.

In response to the above shortfall a need was apparent for the development of a rational

and simple analysis procedure, encompassing the essence of the dynamic behaviour and

thus accounting for a URM wall's 'reserve capacity' to rock. The development of this

analysis procedure was adopted as the research focus for the final component of this

project.

101

6. OUT-OF.PLANE SHAKB TABLE

TESTING OF SIMPLY SUPPORTBI)

URMWALLS

6.1,. Introduction

With the aim of developing a better understanding of the physical processes governing

the dynamic collapse behaviour of simply supported URM walls a series of shaking table

tests were conducted on the earthquake simulator in the Chapman Structural Testing

Laboratory, University of Adelaide. In this experimental study the wall response to

harmonic, transient and pulse excitations was examined with the effect of wall va¡iables

including thickness, slenderness and the level of overburden stress taken into

consideration. In Chapter 7 the resulting dynamic response data is used to confirm the

reliability of a specifically developed non-linear Time History Analysis (THA) procedure

for modelling the semi-rigid rocking response of URM walls.

To complement the shaking table test data, static push tests and free vibration tests ïvere

also conducted. These complementary tests enabled the non-linear force-displacement

(F-^), frequency-displacement (/-A) and damping-frequency ((fl relationships for the

rocking wall to be investigated. In Chapter 7, these experimentally derived relationships

are used to calibrate the specifically developed non-linear Time History Analysis (THA)

program.

For completeness, material tests were conducted even-though the ultimate behaviour of

face loaded URM walls, at low levels of overburden, have not previously been found to

be particularly dependent on the constituent brickwork material properties. Nevertheless,

these results provide an indication of the masonry quality tested.

102

CHAPTER (6)- Out-of-Plane Shake Table Testingof Simply Supported URM Walls

The following chapter presents a description of the experimental study undertaken

highlighting key results and where possible a comparison of experimental results withtheory is also presented. A representative cross section of test results is presented in the

Appendices E and F.

6.2. General Test Set Up

6.2.1. Test Specimens

In total, 14 one-way spanning URM wall panels were constructed for out-of-plane

testing. Where possible, multiple static and dynamic tests were performed on each

specimen. Details of each of the wall specimens are presented in Table 6.4.1. The

height of the wall panels was limited to 1.5m by the height of the laboratory gantry crane.

Consequently, standard 110mm thick wall specimens were constructed at a height of1.5m giving a slenderness ratio of 13.6. For more realistic slenderness ratios to be

examined, 1.5m tall, 50mm thick walls were also constructed. These had a slenderness

ratio of 30.

The bricks used were standard extruded clay bricks having the dimensions 76 x 110 x

230mm and had 3 x Q45mm holes as shown in Figure 6.2.I. A 10mm mortar joint was

adopted for both horizontal and vertical perpends as per normal construction practices in

Australia. The average density of the llOmm thick brickwork was determined to be

1800kg/m3. This was achieved by weighing a representative sample of the brickwork and

dividing by its volume. In this way, the mortar which partially filled the brick holes was

also taken into account.

103

CHAPTER(6)- Out-of-Plane Shake Tøble Testingof Simply SupportedURM Walls

Q45mm

Figure 6.2.1 Ståndard Three Hole Extruded Clay Brick (110mn)

The 50mm bricks used in these tests were solid having been cut from brick pavers, with

dimensions 33 x 50 x 230mm. For the 50mm thick wall specimens, a 5mm mortar joint

was adopted. Since wall geometry rather than material properties w¿ts considered critical

to the rocking behaviour, no attempt was made to model the constituent mortar materials

to half scale. The average density of the solid 50mm thick brickwork was measured at

23}}kstnf .

For all of the wall specimens a typical Australian mix of 1: l: 6 (cement: lime: sand)

mortar was used. Common 'brick' sand and Portland cement were used and water was

added until good workability of the mortff was achieved. No air entraining additives

were used and to improve consistency between mortil batches, 'bucket batching' was

used.

A professional bricklayer was employed to construct the one-way spanning wall

specimens. At the base of each wall an embossed polythene membrane DPC connection

was used (refer Figure 6.2.2). Wall specimens were constructed in three lots with four

110mm thick walls constructed in March 98 and June 98 and three 50mm thick and

110mm thick walls constructed in September 98. All walls \ryere constructed as a

standard veneer with wall ties connected to a timber support frame (refer Figure 6.2.2).

This construction method was adopted after preliminary tests showed that the mortar

bond could be depleted if wall panels \¡/ere constructed without lateral support. This was

attributed to the fact that lower brick layers were disturbed as the upper layers were

r04

CHAPTER (6)- Ourof-Plnne Shùc Tablz Testingof Simply Supponed URM Walls

placed thus breaking the bond. Using the timber wall for support overcame this problem

by providing stability to the wall panel during construction. An added benefit was that

this also prevented accidental damage during curing and provided a more realistic

construction technique. After a minimum of 28 days curing time the wall ties were cut

and the wall panel carefully lifted onto the shaking table.

Throughout the fabrication of the test walls, two-brick and five-brick prisms and

100x100x100mm mortar cubes were regularly constructed for material testing, as

described in Section 6.3.

Veneer wall used forconstruction

Embossed PolytheneDPC connection at base

Figure 6.2.2 Construction of URM Wall Panels

6.22. Test Rig

To provide a representative boundary condition at the top of each of the simply supported

URM wall panels tested, a braced steel frame was rigidly attached to the shake table witha 'cornice' type support connection used to provide lateral restraint at the top of each

brick wall. The 'cornice' support was made up of steel angle and 10mm square, stiffrubber spacers to prevent the wall from binding against the angle at large wall mid-height

displacements (refer Figure 6.2.3). Prior to testing the 'cornice' was fitted snuggly to the

wall. However, to ensure a minimal vertical restraint due to friction the 'cornice' was not

over tightened.

105

CHAPTER (6)- Ourof-Pløne Shake Table Testingof Simply Supported URM Wqlls

l0mm stiffrubber spacer

AdjusEnentbolts

WallSpecimen

Figure 6.2.3Top 'Cornice' Support Connection

The stiffness of the braced frame was designed to represent as closely as possible the in-

plane stiffness of a URM structural shear wall (refer Figure 6.2.4). As a consequence, any

input excitation provided at the table was also applied approximately in phase at the top

of the wall. This w¿rs confirmed by comparison of the absolute displacements of the table

and top of the braced frame for each of the dynamic tests. Using an impulse free

vibration test the natural frequency of the braced frame was determined to be

approximately 10H2. For most of the tests this was not in the range of dominant driving

frequencies so that the small response amplification recorded at the top support was

neglected. For the relatively high un-cracked wall natural frequency tests, however,

where the mid-height of the wall specimen was excited using a mallet strike, the black

frame natural frequency dominated the response and thus was required to be filtered out.

Also, for harmonic tests completed near the frame's natural frequency of 10Hz

significant amplification of the base excitation was observed at the top support of the test

specimen so that an average input excitation had to be considered.

Preliminary tests showed that it was very difhcult, in practice, to apply an overburden

force at the top of the test walls in a realistic manner using weights supported by a

concrete slab. This method produced large overturning moments at the bearing support

rails of the shaking table, leading to a dangerous rocking action during testing that limited

the inertia forces that could be induced into the wall. To oYercome this problem an

106

CHAPTER (6)- Out-of-Plnne Shalce Table TestingofSímply Supported URM Walls

overburden rig was designed which relied on six large springs to develop the required

level of overburden stress (refer Figure 6.2.4). The static deflection of the springs could

be altered by adjustment of the central thread, thus altering the overburden force at the

top of the wall through the base plate of the springs. The overburden test rig therefore had

the advantage of permitting easy changes to the overburden force.

Braced steelframe Cornice

support

URM shearwall action)

Shakingdirection

Table bearingsupport rails X'igrrre 6.2.4 Out-of-plane Test Rig

3mm n¡bber mat between spring plate and wall

Figure 6.2.5 Overburden Rig

I

6 x springs

r07

CHAPTER (6)- Out-of-Plane Shake Table Testingof Simply Supported URM WaIIs

The main disadvantage of using the overburden rig was that with increased mid-height

displacement the total wall height also increased slightly thus increasing the static spring

deflection and hence overburden force. Accordingly, the desired constant overburden

force at the top support was not realised at larger displacements. To overcome this

problem springs were selected so that the additional overburden force developed with the

expected increase in height was not signif,rcant. Further, since the increase in height with

mid-height displacement is inversely proportional to the wall slenderness the additional

overburden force on the 50mm walls was significantly less than that of the 110mm walls.

Correspondingly, for the 50mm wall specimens mid-height displacement changed the

mean overburden force by less than ! SVo so that the constant force assumption was

acceptable. In contrast, for the 110mm thick wall specimens significant increases in

overburden force were observed so that the constant force assumption was only

acceptable for mid-height displacements of less than 207o of the wall thickness. Static

compression tests were performed on the springs to calibrate the spring coefficients

where it was found that a 0.16kN force was developed for each mm of static spring

deflection.

Since the situation with overburden represented a vertical continuation of the wall or a

supported concrete slab, a point load connection was not used at the top of the wall

panels. Thus, the location of the top vertical reaction was governed by the spring base

plate, and with increased wall mid-height displacement the top vertical reaction was

forced to move to the compressive zone (refer Figure 6.2.6).

Test çecirren Top vertical reaction location

Figure 6.2.6Top Yertical Reaction - Overburden Test Rig

108

CHAPTER (6)- Outof-Plnne Shakc Tablz Testingof Simply SupponedURM Walls

The test boundary conditions were therefore considered similar to a concrete support slab

above and below where the vertical reactions are constånt but pushed to the compressive

zone with mid-height displacement.

6.23.Instrumentation

A total of nine channels of data were recorded for each of the dynamic tests in order to

capture the dynamic response characteristics of the rocking URM wall specimens. The

instrumentation consisted of five accelerometers, t'wo Linear Voltage Potentiometer

Transducers (POT), one Linear Voltage Displacement Transducer (LVDT) and the

internal INSTRON hydraulic actuator displacement transducer. For static tests, the same

instrumentation was used with the exception of the five accelerometers. Figure 6.2.7

shows the location of the nine instrument points and Table 6.2.1 presents a summary

description of the application of each instrument.

rffall specimen 5. ACCEL(TA)

Timber wallcatch

(refer Table 6.2.1for instrumentcodes)

4.INSTRON

2LYP(MwD)

3. LVDT(BwD)

I. LVP(TrwD)

Stationaryreference frame:Rigid connectionto súong floor

Figure 6.2.7 Out-o[-plane WaIl Test Instrumentation Locations

7. ACCEL(rwA)

8. ACCEL(MwA)

9. ACCEL(BWA)

6. ACCEL(TTA)

109

CHAPTER (6)- Out-of-Plane Shake Table TestingofSimply Supported URM Walls

ChannelNo.

Location/Description Application InstrumentCode

I Absolute Top Wall Displacement Top wall displacement excitation TWD2 Relative to Frame Mid-height

tWall DisplacementMid-height wall displacement response MWD

J Relative to Table Base WallDisplacement

Base slip check BWD

4 INSTRON internal displacement Base wall displacement excitation INSTRON5 Top Frame Acceleration Top wall acceleration excitation TA6 Table Top Acceleration Base wall acceleration excitation TTA1 Top Wall Acceleration t/+ - wall height acceleration response TWA8 Mid-heieht V/all Acceleration Mid-height wall acceleration response MWA9 Bottom Wall Acceleration r/¿ - wall height acceleration response BWA

Table 6.2.1 Out-of-plane Wall Test Instrumentation Description

One Linear Voltage Potentiometer (POT) was mounted horizontally between the

stationaty reference frame, connected to the laboratory strong floor, and the braced frame

at the level of the top of the simply supported wall specimen to record the total top of

walVframe displacement (TWD). The POT was a Housten Scientifrc model 1850-050

having a maximum displacement of 500 mm and powered by a 10 Volt DC supply. A

similar instrument was used to record the relative mid-height wall response displacement

(MViD) between the wall and braced frame. In Chapter 7, the MWD is used for

comparison with analytical predictions of the mid-height displacement response of

simply supported URM walls using the specially developed THA program. A

Schlumberger Linear Voltage Displacement Transducer (LVDT) having a maximum

displacement of +1Omm was mounted between the base of the wall specimen, just above

the DPC connection, and the shaking table to measure the relative displacement between

the wall base and shaking table (BWD). The data from this instrument was only used to

ascertain if any sliding at the wall base DPC connection occurred during testing.

Kistler Servo Accelerometers powered by a servo amplifier were used to record the top

frame (TA), and tabletop (TTA) accelerations. These accelerometers have a measurable

acceleration range of + 50g and are able to detect accelerations as small as 0.1mm/s2'

These accelerations therefore represented the actual input excitations applied to the wall

specimen and are used in Chapter 7 as input for the non-linear THA. The top frame

accelerations were also compared with the table accelerations to identify how much

amplification of the base excitation was caused by the braced frame's flexibility.

110

CHAPTER (6)- Ourof-Plane Shake Table Testingof Simply Supported URM Walls

The top (TWA), mid-height (MWA) and bottom (BWA) accelerations were recorded

using the 'Analogue Devices' single chip accelerometer, model ADXLO5 which were

adhered to the face of the wall at the 3/t -, mid - and r/¿ - height respectively. This less

expensive semi-disposable accelerometer was selected, as it was possible that should the

wall collapse these devices could be sacrificed. These accelerometers have a measurable

acceleration range of + 59 and a¡e able to detect accelerations as small as 0.019. Alimitation of this method was due to the accuacy of the accelerometers being reliant on a

horizontal datum. Since the accelerometers were glued to the wall surface they rotated

with the rocking of the wall so that as the wall's mid-height displacement increased the

accuracy of the data from these accelerometers decreased. For most of the criticalresponse however the accuracy was adequate for the purpose of the tests. Comparison ofthe BWA and TWA with the mid-height acceleration response was useful incharacterising the total dynamic acceleration response profile. The mid-height

acceleration response was also later used for comparison with THA predictions.

In a similar fashion to the dynamic tests performed on tlRM connections containing a

DPC membrane, described in Chapter 4,the'Microsoft Windows' based data acquisition

system 'Visual Designer' was used to collect the nine channels of response data. Data

was collected at a period interval of 0.01 seconds (100H2).

Where restoring moments were ¡elatively small, in particular for the non-loadbearing

50mm thick wall specimen, care was taken to ensure that the instrumentation did not

influence the test outcome.

6.3. Material Tests

The material tests undertaken have included bond wrench tests to determine the

brickwork flexural tensile strength, fl1, and compression tests of brickwork prisms and

mortar cubes to determine the masonry's modulus of elasticit), Er* and ultimate

compressive strength, f -, and mortar's compressive strength, f". The following section

presents a brief discussion of these tests and their results.

111

CHAPTER (6)- Out-of-Pbrw Shnke Tablz TestingofSimply Supporte d U RM Walls

63.1. Bond Wrench

The bond wrench test is one of two methods permitted in 453700-1998, Appendix (D) to

determine the flexural tensile strength, f t, of the bond between mortar and brick units

perpendicular to the bed joints. As described in Section 5.2.3, for un-cracked walls with

low levels of overburden, f ¡ is often the critical wall parameter for lateral loading. Here

the un+racked elastic lateral force capacity is greater than the cracked force capacity so

that at first cracking an explosive dynamic instability is possible.

Two bond wrenches were specifically manufactured for this project being for the 11Omm

and the 50mm brick specimens. The bond wrench is used to apply a moment to the joint

to be tested by appþing a load at the end of the lever a¡m. From the known applied

moment, f I can be determined with the assumption of an idealised stress distribution

across the bed joint. To best approximate this idealised stress distribution the bond

wrench design, as shown for the ll0mm brick specimen in Figure 6.3.1, was adopted

from research undertaken by Samarasinghe et al (1998). This bond wrench specification

has since been included in 453700-1998, Appendix (D). To simplify the procedure

strain gauges were adhered to the a¡m of the bond wrench with peak strains calibrated to

the applied force at the loading point. Calibration plots for the two bond wrenches are

presented in Appendix (E).

In order to ascertain if the flexural tensile strengths, determined from the two-brick prism

tests, were representative of the test specimens, bond wrench tests were also completed

on pre-dynamically tested LIRM wall specimens, ¿ls shown in

Figure 6.3.2. For each test specimen three prism and three wall tests were completed.

For the pre-dynamically tested walls the vertical perpends on either side of the test joint

were cut using a masoffy hand saw. Comparison of prism and wall test results showed

that the tested walls generally had a slightþ greater f ,. This was attributed to the wall

test including a vertical perpend in the course below as shown in Figure 6.3.2.

112

CHAPTER(6)- Out-of-Plan¿ Shake Tqbl¿ Testingof Simply SupponedURM Walls

l5mr

l6U*

l5m

45m

25m

Strain gauges on ûopand botûom of loadingafm

I-oading Point

l* '* lr

¿t0m8Ouu

¡t0lø

flIlu

Point

Vertical perpendin course below

ãÌ- &lzu

25u

X'igure 6.3.1 Bor¡d Wrench Apparatus Dinænsioru (llllmm Brick)

he-cut vertical perpends

2-brick prism æst

Figure 6.3.2 Bond Wrench Test Set Up

713

Pre-failed wall test

CHAPTER (6)- Out-of-Pbne Shake Table Testingof Simply SupportedURM Walls

Table 6.3.1 presents a summary of the bond wrench test results showing a range of flr

between 0.17 and 0.99 MPa with a mean of 0.49MPa and overall standard deviation of

0.15MPa. The characteristic flexural tensile strength (= mean-1.64 x standard deviation)

is 0.25MPa. A comparison of this with the design fl, permitted by 453700-1998 of

0.2MPa indicates that the design assumption is slightþ conservative. A complete list of

bond wrench test results is presented in Appendix (E).I

X6.32. Modulus of Elasticity

To determine the modulus of elasticity, Er* for each of the masonry specimens a

compressive test was conducted on a five-brick tall prism. Each prism \ryas constructed at

the same time and using the same materials as was used for each test wall. After a

minimum of 28 days a 2-inch set of Demec points was applied vertically at the center

brick and a 8-inch set on the opposite side of the prism thus covering two mortar joints

and the center brick. Following this each hve-brick prism was carefully placed onto the

Tabte 6.3.1 Bond \ilrench Test Resr¡lts Sumrnary

SpecimenNo.

Test SpecimenThiclness

Minimumf . Maximumft

StandardDeviation

Average f,(3 tests)

I Prism 110mm o.22 0.36 0.07 0.28V/all 1lOmm 0.53 0.72 0.10 o.64

2 Prism 110mm 0.30 0.41 0.06 0.36Wall 110mm 0.39 0.54 0.07 0.47

J Prism 110mm 0.30 0.48 0.10 0.40Wall 110mrn 0.42 0.53 0.05 0.47

4 Prism 110mm 0.35 0.48 0.07 o.42V/all l10mm 0.39 0.84 o.22 0.61

5 Prism 110mm 0.40 0.71 o.r7 0.59rWall 110mm 0.5s 0.99 0.25 0.71

6 Prism 110mm 0.41 0.48 0.04 0.43Wall 110mm 0.48 0.53 0.11 0.56

1 Prism 110mm 0.50 0.68 0.09 0.6Wall 110mm 0.27 0.53 0.13 0.41

8 Prism llOmm o.37 0.55 0.09 0.45VfaI 110mm 0.53 0.63 0.05 0.59

10 Prism 5Omm 0.36 0.88 0.30 0.7011 Prism 110mm o.l'l 0.55 0.20 0.32t2 Prism 1l0mm 0.27 o.32 0.03 0.3013 Prism 110mm 0.22 0.40 0.10 0.29l4 Prism 5Omm 0.56 0.86 o.r7 0.76

tr4

CHAPTER(6)- Out-of-Pløw Shalce Tqble Testingof S imply S upported U RM Walls

base compressive platen of a hydraulic actuator. Dental paste was then applied to the topof the prism before gently lowering the top compressive platen onto the dental paste

(refer Figure 6.3.3). This method provided an even loading platform so that stress

concentrations at the loading face would be avoided.

A preparatory compressive test was first undertaken to determine the approximateultimate compressive stength, f* of the prisms. Here strains wers not recorded. Forthe remaining tests Demec strain readings were taken up to approximately 50Vo of theestimated ultimate load. Each specimen was then loaded to f - without further recordingof strains (refer Figure 6.3.3 for tlpical splitting failure). Back calibration of the twoDemec readings allowed the strains in a representative sample of brickwork (one brickand one mortar joint) to be determined. This permitted the stress-strain relationship to be

determined. The brickwork modulus was then calculated for each specimen as the chordmodulus between 5Vo and 33Vo of the ultimate brickwork compressive strength, f -.

{}

-I

DentalPaste

Demecs

Figure 6.33 Five Brick Prism at Ultirmte Conrpressive Load

Table 6.3.2 presents a summary of the modulus test results ranging from 3,300 MPa to16,000 MPa for the 110mm specimens and 6,700 Mpa to 9,800 Mpa for the 50mm

115

CHAPTER (6)- Ourof-Plane Shake Table Testingof Simply Supported URM Walls

specimens. While the results vaded significantly the modulus values were typically

found to be relatively high as expected of modern masonry. For older masonry

constructed with weak lime mortars it is possible that the modulus values would be

lower, being in the order of 500MPa to l,000MPa (Robinson 1985). A complete list of

compressive test results for the five-brick prisms is presented in Appendix (E).

Table 6.3.2 Brickwork Modulus Test Results

The masonry modulus of elasticity, E,* can be represented by the linear relationship

En -kf-

where k is a constant. Drysdale et al (1994) reported that from previous experimental

studies on clay brick prisms, k generally falls within the range of 2lO to 1670. For the

110mm prismtests k was estimated to be9,400113.4=7OO and is therefore within the

range of previous experimental results. For the 50mm bricks k was estimated to be

8,250126.5=310 and is therefore also in the lower range of the proposed values.

'2(/4 touttk/-

U,r dtn^"/,

Specimen No. SpecimenThiclness

ModulusE- (MPa)

Ultimate CompressiveI-oad (N)

Masonry CompressiveStrength, f'* (MPa)

1 ll0mm 330,000 13

2 llOmm 15,00Q 332,OOO 13.1

3 ll0mm . 3;300 \ 336,000 13.3

4 llOmm i 3,380 ' 333,000 13.1

5 llOmm 16,000 360,000 t4.26 110mm 338,000 13.47 l lOmrn 13,900 313,000 t2.48 llOmm 5,400 245,000 9.711 l10mm 6,600 359,000 14.2t2 110mm 11,600 397,000 t5.7t3 l10mm 397,000 15.7

AVERAGE 110mm 9.400 R ¿ 339,000 13.4

STANDARI)DEVIATION

5,322 ) 41,528 t.g

10 5Omm 9,800 307,000 26.7t4 5Omm 6,700 303,000 26.3

AVERAGE 5Omm 8.250 305,000 26.5

STANDARI)DEVIATION

2,192 2,8U 0.28

116

CHAPTER (6)- Out-of-Plane Shake Table Testingof Simply Supported U RM Walls

6.33. Mortar Compressive Strength

Mortar compressive strength, f ",

is often an important parameter for masonry because ithas an influence on the masonry compressive stress, however, it is typically used more as

a measure of quality control. For each test specimen three standard 100x100x100mm

mortar cubes were produced. After 28 days these were removed from their non-

absorptive casing and tested in compression. The typical failure mode was observed to

be a pyramidal shape. Due to the relatively high lime and sand content of the mortar as

compared to the cement content, the mean f "

of 5.17MPa was quite low compared withmortars of a higher cement content, ranging from 3.56MPa to 7.16MPa. A complete listof mortar cube compressive test results is presented in Appendix (E)

6.4. Out-of-Plane Testing of Simply Supported URM WallsTo explore the out-of-plane dynamic response of simply supported URM walls harmonic,

pulse and transient excitation shaking table tests were conducted. The testing program is

best described by grouping the completed tests into the th¡ee construction lots of March98, June 98 and September 98. For both March 98 and June 98, gradually increasing

harmonic excitation tests were performed on both cracked and un-cracked 110mm thickURM walls. These harmonic tests were aimed at developing an understanding of the

basic physical characteristics governing the dynamic behaviour. Once a basic

understanding of the dynamic behaviour \ryas attained, the September 98 test series was

designed to further investigate the previously identifïed specific physical characteristics

and examine the influence of excitation frequency and amplitude on the wall's dynamic

behaviour. Consequently for the September 98 test series both pulse and real earthquake

transient excitations were used.

To complement the dynamic tests and further explore the important physical

characteristics of the out-of-plane behaviour of simply supported tlRM walls, static push

and free vibration tests were also undertaken for each wall configuration. Table 6.4.1

presents the full testing program undertaken.

tt7

CHAPTER (6)- Out-of-Plane Shake Table TestingofSimply Supported URM Walls

CorutructionLot

SpecinrenNo.

Thickness(mm)

SlendernessRatio

Overburden(MPa)

Dynamic Test

March9S I 110 13.6 00

Un-cracked 2Hz Harmonic ExcitationCracked 2Hz Harmonic Excitation

March9E 2 110 13.6 00

Un-cracked 2Hz Harmonic ExcitationCracked 2Hz Harmonic Excitation

March9S J 110 13.6 00

Un-cracked Static Push TestCracked 2Hz Harmonic Excitation

March93 4 110 13.6 00

Un-cracked 2Hz Harmonic ExcitationCracked 2Hz Harmonic Excitation

June98 5 110 13.6 0.15 Un-cracked l0Hz Harmonic ExcitationJune98 6 110 13.6 0.15 Un-cracked 7Hz Harmonic Excitation

Cracked 7Hz Harmonic ExcitationJune98 7 110 t3.6 0.15 Un-cracked 7Hz Harmonic ExcitationJune98 8 110 13.6 0

0.150.15

0

Un-cracked Natural FrequencyUn-cracked Static Push TestCracked Static Push TestTrianqular Displacement Impulse

Sentember9S 9 50 30 Poor Consfruction - DisregardedSeptember9S l0 50 30 0

0.070.07

00070.07

00.15

Un-cracked Natural FrequencyUn-cracked Static Push TestCracked Static Push TestHalf Sine Displacement PulseFree Vibration Release TestsHalf Sine Displacement PulseCracked Static Push TestHalf Sine Displacement Pulse

Septembe19E ll 110 13.6 0.15000

Un-cracked Static Push TestFree Vibration Release TestsHalf Sine Displacement PulseCracked Static Push Test

September9S l2 110 13.6 0000

Un-cracked Static Push TestGaussian PulseTransient ExcitationCracked Søtic Push Test

September9S t3 110 30 0000

Un-cracked Static Push TestGaussian PulseTransient ExcitationCracked Søtic Push Test

September9S t4 50 13.6 000

0.150.15

0

Cracked Static Push TestGaussian PulseTransient ExcitationGaussian PulseCracked Static Push TestCracked Static Push Test

Table 6.4.1 Experimental Phase Test Program

The following section describes each of the test procedures highlighting key results with

a representative cross section of results presented in Appendix (F). Both cracked and un-

118

CHAPTER (6)- Out-of-Plane Shake Table Testingof Simply Supported URM WaIIs

cracked 'quasi-static' analyses of the test specimens are presented as these contribute to

the understanding of the wall response to dynamic loading.

6.4.1. Data Filter

The band-pass filter program, as described in Section 4.3.l,was used to filter noise fromthe simply supported tlRM wall tests.

6.42. Un-cracked Natural Frequency of Vibration

In order to investigate the un-cracked natural frequency of vibration for both non-

loadbearing simply supported 11Omm and 50mm thick wall specimens, a force pulse was

applied to the wall mid-height using a rubber mallet. As displacements were too small

too measure accurately, being only a fraction of a millimeter, mid-height accelerations

were collected using the Kistler Accelerometer. Raw data was then filtered to remove

irrelevant noise frequencies and the natural frequencyresponse ofthe braced steel frame,

which tended to dominate the response.

Figure 6.4.1 shows a representative time trace for one of the tests performed on a non-

loadbearing 50mm thick wall specimen where the natural frequency of vibration is

approximately l9Hz. Similar tests on non-loadbearing simply supported ll0mm thickwalls indicated that the natural frequency of vibration was approximately 42H2.

119

CHAPTER (6)- Out-of-Phne Shake Table Testingo1 Simply Supported URM Wølls

LINCRACKED NATIJRAL FREQUENCY - 0MPa OVERBITRDEN 5OmnTHICK WALLFILTERED

ÐF.Edoooo

ñ

0.04

0.03

0.02

0.01

0.00

4.01

4.02

{.03

{.04Tire (Secs)

\T=0-053sI = t8.9llz

T=0.053sI = tï.gllz

T= 0.053wI = tü.gltz

T = 0.05tuæ

Í =L'l'EHz

I

æ

I

T=0.053sf = tE.9l4z

T= 0.053sI = l8.9llz

I=0.054sf = 18.5Ílz

T=0.056sf =l7.EHz

\¿

Figure 6.4.1Un-cracked Nab¡rat Frequency of Vibration 50mm Nonloadbearing \ilall

Unlike the findings of previous researchers (Lam 1995) the elastic natural frequency

appeared to be constant over the exponential decay of the wall's mid-height

displacement. This therefore supports the theory that URM walls in the un-cracked state

behave essentially as an elastically responding material. To further substantiate this a

comparison of the empirically determined un-cracked natural frequency \¡/ith that

predicted analyticaþ by simple elastic beam theory is presented in the following section.

6.4.2.1. Comparßon w¡th Simple Elastic Beatn Theory

From simple beam theory the square of the angular frequency response for a linear

elastic, simply supported beam is given by Equation 6.4.I (Gere & Timonshenco 1990)

âS'

where

,, - oo(E-1.)vr)o = Angular Frequency =2ú,f = Natural FrequencyE-= Elastic Modulusm =Mass = ytT = Material Densityt = Object ThicknessL = Object LengthI = Second Moment of Area =€t1.2

(6.4.1)

120

CHAPTER (6)- Ourof-Plane 5tu1æ Tablc Testingof Simply Supponed URM Walls

Rearranging and substituting into Equation 6.4.2 the natural frequency of an elastic solid

beam can be shown to be:

r t=-71t IT

,l /48v (6.4.2)

Using the experimentally derived E* and y, Equation 6.4.2 predicts the elastic natural

frequency for the 50mm brick wall as,

r

and for 110mm brick wall as,

r

0.05--19l -5"

0.11--ta'1.5'

.4x10e =50H2800)

As these are of the same order as experimentally derived natural frequencies it was

concluded that simple beam theory provides a reasonable prediction of the elastic natural

frequency of vibration for un-cracked simply supported LJRM walls without overburden

force applied.

6.43. Specimen Lateral Capacity Analysis

The predicted lateral acceleration capacity using the 'quasi-static' linear elastic and rigid

body analyses, as described in Chapter 5, are shown in Figure 6.4.2 for l10mm thick

walls and in Figure 6.4.3 for 50mm thick walls. The range of overburden presented is

relevant for Australian masoffy consEuction.

t2t

CHAPTER (6)- Out-of-Planc Shoke Tøblc Testingol Simply Supported URM Wolls

Yariable IIeigþt(m)

Thiclsress(mm)

Efiective Modulus(Mpa)

Densityftdm1

Flexural Tensile Strength(Mpa)

1.5 110 1000 1,800 o.46

az¡r&Í¡lFlre(J(.)

ârlbâr¡úÈ

8.00

7.O0

6.00

5.00

4.00

3.00

2 00

1 00

0.000.00 0.03 0.05 0.08 0.10 0.13

OVERBURDEN STRESS AT TOPO['WALL

0.1

ELASTIC+RJGIDBODY

ALENERGY

7.7i

'-

)

-/6 ,.1.75

2.30

0.29

Variable Height(m)

Thickrcss(mm)

Efiective Modutus(MPa)

Deruity(kc/m3)

Flexural Tensile Strength(MPa)

1.5 50 5000 2,300 0.73

Figure 6.4.2 Current Available Analysis Comparison - 110mm Thick l{slt

Figure 6.4.3 Current Available Analysis Conrparison - 110mm Thick VYall

aztiúrlEO

âr¡tiOâriúCr

3.00

2.50

2.OO

1.50

1.00

0.50

0.000.00 0.03 0.05 0.08 0.10 0.'13

OVÐRBTJRDEN STRESS ÀT TOP OF IilALL0.

+|-LINEARELASTIC--_RIGIDBODY#EQUALENERGY

#,¿-

1.32¿aé-

1.18

0.98

1-t-t'

0.13 -rtJ-

r22

CHAPTER (6)- Out-of-Plane Shake Table Testingof Simply Supported URM Walls

The predicted lateral acceleration capacity determined by the dynamic 'Equal Energy'

method of analysis is also included in the above plots for comparison.

For the 'quasi-static' elastic analysis prediction of the acceleration to cause cracking, the

average flexural tensile strength, fl,, determined from bond wrench tests, presented inSection 6.3.1, was used with vertical reactions assumed to act at the centerline of the

wall. For the 'quasi-static' rigid body analysis prediction of the 'rigid resistance

threshold' acceleration, vertical reactions were assumed to act at the leeward face of the

wall. Lower values of modulus than those determined by five brick prism tests, presented

in Section 6.3.2, have been used for the 'Equal Energy' method as it was found that the

experimental values provided an unrealistically non-conservative prediction of lateral

acceleration capacity. This is because the test walls are relatively stocky and along withthe relatively high modulus the system period is lower than appropriate for the 'Equal

Energy' observation. Accordingly, the equivalent elastic prediction based on the 'EqualEnergy' observation provides a non-conservative estimate of wall's dynamic capacity.

By assuming a lower modulus the system period moves into the range were the 'EqualEnergy' observation has been shown to be more appropriate so that a reasonable estimate

of lateral capacity is achieved. It is therefore apparent that the 'Equal Energy' procedure

is not particularly relevant to the test walls however it may be more appropriate for tallerwalls havin g a lar ger elastic period.

Examination of the analysis comparison plots show that for the non-loadbearing test

specimens the elastic capacity is greater than the cracked rigid capacity. For walls withlarger overburden sftess, however, the cracked rigid capacity is larger and thus in theory

dominates the behaviour. In all cases the 'Equal Energy' method provides less

conservative predictions as an allowance is incorporated for the walls 'reserye capacity'

due to dynamic stability concepts.

Table 6.4.2 presents a summary of the analytical results for the wall test specimens. The

highlighted analysis results are those which should, in theory, dominate the un-cracked

wall behavior.

123

CHAPTER (6)- Out-ol-Plane Shake Table Testíngof Simply Supported URM Walls

Predicted Lateral Acceleration Capacity (g)

Height(m)

Thickness(mm)

Overburden Stress(MPa)

Un-cracked LinearElastic Analysis

Cracked RigidBody Analysis

'Equal Energy'Method

1.5 110 0 1.75 o.29 2.53

1.5 110 0.15 2.3 3.62 7.721.5 50 0 0.9E 0.13 1.03

1.5 50 0.07 1.ls 0.65 2.15

1.5 50 0.15 1.18 1.32 2.82

Table 6.4.2 Analysis of Test Specirnen

6.4.4. Harmonic Excitation Tests

For the March 98 test series, harmonic excitation tests were conducted on 110mm thick

simply supported URM walls without applied overburden. For walls that fall within this

category the predicted un-cracked elastic lateral acceleration capacity of 1.75g is greater

than the cracked 'rigid resistance threshold' acceleration of 0.29g (refer Table 6.4.2). On

the basis that the peak 'semi-rigid resistance threshold' acceleration occurs at

approximately 2OVo of the incipient instability displacement, the 'semi-rigid resistance

threshold' acceleration was estimated to be approximately 207o kess than for the 'rigid

resistance th¡eshold' acceleration prediction. Consequently, for walls within this

category the cracked semi-rigid lateral acceleration resistance to rocking was estimated at

0.239.

On examination of the 'quasi-static' analysis results for the un-cracked wall specimens

the elastic behaviour was expected to dominate the dynamic response with applied

accelerations of up to 1.75g being withstood by the wall. This was then expected to be

followed by cracking and an explosive instability as the elastic kinetic and stored strain

energy would be sufficient to overcome the potential energy requirement for the wall to

become unstable. For pre-cracked walls the non-linear behaviour was expected to

dominate the response with accelerations at the wall's effective mass of up to

approximately 0.239 withstood prior to rocking, followed by a transient and then steady-

state response. Failure of the wall was then expected to only occur when the table

amplitude was increased sufficiently so that the maximum steady-state displacement

exceeded the incipient instability displacement. The applied acceleration can therefore be

t24

CHAPTER (6)- Out-of-Plane Shake Table Testingof Simply Supported URM Walls

related to the level of displacement amplification and in turn to the wall's dynamic'reserve capacity'.

To examine the physical dynamic response characteristics for both cracked and un-

cracked walls within this category, harmonic tests were conducted on each. In the March98 test series a gradually increasing 2Hzharmonic excitation was selected for input to the

shake table as this was considered representative of what could be expected in URMconstruction where the ground motion is filtered through the building. Of a more

practical concern, at this excitation frequency the predicted lateral accelerations required

were also within the capabilities of the shaking table.

Figure 6.4.4 (a) - (c) presents typical results of a 2Hz harmonic test completed on a non-

loadbearing and un-cracked 110mm thick simply supported URM wall. The

displacement versus time plot, shown in Figure 6.4.4 (a), indicates that prior to t=16

seconds the wall response was elastic and the wall's mid-height displacement responding

in phase with the table excitation. At t=16 seconds the wall was observed to crack. The

input acceleration at the base and top of the wall at this time was recorded as 0.309 (refer

Figure 6.4.4). As the relative elastic mid-height displacements were very small prior to

cracking the mid-height response acceleration was un-amplified at 0.3g. As the input base

ha¡monic displacement at this time was 19mm, the measured harmonic input acceleration

can be checked using a similar procedure to that outlined in Section 4.3.3 and Equation

4.3.4.

ânnx = l-eo' l= l-¡rerrn'l= l-n(+n)21 = ß7.9 A qmm/s2) = 0.0161 A (g)

= 0.0161(19) = 0.30 g

In contrast to the predicted elastic acceleration capacity the input base acceleration to

cause cracking of 0.309 was much lower than the predicted 1.7 59. On examination of the

wall mid-height acceleration data, high frequency spikes of greater than 29 were

observed just prior to cracking. These acceleration spikes were thought to have been a

consequence of the wall initially rocking as a single free body and impacting with the top

'cornice' support. The high impact accelerations are thought to have had sufficient

125

CHAPTER (6)- Out-ol-Plane Shqke Table Testingof Simply Supported URM Walls

energy to crack the wall prematurely. To further substantiate this on cracking at mid-

height and the commencement of rocking as two free bodies the impact at the top support

was reduced and the high frequency spikes no longer observed. This finding highlighted

the possible non-conservative nature of adopting a stress based elastic analysis procedure

for this category of non-loadbearing URM wall.

After the premature cracking the wall's response underwent a transition to steady-state

rocking without becoming unstable as the elastic kinetic and stored strain energy were

insufficient to overcome the potential energy required to cause instability. Following the

transition phase the steady-state mid-height response rocking phase was observed to be

180o out of phase with the table excitation having a mid-height displacement

amplification of 45119 = 2.4. During the steady-state rocking response fhe Vt - and 3/c -

height accelerations were observed to reduce and the mid-height response acceleration

increased (refer Figure 6.4.4(b)). This indicated that the center of gravity (CG) of the two

rocking rigid bodies became closer to being stationary in space. Should the excitation

frequency have been increased further, according to 'equal displacement theory', the CG

would be expected to become completely stationary so that the wall mid-height would

have responded at the same displacement as the table. This would therefore reduce the

effective mid-height displacement amplification thus increasing the walls dynamic

'reserve capacity'.

Figure 6.4.4 (c) shows the hysteretic acceleration-displacement (a-A) behaviour where

initially the un-cracked behaviour was observed to be linear. After cracking the dynamic

wall behaviour switched to follow the non-linear a-À displacement relationship.

Figure 6.a.5 @) - (c) present typical results of a ZHz harmonic test completed on a pre-

cracked non-loadbearing 110mm thick simply supported URM wall. These show that

prior to t=32 seconds the 'semi-rigid threshold resistance' acceleration had not yet been

exceeded at the mid-height of the wall so that rocking had not yet commenced. The test

wall's dynamic behaviour was however governed by the cracked non-linear a-Â

relationship so that mid-height displacements were observed to be larger than for the un-

126

CHAPTER (61 Outof-Plane Shake Table Testingof Simply Supported URM Walls

cracked wall specimens. Here the wall mid-height was responding in phase with the

table motion although some acceleration amplification of the wall mid-height was

observed due to the larger displacement response. At t=32 seconds the 'semi-rigidthreshold resistance' acceleration was exceeded at the mid-height of the wall. At this time

the wall mid-height response acceleration was 0.349 having a displacement amplitude of2lmm. This can again be confirmed using a similar procedure to that outlined in Section

4.3.3 and Equation 4.3.4.

irnnx = l-Ro' l= l-lçzrq¡21= 0.0161 (21) =0.34 g (wall mid-height).

Following the commencement of rocking a transition period prior to steady-state rockingresponse phase occurred. During the steady-state rocking response the wall mid-height

was again observed to have changed to respond 180o out of phase with the table motion.

A displacement amplification of the mid-height respons e of 37114=2.6 was observed.

Although not shown experimentally it can therefore be postulated that once a steady-state

rocking response had commenced without becoming unstable during the t¡ansitionperiod, the amplitude of the 2Hz excitation could then have been increased to ll}12.6 =42mm prior to the instability displacement being reached. This input displacement

excitation corresponds to an input acceleration of 0.679. Thus, for the 2Hz harmonic

excitation this wall would have a 'reserve acceleration' capacity of 0.67-0.33 = 0.34g.Even considering the full predicted dynamic 'reserve capacity' of the wall the 'Equal

Energy' prediction of 2.539 remains extremely non-conservative providing a misleading

assessment of the wall's acceleration capacity for the excitation being considered.

If the full dynamic 'reserve capacity' is to be relied upon for the assessment of cracked

URM walls, as has been proposed by previous researchers (ABK 1984, Priestly 1985), itis important to assess the ability of the rotating mortar joints to sustain repeated loading

cycles during rocking. Throughout the March 98 series of harmonic tests on walls

without applied overburden, the ability of mortar joints to sustain repeated loading cycles

during rocking was found to be very good with only minor degradation observed. As will

127

CHAPTER (6)- Out-of-Plane Shake Table Testingof S i¡nplv Swp orted U RM Walls

be discussed in Section 6.4.5 static push tests have been used to quantify the degradation

of the mortar joints caused by dynamic testing.

Table 6.4.3 presents a summary of results for the March 98 test series. A final

observation was that for cracked walls the mid-height response acceleration at the

coilrmencement of rocking w¿rs typically of the order of 1.5 times the estimated 'semi-

rigid threshold resistance' acceleration (0.341O.23=1.5). This suggests that for a pre-

cracked simpty supported IJRM wall, during dynamic loading a triangular wall

acceleration response relative to the supports is likely, resulting from the larger mid-

height response displacements as compared with the base and top of the wall.

t28

CHAPTER (6)- Out-of-Plan¿ Shak¿ Table Testingof Simply Supponed URM Walls

-stâfe

-INSTRONTWD

o r

rllls(wsr

7060504030

420ëroË0Ê -roË -zoÊ -30i5 ¡o

-50{0-70-80-90

(b

(a)

(c

(l l0mm Wall, 2Hz Ha¡monic Excitation)

Figure 6.4.4 Urrcracked Non-loadbearing URM Wall Harmonic E¡citation Test

0.6

0.5

0.4

0.3

o 0.2

t 0.1.EEOoE ¡.ro< 4.2

4.3444.5{.6

Mid-heieht acceleration at crackinq = 0.3s .t rl I

¡'rllll I t l-t ll lll il.rllI U

-TT/ABWA

-TA-TTA

Initial linea¡ elastic stiffness

At cracking just below 'semi-rigid +

ooô*\oæ

non-linear a-Â relationship

Mid-beigbt Dþlacernt (rnm)

d)

o'Édoooo

Ðo¡¿à

TIYSTERESIS

r29

CHAPTER (6)- Ouçof-Pløne Shake Table Tesrtngof Simply SupportedURM Wqlls

(a)Sæady

90807060

450E¿oË30ËzoHroã.0i5-10

_20

-3040-5060_70

I ¡ llResistance F-xce¡¡led

r

r urÉ \ùecs,

-TWABWA

-TIA-TA

0.6

0.5

0.40.3

0.2

0.1

0{.14.24.34.4{.5{.ó4.7

6

oão

(c

(1 l0mm Wall, 2Hz Harmonic Excitation)

Figure 6.4,5 Pre-cracked Norrloadbearing URM \{all Harmonic Excitation Test

ooooooootn\orooo\ooooor91T17

Mid-beight Displacenent (mm)

d)

ôdooao

¡Ðô¿à

ITYSTERESIS

130

CHAPTER (6)- Out-of-Plan¿ Shakc Table Testingof Simply Supponed URM Wølls

\ilallNo

WallCondition

Predicûed 'Quasi-Static'AccelerationCapacity(Refer Table 6.4.2)

ExperinrcntalResults

Comrrcnt

Un-cracked 1.759 A=20mm (O.32e)(032e)

50t2È2.5

Table input at crackinghockingMid-height acceleration response atcrackinglrocking (no amplification)- High frequency spike (l2Hz) >2g prior tocrackingSteady-state response displacementamplifrcation

I Cracked 0.29e (Rigid)0.23g (Semi-rigid)

A=l5mm (0.2ag)A=2lmm(03ae)

4Ol16=2.5

Table input atrockingMid-height response at rocking- No high frequency spikes observedSteady-state response displacementamplification

) Un-cracked 1.75g A=l6mm (O.Z6e)(o.2ee)

Table input at cracking/rockingMid-height acceleration response atcracking/rocking (small amplifrcation)- High frequency spike (lzHz) >2g prior tocracking- Some elastic acceleration amplification- Wall became unstable immediately aftercracking (no steady-state response)

2 Cracked(refer Figure6.4.s)

0.299 (Risid)0.239 (Semi-rigid)

A=l5mm (O.Ue)A=2lmm (0.3ae)

37114=2.6

Table input at rockingMid-height response at rocking- No high frequency spikes observedSûeady-state response displacementamplification

3 Cracked 0.299 (Rigid)0.23g (Semi-rigid)

A=16mm (0.26e)A=22mm(0.35g)

Table input at rockingMid-height response at rocking- No high frequency spikes obsewedMorta¡ drop out prevented steady-stateresponse from occurring

4 Un-cracked(refer Figure6.4.4)

1.75g A=l9mm (0.30g)(0.30e)

45119=2.4

Table input at cracking/rockingMid-height acceleration response atcracking/rocking (no amplification)- High frequency spike (l2Hz) >2g prior tocrackingSteady-stat€ response displacementamplifrcation

4 Cracked 0.299 (Rigid)0.239 (Semi-rigid)

A=13mm (O.zle)A=19mm (0.30g)

35113=2.7

Table input at rockingMid-height response at rocking- No high frequency spikes observedSæady-state response displacementamplification

Table ó.4.3 llùnm Wall, Non-Iædbearing - Ilarnronic Excitation Test Results

l3t

CHAPTER (6)- Out-of-Plane Shake Table Testingof Simply Supported URM Walls

For the June 98 test series, harmonic excitation tests were conducted on 110 mm thick

simply supported URM walls with 0.15 MPa applied overburden using the spring

overburden rig shown in Figure 6.2.5. As described in Section 6.2.2 for mid-height

displacements greater than approximately 2OVo of the wall thickness the additional static

spring deflection caused an unacceptable increase in overburden force at the top of the

wall. Results were therefore only valid for mid-height displacements less than 2OTo of

the wall thickness. For walls within this category the predicted un-cracked elastic lateral

acceleration capacity of 2.3g is less than the cracked 'rigid resistance threshold'

acceleration of 3.629 (refer Table 6.4.2). Estimates of the 'semi-rigid resistance

threshold' acceleration were approximately 20Vo less than for the rigid case where the

resistance to rocking was estimated to be2.9 g.

Accordingly, even for the un-cracked wall the non-linear cracked wall behaviour was

expected to dominate the dynamic response with cracking of the wall not expected to

have significant impact on the dynamic behaviour. Hence, initially elastic behaviour

was expected up to applied accelerations of 2.3 g followed by cracking with a slight

increase in the wall mid-height displacement response. An increase in applied

accelerations up to 2.9 g at the mid-height of the wall was then expected to be applied

prior to a transient then steady-state rocking response. As per the previously described

March 98 cracked wall response, failure was then expected to only occur when the table

amplitude was increased sufficiently so that the maximum steady-state displacement

exceeded the instabitity displacement. This would therefore again be related to the

displacement amplification and in turn to the wall's dynamic 'reSeIVe capacity'.

Thus, to examine the physical dynamic response characteristics of both cracked and un-

cracked walls within this category, harmonic tests were conducted on each wall

specimen. Much higher inertia forces were required for this test series so 7Hz to 10Hz

harmonic table excitations were selected. These were still considered to be representative

of what could be expected in URM construction due to ground motion. However, since

these frequencies were close to the resonant frequency of the braced steel frame some

amplification of the base excitation was observed at the top support.

t32

CHAPTER (6)- Out-of-Plane Shake Table Testingof Simply Supported URM Walls

Figure 6.4.6 (a) - (c) present typical results for aTHz harmonic test of an un{racked 110

mm thick simply supported URM wall. The displacement versus time plot shown inFigure 6.4.6 (a) indicates that prior to t=4.4 seconds the wall response was elastic and the

mid-height response and table excitation were in phase. At t=4.4 seconds the wall was

observed to crack with displacements increasing slightly. However, the mid-height

response and table excitation remained in phase (refer Figure 6.4.7) indicating that

rocking had not yet commenced. The average input acceleration at the time was recorded

as 1.8 g with the mid-height wall acceleration being 2.I g (refer Figure 6.4.6 (b)). Since

the input harmonic displacement at this time was 9mm this can again be confirmed using

a similar procedure to that outlined in Section 4.3.3 and Equation 4.3.4.

âmax = l-Ro' l= l-4zrç¡'l= l-n(t+n)'l = rg34.4 A (mm/s2) = 0.197 A (g)

= 0.197(9) = 1.8 g

Following cracking the 7Hz-table excitation amphtude was further increased until at

t=19.45 seconds the 'semi-rigid threshold resistance' acceleration was exceeded at the

mid-height of the wall. At this time the wall mid-height response acceleration was 4.3g

having displacement amplitude of 22 mm. This can again be checked by the following

calculation,

Írnnx = l-Ro' l= l-1r2nn2l=0.197(22) = 4.3g (wall mid-height).

Following the commencement of rocking a transition period prior to steady-state rocking

response phase occurred. During the steady-state rocking response the wall mid-height

was again observed to have changed to respond 180o out of phase with the table motion.

A displacement amplification of the mid-height response of 2519=2.77 was observed

(refer Figure 6.4.8).

r33

CHAPTER (6)- Out-of-Plane Shqke Table Testingof Simply Supponed URM Walls

-INSTRONTIVD

ojôioo*\

.,"r ',' 1""" ' l't" r" ll',1 lii¡ti¡ll'ì,lliro\\o

First cracking at 4.4 seconds

50

40

â30g20910o!0À.F -loH

:20

-30

40-50

(a)

(b)

(c) HYSTERISISdue to increased static

ôo

É'Ëdooao

doE¿¿

spnng deflechorcommencementof rockins

-

{.H//5V/'\-7rz"¿ -77

,anilnNon-[neaf a-a fera[onsnrPANAæ--WvMid-height Displacerent (mm)

(110mm V/all, 0.15MPa Overburden, 7Hz Harmonic Excitation)

Figure 6.4.6 Un-cracked NonJoadbearing URMWatl Harmonic Excitation Test

WALL ACCELERATIONS

6

4

.,d)

€ooooo

4

4

Mid-height acceleration at rocking = 4.3g-TWA

BWA

rÉ;l Éhoô''\0 rç É ó\d ..i ñ'pl? ,&;

Ti{r' I ¡ |

Mid-height acceleration at fust crack = 1.99 Tine (Secs)

t34

CHAPTER (61 Ourof-Pl"ane Shake Table Testingof Simply Supported URM Walls

-INSTRONTWD

8

6

4la

Ë0Iro-Ë4À¡5 -o

-8-10

-12

(l10mm Wall, 0.l5MPa Overburden, 7Hz Harmonic Excitation)

Figure 6.4.7 Un-cracked NonJoadbearing URM Wall - First Cracking

(l lOmm ÌWall, O.lSMPa Overburden, 7Hz Harmonic Excitation)

Figure 6.4.8 Un-cracked NonJoadbearing URM Wall - First Rocking

Typically, for the walls tested with applied overburden, once rocking commenced there

was a rapid degadation of the mid-height rotation joint. Physically this could be seen as

mortar being broken from the rotation joints by the impact of the two free bodies. This

was attributed to the rocking frequencies and impact forces being much larger for the

loadbearing walls. As a result of the degradation during rocking an increase indisplacement and reduction in response acceleration was observed, without further

increase in excitation until instability.

Table 6.4.4 presents results of the June 98 test series for 110 mm thick IJRM wall with

0.15 MPa overburden stress. These walls were subjected to an out-of-plane gradually

increasing 7 or 10 Hz harmonic excitation. Consistent with the March 98 tests, a final

-MWD-INSTRONTWT)

A '; f, t^\ I I

æ+l¡ I'l'

-1

V

r rnË \ùcct,

50

40

a30E820F10xõ0oÈ-r0â-zo

-30

40-50

135

CHAPTER (6)- Out-oÍ-Plnn¿ Shake Table TestingofSimply Supponed URM Walls

observation from this test series was that for cracked walls the mid-height acceleration at

the commencement of rocking was again typically of the order of 1.5 times the estimated

'semi-rigid threshold resistance' acceleration.

Table 6.4.4 ll0mm WaIl, 0.15MPa - Ilarnnnic Excitation Test Results

From both the harmonic March 98 and June 98 test series it was concluded that for most

practical cases non-linea¡ cracked behaviour is more relevant to a dynamic loading

scenario than the un-cracked properties. Also, from the identified dynamic mid-height

non-linear cracked F-A relationship, a fiiangular distribution of horizontal acceleration up

the height of the wall assumption relative to the supports has been identif,red as likely to

provide the best approximation of acceleration response.

WaIlNo

Test WallCondition

Predictcd 'Quasi-Static' AccelerationCa¡ncity(Refer Table 6.4.2)

ExperirrcntalResults

Cornrnent

5 IOHzHarmonic

Un-cracked 2.3g (Cracking)3.62e (Rieid)

2.9g (Semi-rigid)

A4mm (1.69)

(2.0e)

A=5mm (2.0g)A=10mm (4.1g)

Average support input atcrackingMid-height accelerationresponse at crackingAverage support input at rockingMid-height response at rocking- Amplification at top support asat black frame resonance

6 7HzHarmonic

Un-cracked 2.3g (Cracking) A=6mm (1.2g)

(1.6e)

Average support input atcrackingMid-height accelerationresponse at cracking

6 7HzHarmonic

Cracked 3.62e (Rigid)2.9g (Semi-rigid)

A=8mm(1.6g)A=10mm (2.0g)

Average support input (rockingnot yetcommenced)Mid-height response (rockingnot yet commenced)

7 7HzHarmonic(referFigure6.4.7)

Un-cracked 2.3g (Cracking)3.62g (Rieid)

2.9g (Semi-rigid)

A=9mm (0.18g)

(2.re)

A=I2mm(2.4g)A=22nm(4.39)25llO=2.5

Average support input atcrackingMid-height accelerationresponse at crackingAverage support input at rockingMid-height response at rockingSæady-state responsedisplacement amplification-Rapid joint degradation duringrockinq

136

CHAPTER (6)- Out-of-Planz Shalæ Tablc TestingofS inply Supporîed U RM Walls

6.45. Static Push Tests

To investigate the out-of-plane non-linear F-Â behaviour of simply supported URM walls

static push tests were conducted on both un-cracked and cracked wall test specimens. The

braced steel support frame was used to simply-support the wall panels in these tests.

Ioading was applied at the wall mid-height using a hand pump driven hydraulic actuator(refer Figure 6.4.9). This was geometrically similar to statically apptyrng the same force

at the wall r/t - and t/¿ - height being the center of gravity (CG) of each of the two free

bodies. The applied static load was therefore related to the 'quasi-static' assumption of arectangularly distributed load having a resultant horizontal force at the free body CG.

A calibrated load cell was inserted between the actuator and the wall at mid-height to

record the resisting force applied by the wall onto the actuator. This force was recorded

for displacements from the vertical position to as near as possible to the incipientinstability displacement, where the resisting force was reduced to near zero. The recorded

data was that of the 'quasi-static' non-linear F-Â relationship by means of a rectangular

distributed load.

Hand operaædhydraulic ram

Figure 6.4.9 Static Push Test

Iilr¡*

Í--

137

CHAPTER (6)- Outof-Plane Shal<e Table TestingofSimply Supported URM Wqlls

A summary of the key results for the static push test and a comparison with static analysis

is shown in Table 6.4.5. Arepresentative cross-section of the experimentally derived F-A

plots is presented in Appendix (Ð. r- ^/rrt^t -

/f,f F i'

* Real 'Semi-rigrdr F = Linear Elastic AnalysisRB = Rigid Body Analysis

Table 6.4.5 Resr¡lt Sumrmry of Static Push Tests

Force

ConstructionLot

WaIlNo.

WallState

Thick-ness(mm)

Over-burden(MPa)

Predicted'Static

Capacity'(kN)

PeakForce*(kN)

Dispat

PeakForce(mm)

Vo o1Rigid

Conr¡rænt

March93 3 Un-cracked

110 0 (r-B)2.@(Pß) 0.41

3.18 0.5

June98 8 Un-cracked

110 0.15 (rÆ) 4.82(RB) 5.31

56.2

0.452I

June98 8 Cracked 110 0.15 ( F)2.32(RB) 5.32

4.36 18.5 82 f .{MPa

September9S 10 Cracked 50 0 (LE) 0.07ßB) 0.r1

0.09 6 82 f ,{MPa

September9S 10 Un-cracked

50 0.075 (LE) 1.07(Rß) 0.59

0.95 0.79

September9S 10 Cracked 50 0.075 (rÆ) 0.2e(RB) 0.62

o.49 8.3 79 fd)MPa

September9S 1l Cracked 110 0 .rl-ÐO.N(RB) 0.41

0.3 12.6 73 fl,{MPa

September9S l1 Un-cracked

110 0.15 (tÐo.n(RB) 0.41

4.55.3

0.6621.5

Increasedspringstaticdeflection

Sepûembcr98 12 Un-cracked

110 0 .o-Ð2.8ßB) 0.41

3.0 0.3

September9S 12 Cracked 110 0 (LE)O.n(RB) 0.41

0.38 8.1 92 f ,=OMPa

September9S T3 Un-cracked

110 0 (rß)2.64ß.8) 0.59

2.2 0.59

Sepûember98 13 Cracked 110 0 (LF.)0.27(RB) 0.41

0.33 10 81 f ,{MPa

September9S t4 Cracked 50 0 (LE) 0.07(RB) 0.11

0.084 8.8 77 f,=0MPa-beforedynamic

September9E T4 Cracked 50 0 (r-E) 0.07(RB) 0.11

0.075 10 68 f,=0MPa-afærdynamic

September9S t4 Cracked 50 0.15 Q-E)0.47(RB) 1.07

o.7l 10 66 f ,{MPa

138

CHAPTER (6)- Outof-Plnne Shakc Tøblc TestingofSimply Supported URM Walls

Examination of the un{racked wall static push test results indicated that the linea¡ elastic

analysis predicted the 'static' cracking load reasonably well, within the limits of accuracy

of the flexural tensile strength prediction.

For the cracked wall specimen tests, the predicted 'rigid threshold resistance' force,

R"(1), determined by rigid body analysis, was observed to overestimate the real 'semi-

rigid threshold resistance' by lÙVo to 4O7o wlnch was attributed mostly to the real 'semi-

rigid' nature of the masonry material. As highlighted in Section 5.3, a simple analytical

method has been proposed for predicting the semi-rigid F-A relationship (Priestþ 1985)

based on the assumption of a proportional relationship between the wall curvature and the

stress gradient across the critical section. This was not found to represent the currenttests well as it overestimated the initial stiffness and 'semi-rigid threshold resistance'

force, R*(1). Figure 6.4.10 presents a comparison of the analytical F-Â prediction for the

non-loadbearing 110mm thick specimen no.10 wall and Figure 6.4.11for the 50mm thickspecimen no.ll wall. Here, moduli of elasticity of 1000MPa were used to maintain the

initial stiffness and 'semi-rigid resistance threshold' force within reasonable limits. Asecond shortfall was that the effect of degradation of the mortar joints could not be

considered.

120

2X r00H

v180

860F

ç,õ40Ê

ÐGERIMENTAL+PRIESTLYMETHoD+-RIGIDBODY

R0nonoÊôtNo nono6rftn

MID IIEIGHT DISPLACEMENT (mm)

Figure 6.4.10 comparison of ll0rnm specimen static Push F-a with anaryticat

r39

CHAPTER (6)- Ourof-Plane Shake Table TestingofSimply Supported URM Wqlls

2H

JFzô.F

Hu¿

400

350

300

250

200

150

r00

50

0oooeQÉcloçn ooooo\¿)ræo\3

MID HEIGTfT DISPLACEMENT

ÐGERIMENTAL+PRESTLYMETHOD

RIGIDBODY

E= 1000MPaSepternber 98Speciræn ll

SmmMortar Rake

Figure 6.4.11 Comparison of S0mm Specimen Static Push F'A with Anatytical

After dynamic testing the degradation of rotation joints was observed and related to a

flattening of the static F-À relationship and thus a lowering of average response

frequencies. To quantify this degradation the wall specimens were catagorised

throughout the dynamic testing as new, moderately degraded or severely degraded by

their appearance as shown in Figure 6.4.12. Using this visual categorisation of the wall

specimens, some broad empirically based predictions of the static F-Â relationship could

be made in relation to the idealised bi-linear rigid F-A relationship. The empirically

determined predictions are discussed further in Chapter 7 as they are related to the

modelling of the non-linear force displacement relationship required for THA.

Tests on non-loadbearing l lOmm thick walls were also performed having displacements

reduced from the incipient instability displacement to investigate the static hysteretic

behaviour as presented in Appendix (F¡. The area encompassed by each hysteresis loop

provided an indication of the energy loss per half cycle caused by joint rotation and

friction at the connections. The resonant energy loss per cycle method of estimating

damping was then used to assess the level of damping within the rocking system. Using

this approach the energy dissipated in a vibrational cycle of the wall was equated to that

of an equivalent viscous system. It was found that the equivalent single degree-of-

freedom (SDOÐ equivalent viscous damping (6sm") was approximately tÙVo,being of a

140

CHAPTER (61 Ourof-Plnne Shake TabI¿ TestingoÍSinply Supported URM Walls

similar value to damping results determined in Section 6.4.6 by free vibration tests.

However, the accuracy of this method is limited as it only considers the response at

resonance. The highly non-linea¡ shape of the F-Â relationship for LIRM walls makes the

effective half cycle stiffness non-unique so that it is also difficult to use this method.

Moderaûe degraded wallVisible crack slightly

rounded

drop outNew condition wall and crack

Severely degraded rvall

Figure 6.4.12 Mid-height Rotation Joint Condition

significantlyrounded

From the static push tests on 110 mm walls with a 0.15 MPa overburden, it was

confirmed that a significant additional restoring force occurred at large mid-height

displacements due to the increased spring deflections. Consequently, for mid-height

displacements greater than approximately 207o of the wall thickness the constant force

assumption \ryas no longer valid.

In Section 6.4.6 the F-À relationships determined by the static push tests have also been

used for comparison with dynamic F-Â relationships, derived in accordance with the

assumption of a uiangula¡ distribution of acceleration. Here the response of the effective

t4r

CHAPTER (6)- Ourof-Plane Shøke Tøblc TestingofSimply Supponed URM Walls

masses at 213 the free body height correlate well with the static push test results. This

further supports the use of a triangula¡ distribution of acceleration.

6.4.6. Free Vibration Tests

Free-vibration tests were performed on test specimens which were pre-cracked at mid-

height to investigate the physical characteristics of the free vibration response of simply

supported URM walls. To enhance the investigation of the free vibration response

additional data points have also been derived from the free vibration phase ofpulse tests,

reported in Section 6.4.7.t. To undertake these tests, the mid-height of the cracked test

panel was displaced statically to near the incipient instability displacement. In effect the

wall was provided with a degree of potential energy equal to that required to move the

wall from its initial vertical position to that of the incipient instability displacement.

From this displacement the wall specimens were released and permitted to vibrate freely

i.e. to rock between their leeward faces. This vibration resulted from a continuous energy

balance comprising an exchange of potential and kinetic energy. During the response the

total system energy was exponentially reduced to zero by energy losses associated with

the incremental damping at the crack closing impact and support friction. At that time

both the potential and kinetic energy are reduced to zero and the vibration ceases with the

wall in the vertical position.

The same instrumentation to that described in Section 6.2.3 was used to record both the

mid-height displacement and acceleration of the free vibration response. A representative

cross-section of the free vibration test results are presented in Appendix (F). For these

tests as well as the mid-height acceleration and displacement response the mid-height

hysteretic behaviour is also presented. From the free vibration tests the a-Â relationship

and thus the mid-height 'semi-rigid resistance threshold' acceleration and approximate

displacement at which this occurred were determined. Further, by adopting the

assumption of a triangular distribution of acceleration relative to the supports, the 'semi-

rigid resistance threshold' acceleration at the effective mass was determined as 213 of the

mid-height 'semi-rigid resistance threshold' acceleration. Table 6.4.6 presents a

summary of the free vibration release results.

r42

CHAPTER (6)- Ow-of-Plarc Shak¿ Tabl¿ TestingofSirrWIy Supported URM Walls

WallNo

Thichress(mm)

Over-burden(MPa)

'Quasi-Static'RigidBody

AccelerationCapacity

(Refer Table6.4.21

Mid-height6Semi-rigidResistanceThreshold'

Acceleration(c)

Efiective Mass'Senú-rigidRcsistanceThreshold'

AccelerationG)

Displacenrcnt at'SemÍ-rigidResistanceIhreshold'

(mm)

l0 50 0 0.13 0.19 o.r2 910 50 0 0.13 0.18 o.t2 810 50 0.07 0.65 0.78 0.52 9ll ll0 0 0.29 0.35 o.23 l51l ll0 0 0.29 0.35 o.23 t6il 110 0 o.29 0.32 o.22 t7

Table 6.4.6 Summry of Release Test Results

As the effective mass 'semi-rigid resistance threshold' acceleration is consistently just

below the predicted 'quasi-static' acceleration this further suggests that the assumption ofa triangular acceleration distribution and thus effective mass location at the 213 freebody

height, is reasonable.

6,4.6. I. N o n-línear F requency - Mid- H eíght Dísplac eme nt Relationship

For all of the free vibration responses analysed, each cycle of the displacement response

was considered in turn. In doing so each mid-height response cycle start amplitude, Â1,

finish amplitude, Lz, and cycle period, T were determined as shown by Figure 6.4.13.

MID-HEIGITT FREE VIBRATION RESPONSE

20

g15ä2rcE]

E]o5

ã0Fi

f;-sóE -10

-15

-20

t\ A1

I \ L2

l \ I/ - - -\ - - J' O È Nló * S Þ...i ..': -.: l-: : l- ..: +# q\ 'r4 q ù../ F Md\.,/NNNddN(

\ IT TIME (SECS

Figure 6.4.13 Free Vibration Calculation

143

CHAPTER (6)- Out-of-Pbne Shak¿ Tabl¿ TestingoÍSimply Supponed URM Walls

The average cycle amplitude, Au, was determined as,

Lo

and the individual cycle frequency as,

2

r =Yr

Having determined this information for each cycle, the non-linear frequency versus Âo

relationship was plotted including an exponential or logarithmic line of best ht. Figure

6.4.L4 presents this relationship for 50 mm thick specimens at various levels of applied

overburden and Figure 6.4.15 for 110 mm thick walls with no applied overburden. A

comparison of the empirically derived /-Au relationships with an analytical prediction

derived by the comparison of the dynamic equation of motion for a SDOF system and

those for the non-linear rocking system is presented in Chapter 7.

80

7 0

oú e.ozot-< 5.0JÈO8 +.o

ð s.ozFIÞg 2.0

É1.0

0.0

0 5 l0 15 20 25 30 35 40 45

AVERAGE CYCLE MID.IIEIGIIT DISPLACEMENT

50

trNOPRECOMP. NOPRECOMPLogfittr0.075MPa¡ 0.075MPa Exp frttr0.15MPa. 0.l5MPaExp fitEPARAPETEItr

¡

tr

. PARAPET fitsF tr

F Ba

o I o.dlÐh

Figure 6.4.14 50mm Specimen Frequency vs Average Cycle Mid-Height Disp.

144

CHAPTER (6)- Out-of-Plane Shake Tøble Testingof Simply Supponed URM Walls

8.0

7.0

se 6.0zoF-f 5.0EO8 ¿.0l&

tr 3.0zÊlÐfl z.oúI&

1.0

0.00 10 20 30 40 50 60 't0 80 90 r00 110

AVERAGE CYCLE MID HEIGI{I DISPLACEMENT (mm)

ltrNOPRECOMP

INO PRECOMP Log [rt

h"*-r-

Figure 6.4.15 1l0mm Specimen Frequerrcy vs Average Cycle Mid-Height Disp.

6, 4. 6. 2. N o n- lin e ar Dy namic F orc e - Mid- H eight Dß plac e m e nt Relatío ns hip

Rearranging the previously established dynamic relationship (Clough et al1993)

a 2d Etl*

"

where o= cycle angular response frequency

IÇ = average cycle secant stiffness

M" - effective mass of the free body

the average cycle secant stiffness can be written as,

K,=(?-t¡f), M"

Following from this an estimate of the response force can then be determined as

F =Ko 1,"= (Zr{), M " L"

where Â. = displacement of the effective mass

(6.4.3)

t45

(6.4.4)

CHAPTER (6)- O*of-Pbne Shakc Table TestingofS imply Supp orted U RM WølIs

Assuming that the acceleration response of each of the rocking free bodies is triangularly

distributed relative to the supports, the effective mass is located at 213 the height of the

free body. Consequently the ayera1e effective mass displacement, Â., can be related to

the average cycle mid-height displacement, Àn, bY

,)o"=ío'

Substituting A" back into Equation 6.4.4 the force response at the effective mass can be

determined as,

, =1*, L"=|Q"f)' M " L^ (6.4.s)

This relationship is therefore directly comparable with static test results. From Equation

6.4.5, the dynamic F-A relationships at the effective mass for the test specimens have

been determined. Each point shown on Figure 6.4.16 shows this relationship for each

free vibration response cycle of the 50 mm thick specimens at various levels of applied

overburden and is compared with the bi-linear static rigid body F-A relationship. The

line of best fit has been derived using the line of best f,rt from the /-Â relationship

discussed in Section 6.4.6.I. Similarly, each point shown on Figure 6.4.17 represents the

relationship for each free vibration response cycle of the 110 mm thick walls with no

applied overburden again compared with the bi-linear static rigid body F-A relationship.

146

CHAPTER (6)- Out-of-Pløne Shake Tqbl¿ Testingof SimPlY StPPorted URM Walls

tzOfj

r000

arll()úl&

800

600

400

200

00 5 10 15 20 25 30 35 40 45 50

AVERAGE CYCLE MID TIEIGIIT DISPLACEMENT (mn)

tr NOPRECOMPO NOPRECOMPLogfit

{-NOPRECOMPRigidBodytr 0.075MPaO 0.075MPaE4fit

0.075MPa Rigid Bodytr 0.15MPaa O.l5MPaExp fit

t0.l5MPaRigidBodytr PARAPET. PARAPETITgfiT

trtr

trD.l¡

t¡

a a

tra

PARAPET

¡p-n

Figure 6.4.16 50mm Wall Dynamic F-A Relationships (Various Overburden)

Figure 6.4.17 110mm Watl Dynanúc F-A Relationship

450

400

350

300

¿H 250OúÊ zoo

150

100

50

0

0 5 1015202530354045 50556065 70 75 80 85 90 95 100 105 110

MID HEIGIIT DISPLACEMENT (mTn)

tr No pnncorvrp

a nopnncoMPlogñt+No pnscoMp Rigid Bodytr

tr

\

147

CHAPTER (6)- Ouçof-Pbne Shak¿ Table Testingof Simply SupportedURM Wqlls

A comparison of the derived dynamic F-Â relationships with the results of the static push

tests also show a good correlation as presented in Figure 6.4.18 and Figure 6.4.19. This

observation further confirms that the assumption of a triangular acceleration response for

rocking free bodies relative to the supports provides a reasonable estimate of the true

acceleration response.

For the remainder of the analytical modelling of the rocking response of pre+racked

simply supported LIRM walls, the free body triangular acceleration response assumption

is adopted.

zt¡¡(JÉÍJ.

800

700

600

500

,t00

300

200

100

0

0 5 l0 15 20 25 30 3s 4D 45 50

AYERAGE CYCLE MID IIEIGIIT DISPLACEMENT (MM)

\1o o¡

EI tr

¡

NO OVER St¿tic Test

NO OVERDynamicNO OVERExp frt0.075MPa Static Test

Dynamic0.075MPaExp frt0.l5MPa Static Testnynar¡¡ctr

a

-+

0.l5MPa frr

tra

Ta

I l\

\t.a

a

I

-oË'f

Figure 6.4.1t 50mm Wall Comparison of Static and Dynamic F-A Relatioruhips

148

CHAPTER(6)- Ourof-Plnne Shakz Tablz TestingoÍSirnply Supported URM Walls

âÊlUút¡r

400

350

300

250

200

r50

100

50

0 10 20 30 40 50 60 70 80 90 100 r10

AVERAGE CYCLE MIDMIGIIT DISPLACEMENT (mm)

?-*:3':

o NoPRECoMpDynamic+tøSepes Shtic Tesr4l-ttsep98 Static Test

A NOPRECOMPLOEFT

oo

o o

Figure 6.4.19 110mm Wall Comparison of Static and Dynamic F-A Relatioruhip

6.4.6. 3. N on-linear Damping- Frequency Relationship

As discussed further in Chapter 7, for a single degreeof-freedom (SDOÐ system, \ryith

l00%o of its mass mobilized, the equivalent viscous damping ratio, (5¡rep, associated withthe per cycle energy loss can be estimated for each response cycle (refer Figure 6.4.13)âS'

n(t,/^ \Ésoop=# 6.4.6)

This estimate can be shown to be reasonable for €soo" less than approximately ZOVo

which is generally the case for building structures. Above this the damped frequency

becomes increasingly significant and must be considered. Since the frequency of each

response cycle was known, the non-linetr €s¡op versus frequency relationship was

developed. Figure 6.4-20 presents this relationship for the 50 mm wall specimens at

various levels of applied overburden and Figure 6.4.22 for non-loadbearing 110 mm wallspecimens. For both sets of walls a lowerbound estimate of 6soou of a¡ound 5Vo was

observed. This is slightly greater than the 3Vo observed by (tam 1995) for tests on

149

CHAPTER (6)- Ourof-Han¿ Shake Tablz TestingofSimply Supponed U RM Wqlls

l l0mm thick parapet walls. A possible reason for this is energy losses associated with

the simply supported wall mid-height rotation joint as well as the additional mass due the

relative heights of the test walls.

From the non-linear relationship an increase it E -u at very low response frequency

(large displacement oscillations) and at high response frequencies (small displacement

oscillations) was observed. Walls having overburden were also observed to typically

have relatively higher hr¡or values than for walls with small axial loads. The increased

energy loss at large displacement oscillations and for walls having overburden can be

explained by the increased impact energy loss per half cycle at the closing of the mid-

height, top and bottom cracks. The increased energy loss at small displacement

oscillation is likely to have been caused by friction losses at the supports becoming

proportionally more si gnificant.

A final observation was that the thicker wall specimens tended to have a slightly higher

energy loss per cycle although this was not proportional to the ratio of thickness since the

density of the two brickwork specimens were not equal.

âøõzô.

oIOEúc),2f¡lU&t¡l

25.Wo

22.5%

2n.o%

t7s%

15.0'lo

t2.5%

to.uk

7.5%

5.Uk

2.5%

0.Wo

0 I 2 3 4 5 6 7 89FREaUm{CY(Hz)

E0.15MPà

O}¡OPRECIIMP!O.Cr/SMP¿

!

^Itd ¡oo^ l^!Ed Ioo oo

EE

o I"teo !ô

-tfirr ,__E_ ¡l ^

LOWERBOUND E=SVo"o -o

0o o

Figure 6.4.20 s0mm\ilatl NonJinear I vs Frequency (Various Overburden)

150

CHAPTER (6)- Out-of-Plønc Shake Table TestingofSimply Supported URM Walls

24.0

17.5

15.0

t2.5

10.0

7.5

5.0

2.5

0.0

I\O;Ø2HC)

Er¡.¡

U(,z.L!,l

zoFúÊúo.

0 1 2 t 4 5 6 7 89FREQ{IE{CY(IIz)

I

OIOPRE@MP

l0.075lvtPa

0.l5Mh

¡¡

f,

^8lol ir¡to8

o^ lal!_ I

A

rl I !J Io !

dp o

To minimise the effect of the specimen density difference the dynamic relationship

(Clough etal1993)

Croo, -4o l6 ,oo,M"

Figure 6.4.21 50mm Wall NonJinear Csnor/t\4 vs Frequency (Yarior¡s OverburdeÐ

was used to derive the ratio of the SDOF proportional damping coefficient, Cs¡op, to the

effective mass, M". This was then plotted against the cycle frequency (refer Figure

6.4.21 and Figure 6.4.23). A comparison of the Csroe/Àft versus frequency relationship

for non-loadbearing 50 mm and 110 mm walls (refer Figure 6.4.23) shows that a good

correlation was found between the energy losses in the two rocking systems.

151

CHAPTER (6)- Outof-Plane Shake Table TestingofSirnply Supported URM Walls

30.v%

25.Wo

2fr.Vo

15.Vo

lO.Mo

5.OVo

0.01o

âv)È.(,zgâc(JFHú(JFz14(JútÐÈ

2 3 4 5FREQIJH{CY(rlz)

60 I

oo

ô^ôô ^:l¡l il I I :;rI

ôo3 8e0 0 o

coo8

tu oo o

0 Eon'õo o

LO\ryERBOUND E= 6Vo

Figure ó.4.22 NonJoadbearing 110nun Wall Non-linear I vs Frequency

Figure 6.4.23 Non-loadbearing 50mm and 1l0mm Wall Cs¡,or/l\¡f. vs Frequency

r4.0

13.0

12.0

lr.0

r0.0

9.0

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

âà(JU)v)

tszI¡}HOÉÍ¡loU(5zÀ

AJzFtsúÀoúÀ

4 5 6I 2 )0FRE@ENCY

a

.l1OMMNOPRECOMP

^ 50MMÌ.¡OPREOCx\4P ôlo

a I

a

a

AaA

^ ¡^

152

CHAPTER (6)- Out-of-Plnne Shnke Tabl-e Testingof Simply Supported URM Walls

6.4.7. Transient Excitation Tests

The shaking table input selected for transient excitation tests included both pulse and real

earthquake excitations. The range of amplitude and frequency content was selected to

permit the rocking wall response to be thoroughly examined over a relevant range ofexcitation scenario. This allowed critical excitation parameters to be identified and

directly related to the wall response. The resulting dynamic data was also used to provide

a basis for comparison with analytical response predictions using THA, as discussed inthe next chapter.

6.4.7.1. Pulse Tests

As part of the September 98 test series both half-sine (Yz SD) and gaussian displacement

pulse tests were performed on pre-cracked simply supported LJRM walls both with and

without applied overburden. Instrumentation as described in Section 6.2.3 was used to

completely record the dynamic response behaviour of the wall specimens.

The displacement pulse frequencies used for the experimental investigation ranged from0.5Hz to 3H2.. This frequency range was selected to cover the lower response frequency

hmit, f¡,¡1, as described in Section 5.2.I, and thus permitted pulse forcing frequency at

which the maximum displacement amplification occurred or the effective wall 'resonant

frequency' to be approximately identified experimentally. Figure 6.4.24 shows a

normalized 0.5H2 input displacement gaussian pulse and Figure 6.4.25 the corespondingacceleration input at the table

For each of the displacement pulse frequencies investigated a normalised displacement

pulse was first determined (e.g. refer Figure 6.4.24). The pulse displacement amplitude

input to the shaking table was gradually increased, at each frequency level, until rockingand ultimately instability of the wall specimen occurred. The peak pulse displacement

(PGD) and acceleration (PGA) were then related to the peak mid-height displacement

response of the test specimen. This permitted the identification the displacement

amplif,rcation (peak mid-height displacement/PGD) of the wall mid-height response.

Table 6.4.7 presents a summary of key results of the pulse tests performed.

153

CHAPTER (6)- O*of-Plane Shalce Tablc Testingof Simply SupportedURM WølIs

t.2

eEl<toN! o.s

7, 0.6

troË o.¿oa9 ntFr

0 c) eì a I e - .ì a I oq d c.ì a 9 e ó q a I aq {oooodNddooóo

Tiæ (secs)

-0.5H2 Gaussian Pulse

At\I \I \

/\

Figure 6.4.A O5ftzNornnlized Gaussian Displacenrent Pulse Input

Figure 6.4.25 Conesponding Acceleration Input

On examination of the results it is evident that for each of the ïvall specimens the

maximum displacement amplification is associated with a particular frequency described

in Section 5.2.1 as the effective resonant frequency,/.ç. For the 1.5m tall, 50mm thick

wall without applied overburden, the maximum displacement amplif,rcation occurs at

pulse frequencies of between lHz and 2Hz. With the application of 0.07MPa overburden

the effective wall resonant frequency increases to between 2Hz and 3Hz and further to

greater than 3Hz with the application of 0.15MPa overburden (refer Table 6.4.7). For the

0 0r5

00

0 005

-0.005

-0.01

-0.0r5

4.02

-0.025

-0.03

^

f9oqô{

It

I

0

è¡)

doNËtroaÒ..ÉdooIoo.adF

Tine (secs)

r54

CHAPTER (6)- Outof-Plønc Shalce Table Testingof S imply Supporte d U RM Walls

l.5m tall, 110mm thick wall without applied overburden the effective resonant frequency

is similar to that of the 50mm wall at l}Jz to ZHz (refer Table 6.4.3). A representative

cross section of the pulse test results where the mid-height displacement response and

input displacements are compared is presented in Appendix (F). The full wall response

including t/t -, mid- and 3/¿ - height acceleration response is also presented. During the

rocking free vibration response phase the mid-height acceleration response is typicallyapproximately twice ther/¿ - and3/c - height acceleration responses.

Table6.4.7 Summry of Key Pulse Test Results (S0mmWalls)

WallNo.

Thick- IreSS(mm)

Over-burden(MPa)

PulseType

PulseFreq.(Hz)

PeakPulseDisp.(mm)

PeakPulseAccel.(mm)

PeakMid-height

ResponseAccel.k)

PeakMid-height

ResporueDisp.(mm)

Mid-heightDisp.

Amp[fication

10* 50 0 Y2SD 0.5 20 0.1 0.15 5 0.25l0* 50 0 Y2SD 0.5 30 0.15 0.18 t3 0.43l0* 50 0 Y2SD 0.5 40 0.r9 0.19 20.5 0.5110* 50 0 %sD 0.5 50 0.225 50 1.0010* 50 0 Y2SD I t3 0.135 0.19 46 3.5410* 50 0 Y2SD I l5 0.155 0.19 3t 2.07l0* 50 0 Y2SD I 17 0.175 0.19 3l 1.8210* 50 0 YzSD 1 20 o.2 50 2.s010* 50 0 YzSD 2 10 o.2s 0.18 28 2.80l0* 50 0 YzSD 2 t3 0.33 0.18 3t 2.38l0* 50 0 Y2SD 2 15.5 0.39 0.18 32 2.0610* 50 0 Y2SD 2 r7.5 0.41 0.18 33 1.8910* 50 0 Y2SD 2 20 0.46 0.18 50 2.50t4 50 0 Gauss 1 5 0.07 o.t2 10.5 2.IOl4 50 0 Gauss I 7.5 0.1 o.t2 16.5 2.20t4 50 0 Gauss I l0 0.125 o.t2 24 2.40t4 50 0 Gauss 1 12.5 0.15 o.t2 33 2.64l4 50 0 Gauss 1 t4 0.18 0.r2 40 2.86t4 50 0 Gauss 1 15 0.2 50 3.33I4 50 0 Gauss I T6 o.2l 50 3.13t4 50 0 Gauss I l4 0.16 0.13 35 2.50t4 50 0 Gauss I l5 0.175 0.13 40 2.67l4 50 0 Gauss 1 t6 0.19 50 3.r374 50 0 Gauss 2 15 0.1 0.09 6 0.40l4 50 0 Gauss 2 2l 0.13 0.1 t7 0.81T4 50 0 Gauss 2 22 0.15 0.r2 23 1.05t4 50 0 Gauss 2 23 0.r6 0.13 29 r.26T4 50 0 Gauss 2 u 0.r75 0.13 50 2.08t4 50 0 Gauss 0.5 5 0.3 0.13 11 2.20t4 50 0 Gauss 0.5 8 0.6 0.13 13 1.63t4 50 0 Gauss 0.5 10.5 o.7 0.13 l5 1.43t4 50 0 Gauss 0.5 T3 0.8 0.13 15.5 t.t9t4 50 0 Gauss 0.5 l5 0.9 0.13 18 r.20

10* 50 0.07 t/2SD 0.5 20 0.19 0.5 3 0.15

155

CHAPTER ( 6 )- O ut- of- PIøne Shake Table'le s t ingofSimply Supported URM Walls

Continued

\ilallNo.

Thick- ness(mm)

Over-burden(MPa)

PulseType

PulseFreq.(Hz)

PeakPulseDisp.(mm)

PeakPulseAccel.(mm)

PeakMid-height

ResponseAccel.

G)

PeakMid-height

ResponseDisp.(mm)

Mid-heightDisp.

Amplification

10* 50 0.07 %SD 0.5 30 0.25 0.6 4 0.13l0* 50 0.07 7z SD 0.5 40 0.31 0.6 5.5 0.14l0* 50 0.07 YzSD 0.5 50 0.375 0.6 6.5 0.1310* 50 0.07 7z SD 0.5 'to 0.4 0.6 l0 0.14l0* 50 0.07 7z SD 1 10 0.18 0.5 3.5 0.3510* 50 0.07 Y2SD I 25 0.38 0.7 l5 0.60l0* 50 0.07 lzz SD I 30 0.39 0.7 8 o.2710* 50 0.07 YzSD I 35 0.4 0.7 10 o.2910* 50 0.07 7z SD I 40 0.45 o.7 t4 0.35l0* 50 0.07 7z SD 1 50 0.5 0.7 25 0.5010* 50 0.07 Y2SD I 55 0.8 o.1 37 0.6710* 50 0.07 %SD 2 l0 0.31 0.7 9 0.9010* 50 0.07 YzSD 2 15 0.41 0.1 16 t.o710* 50 0.07 Y2SD 2 22.5 0.5 0;l 34 1.51

l0* 50 0.07 Y2SD 2 25 0.62 0.7 40 1.60

10* 50 0.07 YzSD J 10 0.7 o;l 2l 2.to10* 50 0.07 %SD 3 l3 0.8 0.1 25 r.92l0* 50 0.07 Y2SD J 16 0.9 0.7 40 2.5010* 50 0.15 YzSD 0.5 30 0.45 1 7 o.2310* 50 0.15 YzSD 0.5 40 0.5 I 8 o.2010* 50 0.15 YzSD 0.5 50 0.55 I I7 o.3410* 50 0. r5 t/z SD 0.5 55 0.6 I ll 0.2010* 50 0.15 Y2SD 0.5 57.5 0.7 I 7 o.t210* 50 0.15 Y2SD 1 60 0.15 I l0 0.17

10* 50 0.15 /z SD I 62.5 0.8 I 36 0.5810* 50 0.15 Y2SD I 62.5 0.8 1 20 o.3210* 50 0.15 Y2SD I 65 0.85 I 30 0.4610* 50 0.15 /z SD 2 20 0.5 I 20 1.00

10* 50 0.15 /z SD 2 22 0.6 I l3 0.59

l0* 50 0.15 Y2SD 2 28 0.8 I t4 0.5010* 50 0.15 /z SD 2 30 0.85 I 1l o.3710* 50 0.15 Y2SD 2 32.5 0.95 I ll 0.34l0* 50 0.15 Y2SD 2 35 1 I 1l 0.31

l0* 50 0.15 %SD 2 37 1.05 I t2 0.32t4 50 0.15 Gaus 0.5 36 N/A 0.9 9 o.25t4 50 0.15 Gaus 0.5 4l N/A 0.9 20 o.49l4 50 0.15 Gaus 0.5 46 N/A 1 24 0.52t4 50 0.15 Gaus 0.5 49 N/A I 34 0.69

156

CHAPTER (6)- Out-of-Plane Shake Tøble Testingof Simply Supported URM WaIIs

WallNo.

Thick- ness(nm)

Over-burdenMPa)

PulseType

P¡¡lseFreq.(Hz)

PeakPulseDisp.(mm)

PeakPulseAccel.(mm)

PeakMid-height

ResponseAccel.

(s)

PeakMid-height

ResponseDisp.

Mid-heightDisp.

Amplification

l1r 110 0 7z SD I l5 0.16 0.28 8 0.531l* ll0 0 YzSD I 18 0.2 0.3 13.5 o.751l* ll0 0 YzSD I 20 0.22 0.3 23 l.l5l1r 110 0 /z SD I 25 0.25 0.3 45 1.80l1* 110 0 /z SD I 27 o.26 0.3 49 1.811l* ll0 0 %SD I 30 0.215 0.31 4l 1.371l* ll0 0 %SD I 32.s 0.3 0.31 40 1.23ll* 110 0 /z SD I 37.5 0.32 0.31 62 1.65ll* ll0 0 Y2SD I 40 0.33 0.31 72 1.8011* ll0 0 %SD I 45 0.3s 0.31 82 1.82l1* 110 0 Y2SD 2 l0 o.2 0.3 20 2.AOl1* 110 0 %SD 2 l5 o.25 0.3 40 2.67ll* ll0 0 YzSD 2 17.5 0.38 0.3 45 2.5711* ll0 0 YzSD 2 20 0.43 0.3 45 2.25l1* 110 0 %SD 2 25 0.5 0.3 58 2.32l1* ll0 0 Y2SD 2 27 0.61 0.3 65 2.41l1 ll0 0 YzSD 3 8 0.5 0.3 l3 1.6311 ll0 0 7z SD 3 l5 0.8 0.3 26 t.731l 110 0 Y2SD J t7 0.9 0.3 27 1.59l1 ll0 0 YzSD J l8 I 0.3 30 1.67ll ll0 0 Y2SD J l6 0.6 0.31 38 2.38ll 110 0 %SD J 20 0.65 0.3r 49 2.4511 110 0 %SD 3 24 o.725 0.31 6t 2.54t2 110 0 Gauss I 16 0.17 0.31 25.5 r.59t2 110 0 Gauss I 2t 0.25 0.31 36 t.7rt2 110 0 Gauss I 26 0.3 0.31 49 1.88t2 ll0 0 Gauss I 28 0.35 0.31 54 1.93t2 il0 0 Gauss I 29 0.375 0.31 57 1.97t2 110 0 Gauss I 30 0.4 0.31 67 2.23t2 ll0 0 Causs I 3l 0.425 0.31 73 2.3slz ll0 0 Gauss I 32 0.45 0.31 77 2.41t2 110 0 Gauss I 31 o.425 0.31 72 2.32l2 110 0 Gauss I 33 0.85 0.31 80 2.42l2 ll0 0 Gauss I 34 0.9 0.31 85 2.50T2 110 0 Gauss I 35 0.95 0.31 88 2.5rt2 ll0 0 Gauss I 39 0.52 0.31 58 r.49t2 ll0 0 Gauss I 4l 0.55 0.31 76 1.85t2 110 0 Gauss I 44 0.58 0.31 78 1.17t2 110 0 Gauss I 46 0.61 0.31 68 1.48l2 110 0 Gauss I 48 0.65 0.31 55 1.15l3* 110 0 Gauss I ll 0.125 0.3 6 0.55l3* ll0 0 Gauss I 12.5 0.15 0.31 9 o.7zl3* ll0 0 Gauss I 15.5 0.175 0.32 15.5 1.0013* 110 0 Gauss I 17.5 0.225 0.33 20.5 t.t7l3* ll0 0 Gauss I 20 0.25 0.33 26 1.30l3* 110 0 Gauss I 22.5 0.275 0.33 30.5 1.36l3* 110 0 Gauss I 25 0.3 0.33 35.5 r.42

Table 6.4.8 Sumrmry of Key Pulse Test Results (110mrn Walls)

r57

CHAPTER (6)- Ourof-Pbne Shake Table TestingofSimply Supported URM Walls

WallNo.

Thick- ness(mm)

Over-burden(MPa)

PulseType

PulseFreq.(Hz)

PeakPulseDisp.(mm)

Peakh¡lseAccel.(mm)

PeakMid-height

ResponseAccel.

(s)

PeakMid-height

ResponseDisp.(mm)

Md-heightDisp.

Amplification

13* 110 0 Gauss I n.5 0.325 0.33 40 r.4513+ 110 0 Gauss I 3L 0.35 0.33 45 r.4513* 110 0 Gauss I JJ 0.4 0.33 57 1.73

13+ 110 0 Gauss 1 36 o.45 0.33 65 1.81

13* 110 0 Gauss 1 38 0.5 0.33 55 1.4513* 110 0 Gauss 1 40 0.55 0.33 50 r.25l3* 110 0 Gauss I 42.5 0.6 0.33 45 1.06

13* 110 0 Gauss 1 44 0.65 0.33 44 1.0013* 110 0 Gauss I 45 o.7 0.33 50 1.1 1

13* 110 0 Gauss 0.5 50 0.225 0.33 20 0.4013* 110 0 Gauss 0.5 55 o.25 0.33 24 o.4413* 110 0 Gauss 0.5 60 o.275 0.33 28 o.4713* 110 0 Gauss 0.5 65 0.3 0.33 4l 0.63l3+ 110 0 Gauss 0.5 70 0.35 0.33 85 t.2rl3* 110 0 Gauss 0.5 70 0.4 0.33 7l 1.01

13* 110 0 Gauss 0.5 75 0.45 0.33 76 1.01

l3r 110 0 Gauss 0.5 80 0.5 0.33 74 0.9313* 110 0 Gauss 0.5 82.5 0.55 0.33 95 1.15

13* 110 0 Gauss 0.5 85 0.575 0.33 69 0.8r13* 110 0 Gauss 0.5 87.5 0.6 0.33 85 0.9713* 110 0 Gauss 0.5 90 0.625 0.33 76 0.84

Continued

Presented in Appendix (F)

The results also indicated that the wall thickness had only a small impact on the effective

resonant frequency but the application of overburden significantþ increased the effective

resonant frequency. This can be explained, as a change in the wall thickness does not

alter the average incremental cycle secant stiffness, Kur", and thus the effective resonant

frequency however an increase in overburden does (refer Figure 6.4.26). For a rigid wall

this is because an increase in wall thickness does not alter the negative stiffness value, as

both of the 'rigid resistance' fotce, R.(1), and instability displacement, A¡¡s¡¡6¡¡y, âfe

increased proportionally. The average incremental secant stiffness and effective resonant

frequency therefore remain the same. In contrast, with an increased overburden applied

at the leeward face, as was the case for the test specimens, Ç(1) is reduced as &(1)

increases however Âinsøbiìity does not alter. Thus, the average incrernental cycle secant

stiffness is increased. This is shown in Figure 6.4.14 where higher response frequencies

for the 50mm wall specimens with overburden are obseryed than without. Where an

158

CHAPTER (6)- Out-ol-Plane Shalcc TøbIe Testingof Simply Supported URM WøIls

increase in overburden is applied at the leeward face of the wall, R"(1) again increases

but to a lesser extent and ¡s¡¿61¡t, is reduced to less than the thickness of the wall. The

reduction in A¡.66i¡s, is dependent on the ratio of overburden to the self weight of the wall(refer Table 5.2.1). Consequentþ, again the average incremental cycle secant stiffness

and thus the effective resonant frequency are increased (refer Figure 6.4.26).

oÊ

Í¡r(l)oÉsaøú.)úclÈc(d

tl

Increasedoverburden atcenterline

Increasedoverburden atleeward face ,,'

Increasing ayera5ecycle secant stiffnessand thus effectiveresonant frequency

a

aa/\ ,aa

2R (1)>K u

K.aa,

R.(1)

Double originalthickness

Âinst¿bility

Mid-height displacement ÂSolid lines represent rigid F-Â relationshipsDashed lines represent ayeruge cycle secant stiffnesses

Figure 6.4.26E,frælíve Resonant Frequerrcy (By rvall rhickress and overburdeÐ

aa

2

159

CHAPTER (6)- Outof-Plane Shake Table Testingof Simply Supported URM Walls

Experimentally the range of effective resonant frequency observed is due to the changing

state of the rotation joints with continued testing and degradation of the rotation joints

flattening the F-À relationship. As such, there is a coresponding decrease in the average

incremental cycle secant stiffness and thus the effective resonant frequency of the wall.

6.4.7.2. Real Earthquake Excitation Tests

To complete the investigation into the response of both loadbearing and non-loadbearing

simply supported URM walls to transient excitations, shaking table tests were performed

using real earthquake accelerogram records to drive the shaking table. A comparison of

recorded table accelerations with the original accelerograms has shown a reasonable level

of correlation. Instrumentation as described in Section 6.2.3 was used to capture the

dynamic response behaviour of the wall specimens.

To investigate wall response over a range of excitation, relevant real earthquake scenario

of both 'low frequency large displacement' and 'high frequency small displacement'

excitation were selected. Table 6.4.9 presents a summary of the earthquake excitations

used for investigation. By comparison of the PGD and PGA an indication of the type and

severity of the earthquake can be attained. For instance it can be seen that the Nahanni

aftershock has a relatively high PGA but a small PGD indicating that this earthquake had

a dominant high frequency component. This was determined from the power frequency

spectrum as approximately l.75Hz to 2.25H2. Although traditionally this would

therefore not be expected to impact greatly on ductile structures the large accelerations

would be expected to impact more severely on stiff brittle structures. The Taft, Pacoima

Dam and ElCentro earthquakes typically have higher PGD and similarly large PGA thus

indicating a lower dominant frequency in the range of 0.7H2 to l.lHz.

In a similar fashion to the pulse tests each earthquake excitation was displacement

normalised setting the peak excitation displacement (PGD) to unity. The Vo of the

original excitation could then be related to the PGD input to the table. For each applied

excitation the 7o of the original excitation, was gradually increased until rocking and

ultimately instability of the wall specimen occurred. The peak transient excitation

160

CHAPTER (6)- Out-of-Plane Shake Table Testingof Simply Supported URM Walls

displacement (PGD) and acceleration (PGA) were then related to the peak mid-height

displacement of the test specimen.

Table 6.4.9 Earthquake Excitation Description

A representative cross section of the earthquake excitation results is presented inAppendix (F). Here the mid-height displacement response and input displacements are

compared. The full wall response includingr/¿ -, mid- and 3/n -heigltt accelerations are

also presented. The recorded input excitation accelerations at the base and top of the wall

specimen are also presented as these are used in Chapter 7 for analytical THA predictions

and should be used for future analytical comparison with these experimental results.

Table 6.4.10 and Table 6.4.11present a summa¡y of key results of the earthquake tests

performed for the 50mm and l lOmm thick walls respectively.

Transient Excitation Description Abbr. ItÙVoPeak GroundDisplacenrent

(PGD)

lAOToPeak GroundAcceleration

(PGA)NAHANNI, Canada:Recorded at Iverson during an aftershock of the Nahanni EQ23'd December 1985Magnitude 5.5Epicentral distance 7.5krnSoil type rock

NH 4.2mm 2.24mJs'(o.23e)

PACOIMA DAM, California:Recorded at Pacoima Dam, downsteam during Northridge EQlTth January 1994Magnitude 6.6Epicenral Distance I thnSoil Type: Rock

PD 53.9mm 4.26¡nls'(0.43e)

ELCENTRO, California:Recorded atElCentro during the Imperial Valley EQl8'h May 1940Magnitude 6.6Epicennal Distance 8l¡nSoil rype: RockAccelerogram component NS

EL 163.0mm 3.42m1s"(0.3se)

TAFT, California:Recorded at Kern Counfy, TaftLincoln School Tunnel21"'JDly 1952Accelerogram component S69EEpicenter 35 00 00N I 19 02 00rr)YSeismograph station 35 09 00N ll9 27 ODW

TF 98.5mrn I.76rnls"(0.18e)

161

PGD(mm)

PGAG)

PeakMid-height

ResponseAccel. (s)

PeakMid-height

ResponseDisp. (mm)

Mid-heightDisp.Amo.

WallNo.

Thickness

(mm)

Over-burden(MPa)

WâtlCond-ition

Excitation(referTable6.4.9)

2.t7l2* 110 0 NEV/ 1007o NH 4.2 0.23 0.26 90 NEW 200% NH 8.3 0.46 0.26 zt 2.5312" ll00 NEVT 3007o NH 12.5 0.69 0.26 28 2.2512" 110

4007o NH 16.6 0.92 o.26 32.5 1.96l2* 110 0 NEW0.18 0.26 16 0.20t2 110 0 MOD 5OVoEL 81.50.23 Failedl2* 110 0 MOD 66VoEL t01.6

t2 110 0 MOD SOVoEL 130.4 0.28 FailedMOD 1007o TF 98.5 0.18 0.33 3t 0.3rt2 110 0NEV/ 50VoPD 2',1.0 0.22 0.36 32 1.19t2 110 0

66VoPD 35.6 0.28 0.35 65 1.83t2 110 0 NEV/l2 110 0 NEW 8O7oPD 43.1 o.34 0.35 80 1.8612 ll0 0 NEW I00VoPD 53.9 o.43 0.34 105 1.95t3 110 0 NEW 5OVoPD 27.0 o.22 0.31 5l 1.89

0 NEW 667oPD 35.6 0.28 0.30 66 1.86l3* ll0110 0 NEW 8O7oPD 43.1 0.34 0.32 70 t.62l3*

NEìW IOOVoPD s3.9 o.43 Failed13* 110 081.5 0.18 0.29 7I 0.87t3 110 0 MOD 5OVoEL

667oEL r07.6 0.23 Failedl3* 110 0 MOD163.0 0.35 FailedT3 110 0 MOD IOOVoEL

13 110 0 SER SOVoPD 43.1 0.34 Failed

CHAPTER (6)- Ouçol-Plane Shake Tøble Testingof Simply Supported URM Walls

Table 6.4.10 Sumrnary of Key Earthquake Excitation Test Results (50mm Walls)

*Presented rn (F)

Table 6.4.11 Sumnrary of Key Earthquake Excitation Test Results (l10mmWalls)

r62

f' ,? .t - L .,î ' j'ff"{-o. 'f .- \..4 a-l\ '' . r ':' t t i t..''

WallNo.

Thick- ness(mm)

Over-burden(MPa)

WallCond-ition

Excitation(referTable6.4.91

PGD(mm)

PGAG)

PeakMid-height

ResponseAccel. (s)

PeakMid-height

ResponseDisp. (mm)

Mid-heightDisp.Amp.

t4 50 0 MOD l5VoEL 24.5 0.05 0.r5 l5 0.61t4 50 0 MOD 2OVoEL 32.6 0.07 Failedl4 50 0 MOD 25VoEL 40.8 0,09 Failedt4 50 0 MOD 3O7oEL 48.9 0.1l Failedl4 50 0 NEV/ 2OVoPD 10.8 0.09 0.18 28 2.6014 50 0 NEV/ 25VoPD 13.5 0.1I Failedt4 50 0 NEV/ 307oPD 16.2 0.13 Failedt4 50 0 NEV/ 5OVo TF 49.3 0.09 0.15 13 0.26l4 50 0 MOD 60VoTF 59.1 0.11 Failedt4 50 0 MOD TOVoTF 69.0 0.13 Failedt4 50 0 MOD 50% NH 2.1 o.t2 0.05 6 2.88t4 50 0 MOD 70VoNH 2.9 0.16 0.1 8.5 2.92t4 50 0 MOD 100% NH 4.2 0.23 0.23 l1 2.65t4 50 0 MOD 2007¿ NH 8.3 0.46 0.4 22 2.65t4 50 0 MOD 3007o NH 12.5 0.69 0.5 38 3.05t4 50 0.15 SER IOOVoPD 53.9 o.43 0.9 t3 0.24l4 50 0.15 SER I25VoPD 67.4 0.54 1.0 38 0.56t4 50 0.15 SER l35VoPD 72.8 0.58 1.0 30 0.41t4 50 0.15 SER l5OToPD 80.9 0.65 0.9 44 0.54t4 50 0.15 SER l75Vo PD 94.3 0.7s Failed

*'-ì *

7. NON.LINEAR TIME HISTORY

ANALYSIS DBVELOPMENT

7.1. Introduction

Non-linear time-history analysis (THA) based on time-step integration is the most

representative and reliable method of accounting for the time-dependent nature of URM

wall response to applied excitations provided that the non-linear (F-Â) and damping

properties are accurately represented in the analyical model.

Time-stepping procedures have been developed for basic linear single degree-of-freedom

(SDOÐ systems having a known linear stiffness and damping component. This method

relies upon an assumption on the response behaviour between consecutive time steps

which permits the dynamic response to be estimated from the applied excitation. One

such assumption is the 'Newmark' constant acceleration assumption. For the rocking

response of 'semi-rigid' URM walls, since both the stiffness and damping properties are

highly non-linear and because the entire system mass is not mobilized evenly, the

response behaviour does not strictly follow the basic linear SDOF equation of motion.

Consequently, to permit the use of time-stepping procedures by substtution of the linear

SDOF damping and stiffness components with non-linear damping and stiffness

properties, correlation between the non-linea¡ 'semi-rigid' rocking and basic linear SDOF

system equations of motion must be established.

The following chapter presents the development of a specialised non-linear THA

program for the 'semi-rigid' rocking response of simply supported URM walls. This

includes the development of algorithms by comparison of the SDOF and non-linear

rocking equations of motion. Consideration to the various support conditions identihed

for Australian URM construction in Chapter 2 is also provided for in the non-linear THA

163

CHAPTER (7) - Non-Linear Time HistoryAnalysis Development

program. Calibration of the stiffness and damping properties and confîrmation ofanalytical predictions by comparison with experimental results described in Chapter ó are

also presented.

In the past the use of TIIA for the analytical prediction of the 'semi-rigid' rocking

response of simply supported URM walls has been restricted to commercially available

softwa¡e not designed specihcally for URM wall analysis. Consequently these

predictions have been limited and have not been adequately confirmed by experimental

studies. The main advantage of the current THA program is that it has been designed to

specifically take into account the critical non-linear stiffness and damping properties

which have been calibrated using the experimental results presented in Chapter 6. The

effect of various support conditions and degradation of rotation joints on the non-linear

stiffness component was also examined so that analytical comparisons of various realistic

situations are possible.

Although THA has limited application in design, as loading scenarios are diverse, itremains a valuable resea¡ch analysis tool. In Chapter 8 the developed THA program is

used to undertake an in-depth parametric study of the 'semi-rigid' rocking response ofsimply supported URM walls to further investigate the physical parameters whichinfluence URM wall response. Having developed an understanding of these criticalparameters a simplihed analysis procedure is then proposed and its effectiveness assessed

against the more comprehensive THA predictions.

7.2.ßnef Description of Basic Linear SDOF System

To permit the use of time-stepping procedures for the highly non-linear 'semi-rigid'

rocking response of simply supported URM walls an understanding of the development

of the dynamic equation of motion for a basic linear SDOF system is first required. Later

this will be expanded into the development of dynamic equations of motion for the non-

linear 'semi-rigid' rocking of the simply supported URM walls having various support

conditions.

164

CHAPTER (7) - Non-Linear Time HistoryArwlysis Development

The equation of motion of a dynamic system is a representation of Newton's second law.

That is, the rate of change of momentum of any mass particle equals the force acting on

it. Together with d'Alemberts principle that a mass develops an inertial force opposing itproportional to its acceleration the equation of motion can be expressed as an equation of

dynamic equilibrium. The essential properties governing the displacement response, A(t),

of a system subjected to an external excitation, P(t), are its mass, M stiffness and energy

loss mechanism or damping. For a basic linear SDOF system each of these properties is

concentrated into a single physical element as shown in Figure 7.2.1. Although the true

damping characteristics of real systems are typically very complicated and difficult to

define it is common to express the damping of real systems in terms of an equivalent

viscous damping, which shows a similar decay rate under free vibration conditions.

Therefore, in this case the elastic resistance is provided by the spring stiffness, /<, and the

energy loss mechanism by the velocity proportional viscous damper, c.

Linear springk ^(t)

P(t)

cLinear damper

Figure 7.2.1 B,asic Linea¡ SDOF System

The motion-resisting forces are therefore the damping force being the product of the

damping constant, c, and velocity, v(t), the elastic force being the product of the spring

stiffness, ft and the response displacement, A(t) and the inertia force in accordance with

d'Alambert's principle being the product of the system mass, M and response

acceleration, a(t). Equating these motion-resisting forces to the external dynamic loading

provides the SDOF equation of motion as, \

Ma(t) + cv(t) +kA(t)= P(t) (7.2.1)

165

CHAPTER (7) - Non-Linear Tilne HistoryAnalysis Development

If the loading to be considered is due to ground or support excitation this can be included

by expressing the inertial force in terms of the two acceleration components. By

re¿uranging and substit uting ø,z=!rh" basic linear SDOF system dynamic equation of"Mmotion becomes,

aQ) + -L vlt) + a2 L(t¡ = - a, (t) (7.2.2)

where ú) = un-damped elastic angular natural frequency

By solving the dynamic equation of motion (Equation 7.2.2) it can be shown (Clough and

Penzien 1993) that for an under-critically damped system the critical damping coeff,rcient,

c., is,

cc=2M@=4Mnfwhere/- un-damped elastic natural frequency

(7.2.3)

Therefore by definition the SDOF equivalent viscous damping, 6sno¡, is,

€soor = c/cr= c/4 M nf (7.2.4)

and the SDOF proportional damping coefficient, csDoF,

Csoor=4MnfSnor (7.2.s)

Further to this by substituting zero initial conditions in to the SDOF dynamic equation ofmotion solution it can be shown that for €,spor less than approximately 20Vo,,

r, = 1 ,rrl^'l5soor -fi ",[O* J

where 7ç = peak amplitude at the nù cycle

Ân+r = peak amplitude at the (n+1)ù cycle

(7.2.6)

166

CHAPTER (7) - Non-Linear Time HistoryAnalysis Development

It should be noted that both the SDOF based equations 7.2.4 to 7.2.6 were used to

determine c and ( respectively for the experimental rocking wall in Section 6.4.6.2.

Since for the rocking v/all the system mass is not mobilized evenly as is assumed above a

conversion is required, as will be discussed in Section 7.3.

7.3. Negative Stiffness System Modelled as a Basic Linear SDOF System

In the following discussion a negative stiffness system is dehned as a system having a bi-

linea¡ F-Â relationship (refer Figure 7.3.I) comprising an initial infinite stiffness

component followed by a negative stiffness component. On application of a force to the

negative stiffness system, initially the infînite stiffness governs the behaviour until the

'threshold resistance' force, R.(1), is exceeded. Following this a negative stiffness,

IÇ(1), takes effect so that the force resistive capacity is reduced with increased

displacement. As described in Chapter 5, for 'semi-rigid' rocking the non-linear F-A

relationship has a negative stiffness component. It is thus pertinent to first examine the

modelling of a negative stiffness system as a basic linear SDOF system to determine ifexisting time-stepping procedures can be utilised.

R"(1)Half cycle under consideration

Negative stiffness

K(1)

Âvo DisPlacement Âr"o¡¡¡y

Figure 7.3.1 Negative Stiffness F-Â Relationship

(.)oHoq)oclaØ(,)úc)Ø>¡U)

^(r)

1)+IÇ(1)^(t)

t67

CHAPTER (7) - Non-Lineør Titne HistoryAnalysß Development

For all displacements, ^(t),

greater than zero, at any given time the instantaneous secant

stiffness, Kdt), can be derived as,

K" 1r¡ =Ul)- + K, (1) for L(t) > 0 (7 .3 .t)^(/)

This non-linea¡ instantaneous secant stiffness relationship is then used to derive the non-

linear frequency-displacement ff-L) relationship for the negative stiffness system whichbecomes,

a=2nf= K"(t)(7.3.2)M

Rearranging this and substituting in the non-linear instantaneous secant stiffnessrelationship gives the generic response frequency,

R,(1)

^(r)

+ K"(l)

Mfor L(t) > 0

2n(7.3.3)

Assuming that the entire system mass is evenly mobilized the complete equation ofdynamic equilibrium for the negative stiffness system is derived as,

Ma(t) + cv(r) + R "(1)

+ rK" (1)^(r) = - Ma, (t) for L(t) > 0 (7 .3.4)

By rearranging and substituting the non-linear instantaneous secant stiffness relationship

the equation of dynamic equilibrium for a negative stiffness system subjected to a base

excitation is,

a(t)+#rrrr*K"!)-tç)=-ar(t) for L(t) > 0 (7.3.5)

Thus, by comparison of the dynamic equation of motion for a basic linea¡ SDOF system(Equation 7.2.2) and for the negative stiffness system (Equation 7.3.5) it can be seen that

f

168

CHAPTER (7) - Non-Linear Time HistoryAnalysis Development

a similarity exists provided that the non-linear instantaneous secant stiffness relationship

is substituted for the linear stiffness. Thus by adopting this substitution the time-stepping

procedure can be applied to the negative stiffness system.

7.4. Rigid simply supported object Rocking Response About Mid-

height - Dynamic Equation of Motion

As a second phase in the modelling of the real 'semi-rigid' URM wall rocking response

for illustrative purposes we now consider the idealised simply supported rigid rocking

scenario. Here, as was the case for the negative stiffness system the idealised rigid F-À

curve is comprised of a bi-linear F-A relationship having an initial infinite stiffness

followed by a negative stiffness component due to P-A effects (refer Section 5.2.1). The

defining terms of the bi-linear F-Â curve, the 'rigid resistance threshold' force, R"(1), and

negative stiffness IÇ(1) are functions of the wall geometry and applied overburden at the

top of the simply supported object. Also influencing R.(1) and Ç(1) are the support

conditions as these govern the eccentricity of the vertical reactions.

For the rigid rocking of a simply supported object about it's mid-height it must also be

recognised that during the dynamic response the full system mass is not mobilized

evenly. Consequently, this must be considered when deriving the systems dynamic

equation of motion. As was concluded from the experimental study (Chapter 6) a

triangular acceleration distribution relative to the supports provides a good assessment of

the rocking object's acceleration response and is thus adopted. This therefore impacts on

both the dynamic stiffness and damping components of the dynamic equation of motion.

The following calculation illustrates the derivation of the dynamic equation of motion for

a rigid non-loadbearing simply supported wall rocking about a mid-height crack. This is

further related to the generic dynamic equation of motion for various rigid rocking

objects having other support conditions relevant to Australian masonry construction.

For any rigid rocking object the static bi-linear F-À relationship can be generically

defined as Equation 7.4.1 where R. (1) represents the 'rigid threshold resistance' force,

769

CHAPTER (7) - Non-Linear Time HistoryAnalysis Development

IÇ(1) the negative stiffness component (-R*(1)/Ai"søuiuty) and Fr(t) the evenly distributed'quasi-static' force. Further, the bracketed termrepresents the instantaneous static secant

stiffness, K,(t) at the mid-height displacement Â(t).

(7.4.1)

For a rigid non-loadbearing simply supported wall the static F-A relationship is derived

âS'

-FsQ)--Mo,(t)=[#*K"cl]r'l forL(t)>0

- F rt) - - Ma c Q) = M[f t# -'1)^,,, for A(t) > 0 (7.4.2)

The generic defining terms of the static a-a relationship are therefore,

'Rigid Threshold Resistance' force n "e)=ß#

K "(t)=-49Negative Stiffness

Displacement at static incipient instability Linsøa;tiryK"(t)

'Where the load is applied dynamically the acceleration response also comprises atriangular acceleration component, a-(t), as shown in Figure 7.4.1. The dampingcomponent of the equation of motion will be neglected at this stage but will be discussed

in more detail following the derivation.

170

CHAPTER (7) - Non-Linear Time HistoryArnlysis Development

Triangularacceleration responsedue to rockingdisplacementsrelative to supports

t€dacceleration

.(-..Ð responsedueto ht4motion ofsupports

w4

a.(t) Cr0)

-

ht4

ht4

<¡.+

INERTIALOADtÍ2-N2 M=mxh

Figure 7.4.1 NonJmdbearing Simply Supported Object at RocHng at Mid-height

The top support horizontal reaction Rr is determined by taking moments about the base

vertical reaction.

2M ^, R' __ar(t)mh _a^(t)mh _!n(t) gt +m(t) gLG)

2422

Then horizontal equilibrium is used to determine the base support horizontal reaction as,

h a,(t)mh a^(t)mh , mgt mg\(t)nt=-a- 2 - z

777

CHAPTER (7 ) - Non-Linear Time HistoryAnnlysis Developrnent

Now considering the dynamic equilibrium of the top free body, by taking moments about

the mid-height vertical reaction, the mid-height dynamic equation of motion is,

"^ur.}(+h ,]\¡a>=-)",a> ror*(t)>, (7 43)

Writing this in generic terms becomes,

Including the damping component,

"^@*1;[[#. r,rrr]Jnr')=-2o,(t) rora(t)>o (7.4.4)

-̂tt) ,(t) for L(t) > 0 (7.4.5)2

where the proportional damping coefficient has been measured at the effective mass, Mr,of the responding wall.

In order to continue to use the mid-height wall response as in Chapter 6 rather than the

response at the position of the effective mass the damping term must be multiplie dby 213

to compensate for the relative velocities.

The dynamic equation of motion for the rigid non-loadbearing simply supported objectrocking about its mid-height therefore becomes,

a ^

Ø + L* v e) + i(+l#-'] )^,

"^u,.1(ø1,,,, . i(+lh-'] )^r,, =- 1o,,,, for L(t) > O (7 .4.6)

172

CHAPTER (7) - Non-Linear Time HistoryAnalysis Development

This can again be rewritten in generic terms as,

a^(t).i(t\.,v (' ) + i;(H+ r' or )n'

) = - |a,(t) lor L(t) > o (7 .4.7)

and by substituting the instantaneous static secant stiffness, K(t), as,

,, zf r I 'rr\+ 1K"(t) 3 .."^Ø*;ln

" )",rr,r* ZËo(t)=-ia,(t) forL(t)>0 (7.4.8)

Comparing the basic linear SDOF equation of motion (Equation 7.2.2) previously

developed for the system shown in Figure 7.2.1 and the generic dynamic equation of

motion for rigid rocking objects (Equation 7.4.6) it is evident that the following

substitutions can be made to permit the use of time stepping procedures and the mid-

height response of the wall.

l. Substitute the linear SDOF proportional damping with 213 of the experimentally

derived values

2. Substitute the linear stiffness component with the dynamic non-linear instantaneous

secant stiffness, IÇr(t), represented by 312 times the static instantaneous secant

stiffness. This is achieved by applying a factor of 312 to the static F-A relationship.

K^çt¡=1y,ç¡¿

3. Apply a conversion factor of 312 to the applied ground acceleration.

Also from Equation 1.4.7 the theoretical rigid mid-height fA relationship without

K"(t)damping can be derived in accordance with a =2n f = in generic terms as,

M"

l(ffi.*"r,M.f (7.4.e)2n

173

for L(t) > O

CHAPTER (7) - Non-Linear Time HistoryAnalysß Development

Since each set of support conditions alters the F-Â relationship by changing the value ofR.(1) and Ç(1) this also influences the dynamic equation of motion. The genericdefining terms R"(1) and IÇ(l) are shown in Table 5.2.1 and. can be substituted directlyinto the above equations.

7.5. Semi-rigid URM Loadbearing Wall Dynamic Equation of MotionAs discussed in Chapter 5, the real 'semi-rigid' non-linear F-Â relationship of a face

loaded URM wall results from the complicated interaction of gravity restoring moments,

the movement of vertical reactions with increasing mid-height displacement and p-A

overturning moments. The wall properties that therefore dictate the shape of the curve are

wall geometry, support conditions, overburden stress, material modulus and importantlythe condition of the morta¡ joint rotation points. As described in Section 6.4.5 theories

have been postulated by previous researchers to define this complex behaviour howeve¡these were not found to correlate well with the experimental results as based on simple

and often unrealistic support conditions. Consequently a more empirically based method

was adopted in this study.

From the experimental study presented in Chapter 6 the real 'semi-rigid' non-linear F-Àrelationship was found to approach that of the idealised rigid bi-linear relationship at

large mid-height displacements. This was due to the vertical reactions being pushed

nearly to the extreme compressive face of the wall. As the applied overburden was small

the influence of the hnite compressive stress blocks at vertical reactions was not

significant. Since the bi-linear F-A relationship is simply a function of geometry,

overburden and support conditions, this was used as a basis for development of an

approximation of the real non-linea¡ F-Â relationship.

A parametric study was undertaken to dete¡mine which of the non-linear F-Â relationshipproperties governed the response behaviour. It was found that the initial stiffness, K¡o,

and 'semi-rigid threshold resistance' force plateau, R*(l), were critical. Thus to model

the non-linear F-A relationship at smaller mid-height displacements a tri-linear F-À

174

CHAPTER (7) - Non-Linear Time HistoryAnalysis Development

approximation was selected (refer Figure 7.5.1). Since the rigid bi-linear relationship is

set the tri-linear approximation is defined by the displacements ratios , Â(1) *O

Lircøuitity

,L(z) , which govern Kn and zu(1) respectively. The value of , ^(t) -¿ -^(2)-L;nsøtitity Linøaitity Linsnbitig

are therefore related to material properties, predominantly being the less stiff mortar, and

the state of degradation of the rotating mortar joints.

R (1)

'semi-rigid thresholdresistance' force plateau

=R"(1)+K(1)^(2)

^(l)L(2) A¡n5¡aþ¡¡¡¡y

Mid-height Displacement (Á)

Figure 7.5.1 TriJinear 'Semi-rigid' Non-linear F-A Relationship Approxinntion

Table 7.5.1 presents the empirically derived defining displacements of the tri-linear

approximation from the experimental static push tests presented in Chapter 6. Here the

support conditions considered included NLBSSCL and LBSSLL (refer Table 5.2.1), so

that ¡os¡n5¡¡ty wâs taken as the thickness of the wall. Since the materials used did not

change, an increase in degradation of the rotating mortar joints was related to an increase

Tri-linear F-ÂApproximation

Bi-linear F-ARelationship

Real Semi-rigidNon-linea¡ F-ÂRelationship

q)okof¡rcdk()ctr'l!d)

ÈÈ

Initial stiffness == R-11)+ICll)Â2)

^(1)

ç(1)

175

CHAPTER (7) - Non-Lin¿ar Time HistoryArulysß Developmcnt

in both displacement ratios t ^(t) -¿ --^Ø-. This represented a decrease in Ki,r andLinsøuitiry L;nsøuit;ty (

R*(1) and a corresponding flattening of the 'semi-rigid' non-linear F-A relationship (referFigure 7.5.2). The resulting decrease in the overall response frequencies also led to adecrease in the instantaneous dynamic secant stiffness.

Table 7.5.1 Defining Displacenrents of the Tri-linear F-A ApproxirmtionState of Rotation Joint Degradation a(1)

A^t"m.yLA)

4-t UUtt

New 6Vo 28VoModerate l37o 4O7o

Severe 2OVo 5O7o

10O7oR.( Tri-linea¡ F-ÂApproximationVarious DegradationBi-linear F-ÂRelationship

New6O4o

Moderaæ

Severe

K(1)

(1)úèaq)oLo

f¡.ñtc)

sE(¡)ÞrÞr

727o

5OVo

ñs s s\OÈNNñòeOA.+ !ñ

l(X)7o \,65¡1,

Mid-height Displacement ( VoA¡", )Figure 7.5.2 Tri-linear F-A Approximation for Various Wall Degradation

After adopting the tri-linear 'semi-rigid' F-A relationship approximation, the rockingresponse was governed by three discrete equations of motion. At any given time the

I I

II

/I

176

CHAPTER (7) - Non-Linear Time HistoryArnlysis Development

governing dynamic equation of motion is dependent on the instantaneous displacement.

In generic terms the three governing equations of motion are,

R"(1) + K"(I)L(2)

^(1)

J

2

3(t

2

, (r) forl < ^(r)

< A(l)

(7.s.Ð

) ) for L(I) < Â(r) < L(2)

(7.s.2)

for L(2) < Â(r) < Lirctøitity

(7.s.3)

relationship in accordance with @ =21c, = W

As each stiffness term is represented by the instantaneous dynamic secant stiffness the

overall generic dynamic equation of motion again takes the form of Equation 7.4.8.

Thus, by comparison with the basic linear SDOF equation of motion (F,quation 7.2.2) itisobserved that the required substitutions to allow the use of previously developed time-

stepping procedures highlighted in Section 7.4 are still applicable. This is provided that

the governing dynamic equation of motion at any time is dependent on the instantaneous

displacement.

By adopting the tri-linear F-A relationship approximation for the 'semi-rigid' rocking

response of URM walls allows an estimate of the frequency-displacement response to be

made. Since the approximate response is governed by the three dynamic equations of

motion, which are dependent on the instantaneous displacement, the frequency response

is also dependent on the instantaneous displacement. The relevant instantaneous dynamic

secant stiffness can therefore be used to determine the frequency-displacement

177

Thus from Equation 7.5.1 to

CHAPTER (7) - Non-Linear Time HßtoryAnalysß Developmcnt

7.5.3 the generic 'semi-rigid' rocking frequency response can be approximated when

neglecting damping as,

12r

r

2n

3 R,(1) + K (1)^(2)

forï<^(f)<^(1) (7.s.4)

for L(t) < A(r) < L(2) (7.s.s)2

3

2

L(t)M "

R"(1) + K,(1)^(r)L(t)M

"

2n

f- 2n for L(2) < ^(/)

< L;rcøuinry Q .5.6)

Figure 7 .5.3 to Figure 7.5.6 present a comparison of the analytical best fit/-^ relationship

without damping, each derived from Equation 7.5.4, Equation 7.5.5 and Equation 7.5.6

with the experimentally derivedf relationships as presented in Section 6.4.6.1.

îoÉÐásl!

7

6

5

4

3

2

I0

O ExperirænøI ll0mm

-oet1t¡6 vo DELe)2Bvo

il

o oaoooooNo<tnËÉ aoooæO\c)Midheight displacerrent (mm)

Figure 7.53 Analytical vs Experirnental F-Á- 110mrn, No Overburden

178

CHAPTER (7) - Non-Linear Timc HistoryAnalysis Development

N

àaoøotL

7

6

5

4

3

2

1

0

o Experiæntal 50mm

-DEL(I)6 % DELe)zBEo

ononoÊclôlm nonoo{snMidheigbt displacement (mm)

Figure 7.5.4 Analytical vs Experimental F-Á- 50mr¡t, No Overburden

'N'

>'oEIru

dc)Lt\

II765432I0

o Þçerlmental r.5

-DE {r) zolo DEr-{22Ít96

o rO otôorootootooÊÊcìN(l)Cl)++loMidherght dlÐlacem¡t ( mm)

Figure 7.5.5 Analytical vs Experirnental F-Á- 50mnr,0.û7MPa Overburden

ñ

oÉoõoÈ

9

8

7

6

5

4

3

2

I0

o Experirental 50mm

-pgr(l) to% DFt (2)3oEo

o ononon ÊNCIOO onoËThMidheight displacemont (mm)

Figure 7.5.6 Anatytical vs Experinrental F-A- 50mnt' 0.15MPa Overburden

t79

CHAPTER (7) - Non-Lineqr Tilne HistoryAnalysis Development

7.6. Modelling of Non-Linear Damping

Although the F-Â relationship is the most critical factor for modeling of the rocking

frequency response, damping also has an influence on the f relationship. Due to the

complex physical nature of damping it is usually represented in a highly ideahzed fashion

as an equivalent viscous (velocity proportional) damping force with a similar decay rate

under free vibration conditions to that of the real system being modelled. Thus, the

proportional damping coefficient used in formulating the equation of motion (Equation

7.2.2) is selected so that the vibration energy dissipated is equivalent to the energy

dissipated in all of the damping mechanisms of the rocking system. For an URM wallthese mechanisms would include elastic, friction, impact and joint rotation energy losses.

Although not strictly an accurate representation of the system behaviour any

disadvantage of using this approximate method is far outweighed by the simplificationachieved in applying the equivalent viscous damper.

Commonly the damping in most structures can adequately be modelled by using Rayleigh

damping.

Rayleigh damping is a linear combination of both mass and stiffness proportional

damping so that,

C = ooM *Kcr,1 = cloM + crr(Mco2) = M(r,.,* a{2n1l2) (7.6.1)

= C/M = ob+ a[2úf2

By substituting C/l\4 = 4rf I the theoretical Rayleigh equivalent viscous damping

becomes,

Iao

4ú +atÚ (7.6.2)

By comparison with experimental results presented in Section 6.4.6.3 and careful

selection of oo, and o,1, Rayleigh damping was found to best represent the physical nature

of the real non-linear system damping mechanisms. Figure 7.6.1 presents a compa¡ison

180

CHAPTER (7) - Non-Lineør Time HistoryAnalysis Development

of the experimental equivalent viscous damping versus frequency with that calculated

using a theoretical Rayleigh damping (Equation 7.6.2) for a 50 mm thick wall specimen

having no applied overburden.

Figure 7.6.1 Experimental I vs Rayleigh | - 50mm \üatl, No Àpplied Overburden

Although the mass and stiffness proportional damping coefficients were found to be

higher for both the 50 mm thick walls with overburden and the 110mm thick walls than

the coefficients shown in Figure 7.6.1 these provided a reasonable lower bound estimate

of the equivalent viscous damping. Thus to be conservative these coeff,rcients were

adopted for the parametric study presented in Chapter 8.

If system damping were truly of the linear viscous form then any set of m consecutive

cycles would give the same viscous damping ratio. For the case for rocking of URM

walls m consecutive cycles in a high amplitude response section will yield a different

damping ratio than that of m consecutive cycles in a lower amplitude section of free

response. The equivalent viscous damping ratio is therefore non-linear amplirude or

frequency dependent (refer Figure 7.6.1). Thus, we are unable to assume a linea¡ viscous

damping within the THA so that either an average proportional damping coefficient or an

iterative approach must be invoked into the THA.

oÐoeRIÀæNTALpSI. RAYLEIGHPSIo

toô ooo ooa

o8

o

e ¡t'

(I¡ = 1.0c[r = 0.002

18.070

16.0lo

14.0%

t2.o%

10.07o

8.O7o

6.07o

4.O%

2.O%

0.ïVo

âØÀzÀ

oI(-)F7,(JFzfIl(Júf!o.

) 3 4 5 6FRBQIJENCY

70 1

181

CHAPTER (7) - Non-Lineør Time HistoryAnalysis Development

While adopting an average proportional damping coefñcient method for the entteresponse is the simplest and least intensive method the main disadvantage is that itrequires an average response frequency,f, to be estimated prior to the THA. From this an

estimate of c/lM is made from Equation7.6.l. The consequence of this is that the analysis

outcome can be subjective as it is related to the assumed average response frequency.

For the iterative approach an initial estimate of the proportional damping is made at the

colffnencement of each haH cycle of the response. The instantaneous frequency is then

determined at the completion of each half cycle and the resulting proportional dampingcalculated. This is then tested against the estimated proportional damping at the

beginning of the cycle. If the estimate and resulting proportional damping coefficientmatch then the next half cycle is considered. If not the THA returns to the beginning ofthe half cycle under consideration and the initial conditions are reset. Another estimate ofthe proportional damping coefficient is made and the iterative process continues. Thisiterative process is shown in Figure 7 .6.2. The only disadvantage of the iterative methodis that the computing time is increased, however, this was not found to be significant forthe SDOF system. Comparison of anal¡ical and experimentally response showed thatthe iterative procedure was the most effective and least sensitive to initial assumptions.

()'1'

ÈÊ{q)

&øc)ú

FinalPrediction

ç21

Time

Figure 7.6.2 lterative Damping

Estimate c1-+f¡ft--xnC11)€St C1

Return to start of half cycle-new estimate

Estimaæ cr4r{crr2

Esttmaæ c2+f2Íz*.ztC21(9St C2

Rehrrn to start of half cycle-new estimate

Estimate cs@2

Estimate ca+frfs--xstC314St C3

Continue next half cycle

\acÍt2

T^=ttf,2

LpÍ'2

r82

CHAPTER (7) - Non-Linear Tim¿ HistoryAtwlysis Development

7 .7 . Event Based Time-Stepping Analysis

Since at any time the dynamic response is dependent on the instantaneous displacement

an event based time-stepping analysis was required to distinguish between the governing

dynamic equation of motion. As part of the time-stepping procedure the dynamic

response was considered by conversion of the static non-linear F-Â curve into a 'pseudo

static' F-A relationship. This procedure was based on the constant acceleration

assumption between time steps and takes into account the proportional damping. By

adopting the tri-linear F-A model, the 'pseudo static' F-Â relationship was made up of the

three 'pseudo static' stiffness' being ktsl, ktsp and kts2 (refer Figure 7.7.1). To permit

the use of the time-stepping procedure as described in Section 7 .5 the conversion factor

of 312 was applied to both the input ground acceleration, ac(t) and the three 'pseudo

static' stiffness'.

Re(1)

Re( 1 )+Â(2)Ke( I )+Â( I )ktsp

Re(1ÌrÂ(2)Ke(1

1

^(1) L(2)

Figure 7.7.1 'Pseudo Static' F-A relationship

Âioro¡lity

Mid-height Displacement, Âc)octØØc)úoohol¡r(dÈO

rl

s1

a\

/ITrilinear'pseudo static'

stiffness

ktsp-4M +2pat? ¿t

where dt is the timeincrement

kts 1 =Re( 1 ÞÂ(2)Ke( 1 )+ktsp

^(1)kts2=ke(lþktsp

183

CHAPTER (7) - Non-Linear Time HistoryAnnlysis Development

The time-stepping procedure is then applied to the 'pseudo static' system. The first step isto convert the input excitation, 312(ar(t)), to an incremental'pseudo static' force (dps)

which takes into account the previous incremental acceleration. Once this has been

determined it is used to calculate the incremental 'pseudo static' force displacement using

the respective 'pseudo static' stiffness. If ^(tl)

or ^(+2)

is reached within the time

increment this is recognised as an event and the dynamic equation of motion and the'pseudo static' stiffness is updated. Any remaining 'pseudo static' resistance force isthen used to determine the remaining incremental displacement according to the new'pseudo static' stiffness so that the displacement at the completion of the time incrementis determined. This process is continued until the incremental 'pseudo static' force and

thus the remaining system energy is reduced to zero. Alternatively, if the instabilitydisplacemerìt, *¡s¡¿5¡¡ty, has been exceeded this indicates failure and the THA process is

terminated.

The Fortran 77 program developed to run the non-linear rocking LJRM wall THA ispresented in Appendix (G).

7.8. Comparison of Experimental and Analytical Results

Conhrmation of the non-linear time history analysis (THA) softwa¡e developed for the'semi-rigid' rocking response of URM walls has been conducted by comparison ofanalytical results with both pulse and earthquake excitation shaking table test results(refer Chapter 6). Figure 7.8.1 presents an indicative comparison of an analytically and

experimentally derived response for a 110mm thick, 1.5m tall wall with no overburdenhaving been subjected to a lHz,37mm amplitude pulse excitation. Further details of the

parameters used within the THA are presented in Appendix (H). Figure 7.8.1 (a) provides

a comparison of the experimental mid-height displacement, MWD, relative to the shakingtable compared with the THA, (u). Figure 7.s.1 (b) provides a comparison of the

experimental mid-height acceleration, MrilA, compared with the absolute mid-heightacceleration derived through THA, (at). Figure 7.8.1 (c) provides a comparison ofexperimental and anal¡ical hysteretic behaviour.

184

CHAPTER (7) - Non-Linear Timc HistoryAnalysis Development

u(m)

-MWD!ñ

(\ c.l cô ú) c.) c1

0)

q)()(lÈØ

Eèo0).ÉËÀ

0.04

0.03

0.02

0.01

0

-0.01

-0.02

-0.03

-0.04Time(secs)

(a)

(b)

oGIÊoc)()^O C.l

ðo0.)3

*at(m/s/s)+MwA

o O OO(OOO

Mi¿l [Ieioht T']isnlacement fmì

(c)

Figure 7.8.1 Comparison of Analyticat and Experimental Pulse Test Results

Figure 7.8.2 presents a comparison of the THA and experimental peak mid-height

displacements for a non-loadbearing simply supported 110mm thick, 1.5m tall LJRM

wall. For the THA the wall condition was assumed to be moderately degraded. Here itis observed that the peak displacement response for the tested pulse frequencies and

amplitudes is well represented by the THA. It is observed that the maximum

54J,,

I0

-1_1

-3-4

c)

Ra<*t9ÒO

c)¡€à

Time(secs)

-at(m/Vs)-MIWAÁ I

-/\ t.tô ô ) I ) ( c

IC ó CñI N \ V

yqv

185

CHAPTER (7) - Non-Linear Time HistoryArnlysis Development

displacement amplification occurs for pulse frequencies of around lHz to 2Hz. Thus theeffective resonant frequency,fit, for the 110mm thick, 1.5m tall simply supported walls

with no applied overburden is also approximately lHz.

Figure 7.8.2 THA and Experinrental Peak Pulse Mid-height Disp. Response

Figure 7.8.3 presents an indicative comparison of an analytically and experimentally

derived response for a 110mm thick, l.5m tall wall with no overburden having been

subjected to an earthquake excitation representin g 80Vo of the Pacoima Dam earthquake

(refer Table 6.4.9). Further details of the parameters used within the THA are presented

ln Appendix (Ð. Figure 7.8.3 (a), (b) and (c) provide comparisons of mid-heightdisplacement, acceleration and hysteretic behaviour respectively.

ll0

100

90

gBoËq¡

Hzooô.É60gEsooúË40ÐE¿30= 20

l0

0

0 l0 20 30 4 50 60 70 80 90Peak Base Displacernent (mm)

r00 I

Amplifieddisplacements

E

\fl o II1

o

oo - THEOREICAL 0.5FIz Pulse

- TI{EORETICAL lFIz Pulse

- TI{EORETCAL 2IIz Pr¡lse

- THEORETCAL 3.0H2 R¡Ise

troootrEtr

Ð(P I IIz 1/2 Sine Disp pulse

FXP 2llz 1/2 Sine Disp pulseEXP 3I{z 1/2 Sine Disp pulseEXP 0.5 [Iz Gaussian R¡lseÐ(P I tlz Gaussian Pulse

tr

tro

EXP R.¡lse

186

CHAPTER (7) - Non-Lincar Tim¿ HistoryAnalysis Development

-at(r/s/s)-MV/A

lô

O\ Êt,,-Ê CO ìa¡

ilt Itttt rt'lt t t It

Irme(secs)

4É?€)()E^ 1åq o-Èrtr _1ooO^-c -L

4-5

u(ml

-MWDI iltI

(a¡ O ìô Iht--ol\-cl+\c)æO\-ú)J:Êeì(.lNelN(.lcq(.)al !a)

uvTime(secs)

0.08Àg 0.06ËË 0.04

Ë o.o2o,.Ä0Ë -0.02bo

E -o.o¿E> -0.06

-0.08

(a)

(b)

(c)

Figure 7.8.3 Comparison of Analyt¡cåt and Experimental Earthquake Test Resr¡lts

A representative cross section of analytical and experimental, pulse and earthquake

results is presented in Appendix (Ff¡. This shows that the THA is capable of accurately

predicting both the forced and free vibration rocking response provided that the non-

linear (F-À) and damping properties are adequately represented in the analytical model.

,)

.9c!Ê(,)oo^o e.¡

.Ëgè0c)EI€

*at(rn/s/s)+MwA r

O (

-lMid Heisht l)isnlacement fm'

187

8. LINEARISED DISPLACBMENT-BASBD

(DB)ANALYSIS

8.L. Linearised DB Analysis Methodology

The displacement-based (DB) analysis methodology provides a rational means for

determining seismic design actions as an alternative to the more traditional 'quasi-static'

force-based approach. In the DB procedure the dynamic lateral capacity of a structure is

determined on the basis of a comparison of a pre-determined failure displacement with

the displacement demand imposed on the structure by a seismic event.

To simplify the DB analysis procedure for highly non-linear systems the 'substitute

structure' methodology, proposed by Shibata and Sozen (1976), is often adopted. This

involves the substitution of the real structure's stiffness and damping properties with the

linear properties of a characteristic elastic SDOF oscillator. Here the characterising

linear properties are selected so that the linear and real non-linear systems are ftkely to

reach the failure displacement under the same applied excitation. The elastic system's

response to failure, as can be determined from the elastic response spectrum, is therefore

representative of the displacement demand on the real structure.

For elastic perfectly plastic systems (refer Figure 8.1.1) the bi-linear F-À relationship to

the failure displacement is characterised by the elastic stiffness related to the real

structure's secant stiffness at the in-elastic failure displacement (Priestly 7996:1997 ,Iudiet al 1998, Edwards et aI 1999). Thus, the characterising SDOF oscillator stiffness

component is approximated by the lowest secant stiffness analogous with the real

structure's dynamic response and is associated with the lowest feasible response

frequency. Using this characteristic 'substitute structure' property for elastic perfectly

plastic systems and an appropriate level of equivalent viscous damping during the non-

188

CHAPTER (8) - Linearised Displacement-based Analysis

linear response, the linea¡ised DB analysis has been found to provide a reasonable

prediction of these system's dynamic lateral capacity.

FailureDisplacement

\ 'Substiu¡teSEuch¡re'

Kubgi¡¡æ or¡ua¡rc

Mid-height Displacement ( A) A¡oitrrc

Figure 8.1.1 Lineadsed DB Analysis for Elastic perfectly plastic System

Unlike the more comprehensive non-linear time history analysis (THA), the linea¡isedDB procedure does not provide an accurate representation of the complete dynamicresponse but rather an indication of the excitation (load) required to reach the pre{efinedfailure displacement. To illushate, during the elastic response phase the tangentialstiffrress is underestimated however during the in-elastic response phase the tangentialstiffness is overestimated. As a consequence of this a 'period lag' may deveþ between

the 'substitute structure' and the real system displacement response so that at the criticalresponse cycle the DB analysis initial conditions may not represent the real initialconditions.

The DB analysis effectiveness is dependent on the probability that the 'substitute

structure' and real system will reach the predetermined failure displacement whensubjected to the same excitation. It is therefore evident that for the DB analysis toprovide a reasonable estimate of the excitation required to cause the structure to reach the

failure displacement an integral part of the procedure is the selection of the cha¡acteristic

c)()o

t¡rñtk()dËq)

o¡Þ. F-^

¡.- Elastic Perfectly\Plastic Non-linea¡

189

CHAPTER (8) - Linearised Displacement-based Arnlysis

SDOF oscillator or 'substitute structure' Iinear stiffrress. To confirm that the selected

'substitute structure' properties represent the real system at the critical displacement for

any linearised DB analysis procedure an extensive comparison of the DB prediction with

experimental and THA results was required.

The following chapter presents a proposed linearised DB analysis procedure for the

ultimate limit state analysis of simply supported URM walls including a procedure for the

definition of the characterising linear SDOF oscillator stiffness. The displacement

capacity and damping properties of the simply supported walls are discussed in

conjunction with the implication on the modeling of the real structure as a characteristic

SDOF oscillator. An extensive comparison of the linearised DB analysis predictions of

dynamic lateral capacity with THA and experimental results is then presented to confirm

the procedure' s suitability.

Similar to the above, a comparison of THA predictions with the existing 'quasi-static'

rigid body and 'semi-rigid resistance threshold' force prediction of lateral capacity is also

conducted. This highlights the limitations of not considering 'dynamic stability' concepts

for the dynamic analysis of simply supported URM walls. He¡e the 'quasi-static'

analysis results are shown to often fall outside of the limiting tolerance assumed for the

DB anaþis.

8.2. Proposed Linearised DB Analysis

In accordance with the DB procedure, the 'substitute structure' displacement demand

relative to the top and bottom wall supports is determined from the response spectral

displacement (Aps¡), as obtained from the corresponding elastic displacement response

spectrum and characteristic 'substitute structure' frequency and damping. As is shown

by the typical relative elastic displacement response spectrum in Figure 8.2.1, for flexible

(low natural frequency) elastic systems the maximum relative displacement imposed by

an excitation is equal to the peak ground displacement (PGD). For elastic systems with

natural frequencies near to the excitations dominant frequency, displacement

190

CHAPTER ( 8 ) -' Linearised Displacement- based Analysis

amplification and resonant effects increase the Ânso to a maximum greater than the PGD.

The displacement amplification is thus defined as Ânso,/PGD. For elastic systems withnatural frequencies greater than the excitation's dominant frequency ¡þs ÂRsp and

displacement amplification is reduced. For rigid elastic systems with large natural

frequencies (i.e. infinite stiffness), Ânsp approaches zero.

(tËod)Ê.

U)o-,É

"Tl*Ëo()úÊËË€Àõ.9úÀ

(A) natural frequency <dominant excitation frequency

(C) nan¡ral frequency >dominant excitation frequency

(B ) RESONANsT FREQUENCYnaû¡ral frequency = dominant excitation frequencyMaximum displacement amplification

Elastic System Natural Frequency

.J

PGD

PGD

rJ

In*l Hishff =fæResonantfrequency

PGD^RsD

> PGD

Figure 8.2.1 Typical Elastic Displacenrent Response Spectrum

Åns¡ = PGD

191

Âqso = 0

CHAPTER (8) - Lineørised Displacement-bøsed Arnlysis

This indicates that for ground motions where the dominant frequencies are much greater

than the elastic system's natural frequency the system will be safe from failure provided

that the PGD does not exceed Âinsrau¡iry. On the other hand should the dominant ground

motion frequency be nea¡ that of the natural resonant frequency, the Ans¡ may be

significantly amplified above that of the PGD depending on damping. In this case failure

may occur under excitations with much lower PGD.

THA and shaking table tests have shown the maximum relative mid-height displacement

amplification to be 1.5 to 3.3. This corresponds to a dynamic amplif,rcation of I to 2.2 at

the wall's effective mass, which is the point located at 213 of the free body height from

the point where the wall is stationary. This suggests that during ground motion with

dominant frequencies in the vicinity of the walls resonant frequency the wall will be safe

from overturning provided that the PGD does not exceed 0.3 of the wall thickness

(0.6612.2). For design, safefy factors would also need to be applied.

8.2.1. Derivation of Characteristic SDOF 6Substitute Structure' Stiffness

Provided that the selected SDOF 'substitute structure' stiffness, Kn (refer Figure 8.2.2)

linearly characterises the real structure for response at the incipient instability

displacement the real structure's displacement demand can be determined in accordance

with the relative elastic displacement response spectrum. The selection of Ç6 must

therefore be made so that it is probable that the 'substitute structure' and rocking wall

system will reach their respective displacement capacity under the same excitation.

Unlike the elastic perfectly plastic system presented in Section 8.1, where the lowest

secant stiffness analogous with the real structures dynamic response is used to

characterise the non-linear, this is not appropriate for rocking objects as at the failure or

instability displacement, ¡s65¡¡¡y, the secant stiffness is zero. It was therefore necessary

to develop an alternative procedure for deriving the characterising linear stiffness for

rocking simply supported URM walls.

192

CHAPTER (8) - Linearised Displacement-based Analysis

For same excitation the 2 systemsreach instability displacement

'SubstiûlteSEuch¡re'

Mid-height Displacement ( A)

tr'igure 8.22 Linearised DB Analysis Characteristic StifÊress, K.¡

During the response of a simply supported URM wall subjected to a transient excitation,it has been observed that incipient instability is most likely to be reached as aconsequence of the large displacement amplif,rcations associated with the effectiveresonant frequency of the wall. This is because unrealistically large ground motions are

required at or near resonance to cause the wall response to reach incipient instability.Consequently, the resonant behaviour of the simply supported URM walts should be

modelled by the linea¡ 'substitute structure' stiffness. Thus, the characteristic linearstiffness that will most likely best model the real wall behaviour at instability is the realstructure's effective resonant frequency. As was discussed in Chapter 5, the effectiveresonant frequency, ,Ên of a simply supported wall is associated with the aveÍage

incremental secant stiffrress, K"r", of the dynamic F-Â relationship. By again assuming

the tri-linear approximation of the static F-Â relationship K u"" is determined in generic

terms as,

o()!ol¡.ctkí)ctEIt)o¡Êr

A¡rr¡o6¡¡¿¡y

Krou" =K" r+2LQ)- L(r) +

Liwøøniry - LQ)Â(2) + Â(1) Linsøbitiry + L(2)

Here Ç(1) is dehned by Table 5.2.1andÂ(l) and L(Z)by Tabte 7.5.1

Real Semi-rigidNon-linear F-ÀRelationship

t93

(8.2.1)

CHAPTER (8) - Linearised Displacement-based Arnlysis

As the average dynamic secant stiffness, & ou" = 312 K" un" (again assuming a triangular

acceleration response relative to the wall supports) an estimate of the effective resonant

frequency without considering damping is therefore derived in accordance with

a=2nf=M

3 K,o,"

lqr2 M"

(8.2.2)2n

Since this estimation of/.6 by Equation 8.2.2 does not consider the damping component,

the true effective resonant frequency is expected to be slightly higher than the estimation.

This is confirmed by comparison with THA in Section 8.3.1.

8.22. Simply Supported URM Walls Modelled as a SDOF Oscillator

Prior to DB analysis being applied to a simply supported URM wall the substitutions

required for the modeling of the rocking system as an SDOF oscillator must be

recognised. These substitutions are required as for SDOF oscillator it is assumed that

lÙOVo of the system mass is mobilized whereas for rocking bodies this is not the case. As

a result the effective mass location relative to the supports must be considered.

8.2.2.1. Modelled Displac eme nt Capacity

As discussed in Section 5.2.1, for rigid simply supported objects the instability mid-

height displacement, A¡r¡¿6i¡1y, is considered to have been reached when the resultant

vertical force above the mid-height crack, due to self weight and overburden, is displaced

outside of the back mid-height edge of the wall. The mid-height displacement at which

this occurs is dependent on the support conditions (Table 5.2.1). For simply supported

'semi-rigid' URM walls with relatively low levels of applied overburden the finite

vertical reaction stress blocks a¡e small atlarge mid-height displacements. Consequently,

the rigid incipient instability displacement, ¡s¡¿6i¡¡y, can also be assumed for the analysis

of 'semi-rigid' simply supported URM walls.

âS'e

t94

CHAPTER (8 ) - Linearised Dßplacement-based Analysis

As was discussed in the development of the THA algorithm in Chapter 7, to represent a

simply supported rocking object as an SDOF oscillator a triangular acceleration responseis appropriate relative to the supports. Consequently, the effective masses of the tworocking free bodies are located at the 213 of the free body heights as measured from thesupports. The effective displacement capacity of the modelled SDOF 'substitute

structure', 4r rsøuility, is therefore reduced to 2/3 of the wall's static mid-heightdisplacement capacity so that:

Anmstauitity = 2/3 A¡.¡¿5¡¡1,

8.2.2.2. Modelled Damping Appropriate During Rocking Response

To take into account the reduced response velocity at the effective mass the level ofdamping associated with the elastic displacement response spectrum is taken as 213 thatdetermined experimentally from the mid-height response of the wall. As was presented inSection 6.4.6.3, a lower bound mid-height experimental equivalent viscous damping,

€soo", of approximately 57o was observed for both the 50 mm and 110 mm thick wallspecimens (refer Figure 6.4.20 and Figure 6.4.21). For simplicity and to be slightlyconservative an equivalent viscous damping of 57o for all frequencies was adopted. Theproportional damping coeffltcient, c, therefore varies linearly with frequency. Thecorresponding equivalent viscous damping assumed for the DB analysis to determine theelastic RSD was therefore 3Vo (=2¡3 5Eo¡.

8.3. Effectiveness of the Linearised DB Analysis

To test the effectiveness of the proposed DB analysis for face loaded simply supportedURM walls an extensive analytical study was conducted using the non-linear THAsoftware ROWMANRY presented in Chapter 7. In this study wall configurationsselected for examination included simply supported URM walls l.5m tall, beingrepresentative of the experimental study presented in Chapter 6, 3.3m tall, being acommon height found in Aust¡alian masonry construction and 4.0m tall, as permitted bythe South Australian Housing Code, 1996. For each wall height, wall thickness

195

CHAPTER (8) - Linearised Displacement-based Analysis

considered included 50mm, 110mm and 220mm. Iævels of applied overburden included

0MPa, 0.075MPa, 0.15MPa and 0.25MPa being representative of Australian masonry

construction. For all wall configurations having applied overburden, the top vertical

reaction was assumed to be pushed to the leeward face of the wall so that the mid-height

Ainstability was the thickness of the wall (refer Table 5.2.1) being representative of a

concrete slab above boundary condition. Finally, the three levels of mortar joint

degradation defined in Section 7 .5 were also examined for each of the wall configuration

considered. As the tri-linear F-A approximation is again used Table 7.5.1 presents the

defining displacements Â(1) and A(2) associated with each of the three levels of joint

degradation.

The first stage in testing the effectiveness of the proposed linearised DB analysis

procedure was to determine the estimated effective resonant frequency for each of the

wall configurations based on the average cycle secant stiffness to ¡r¡u6¡¡¡r, without

considering damping in accordance with Equation 8.2.1. Following this, an extensive

THA study using gaussian pulse input was conducted to confi¡m that the estimate of the

effective resonant frequency derived was appropriate. A linearised DB analysis was then

conducted on each of the simply supported wall configuration subjected to the transient

excitations as presented in Table 6.4.9. Here the percentage of the normalised transient

excitations required to cause instability of the simply supported URM wall under

consideration was predicted. As part of the linearised DB analysis procedure the derived

estimate of effective resonant frequency using Equation 8.2.2 was used as the

characteristic 'substitute structure' frequency. As discussed in Section 6.4.7.2 the

earthquake excitations used were selected to provide a representative cross section of

frequency and amplitude contents of plausible ground motions.

Comparison of the DB analysis is then made with results derived using the

comprehensive THA softwa¡e. The following sections present each stage of the study.

196

CHAPTER (8) - Linearised Displacement-based Analysis

8.3.1. Effective Resonant Frequency of simpry supported URM wallsThe first stage of the study was to determine the effective resonant frequency of thesimply supported wall configurations selected. Initially an estimate of effective resonantfrequency based on the average static secant stiffness determined from Equation g.2.1

was made from Equation8.2.2.

A THA study was then conducted to confirm the effective resonant frequency for theselected wall configurations. This was achieved by running a series of 500 gaussian

pulse THA at frequencies ranging from 0.25Hzto l}Hz and amplitudes from 2.5mm to11Omm for each of the wall configurations under consideration. From the resulting RSDversus PGD plot the frequency associated with maximum displacement amplification wasidentified as the effective resonant frequency. To illustrate, Figure 8.3.1 presents theRSD versus PGD for a 500 gaussian point THA run for a non-loadbearing 3.3m tall,l lOmm thick simply supported wall having moderately degraded rotation joints. Fromthis plot it is observed that the maximum mid-height displacement amplification oflt0l40 = 2.75 is associated with gaussian pulse frequencies of between 0.75H2 and,

1.0H2. This is compared with the estimated effective resonant frequency derived inaccordance with Equation 8.2.2 for the 3.3m tall simply supported LIRM wall havingmoderately degraded rotation joints of 0.81H2. For pulses with a much higher frequencythan the system natural frequency (>2.5H2) it can be seen that the plot converges to astraight line where the PGD is equal to approximately 213 of the relative response mid-height spectral displacement. Alternatively this line indicates where the pGD is

approximately equal to the Âns¡ measured at the 213 free body height beingrepresentative of the effective mass location relative to the supports due to the triangularacceleration response. This can be related to the lower part of zone (A) shown in Figure8.2.1). For these higher frequencies it is evident that instability can only occur when the

PGD is equal to or greater than 213 of ¡or¡u6¡1, (measured at the mid-height).Accordingly, much higher forces can be withstood by the wall at the higher excitationfrequencies than at frequencies near to the effective resonant frequency. This illustratesthe dependence of the walls dynamic reserve capacity on the dominant excitationfrequency.

r97

CHAPTER (8) - Linearised Dßplacement-bøsed Analysis

110

r00

90

€Í soEÊó2ioËEÉ8 ¿oo:øáãäsoE:d¡3åË 40

EåË' ,o

20

10

0

0102030405060708090 100

PGD(mrn)

MaximumDisplacement/Amplification

I / rYI I

)

,{

Poc!PGD=2ß ofthe relativemid-heightdisp. response

J

) *o.zsw,1n

-l.75Hz3Hz*:l- loHz

0.5IIz-#t.259"

-zHze''4Hz

*o.lsH"#t.5H"#2.5H"

À sl¡"

1

f âaãl Ðooê

Í Ðêê(; Ðoêê froë'

Figure 8.3.lGaussian Pulse; 33m Tall, 110mm Thicþ Moderate Degradation TIIA

As a result of this study it was determined that the effective resonant frequency of simply

supported URM walls derived using THA was approximately that predicted from the

average secant stiffness to A¡5¡¡5i¡¡y (refer Equation 8.2.1). A slight va.riation was

predicted to be due to the small influence of including damping in the THA increasing

the response frequency slightly. In summary, it was found that the frequency derived

using Equation 8.2.1 provided a good assessment of the estimate of effective resonant

frequency derived from the THA study which itself correlated well with the experimental

results (refer Figure 7.8.2). Consequently, it was postulated that the approximate

effective resonant frequency for simply supported URM walls determined in accordance

with Equatto¡ 8.2.2 for use as the characteristic 'substitute sffucture' frequency is

adequate considering the approximations made within the linearisation procedure.

The estimated effective resonant frequency (Equation 8.2.2) determined for the 1.5m,

3.3m and 4.0m height walls at various levels of overburden stress and joint degradation

198

CHAPTER (8) - Linearised Displacement-based Analysis

are presented in Table 8.4.1 to Table 8.4.12. In most cases the effective resonant

frequency is associated with the secant stiffness at instantaneous displacements at around

30 to 40Vo of the incipient instability displacement. The wall thickness was found to have

little influence on the effective resonant frequency (the reasons for this are discussed inSection 5.2.1).

By comparison with experimental results it was also found that the analytically derived

effective resonant frequencies correlated well with frequencies observed experimentally

as the minimum asymptotic frequency, friroit.

8.32. Linearised DB Analysis

The second stage of the study was to conduct the linearised DB analysis on each of the

simply supported tlRM wall configurations subjected to the transient excitationspresented in Table 6.4.9 including Elcentro, Pacoima Dam, Nahanni and Taft earthquake.

Here the effective resonant frequency determined in the fîrst stage of the study, and the

elastic displacement response spectrum at 3Vo damping (=2l3x5%o) were used todetermine the displacement demand on each of the modelled wall configurations. Using

the effective resonant frequency as the cha¡acterising elastic SDOF stiffrress the percent

normalised earthquake excitation required for the modelled displacement demand toequal the modelled displacement capacity was determined. This therefore represented the

excitation required for ultimate instability of the wall to be reached. For illustrativepurposes the linearised DB procedure for the 3.3m tall, 110mm thick wall with 0.075MPa

applied overburden stress having moderately degraded rotation joints and subjected to the

ElCentro earthquake is described.

Figure 8.3.2 presents the relative elastic displacement response specfum (3Vo damping)

for the Elcentro earthquake comprised of displacement-normaltzed spectrum ranging

from 25Vo to 500Vo in 25Vo increments. The horizontal line shown at 73mm (ll0x2l3)displacement is representative of the displacement capacity of the elastic SDOF'substitute structure' representing the 110mm thick wall both with and without

199

CHAPTER (8) - Linearised Displacement-based Analysis

overburden. The estimate of effective resonant frequency, determined in accordance with

Equation 8.2.1 (refer Table 8.4.2) is l.23Hz. As frequencies gteater than the assumed

characteristic SDOF oscillator frequency are relevant to the response, to be slightly

conservative the lowest percent displacement normalised ElCentro earthquake is adopted

from all frequencies greater than the estimated effective resonant frequency. Thus, using

the characteristic 'substitute structure' stiffness compatible with the l.23Hz resonant

frequency the percent displacement normalised ElCentro earthquake predicted to cause

instability of the wall is determined as 7OVo.

Results of the linearised DB analysis for all of the considered wall conf,rgurations are

presented in Table 8.4.1 to Table 8.4.12.

Figure 8.3.2 Relative ElCentro Earthquake Elastic Response Spectrum (37o damp¡ng)

8.33. TIIA for Various Transient Excitation

The next stage of the study to test the effectiveness of the DB criterion \ryas to predict the

percent displacement normalised earthquake to cause ultimate instability using the non-

linear THA software described in Chapter 7. For each wall under consideration a THA

was performed gradually increasing the displacement-normalised earthquake by l7o at a

ïa

I

ï

-+- +

*t

xt¡

1¿t\b¡

I

t \

1IY I 7Qïo 1

¡I FT Lt\ )aa Ai'l(

P( Ntf.++.

ÊÈ

e 200É

ãft rzs

.s

'ã rtEIH lzs

€E roo

8"

75

50

25

0hhih6hNhhhóhhhthhhhñhJtìcl..jrìclñrì.ìGiìcl+lqviOÉÊddoOçth

'SUBSTITUTE STRUCTIJRE' FREQTJENCY

200

CHAPTER (8) - Lineørised Dßplacernent-based Analysis

time. Figure 8.3.3, Figure 8.3.4 and Figure 8.3.5 present the peak mid-heightdisplacement result, relative to the supports, for the 1.5m, 3.3m and 4m wall respectively

at va¡ious overburden and with moderately degraded bed joints subjected to the ElCentroearthquake. From Figure 8.3.4 it can be observed that for the 3.3m wall with 0.0Z5Mpaapplied overburden stess the THA prediction for ultimate instability is 85Vo of thedisplacement normalised ElCentro earthquake. This compares reasonably well with theDB analysis prediction of 70Vo ElCentro as described in Section 8.3.2. Dampingassumed for all THA was Rayleigh damping with the mass proportional coeff,rcient of 1.0

and stiffness proportional coefficient of 0.002 as these represented the lower bound of theexperimental results presented in Section 6.4.6.3.

ll0100

E90tsY80É8zos60ÉsoÂË40Ð'õ. 30¡Ézo

0

+0MPa{-0.075MPa

0.l5MPaJê0.25MPa

a

0 50 100 150 200 250 300 350 400 4507o Normalised Accelerogram

Figure 8.3.3 THA ElCentro Earthquake: 1.5m Tall, Moderate Degradation

110

100

Ee0YaoEzooR60ås0åûõ830þzo

00 25 50 75 100 t25 150 175 200 225 250

% Normalised Accelerogram

vt t -"

<-OMF¿{-0.075MPa

0.15MPa

-)ts0.25MPara¡'tr tJ

Figure 8.3.4 ElCentro Earthquake: 33m Tall, Moderate Degradation

201

CHAPTER (8) - Linearised Displacement-based Anølysis

110

^100Ëe0ãaoËro-E ooÞ.

É50z,ÆilEso€ro'' 10

0

'ìl" t^ 'I/ : -

0 15 30 45 60 75 90 r05 r20 135 150 165% Normalised Accelerogram

-#OMPa#0.075MPa

0.l5MPa-X-0.25MPa

,t.fl it-

Figure 8.3.5 ElCentro Earthquake: 4.0m Tall, Moderate Degradation

The analysis results for the THA study are presented in Table 8.4.1 to Table 8.4.12.

8.3.4. Comparison of Predictive Model Results

The final stage of the study to test the effectiveness of the DB criterion was to compale

the linearised DB and non-linear THA predictions of the percent displacement

normalised eafthquake to cause ultimate instability as derived in 8.3.2 and 8.3.3

respectively. Figure 8.3.6 graphically presents these comparisons where it is observed

that almost all of the results fall within the bounds of the 1507o tolerance lines. That is,

the linearised DB analysis, using the estimate of effective resonant frequency derived in

accordance with Equation8.2.2 as the characterising 'substitute structure' frequency, will

provide an ultimate instability prediction not more than 1.5 times and or less than2l3 of

that predicted by the more comprehensive non-linear THA. The scatter of results

observed is a function of the linearisation of the real non-linear stiffrress and damping

components of the real rocking wall system.

Further to this comparison, the more traditional 'quasi-static' rigid body prediction of

lateral resistance capacity and the 'semi-rigid resistance threshold' acceleration (refer

Table 8.4.1 to Table 5.4.12) are compared with the THA predictions.

202

CHAPTER (8) - Linearised Displacement-based Analysis

d

oõÉIoo(È

H

o'ÉdoJ

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00Òo el

oono Io o eì oI rì o

elclN

oN

THAG)

.ELCENTROIPACOIMADAM

TAFT

ONAHANM

15O4"'ît llønæI.i w ,me

o o ôUn-conserPredicti@

¡ativeDB r nalysis a -7/r r.¡r r l5Ocr'oTo terance Lir

t arl)/

Cons rvativÊ DI

I

Figure 8.3.6 Comparison of DB Analysis and THA Ultirmte Instability Prediction

Figure 8.3.7 presents graphically the compa.rison of the 'semi-rigid resistance threshold'

acceleration with the THA ultimate instability prediction. Here it is observed that for the

transient excitations with lower dominant frequencies (Taft, ElCentro and Pacoima Dam)

near to the wall's effective resonant frequency the 'semi-rigid resistance threshold'

acceleration provides a good prediction of the lateral acceleration capacity of the wall.This is because at these dominant excitation frequencies there is little benefit gained

through 'dynamic stability' concepts so that the URM wall's reserye capacity is small.

Thus, this 'quasi-static' analysis provides a reasonable prediction oflateral capacity. Forexcitations having dominant frequencies greater than the effective resonant frequency(Nahanni) the dynamic reserve capacity is far more significant. As this is not accounted

for by the 'quasi-static' analysis the ultimate instability prediction is conservative.

203

CHAPTER (8) - Linearised Displacement-based Analysis

d)ob

ç¡.os.s.2oúËè0dEo(t)

2.50

2.25

2.00

1.75

1.50

t.25

1.00

0.75

0.s0

0.25

0.00

aeI-cENTRolpeconuRo¡r"t

TAFToNRnnr.INI

l50%oTolT -imit

erance

I ?I I Equ Lity Line

Un-colanalys

servative I

s PredictioRR

a

I

lla

aa

a

Cons )rvative lredictic

II !^lt^--^^

T¡

Limit

ì TT ot.ì

Consa¡al:

:rvative Slris Pr€dict

R)n

I oâôo

ôeo

o oBô ooo

oÊ

(J

onÔnahonanoõñnrôNhroe{nððoo-'iôi ñõi

THAG)

Figure 8.3.7 R*(1) vs THA Ultirnatc Instability Prediction

Figure 8.3.8 presents graphically the comp¿ìrison of the 'quasi-static' rigid body ultimate

instability prediction. Here it is observed that for the transient excitations 'with lower

dominant frequencies near to the wall's effective resonant frequency the 'quasi-static'

rigid body analysis provides an un-conservative prediction of the lateral acceleration

capacity of the wall. This is attributed to the overestimation of the 'semi-rigid resistance

threshold' force by the rigid assumption and ths in-significant wall dynamic reserve

capacity. For transient excitations with higher dominant frequencies than the wall's

effective resonant frequency, like the 'semi-rigid resistance threshold' force prediction,

the 'quasi-static' rigid body analysis provides a conservative prediction of the lateral

acceleration capacify of the wall.

204

CHAPTER (8) - Lineørised Displacement-based Analysis

€9

õÊ

atoÉËè0ú-a

su)

aa

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00ôo cì

ooVlo ¡l

o a cl ou] ì Eelcle.l e{

THAG)

.ELCENTROTPACOIMADAM

TAFTONAHANNI

RB

a

150%1 ollerance I {

I t a

^,AI

ity Line

I Io

o

ßOqtLimit

Tolleranq

ltI o

,'l,) /l

oCmserv¿anatysis J

ive RBTediction o

o oo oo o ôo o

o o" oo

Figure 8.3.8 'Quasi-static' Rigid Body vs THA llltirnate Instability Prediction

8.4. Conclusion

Linearised DB analysis using the wall's effective resonant frequency as the 'substitute

structure' natural frequency provides predictions of ultimate instability \ryithin + 5OVo ofthe more comprehensive THA. Equation 8.2.1, which represents the generic average

secant stiffness to the incipient instability displacement, has been found to provide areasonable estimate of the simply supported IJRM walls effective resonant frequency.

The linearised DB analysis therefore provides a rational and relatively straight forwardprediction of the dynamic lateral capacity for simply supported URM walls. Since this

takes into account the true dynamic behaviour of the rocking wall system, the dynamic

reserve capacity for excitations having dominant frequencies greater than the effectiveresonant frequency is accounted for.

In conclusion the linearised DB analysis using the wall's effective resonant frequency

determined in accordance with Equation 8.2.1 as the 'substitute structure' characteristic

205

CHAPTER (8) - Linearised Dßpbcement-based Analysis

frequency provides predictions within limiting tolerances of + 50Vo of the more

comprehensive THA results. This method therefore provides the most rational and

simple approach for assessing the dynamic lateral capacity of simply supported URM

walls subjected to transient excitations.

Table 8.4.1 ElCentro Analysis Conrparison: 1.5m Height Wall

GEOMETRY OVER-BURDEN

(MPa)

WALL CONDITION RIGIDBODY

(g)

SEMIRIGID

G)

THA DBA(t)

(mm)(h)(m)

(referFigure6.4.12)

ag)A^

&tA*

ToEQ PGAG)

l*(Hz)

>FREQToEQ

>FREQPGAk)

50 1.5 0 NE}V 67o 287o 0.13 0.10 33Vo 0.11 1.45 307o 0. l0

50 1.5 0 MOD l37o 4OVo 0.13 0.08 197o 0.07 t.2t 25Vo 0.09

50 1.5 0 SEV 2O7o 5O7o 0.13 0.07 217o 0.07 1.04 20Vo 0.07

50 1.5 0.075 NEW 67o 28Vo 0.89 0.64 l3O7o 0.45 2.U l4OTo 0.49

50 1.5 0.075 MOD l3%o 4OVo 0.89 0.53 924o 0.32 2.X lOO9o 0.35

50 1.5 0.075 SEV 2O4o 5O7o 0.89 0.44 767o 0.26 LM 6OVo o.2t

50 1.5 0.15 NEW 6Vo 28Vo 1.64 1.18 5407o 1.14 t.74 2OOTo 0.70

50 1.5 0.15 MOD 13Vo 4OVo 1.64 0.99 LSO4o 0.52 3.r2 lSOTo 0.52

50 1.5 0.15 SEV 2OVo 5OVo 1.64 0.82 lXZ7o 0.42 2.69 ll57o 0.40

50 1.5 0.25 NE}V 6Vo 28Vo 2.65 1.91 NF NF 4.62 4001o 1.39

50 1.5 o.25 MOD l3Vo 4OVo 2.65 1.59 I{F NF 3.9 2OOVo 0.70

50 1.5 o.25 SEV 2OVo 5OVo 2.65 1.33 1939o 0.67 337 2NVo 0.70

110 1.5 0 NEV/ 6Vo 287o o.29 o.2l 80Vo 0.28 1.45 85Vo 0.30

ll0 1.5 0 MOD 13Vo 4OVo 0.29 0.18 457o 0.16 t2r 6OVo 0.21

110 1.5 0 SEV 2O7o 5O7o 0.29 0.15 457o 0.16 1.04 45Vo 0.16

110 1.5 0.075 NEW 67o 28Vo 1.95 l.4l 3757o t.3l 2.U 3tOVo 1. r5

110 1.5 0.075 MOD 13Vo 4O7o 1.95 t.t7 3257o 1.13 2.36 250Vo 0.87

110 1.5 0.075 SEV 2OVo 5OVo 1.95 0.98 2107o 0.73 2.M \23Vo 0.43

110 1.5 0.15 ' NEW 67o 287o 3.62 2.60 Nr. NF 1.74 425Vo 1.48

110 1.5 0.15 MOD 131o 4OVo 3.62 2.17 NF NF 3.12 3257o 1.13

110 1.5 0.15 SEV 2OVo 5OVo 3.62 l.8l 3854o 1.34 2.69 250/o 0.87

110 1.5 0.25 NEV/ 67o 28Vo 5.83 4.20 ¡m NF 4.62 NT' NF

110 1.5 0.25 MOD 137o 4OVo 5.83 3.50 NF NF 3.9 ASTo 1.48

r10 1.5 0.25 SEV 2O7o 5OVo 5.83 2.92 NF NF 337 4254o 1.48

220 1.5 0 NEW 6Vo 28Vo 0.59 o.42 1557o 0.54 1.45 lTOVo 0.59

220 1.5 0 MOD l3Vo 4OVo 0.59 0.35 85Vo 0.30 l.2l 125Vo 0.44

220 1.5 0 SEV ZOVo SOVo 0.59 0.29 N7o 0.28 1.04 85Vo 0.30

220 1.5 0.075 NEW 6Vo 284o 3.91 2.8r NF NF 2.U NT' NF

220 1.5 0.075 MOD I3Vo 404o 3.91 2.35 NF NF 236 NF NF

220 1.5 0.075 SEV 2OVo 5O1o 3.9t 1.95 4l5Vo 1.45 2.M 4707o t.&220 1.5 0. l5 NEW 6Vo 28Vo 7.23 5.2r NF NF 3.74 NT' NF

220 1.5 0.15 MOD 13Vo 4O7o 7.23 4.34 I\F NF 3.12 NT' NF

220 1.5 0.15 SEV 2OVo 5O7o 7.23 3.62 NF NF 2.69 NF

220 1.5 0.25 NEW 61o 28Vo 11.66 8.40 NF NF 4.62 NF NF

220 1.5 0.25 MOD l31o 4OVo 11.66 7.00 NF NF 3.9 NT' NF

220 1.5 0.25 SEV 2OVo SOVo 1r.66 5.83 NF NF 3.37 NT' NF

*NF - No Fail within limits of study

206

CHAPTER (8) - Lineørised Displacernent-based Arnlysis

Table 8.4.2 ElCenho Analysis Conrparison: 3.3m Height Wall

GEOMETRY OVER.BURDEN

0\,rPa)

WALL CONDITION RIGIDBODY

G)

SEMIRIGID

G)

THA DBA(r)

(mm)(h)(m)

(referFigure6.4.12)

a(1)A^

&I4^

VoEQ PGAG)

l"n(Hz)

>FREQloEQ

>FREQPGAk)

50 3.3 0 NE\Y 67o 28Vo 0.06 0.04 2O7o 0.07 0.96 257o 0.0950 3.3 0 MOD 13Vo 4OVo 0.06 0.04 tLVo 0.08 0,81 25Vo 0.(D50 3.3 0 SEV 2OVo 5O7o 0.06 0.03 267o 0.09 t.7 25To 0.0950 3.3 0.075 NEW 6Vo 28Vo o.22 0.r6 327o 0.1I t.46 3O7o 0. r050 3.3 0.075 MOD 13Vo 4OVo 0.22 0.13 27Vo 0.09 t.?.3 25y'o 0.0950 3.3 0.075 SEV 2OVo 5OVo 0.22 0.11 2OVo 0.07 1.0ó 2OVo 0.0750 3.3 0.15 NEW 6Vo 287o o.37 0.27 547o 0.19 1.82 45lo 0.1650 3.3 0.15 MOD 13Vo 4OVo 0.37 0.22 377o 0.13 1.54 357o tJ.12

50 3.3 0.15 SEV 2OVo 5O7o 0.37 0.19 327o 0.11 r33 3O9o 0.r050 3.3 o.25 NEW 6Vo 28Vo 0.58 0.42 93Vo 0.32 2.72 TOVo 0.2450 J.J 0.25 MOD l3Vo 4O7o 0.58 0.35 6Vo 0.23 SOVo o.t750 3.3 o.25 SEV 2O7o 5O7o 0.58 0.29 439o 0.15 L6¿ 4O7o 0.14110 3.3 0 NEW 6Vo 28Vo 0. 13 0.10 457o 0.16 0.96 457o 0. lóll0 3.3 0 MOD l37o 4OVo 0.13 0.08 45Vo 0.16 0.81 451o 0.1óll0 3.3 0 SEV 2OVo 50% 0.13 0.07 457o 0.16 0.7 457o 0. l6110 3.3 0.075 NEW 6Vo 28Vo 0.48 0.34 üVo 0.28 1.46 EOVo 0.28110 3.3 0.075 MOD 137o 4OVo 0.48 o.29 85Vo 0.30 t.?ß 7O7o 0.24ll0 3.3 0.075 SEV ZOVo SOVo 0.48 o.24 5O7o 0.17 1.06 S54o 0.19110 3.3 0.15 NEW 6Vo 28Vo 0.82 0.59 lffiVo 0.56 1.82 lOOTo 0.35110 3.3 0.15 MOD l3Vo 4OVo o.82 0.49 l30Vo 0.45 1.54 917o 0.31ll0 3.3 0.15 SEV ZOVo 5O7o 0.82 0.41 1257o o.44 1.33 EOVo 0.28ll0 3.3 0.25 NEW 67o 28Vo 1.28 0.92 ttsvo 0.78 2.?:2 l5O7o 0.52110 3.3 o.25 MOD l3Vo 4O7o 1.28 0.77 1757o 0.61 1.87 llïVo 0.38110 3.3 0.25 SEV 2OVo 5OVo 1.28 o.& l45Vo 0.51 1.62 9O7o 0.31220 3.3 0 NEW 6Vo 28Vo 0.27 0.19 7íVo 0.26 0;96 9OVo 0.3r220 3.3 0 MOD 137o 4OVo 0.27 0.16 80Vo 0.28 0;81 9{Vo 0.31220 3.3 0 SEV 2O7o 5O7o o.27 0.13 lA07o 0.35 0.7 9OVo 0.31220 3.3 0.075 NEW 6Vo 28Vo 0.95 0.69 16OVo 0.56 1.46 16OVo 0.56220 3.3 0.o75 MOD 13Vo 40Vo 0.95 0.57 lffiVo 0.56 1.23 l25lo 0.44220 3.3 0.075 SEV 2OVo 5OVo 0.95 0.48 l05Vo 0.37 1:06 9X)7o 0.31220 3.3 0. l5 NEW 67o 28Vo 1.64 1.18 3357o l.t7 1.82 2OOVo 0.70220 3.3 0.15 MOD 13Vo 4OVo 1.64 0.98 2757o 0.96 1.54 17SVo 0.61220 3.3 0.15 SEV 2OVo 5OVo 1.64 0.82 2357o 0.82 1.33 17SVo 0.ól220 3.3 0.25 NEIW 6Vo 28Vo 2.55 1.84 4SSVo 1.58 2.X2 3507o 1.22220 3.3 0.25 MOD 13Vo 4OVo 2.55 1.53 SOOVo 1.74 1.87 25O7o 0.87220 3.3 o.25 SEV 2OVo 5OVo 2.s5 1.28 29n7o t.0r 1.62 17íVo 0.61

*NF - No Fail within limits of study

207

CHAPTER (8) - Linearised Dßplacement-based Analysis

Table 8.4.3 ElCentro Analysis Comparison: 4.0m Height \üall

GEOMETRY OYER-BURDEN

(MPa)

WALL CONDITION RIGIDBODY

G)

SEMIRIGID

G)

THA DBA(t)

(mm)(h)(m)

(referFigure6.4.12\

4ú)A^

AG)4^

VoEQ PGAG)

f*(IIz)

>FREQToEQ

>FREQPGAG)

50 4 0 NEW 6Vo 287o 0.05 o.04 32Vo 0.1r O.EE 254o 0.09

50 4 0 MOD 13Vo 4O7o 0.05 0.03 3O4o 0.10 o.74 259o 0.09

50 4 0 SEV 2O4o 5OVo 0.05 0.03 33Vo 0.n 0.64 25(o 0.09

50 4 0.075 NEW 6Vo 28Vo 0. 16 0.ll 32Vo 0.11 1.26 257o 0.09

50 4 0.075 MOD 137o 4OVo 0.1ó 0.09 L9Vo 0.07 1.06 22Vo 0.08

50 4 0.075 SEV 2OVo 5O7o 0. ló 0.08 2lVo 0.07 0.92 22(o 0.08

50 4 0.15 NEW 6Vo 287o o.26 0.19 5O7o o.t7 1.55 4O9o 0.14

50 4 0.15 MOD l37o 4O7o o.26 0. 16 347o o.t2 1.31 35Vo o.t2

50 4 0. 15 SEV 2OVo 5OVo [J.26 0.13 22Vo 0.08 1.13 251o 0.u,

50 4 o.25 NEW 6Vo 287o 0.4{) o.29 62Vo 0.22 1.01 5O7o 0. 17

50 4 o.25 MOD l3Vo 4OVo 0..!0 0.24 417o 0.14 l.5E 4OVo 0.14

50 4 0.25 SEV 2OVo 5O7o 0.40 o.zo 377o 0.13 1.36 35To 0.12

ll0 4 0 NEW 6Vo 28Vo 0.11 0.08 757o tJ.26 0.8E 45Vo 0. 16

110 4 0 MOD 13Vo 4OVo 0.il 0.07 45Vo 0. l6 0.74 45Vo 0.16

110 4 0 SEV 2OVo 5OVo 0.ll 0.06 55lo 0.19 0.64 457o 0. 16

110 4 0.075 NEW 6Vo 287o 0.34 0.25 757o 0.26 70Vo o.24

110 4 0.075 MOD l3Vo 4OVo 0.34 o.2t 55Vo 0.19 l;06 5O7o 0.17

110 4 0.075 SEV 2OVo 5OVo 0.34 0.17 457o 0.16 0,92 457o 0.16

110 4 0.15 NEW 67o 28Vo 0.5E o.42 lO5Vo 0.37 1.55 ESVo 0.30

ll0 4 0.15 MOD l3Vo 4O7o 0.58 0.35 757o o.26 131 lSVo 0.26

110 4 0. 15 SEV 2OVo 5OVo 0.s8 0.29 TOVo o.24 1.13 60?o 0.21

ll0 4 0.25 NEW 6Vo 287o 0.89 o.g lEïVo 0.63 1.01 IIOVo 0.38

110 4 o.25 MOD l3Vo 4OVo 0.89 0.53 l35Vo o.47 1.sE 9OVo 0.31

110 4 o.25 SEV ZOVo 5O7o 0.89 o.44 9Oio 0.31 136 9O7o 0.31

220 4 0 NE}V 6Vo 281o 0.22 0.16 t457o 0.51 0.8E 9nVo 0.3r

220 4 0 MOD 13Vo 4OVo o.22 0.13 too% 0.35 0.74 9OVo 0.3r

220 4 0 SEV 2OVo 5OVo o.22 0.11 llSVo 0.,1{J 0.64 9O4o 0.31

220 4 0.075 NEW 6Vo 287o 0.69 0.49 l25Vo o.44 1.2Íi lSOlo 0.52

220 4 0.075 MOD 13Vo 4O7o 0.69 0.41 160Vo 0.56 1.06 9OVo 0.31

220 4 0.075 SEV 2OVo 5OVo 0.69 o.34 9O9o 0.3r 0.92 90?o 0.31

220 4 0.15 NEW 6Vo 28Vo l 15 0.83 2to?o o.13 1.55 17SVo 0.61

220 4 0.15 MOD 137o 4OVo 1.15 0.69 2207o 0.77 131 16O7o 0.56

220 4 0. 15 SEV 2OVo 5O7o l.l5 0.58 l35Vo o.47 1.13 llSVo 0.,1O

220 4 o.25 NEW 6Vo 28Vo 1.78 1.28 370Vo 1.29 1.01 2lO7o 0.73

220 4 0.25 MOD 13Vo 4OVo l.7E r.07 2E07o 0.98 l5E IEOVo 0.63

220 4 o.25 SEV 2O7o SOVo 1.78 0.89 lEOTo 0.63 136 lTOVo 0.59

*NF - No Fail within limits of study

208

CHAPTER (8) - Linearised Displacement-based Analysis

Table 8.4.4 Taft Analysis Conrparison: l.5m Height \ilall

GEOMETRY OYER.BURDEN

(MPa)

\ilALL CONDITION RIGIDBODY

G)

SEMIRIGID

G)

THA DBA(r)

(mm)(h)(m)

(referFigure6.4.12)

ag)4*

AQT4^

TIEQ PGAG)

.r"n(Hz)

>FREQloEQ

>FREQPGAk)

50 1.5 o NEIW 6Vo 28Vo 0.13 0.10 72Vo 0.13 1.45 öo"h 0.1450 1.5 0 MOD 13Vo 4OVo 0.13 0.08 58% o.10 1.21 55Uo 0. t050 1.5 0 SEV 20% 50Vo 0.13 0.07 4OUo 0.07 1.04 45% 0.0850 1.5 o.o75 NEI9V 6Vo 28Vo 0.89 o.M NF NF 2.84 190% 0.3450 1.5 0.075 MOD l3Vo 4OVo 0.89 0.53 1360/o o.24 2.36 180ch 0.3250 1.5 0.075 SEV ZOVo 5OVo 0.89 0.44 IOZYo 0.18 2.O4 95"/" o.1750 1.5 o.15 NE}V 6Vo 28Vo '1.64 1.18 NF NF 3.74 410% o.7450 1.5 0.15 MOD 13Vo 4OVo 1.64 0.99 NF NF 3.12 21OUo 0.3850 1.5 0.15 SEV 2OVo 50% 1.64 0.82 19170 0.34 2.69 190% 0.3450 1.5 o.25 NE\ry 6% 28Vo 2.65 1.91 NF NF 4.62 s00% o.9050 1.5 0.25 MOD l37o 4OVo 2.65 1.59 NF NF 3.9 455% 0.8250 1.5 0.25 SEV 2O7o 5O7o 2.65 1.33 NF NF 3.37 31O"/" o.56110 1.5 0 NEW 67o 28Vo 0.29 o.21 155"h 0.28 1.45 190To o.34110 1.5 0 MOD l3Vo 4OVo 0.29 0.18 145Vo o.26 1.21 12OYo o.22110 1.5 0 SEV ?-OVo 5OVo 0.29 0.15 1OO"/" 0.18 1.04 120% o.22ll0 1.5 0.075 NEW 6Vo 28Vo 1.95 1.41 NF NF 2.84 42Ùo/o 0.75ll0 1.5 0.o75 MOD l37o 4OVo 1.95 1-17 4OOUI 0.72 2.36 350% 0.63110 1.5 0.075 SEV 20Vo 5O7o 1.95 0.98 38OYo 0.68 2.O4 2OOe/o 0.36110 1.5 0.15 NE}V 67o 28Vo 3.62 2.60 NF NF 3.74 1000% 1.79110 1.5 o.15 MOD l3Vo 4OVo 3.62 2.11 NF NF 3.12 550o/" o.99ll0 1.5 0.15 SEV 2OVo 5OVo 3.62 1.81 600"h 1.08 2.69 45O7o 0.81110 1.5 o.25 NE\ry 6Vo 28Vo 5.83 4.20 NF NF 4.62 NF NFr10 't.5 0.25 MOD 137o 4OVo 5.83 3.50 NF NF 3.9 NF NF110 1.5 o.25 SEV 2OVo 5OVo 5.83 2.92 NF NF 3.37 TOVo o.13220 1.5 0 NEIW 6Vo 28Vo 0.59 o.42 31OYo 0.56 1.45 390% 0.70220 1.5 0 MOD 13Vo 4OVo 0.59 0.35 290% o.52 1.21 260% 0.47220 1.5 0 SEV 2OVo 50Vo 0.s9 0.29 ZOOYo 0.36 1.04 22O'/o 0.39220 1.5 0.o75 NEW 6% 28% 3.91 2.81 NF NF 2.84 8OO"/" 1.43220 1.5 0.075 MOD 13Vo 4OVo 3.91 2.35 1050% 1.88 2.36 650% 1.17220 1.5 0.075 SEV 2O7o 5O4o 3.91 1.95 725Yo 1.30 2.O4 400% 0.72220 't.5 o.15 NEW 6Vo 28Vo 7.23 5.21 NF NF 3.74 NF NF220 1.5 0.15 MOD 13Vo 4OVo 7.23 4.34 NF NF 3.12 NF NF220 't.5 o.15 SEV 2OVo 5OVo 7.23 3.62 NF NF 2.69 81OYo 1.45220 'L5 o.25 NEW 6Vo 28Vo 11.66 8.40 NF NF 4.62 NF NF220 1.5 0.25 MOD 137o 4OVo 11.66 7.00 NF NF 3.9 NF NF220 1.5 0.25 SEV 2O7o 5OVo 11.66 5.83 NF NF 3.37 NF NF

*NF - No Fail within limits of study

209

CHAPTER (8) - Linearised Displncement-based Analysis

Table 8.4.5 Taft Analysis Comparison: 3.3m Height Wall

GEOMETRY OVER-BURDEN

(MPa)

WALL CONDITION RIGIDBODY

G)

SEMIRIGID

G)

THA DBA(t)

(mm)(h)(m)

(referFigure6.4.12)

Â(1)A*

ae)A*

loEQ PGAG)

f"n(Hz)

>FREQVoßQ

>FREQPGAk)

50 3.3 0 NEW 6% 28V" 0.ott 0.04 53Vo 0.10 o.96 SOYI 0.09

50 3.3 0 MOD 13% 40% 0.06 0.04 46"/" 0.08 0.81 SOYI 0.09

50 3.3 0 SEV 2O"/o 50% 0.06 0.03 41Yo 0.07 o.7 5O"/" 0.09

50 3.3 0.075 NEV/ 6"/o 24"/" 0.22 0.16 91"/o 0.16 1.46 95% 0.17

50 3.3 0.075 MOD 13"/" 4OYo 0.22 0.13 66% 0.'t2 1.23 95"/o 0.17

50 3.3 0.075 SEV 2O"/o 5Oo/" 0.22 0.11 SAYI 0.10 1.0ö 5OV" 0.09

50 3.3 0.'t5 NEV/ 6% 24"/o 0.37 0.27 91"h 0.16 1.42 95% 0.17

50 3.3 0.15 MOD 13"/o 40% 0.37 o.22 66% 0.12 1.54 95% 0.17

50 3.3 0.15 SEV 2O"/o 5OTo 0.37 0.19 TOYo 0.13 1.33 95"/" o.'17

50 3.3 0.25 NEVT 6% zAV" 0.58 0.42 115"/o o.21 2.22 ro0% 0.'t8

50 3.3 0.25 MOD 13% 40% 0.58 0.35 104?/" 0.19 1.87 95"/o 0.17

50 3.3 0.25 SEV 2O"/" 50% 0.58 0.29 88e/o 0.16 1,62 95"/" 0.17

110 3.3 0 NEW 6"/0 28Y" 0.13 0.10 1O2"/o 0.18 0.96 11Oo/o 0.20

110 3.3 0 MOD 13o/" 40% 0.13 0.08 95% 0.17 0:81 11OYo 0.20

ll0 3.3 0 SEV 2O"/o 50% 0.13 0.07 SOUo 0.16 1,00% 0.18

110 3.3 0.075 NEIW 6% 28"/o 0.48 0.34 17sVo 0.31 1.46 190% 0.34

110 3.3 o.o75 MOD 'l3o/" 40% 0.48 0.29 1750h 0.31 1.23 145Yo

110 3.3 0.075 SEV 20% 50% 0.48 o.24 11sYo 0.31 1.06 11OYo o.20

110 3.3 0.15 NEV/ 60/" 28% 0.82 0.59 21OYo 0.38 1.82 190% 0.34

110 3.3 0.15 MOD 13o/" 40% o.a2 0.49 21O"/o 0.38 1.54 190% 0.34

110 3.3 0.15 SEV 20% 50% 0.82 0.41 175"/o 0.31 1.33 190% 0.34

ll0 3.3 o.25 NEV/ 6o/o 28% 1.28 0.92 365% 0.65 2.22 1 907o 0.34

110 3.3 0.25 MOD 13% 4OVo 't.28 0.77 27sVo 0.49 1.At 190% 0.34

110 3.3 0.25 SEV 20o/" 50% 1.24 o.64 210% 0.38 1.02 190% 0.34

220 3.3 0 NEV/ 6"/o 28Y" o.27 o.19 20O/" 0.36 0.96 21OYo 0.38

220 3.3 0 MOD 13"h 4oo/o 0.27 0.16 189"h o.32 0.81 240% 0.43

220 3.3 0 SEV 2O"/o 50% 0.27 0.13 2OO"/o 0.36 o,t 200% 0.36

220 3.3 0.075 NEW 6o/" 28% o.95 0.69 325o/o 0.58 1.46 370"h 0.66

220 3.3 0.075 MOD 13" 40% 0.95 0.57 ßOU. 0.77 1.23 300% 0.54

220 3.3 0.075 SEV 2OVo SOVI 0.95 0.48 300% 0.54 l.06 230% 0.41

220 3.3 0.15 NEW 6o/" 28% 1.64 1.18 44OYe 0.79 1.42 390% 0.70

220 3.3 0.15 MOD 13"/" 40% 1.64 0.98 525o/o 0.94 1.54 390% 0.70

220 3.3 0.15 SEV 2O"/o 5O"/o 1.64 0.82 360% 0.65 1.33 210% 0.38

220 3.3 o.25 NEIù/ 6o/" 28"/" 2.55 1.84 73OYo 1.31 2.22 390% 0.70

220 3.3 0.25 MOD 13% 40% 2.55 1.53 6250/" 1.12 1.87 3907o 0.70

220 3.3 0.25 SEV 2O"/" 5Oo/" 2.55 1.28 41OYo o.74 1.62 390% 0.70

*NF - No Fail within limits of study

2to

CHAPTER (8) - Linearised Displncement-bøsed Arnlysis

Table 8.4.6 Taft Analysis Comparison: 4.0m Height Wall

GEOMETRY OVER.BURDEN

(MPa)

WALLCONDITION RIGIDBODY

G)

SEMIRIGID

G)

THA DBA(r)

(mm)(h)(m)

(referFigure6.4.12)

AG)A^ ^QlA^

ToEQ PGAG)

f.n(Hz)

>FREQToEQ

>FREQPGAk)

50 4 0 NEW 6Vo 28Vo o.05 0.04 4ïo/o 0.07 o.88 50% 0.0950 4 0 MOD I37o 4OVo 0.05 0.03 4270 0.08 o.74 SOY' 0.0950 4 0 SEV 2OVo SOVo 0.05 0.03 58Uo 0.10 0:64 4g7o 0.0750 4 0.075 NEW 67o 287o 0. t6 0.11 TOYo 0.13 1.2õ 60% 0.11

4 0.075 MOD l3Vo 40Vo 0.16 0.09 60% o.11 1.06 sOVò 0.0950 4 0.075 SEV 2OVo 50Vo 0.16 0.o8 SAYI 0.10 0.92 50o/o 0.0950 4 0.15 NEW 6Vo 28Vo 0.26 0.19 Ez"/o 0.15 1.55 9OYo 0.1650 4 0.15 MOD l3Vo 4O7o o.26 0.16 73% o.t3 1.31 85Yo 0.1550 4 0.15 SEV 2OVo 50Vo 0.26 0.13 6AUo o.12 f.13 5O"/o 0.0950 4 0.25 NEW 6Vo 28Vo 0.40 0.29 86Uö 0.15 1.01 SOYo 0.0950 4 0.25 MOD 13Vo 4OVo 0.40 o.24 9Oe/o 0.16 1.58 95o/" o.'1750 4 0.25 SEV 2OVo 5OVo 0.40 o.20 76"/o 0.14 1.36 9OYo 0.16110 4 0 NEW 6Vo 28Vo 0.11 0.08 100"h 0.18 O¡EE 11'gUo 0.20110 4 o MOD l3Vo 4OVo o.11 0.07 f05% o.19 o.74 1O5e/o 0.19110 4 0 SEV 2OVo 5OVo 0.11 0.06 lOge/o 0.18 O:64 80% 0.14110 4 0.075 NEW 6Vo 28Vo 0.34 0.25 1il.O"/o 0.30 1.2e 11O7o o.20110 4 0.075 MOD l3Vo 4OVo 0.34 o.21 lV5"/o 0.31 1.O6 11O7o 0.20110 4 0.075 SEV 2O7o 5OVo 0.34 0.17 125o/o o.22 0.92 1,100h 0.20ll0 4 0.15 NEW 6Vo 28Vo 0.58 0.42 17Oo/" o.30 1.55 1900h 0.34110 4 0.15 MOD 13Vo 40Vo 0.58 0.35 185c/o 0.33 1.31 19070 0.34110 4 o.15 SEV 2OVo 5OVo 0.58 0.29 145o/o o.26 1 .13 0.20il0 4 o.25 NEW 6Vo 28Vo 0.89 0.64 23O/o o.41 1.01 1'1Oo/e 0.20ll0 4 0.25 MOD l3Vo 4O7o 0.89 0.53 21OUo 0.38 1.58 19O'/o o.34ll0 4 0.25 SEV 2OVo 5OVo o.89 o.44 185Yo 0.33 1.36 r90% 0.34220 4 0 NEW 6Vo 28Vo o.22 0.16 2D5o/o 0.37 O;EE 22OYo 0.39220 4 0 MOD 13Vo 4OVo o.22 0.13 lVSVo 0.31 o.74 21O7o 0.38220 4 0 SEV 2OVo 5O7o 0.22 o.11 185% 0.33 0.64 15O'/o o.27220 4 0.075 NEW 6Vo 287o 0.69 o.49 285e/o 0.51 1.26 25O'/o o.45220 4 0.075 MOD 13Vo 40Vo 0.69 0.41 315"/" o.56 1.06 22OYo 0.39220 4 0.075 SEV 2OVo 50Vo 0.69 0.34 25OYo 0.45 0.92 21Oo/" o.38220 4 0.15 NEW 6Vo 28Vo 1.15 0.83 380% 0.68 f .55 3AO7o 0.68220 4 0.15 MOD 13Vo 407o 1.15 0.69 385% 0.69 1.31 3SO"h 0.68220 4 0.15 SEV 2OVo 5O7o 't. t5 0.58 300"h 0.54 1 .13 38096 o.68220 4 0.25 NEW 6Vo 28Vo 1.78 1.24 47Dch 0.84 1.0t 6OO"/o 1.43

4 0.25 MOD 13Vo 4O7o 1.78 1.O7 550% o.99 1.58 3AOYI 0.68220 4 0.25 SEV 2OVo 5OVo 1.78 0.89 365% 0.65 1.36 38O"/" 0.68

*NF - No Fail within lirnits of study

2tr

CHAPTER (8) - Linearised Displacement-based Analysis

Table 8.4.7 Pacoima Dam Analysis Conrparison: l.5m Height Wall

*NF - No Fail within limits of study

GEOMETRY OVER-BURDEN

(MPa)

WALL CONDITION RIGIDBODY

G)

SEMIRIGID

G)

THÄ DBA(t)

(mm)(h)(m)

(referFigure6.4.12)

4ú)À."

ae)A*

VoßQ PGAG)

Í.n(Hz)

>FREQVoEQ

>FREQPGA

(e)

50 1.5 0 NEW 6"/" 28o/" 0.13 0.10 43Yo 0.19 1.45 SgYo o.22

50 1.5 0 MOD 'l3Yo 4O"/o 0.13 o.08 33% 0.14 1.21 SOYo o.22

50 1.5 0 SEV 20% 50/. 0.13 0.07 48Yo o.21 1.04 35"/o 0.15

50 1.5 0.075 NEVT 6Vo 28o/" 0.89 0.64 118"h 0.51 2.4¿I 100% 0.43

50 1.5 0.075 MOD 13o/" 40% o.89 o.53 97% 0.42 2.36 7O7o 0.30

50 1.5 0.075 SEV 2Oo/" 50y. 0.89 0.44 67Uo o.29 2.O4 65"/c 0.28

50 '1.5 0.15 NEW 6"/o 28% 1.64 1.18 NF NF 3.74 25.O?/" 1.08

50 1.5 0.'t5 MOD 13% 40% 1.64 o.99 136% 0.59 3:12 140e/o 0.61

50 1.5 0.15 SEV 2Oo/" 50% 1.64 o.82 1sOYo 0.5tt 2.69 85"/" 0.37

50 't.5 0.25 NEW 6% 28"/o 2.65 't.91 NF NF 4.62 zfJlJ7o 1.21

50 't.5 0.25 MOD 13% 4Oo/o 2.65 1.59 NF NF 3:9 28OVo 1.21

50 1.5 0.25 SEV 2O"/o 50o/o 2.65 1.33 163% 0.71 3.37 175'h 0.76

ll0 'L5 0 NEW 6"/" 28"/o 0.29 0.2'l 105% 0.46 1.45 115% 0.50

110 1.5 0 MOD 'lSYo 40% 0.29 o.18 I 057c 0.46 1.21 125Vo 0.54

110 '1.5 0 SEV 2Oo/" 50/" 0.29 0.15 7veh 0.30 1.04 75o/o 0.33

110 1.5 0.075 NEW 6"/o 28% 1.95 1.41 340"h 1.48 2.84 22O"/" 0.95

110 1.5 0.075 MOD 13"/o 4OVo 't.95 1.17 28O"/o 1.21 2.3õ 0.65

ll0 1.5 0.075 SEV 20% 50"/" 1.95 0.98 2154/o 0.93 2.O4 13OYo o.56

110 1.5 0.15 NEW 6% 28% 3.62 2.60 NF NF 3.74 NF NF

110 1.5 0.'t5 MOD 13"/" 4O"/o 3.62 2.17 460"/o 2.00 3.12 300% 1.30

110 1.5 o.15 SEV 20% 50"/ 3.62 1.81 430"/" 1.87 2.69 2OO"/o 0.87

110 1.5 o.25 NEW 6Y" 28% 5.83 4.20 NF NF 4,62 NF NF

110 1.5 0.25 MOD 13"/" 40o/o 5.83 3.50 NF NF 3.9 NF NF

ll0 1.5 o.25 SEV 20% 50% 5.83 2.92 NF NF 3.37 4OO7o 't.74

220 1.5 0 NEVT 6Yo 28% 0.59 o.42 325"/" 1.4',1 1.45 225"h 0.98

220 1.5 0 MOD 13% 4Ùo/o 0.59 0.35 225Yo 0.98 1.21 27s%o 1.19

220 't.5 0 SEV 2O"/o 50% 0.59 0.29 135% 0.59 1.O4 14O"/" 0.61

220 1.5 0.075 NEVT 6% 2A7o 3.91 2.81 NF NF 2.44 425"/" 't.84

220 1.5 0.075 MOD 13% 4Oo/o 3.91 2.35 500% 2.17 2.36 28OYo 1.21

220 1.5 0.075 SEV 2O"/o 50o/o 3.91 1.95 43O"/o 1.47 2.Ott 260% 1.13

220 1.5 0.15 NEW 6% 28"/o 7.23 5.2'l NF NF 3.74 NF NF

220 1.5 o.15 MOD 13% 40% 7.23 4.U NF NF 3.12 NF NF

220 1.5 0.15 SEV 2O"/o 500/" 7.23 3.62 600% 2.60 2.69 375"/" 1.63

220 1.5 0.25 NEW 6% 2fj"/o 11.66 8.40 NF NF 4.62 NF NF

220 1.5 o.25 MOD 13% 40% 11.66 7.OO NF NF 3.9 NF NF

220 1.5 0.25 SEV 2Oo/" 50% 11.66 5.83 NF NF 3.37 NF NF

212

CHAPTER (8) - Lineørised Displacement-bøsed Analysis

Table E.4.8 Pacoirm Dam Analysis Conrparison: 3.3m Height Wall

GEOMETRY OVER-BURDEN

(MPa)

1VALL CONDITION RIGIDBODY

G)

SEMIRIGID

G)

THA DBA(t)

(mm)ft)(m)

(referFigure6.4.12)

AG)4* ^(2)A^

ToEQ PGAG)

.f.n(Hz)

>FREQToEQ

>FREQPGAk)

50 3.3 0 NEW 6Vo 28% 0.06 0.04 29"/o 0.13 o.96 35"/o 0.1550 3.3 0 MOD 13o/o 4Oo/" 0.06 0.04 ¿ |"/c o.12 0.81 3Ùo/o 0.1350 3.3 0 SEV 20% 50o/o 0.06 0.03 33Uo 0.14 o.7 SOUI 0.1350 3.3 0.075 NEW 60/" 28"/" 0.22 0.16 4TYo 0.20 1.46 5O!/o 0.2250 3.3 0.075 MOD 13% 4Oo/o o.22 0.13 36"/" o.16 1.23 50"/" o.2250 3.3 o.075 SEV 2Oo/o 5O"/" o.22 0.11 33Yo 0.14 1¡06 35"h 0.1550 3.3 0.15 NEW 6o/" zAVo 0.37 0.27 5BUo 0.25 1.82 6Ðolo 0.2650 3.3 0.15 MOD 13% 40% 0.37 o.22 46"/o 0.20 1.54 55o/o 0.2450 3.3 0.15 SEV 20% 5Oo/" o.37 0.19 49/" 0.21 1.33 50"/" o.2250 3.3 o.25 NEW 6% 28% 0.58 0.42 ATUo 0.38 2.22 607o o.2650 3.3 0.25 MOD 13% 40"/" 0.s8 0.35 63% o.27 1.87 6OVo 0.2650 3.3 o.25 SEV 2oo/o SOVo 0.58 0.29 49"h 0.21 1.62 55"h o.24110 3.3 0 NEW 6% 28% 0.13 0.10 6O."/o 0.35 0:96 7Oe/o 0.30ll0 3.3 0 MOD 13Yo 4Oo/" 0.13 0.08 65% 0.28 o.81 TOYo 0.30110 3.3 0 SEV 2Oo/" 5Oo/" 0.13 0.07 g7o o.22 o,7 70V" 0.30ll0 3.3 o.075 NEV/ 6% 28o/" 0.48 0.34 Í05% 0.46 1.46 l:1Se./o 0.50110 3.3 0.075 MOD 13o/" 40% 0.48 0.29 9.57o 0.41 1.23 1157o 0.50ll0 3.3 0.075 SEV 20% 50% 0.48 o.24 75o/o 0.33 1:06 7Sc/o 0.33110 3.3 0. t5 NEW 6% 28o/o 0.82 0.59 150% 0.69 1.42 135o/o 0.s9110 3.3 0.15 MOD 13o/" 4oo/o 0.82 0.49 1zOYo 0.52 1.54 125Yo 0.54ll0 3.3 0.15 SEV 2O"/o 5Oo/o 0.82 o.41 1OO7o 0.43 1.33 11iYo 0.50110 3.3 0.25 NE}V 6% 28% 't.28 0.92 215o/o 0.93 2.22 135o/o 0.59110 3.3 o.25 MOD 13% 4O"/o 1.28 o.77 ISOYo 0.78 1.87 f3O7o 0.56ll0 3.3 o.25 SEV zOV" 50% 't.28 o.64 1sOUo 0.56 1.62 1sOYo 0.56220 3.3 0 NEIù/ 6V" 284/o o.27 o.19 17O"/o 0.74 o.96 140c/c 0.61220 3.3 0 MOD 13o/o 40o/o o.27 0.16 125o/o o.54 O:81 13Ùo/o o.56220 3.3 0 SEV 20% 50% o.27 0.13 1OsYo 0.46 o.7 11sYo 0.50220 3.3 0.075 NEW 6o/" zAV" 0.95 0.69 ZIOUo 0.91 1.46 220"h 0.95220 3.3 0.075 MOD 13% 4Oo/" 0.95 0.57 2OOo/o 0.87 1.23 14Ùo/o 0.61220 3.3 o.o75 sEv 20o/" 50"Â 0.95 0.48 15Ùo/o 0.65 1.06 150Y" 0.65220 3.3 0.15 NEW 6o/o 28"/" 1.64 1. t8 325Yo 1.41 1.82 2607o 1.13220 3.3 0.15 MOD 134/o 40o/o 1.64 o.98 29OUo 't.26 1.54 26OYo 1.13220 3 o.15 SEV 2Oo/o SOVo 1.64 0.82 190U" o.82 1.33 26lJ7o 1.13220 3.3 o.25 NEW 6/" zAVo 2.55 1.84 435?/o 1.89 2.22 275'/o 1.19220 3.3 0.25 MOD 13"/" 4Oo/o 2.55 1.53 4257o 1.U 1.87 26OVo 1.13220 3.3 0.25 SEV 2Oo/o 5O"/" 2.55 1.28 265% 1.15 1.62 26OYo 1.13

*NF - No Fail wirhin limirs of study

213

CHAPTER (8) - Linearised Displacement-based AnøIysis

Table 8.4.9 Pacoinra Dam Analysis Conrparison: 4.0m Height Wall

*NF - No Fail within limits of study

GEOMETRY OVER-BURDEN

(MPa)

WALL CONDITION RIGIDBODY

G)

SEMIRIGID

G)

THA DBA(t)

(mm)(h)(m)

(referFigure6.4.12)

^(1)A^a(2)4^

ToEQ PGAG)

f"n(IIz)

>FREQVoEQ

>FREQPGA(e)

50 4 0 NEW 6% 2a% o.05 0.04 36/" 0.16 0.88 SOYI 0.13

50 4 0 MOD 13o/" 40% 0.05 0.03 23"/o 0.10 o.74 zAYo o.12

50 4 0 SEV 2O"/o 50% 0.05 0.03 31% 0.13 0.64 28e/o 0.12

50 4 0.075 NEW 6"/0 28"/o o.1tt 0.11 40"/" 0.17 1.26 55Yo 0.24

50 4 o.075 MOD 13o/" 40% 0.16 0.09 32"/o 0.14 r.oõ 35"fo 0.1 5

50 4 0.075 SEV 2O"/" 50% 0.16 0.08 33"/" 0.14 0.92 3O"/o 0.13

50 4 0.15 NE\M 6"/o 28Y" o.2tt 0.19 53V" 0.23 1.55 55Yo o.24

50 4 o.15 MOD 13o/" 40% o.26 0.16 37Uo 0.1tt t.3t slJ"h 0.22

50 4 0.15 SEV 2O"/o s0% 0.26 0.13 47Vo 0.20 1.13 45Uo 0.20

50 4 0.25 NEVT 6"/" 28% o.40 0.29 60/" 0.26 t.0f 6O"/o 0.26

50 4 o.25 MOD 13"/" 40% 0.40 0.24 48Yo 0.21 1.58 55% 0.24

50 4 0.2s SEV 2O"/o 50% o.40 o.20 5O1" 0.22 1.36 50?/o 0.22

110 4 0 NEW 6% 28% o.11 0.08 70e/" 0.30 0.88 70% 0.30

110 4 0 MOD 13o/" 40% 0.11 0.07 50"h o.22 o.74 70% 0.30

110 4 0 SEV 2O"/o 50% 0.11 0.06 7Oe/o 0.30 0.64 7lJ"h 0.30

ll0 4 0.075 NEW 6o/o 28"/o 0.34 0.25 85"h 0.37 1.26 115"/o 0.50

110 4 0.075 MOD 13% 40% 0.34 o.21 lSYo 0.33 r.06 75% 0.33

110 4 0.075 SEV 2Oo/o 5O"/" 0.34 o.'t7 TQYo 0.30 0.92 TOYo 0.30

110 4 0.15 NEV/ 6Vo 28o/" 0.58 0.42 12O7o 0.52 1.55 125Yo 0.54

110 4 0.15 MOD 13"/" 40% o.58 o.35 99"/o 0.39 1.31 115"/o 0.50

110 4 0.15 SEV 2oo/o 5O"/o 0.58 0.29 80?/o 0.35 1 .13 100% 0.43

r10 4 0.25 NEW 6% 280/ 0.89 0.64 17sch 0.76 1.O1 130"/" 0.56

110 4 o.25 MOD 1sVo 4O"/" 0.89 0.53 130o/o 0.56 1.58 130% 0.56

110 4 o.25 SEV 20"/" 50% 0.89 o.44 105% o.4tt f .36 115% 0.50

220 4 0 NEW 60/" 28"/" o.22 0.16 135e/o 0.59 0.88 135e/o 0.59

220 4 0 MOD 13"/o 40% 0.22 0.13 125Vo 0.54 o.74 125Yo 0.54

220 4 0 SEV 2O"/o 50% o.22 0.11 13s% 0.s9 0.64 12O7o 0.52

220 4 0.075 NEIW 6Y" 2A% o.69 0.49 20O."/" 0.87 1.26 22OYo 0.95

220 4 0.075 MOD 13"/o 40% 0.69 0.41 155% 0.67 1.06 r50% 0.65

220 4 0.075 SEV 2O"/o 5O"/o o.ttg 0.34 135"/o 0.59 0.92 135% 0.59

220 4 0.15 NEV/ 6% 2A% 1.15 0.83 255"/" 1.'t 1 1.55 255% 1.11

220 4 0.15 MOD 13o/o 40o/o 1.15 0.69 225o/o 0.98 1.31 220"/" 0.95

220 4 0.15 SEV 2O"/o 5O"/o 1.15 0.58 165% 0.72 1.13 19OYo o.a2

220 4 o.25 NEW 6o/" 28"/" 1.18 1.24 345"/" 't.50 1.01 260% 1.13

220 4 o.25 MOD 13% 40o/o 1.78 1.07 31Oo/o 't.34 1.58 260% 1.13

220 4 0.25 SEV zOV" 50o/o 1.78 0.89 215V. 0.93 1.36 220"h 0.95

2t4

CHAPTER (8) - Linearísed Displacement-based Analysis

Table 8.4.10 Nahanni Analysis Conrparison: l.Sm lleight WaltGEOMETRY OVER.

BURDEN(MPa)

\ryALL CONDITION RIGIDBODY

G)

SEMIRIGID

G)

THA DBA(r)

(mm)(h)(m)

(referFigure6.4.12)

AG)4^

AQ)4^

VoEQ PGAG)

l.n(Hz)

>FREQToEQ

>FREQPGAG)

50 1.5 o NEW 60/o 28Y" 0.13 0.10 24Ùe/o 0.55 1.45 400% 0.9150 1.5 0 MOD 13"/õ 4OV" 0.13 0.08 41Oe/o 0.94 1.21 400?/o 0.9150 1.5 0 SEV 2Oo/" S0o/o o.13 0.07 500% 1.14 1.04 400"h 0.9150 1.5 0.075 NEW 6Yo 28T" 0.89 0.64 33O"/" 0.75 2.84 475"/o 1.09

1.5 0.075 MOD 13o/" 4Ùo/o 0.89 0.53 32OYo 0.73 236 420% 0.9650 1.5 0.075 SEV 20% 50% 0.89 o.44 41och 0.94 2.W 41Oe/o 0.9450 1.5 0.15 NEW 6% 28o/o 1.64 1.18 38OYo 0.87 3.74 6007o 1.3750 1.5 0.15 MOD 13/' 4O"/" 1.64 0.99 360% o.a2 3.1,2 550e/" 1.2650 1.5 0.15 SEV 20% 50% 1.64 o.82 3$OYo 0.78 2.69 420"h 0.9650 1.5 o.25 NETW 6Y" 28o/" 2.65 1.91 4OO"/" 0.91 4:62 900% 2.0650 1.5 0.25 MOD 13Vo 40% 2.65 1.59 NF NF 3.9 750eh 1.7150 1.5 0.25 SEV 20% SOT' 2.65 1.33 NF NF 3.37 6007o 1.37110 1.5 0 NEW 6a/o 28Yo o.29 o.21 55OYo 't.26 1.45 900% 2.06110 't.5 0 MOD 13% 40e/o 0.29 0.18 900% 2.06 1.21 900% 2.06110 1.5 0 SEV zOV" SOY" 0.29 o.15 1050% 2.40 1-04 900e/o 2.06110 1.5 0.075 NEW 6% 28o/o 1.95 1.41 7íOVo 1.71 2.84 900% 2.06110 't.5 o.075 MOD 13% 4Oo/" 1.95 1.17 9OO"/" 2.06 2.36 900% 2.06ll0 1.5 0.075 SEV 2Oo/" 50% 1.95 0.98 7sOYo 1.7'l 2.O4 900% 2.06ll0 1.5 0.f 5 NEW 6"/o 28% 3.62 2.60 NF NF 3.V4 1500% 3.43110 't.5 0.15 MOD 13% 40Yo 3.62 2_'t7 950e/" 2.'t7 3.1.2 1200"/o 2.74ll0 1.5 0.15 SEV 2O"/o s0% 3.62 1.81 E50% 1.94 2.69 lOOO7o 2.24110 1.5 0.25 NEW 6Vo 28% 5.83 4.20 NF NF 4.62 NF NFll0 1.5 o.25 MOD 13% 4Oo/" 5.83 3.50 NF NF 3.9 16O0e/¿ 3.66ll0 1.5 o.25 SEV 2Oo/" 50% s.83 2.92 NF NF 3.37 1300% 2.97220 1.5 0 NEW 6% zAVo 0.59 o.42 11OO/" 2.51 1.45 l76Oo/" 4.02220 1.5 0 MOD 13Vo 40% 0.s9 0.3s IAOOUo 4.'t 1 1.21 17öO7o 4.02220 1.5 0 SEV 2Oo/" 5Oo/" 0.59 o.29 2200yo 5.03 r.04 176OUo 4.O2220 1.5 0.075 NEW 6% 28o/" 3.91 2.81 14OOYI 3.20 2.Vt NF NF220 1.5 0.075 MOD 13"/o 4oo/o 3.91 2.35 r3u¡% 2.97 2.36 1800% 4.11220 1.5 0.075 SEV 20% 50% 3.91 't.95 1600% 3.66 2.O4 IAOOYI 4.11220 1.5 0.15 NEW 6% 28% 7.23 5.21 NF NF 3.74 NF NF220 1.5 0.15 MOD 13"/o 4OV" 7.23 4.U zOltOTo 4.57 3.12 NF NF220 1.5 0.15 SEV 20% 50% 7.23 3.62 1700ch 3.88 2.69 19OOYI 4.34220 1.5 0.25 NEW 6% 28% 11.66 8.40 NF NF 4.62 NF NF220 1.5 o.25 MOD 13y" 4Ùo/o 1 1.66 7.00 NF NF 3.9 NF NF220 1.5 0.25 SEV zOVo 50% 11.66 5.83 NF NF 3.37 NF NF

*NF - No Fail within limits of study

215

CHAPTER (8) - Linearised Displacement-based Annlysis

Table E.4.11 Nahanni Analysis Conparison: 3.3m lleight \{all

GEOMETRY OYER-BURDEN

(MPa)

WALL CONDITION RIGII)BODY

G)

SEMIRIGII)

(e)

THA DBA(t)

(mm)(h)(m)

(referFigure6.4.12)

A(ÐA^ ^3rA*

VoEQ PGAG)

Í.n(Hz)

>FREQToEQ

>FREQPGAG)

50 3.3 0 NEV/ 6o/o 28o/o 0.06 0.04 360% 0.82 0.96 4OO"/o 0.91

50 3.3 0 MOD 13"/o 4O"/o o.ott o.o4 500% 1.14 O;El 4OO7o 0.9'l

50 3.3 0 SEV 20% 50% 0.06 0.03 NF NF o.7 4OOYI 0.91

50 3.3 0.075 NEV/ 6Yo 28Yo o.22 0.16 360% 0.82 1.46 400"h 0.91

50 3.3 0.075 MOD 'l3Yo 40% o.22 0.13 42O/" 0.96 1.23 4OOe/" o.91

50 3.3 0.075 SEV 20% 50"/o o.22 0.11 44OYo 1.01 1.06 400?/o 0.91

50 3.3 0.15 NEW 6% 28T" 0.37 o.27 360% o.82 1.82 4OO"/o 0.91

50 3.3 0.15 MOD 131" 40% 0.37 0.22 340?/" 0.78 1.54 400% 0.91

50 3.3 0.15 SEV 2OVo 50% o.37 0.19 28o9h 0.64 1.33 4OOUo o.91

50 3.3 0.25 NEV/ 6Y" 28% 0.58 0.42 360% 0.82 2.22 41vch 0.94

50 3.3 0.25 MOD 13o/" 4Oo/" 0.58 0.35 NF NF 1.r 4OOo/o 0.91

50 3.3 0.25 SEV 20% 50% 0.58 0.29 360% 0.82 4OOe/o 0.91

110 3.3 0 NEW 6o/" 28% 0.13 0.10 1050e/o 2.40 t 900e/" 2.06

110 3.3 0 MOD 13"/o 4OYo 0.13 0.08 NF NF 90Oe/o 2.06

ll0 3.3 0 SEV 2O"/" 50% 0.13 0.07 NF NF o.7 900e/o 2.06

110 3.3 0.075 NEW 6% 28% 0.48 0.34 1O5OYI 2-40 1.¡ 9OO9/o 2.06

110 3.3 o.075 MOD 13% 40% 0.48 0.29 600% 1.37 2.06

110 3.3 0.075 SEV 2OV" 5O"/o o.48 o.24 ro00% 2.24 r.06 2.06

110 3.3 0.15 NEW 60/" 24" o.a2 0.59 1050% 2.40 9OOe/o 2.06

110 3.3 0.15 MOD 13% 40o/o 0.82 0.49 980% 2.24 1.54 900% 2.06

ll0 3.3 0.15 SEV 2O"/o 50% o.a2 o.41 1000% 2.28 Lr 9009/o 2.06

110 3.3 o.25 NEV/ 6Vo 24"/o 1.28 0.92 1050% 2.40 2.22 9OOe/" 2.06

110 3.3 0.25 MOD 13% 40% 1.28 0.77 75O"/o 1.71 1.87 900% 2.06

110 3.3 0.25 SEV 2O"/o 50"/" 1.28 0.64 1000% 2.28 1.1 2 2.06

220 3.3 0 NEW 6"/o 24"/o o.27 0.19 2O5O"/" 4.68 0.96 1.76070 4.O2

220 3.3 0 MOD '13"/o 40% o.27 0.16 2O5OVI 4.68 o.E1 1760% 4.02

220 3.3 0 SEV 2Oo/" 50% 0.27 0.13 NF NF o.7 176OUo 4.O2

2ZO 3.3 o.075 NEfW 6o/" 2Bo/" 0.95 0.69 2050% 4.68 L46 176OYo 4.O2

220 3.3 0.075 MOD 13% 40"/" o.95 o.57 1600e/o 3.66 1.23 176O0/" 4.O2

220 3.3 0.075 SEV 20% 50% 0.95 0.48 2OOO"/o 4.57 1.06 17607o 4-O2

220 3.3 0.15 NEV/ 6% 28"/o 1.64 1.18 2O5O"/o 4.68 1.82 1800% 4.11

220 3.3 0.15 MOD 13Vo 4O"/o 1.tt4 o.98 1800% 4.1'l f .54 1800% 4.'t1220 3.3 0.15 SEV 2oo/o 50% 1.64 0.82 2000% 4.57 1.33 17607o 4.O2

220 3.3 0.25 NEW 6o/" 28% 2.55 1.84 2100% 4.80 2.22 1800% 4_11

220 3.3 o.25 MOD 13"/o 4O"/o 2.55 1.53 15007" 3.43 1.87 18000/" 4.'t1220 3.3 0.25 SEV 20% 50% 2.55 1.28 2O5O"/o 4.68 1.62 1600% 4.',t1

*NF - No Fail within limits of study

216

CHAPTER (8) - Linearised Displacement-based Annlysis

Table 8.4.12 Nahanni Analysis Comparison: 4.0m lleight rildl

*NF- No Fail within limits of study

GEOMETRY OVER.BURDEN

(MPa)

WALL CONDITION RIGIDBODY

G)

SEMIRIGID

G)

THA DBA(t)

(mm)(h)(m)

(referFigure6.4.12)

ag)4^ ^(2\4^

ToEQ PGAG)

f.n(Hz)

>FREQVoEQ

>FREQPGAG)

50 4 0 NEW 6% 28% 0.05 0.04 NF NF 0.88 4OOYI 0.9150 4 0 MOD 13Y" 40% o.05 0.03 NF NF o.74 4OOYI 0.9150 4 0 SEV zOVo 50% 0.05 0.03 24O'/o 0.55 0.il 4OO/o 0.9150 4 0.075 NEW 6"/" 28% 0.16 0.11 3E096 o.87 1.26 4OO"/" 0.9150 4 0.075 MOD 13% 4O/o 0.16 0.09 41OYo 0.94 1.06 4g0e/o 0.9150 4 0.075 SEV 20% 50% 0.16 0.08 NF NF o92 4OOTI 0.9150 4 0.15 NEV/ 60/o 28% o.26 0.19 SEO"/o 0.87 1.55 4OOYo 0.9150 4 0.1s MOD 13o/" 4Oo/" 0.26 0.16 26O"/o 0.64 1.31 4OO"/o 0.9150 4 0.15 SEV 20Io 50% o.26 0.13 420o/o o.96 1.13 4OOo/o 0.9150 4 0.25 NEW 6"/o 28% 0.40 0.29 3E07ö o.87 1.01 4OOo/o 0.9150 4 o.25 MOD 13Y" 40io 0.40 o.24 380o/o 0.87 1.58 4OO"/o 0.9150 4 o.25 SEV 2Oo/" 5O"/" 0.40 0.20 3OOe/o 0.69 1.36 4OOo/o 0.91ll0 4 0 NEV/ 6"/o 28"/o 0.11 0.08 fO5O7o 2.40 0.88 900% 2.06110 4 0 MOD 13% 4Oo/" 0.11 o.o7 NF NF 0.74 900% 2.06ll0 4 0 SEV 2Oo/" 5Oo/" 0.11 0.06 NF NF 0.õ4 900% 2.06110 4 0.075 NEW 6/o zAVo 0.34 0.25 r050% 2.40 1.26 90O.e/o 2.06ll0 4 0.075 MOD 13V" 40% 0.34 0.21 SOOYo 1.14 1.06 90070 2.06110 4 0.075 SEV 20% 5Oo/" 0.34 o.17 1000e/o 2.28 o.g2 9POYo 2.06ll0 4 0.'t5 NEIù/ 6o/o 28% o.58 o.42 1050e/o 2.40 r.55 90OYo 2.06ll0 4 0.15 MOD 1sYo 40% 0.58 0.35 759'/o 1.71 1.31 9OO"/" 2.06ll0 4 0. t5 SEV 2OYo 50% 0.58 o.29 55OYo 1.26 l.l3 900% 2.06110 4 0.25 NEW 60/" 28% 0.89 o.64 1O5OYI 2.40 1.01 900% 2.06ll0 4 0.25 MOD 13o/" 4OV" 0.89 0.53 11OOo/o 2.51 r.5E 90OYo 2.06110 4 o.25 SEV 2OYo 50% 0.89 o.44 800% 1.83 1;36 900% 2.06220 4 0 NEW 6% 28o/o 0.22 0. t6 NF NF 0.88 176OY" 4.O2220 4 0 MOD 13% 4Oo/" Q.22 0.13 NF NF o.74 1760e/o 4.O2220 4 0 SEV 2Oo/" 5Oo/" 0.22 0.11 NF NF 0.64 1760eh 4.O2220 4 0.075 NErty 6"/o 28% 0.69 0.49 2000/" 4.57 1.26 176OYo 4.02220 4 0.075 MOD 13o/o 40o/o 0.69 0.41 110070 2.51 r.0õ 17.6OU. 4.02220 4 0.075 SEV 2Oo/" 50% 0.69 0.34 r950% 4.45 o.92 l76Ùyc 4.O2220 4 0.15 NE\ry 6% 28o/" 1.15 0.83 2OOO/o 4.57 1.55 176o0/o 4.02220 4 0.15 MOD 13% 4Oo/o 1.15 0.69 17OOYo 3.88 f .31 176lJ"h 4.O2220 4 0.15 SEV 20% 50% 1.15 0.58 11OOo/c 2.51 1.13 176OYo 4.O2220 4 o.25 NEW 60/" 28% 1-78 1.28 2OOOo/o 4.57 1.01 1800% 4.11220 4 0.25 MOD 13% 4Oo/o 1.78 1.07 1600% 3.66 1.s8 176lJ"h 4.O2220 4 o.25 SEV 2Qo/o 5Oo/" 1.78 0.89 1600% 3.66 1.36 176OYo 4.O2

217

9. SUMMARYAND CONCLUSIONS

This report has presented the findings of an investigation into the weak links in the

seismic load path of unreinforced masonry buildings specifically aimed at Australian

masoffy construction being:

(1) The limited force capacity of connections betvveen floors and walls, in particular the

friction dependent connections containing damp proof course (DPC) membranes and

(2) the out-of-plane failure of walls in the upper stories of URM buildings.

The two prime objectives of this investigation were thus to provide designers with the

appropriate tools to avoid these brittle 'weak link' failure modes in the design of new and

the assessment of existing URM buildings. Once adequate seismic load paths have been

developed and these 'weak links' successfully avoided it is expected that carefully

designed, detailed and constructed regular URM buildings will behave adequately during

moderate intensity earthquakes.

The first of the above objectives was fulfilled by an extensive series of shaking table tests

on URM connections containing DPC membrane typical found in Australian masonry

construction being aimed at providing data on the connections dynamic capacity

applicable (refer Chapter 4). The main purpose of these tests was therefore to evaluate

the connection performance under dynamic loading in order to assess their seismic

integrity. Dynamic friction coefficients determined from these tests were then compared

with quasi-static friction coefficients determined by previous research (Griffith et al

1998) to assess to what extent the quasi-statically determined friction coefficients

represented those which could be expected in seismic events. Here it was found that the

dynamic friction coefficients were not more than 20Vo less than those determined quasi-

218

CHAPTER (9) - Summary and Conclusions

statically. Further with the exception of greased galvanised sheets no connection had afriction coefficient less than the 453700-1998 code prescribed design value of 0.3.

The second of the above objectives was achieved by the development of a simplisticrational analysis procedure for face loaded simply supported IJRM walls for practical

applications which considers the essence of the true dynamic response behaviour. Since

the simplified procedure was required to be both user friendly and readily codified it was

developed from the increasingly popular linea¡ised 'Displacement-based' method.

Various boundary conditions for URM walls are often encountered which can

significantly impact on the \ryall's dynamic behaviour. The analysis procedure thereforeneeded to have the ability of easily accounting for these conditions. Also, with poor

quality masonry, lack of maintenance and poor workmanship arising as major issues fromprevious earthquake reconnaissance documentation, the analysis needed to have the

capability of allowing for rotation joint condition over the life of the wall. Both of these

requirements were taken into account by modifications to the modelled F-A relationship(refer Chapter 8). The following paragraphs briefly describe the steps undertaken to

develop this procedure:

To gain a better understanding of the physical process governing the out-of-plane

behaviour of URM walls an extensive series of out-of-plane static and dynamic tests were

undertaken on one-way spanning wall panels as presented in Chapter 6. Test variablesincluded the level of overburden stress and wall aspect ratio, however, only one set ofboundary conditions was examined. Joint degradation was also examined as pa-rt of the

experimental phase.

A comprehensive THA program was then developed to accurately model the dynamic

wall behaviour, as presented in Chapter 7. Here the rocking wall was modelled as a single

degree of freedom (SDOÐ system having a non-linear spring and frequency dependent

damper. The relationships between the real and SDOF systems were determined by

comparison of the dynamic equations of motion. The modelled non-linear spring and

frequency dependent damper were then calibrated by comparison with experimentally

determined F-Â and /-Ç relationships. Results of the THA were then confirmed by

219

CHAPTER (9) - Summary and Conclusions

comparison with experimental results including free vibration tests, single pulse,

harmonic and transient excitation tests.

Following confirmation of the THA, results were used to undertake parametric studies to

further identify key properties of URM wall behaviour without the expense of continued

experimental testing. In total over two hundred thousand THA were completed as part of

this process.

The simplihed analysis procedure was based on the linearised 'Displacement-based'

procedure, used to predict the input excitation required to force the post-cracked URM

wall to incipient instability (refer Chapter 8). For the simplifred analysis, as most

realistic failures are associated with the large displacement amplifications associated with

resonance, the characteristic 'substitute structure' linear stiffness was related to the

effective resonant frequency of the simply supported wall to permit the wall's resonant

behaviour to be modelled. The effective resonant frequency was in turn related to the

average incremental secant stiffness of the failure half cycle. Damping was related to a

constant lowerbound observed during the experimental phase. As this method linearises

a highly non-linea¡ problem it has an inherent degree of inaccuracy for transient

excitations where a 'period lag' between the modelled linear SDOF oscillator and the real

system. Consequently, the suitability and accuracy of using the simplified method was

determined by comparison with THA and experimental results. Although, as expected

some result scatter was observed the correlation was substantially better than that of a

comparison with 'quasi-static' methods which are currently in use. Therefore, with the

provision of suitable safety factors it appears that the proposed linearised DB procedure

in conjunction with a 'quasi-statically' determined lowerbound force provides an

improved method for assessing the dynamic capacity for the design of new and the

assessment of existing URM buildings.

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RIDDINGTON, J., R., ruKEs, P., "A Masonry Joint shear strength rest Method",Proceedings of the Institution of Civil Engineers, 104,1994,pp.267-274RIDDINGTON, J., R., GHAZALI, M, 2., "Hypothesis for shear Failure in MasonryJoints", Proceedings of rhe Institution of civil Engineers, part2,l990, pp.89-102RODOLICO, 8., DOI{ERTY, K., LAM, N., GRTFFITH, M., WILSON, J., "SEiSMiCResponse Behaviour of Unreinforced Masonry Slender \ilalls Revealed By ShakingTable Testings and Time-History Analyses", Proceedings of the 16ù AusgalasianConference on Mechanics of Structures and Materials, Sydney,lgggRoMANo, F., GANDUSCIO, s., zNGoNE, G., "Analysis of Masonry walls Subjectto Cyclic L-oads", Proceedings of the 10th European Conference on EarthquakeEngineering, Vol. 3, Rotterdam, 1995, pp. 1675 - 1680

ROSATO, Donald, V., MATTIA, D., P., ROSATO, Dominick, V., ..Designing withComposites and Plastics: A Handbook", Van Nostrand Reinhold, l99l

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SAA Earthquake Loading Code, AS2l21, Standards Association of Australia, Sydney,1979

SAA Loading Code, Minimum Design Loads on Structures - Part 4 - Earthquake [¡ads,4S1170.4 - 1993, Standa¡ds Australia, Sydney 1993

SAA Masonry Code 453700-1988, Standa¡ds Australia, Sydney 1988

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SAA Masonry Code Commentary, 453700 Supplement l, Standards Australia, Sydney,t99lSAA Strengthening Existing Buildings for Earthquake, 453626 - 1998, StandardsAustralia, Sydney 1998

SAMARASINGHE, W., LAWRENCE, S., J., PAGE,4., W., "Investigations of the Bond'Wrench Method of Testing masonry", Proceedings of the 15th Australasian Conferenceon The Mechanics of Structures and Materials, Melbourne, Victoria, Australia, 1997,pp.651-656

SAÀ4AIù\SINGHE, W., LAWRENCE, S., J., PAGE,4.,'W., "Standardising the Bond'Wrench", Proceedings of the 5th Australasian Masonry Conference, Gladstone,Queensland, 1998, pp. 335-344

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REFERENCES

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REFENZNCES

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REFERENCES

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240

APPENDIX (A): Band Pass Filter Program ForttanTTCode

PROGRAM filtlC Fourier Transform of single real function

INTEGER n, no, isignREAL del, botd, ûopdREAL a(0: I 63 84), ai(O: I 63 84), afdu(O: I 6384), afdf(O: 1 6384)REAL freq(O:16384)REAL del(0:16384)CHARACTER *50 IG[¡, OFIIß

C

'Write(*,*) " BAND PASS FILTER PROGRAM"\Vrite(*,*) " FILTI.Write(*,*) " FILTERS I COLUMN OF DATA"V/riæ(*,*)V/riæ(+,x) "Type filename of input time domain data file (.csv)"Read(*,'(a)') )GILEV/rite(*,*) "Type filename for filtered data output (.csv)"Read(*,(a)') OFII¡Write(*,*) "Type input data time increment (secs)"Read(*,*) delrWrite(*,*) "Type bottom band pass filter frequency"Read(*,*) botdWrite(*,*) "Type top band pass filter frequency @isplacements)"Read(+,+) topdOpen(30,file=XFllE,staûrs='old',err= I I 0)no=O

CC Here the data array is read from external file XFILE

Do 1k=1,16384Read(30,*,END=2) a(k)ai(k)=a(k)no=no+1

I Continuec

Close(30)2 Continue

n=13 Continue

If(no.gLn)thenn=2*ngoto 3

end ifC Anays are augmented with zeros to get a function of 2

Do 4 k=netl, na(k)=O-0ai(k){.0

241

APPENDD( (A)-Band Pass Filter Forrran hogram

4 ContinueC Transform to frequency domain compleæd giving data(n) array

isign=lcall realft(a,n,isþ)Do 5 k=l,n

afdu(k)=¿(þ)5 Continue

C Frequencies a¡e calculatedDo 6 j-l,n/2Freq$=y'(n*del)

6 ContinueC Frequency domain daø is filæredC acceleration band pass filær frequencies

call genfil(a,freq,n,botd,topd)Do 7 k=l,n

afdf(k)=a(k)7 Continue

C Realft is called to perform the inverseC Eansform of the filtered data

isign = -1ca-ll realft(a,n,isign)Do 8 k=l,ndell(k)-del*ka(k)=2+¿1¡¡7n

8 ContinueC Data ouput

Open(35,file=OFILE,staüls='new',en= 1 20)Write(35,*) "INPUT FILENAME : ",XFILEWrite(35,9) del

9 Format ('SAMPIÆ RATE USED IS =',F6.3,'seconds')Write(35, l0) botd, topd

10 Format (tsand pass filter range',F5.2,' Hz -'+,F5.2,TI2')Wriæ135,*¡ "'Write(3 5, *) "FREQUENCY DOMAIN,,,,,TIME DOMAIN"Writ€(35, *) "No.,Frequency,Data,Data,,Time,Data"Data"Write(35,*) ",,unfilt filt,,,unfilt filt"Write(35, l2) afdu(1),afdf(l ),del( 1),ai( 1),a( l)

l2 Format ('1,0,'"F15.3,',',F15.3,',,',F15.3,',',F15.3,',',F15.3)rWrite(35, I 3) freq(n2),afdu(2),afdf(2),detJ¡(2),u(2),a(2)

l3 Format (2,',F15.3,',',F15.3,','"Fl 5.3,',,',F15.3,',',F15.3+,',',Fll.3)Do 14 k=3,n-1,2

Write(3 5, I 5) Þ,,freq(kÍ2- I l2),afdu(k),afdf(k),del(k), ai(k), a(k)rffrite(35, I 5) k+l,freq(V2- 1/Z),afdu(k+l ),afdf(k+ I ),denG+l )

+ ,ai(k+l),a(k+l)15 Format (I4,',',F15.3,',',F15.3,',',F15.3,',,',F15.3,',',F15.3,',+ ',F15.3)

14 Continuelù[rite1*,*¡ " "Wriæ(*,16) no

16 Forma('Number of inputdata lines =',I10)Write(*,17) n

17 Format('Number of ouþut data lines = ',I10)lVriæ(*, *) "PROGRAM RIJN COMPLETED"

100 Stop

242

APPENDD( (A) - Band Pass Filter Fortran Program

110 Vtrire(*,*) 'ERROR OPENING INPUT FILE"105 Stop120 Wriæ(*,*) "ERROR OPENING OUTPUT FILE"

END

PROGRAM filtlsC Fourier Transform of single real function

INTEGER n, no, isignREAL del, botd, topd, æmpREAL a(0: 1 63 84), ai(O: I 63 84), afdu(0: I 6384), afdf(O: 1 6384)REAL freq(0:16384)REAL dell(O:16384)CHARACTER *50)CITIF, OFTÍ F, TEXT

CìVriæ1*,x¡ " "Wriæ(*,*) ¡---------------Write(t,*) " BAND PASS FILTERPROGRAM"Write(*,*) " FILTI"Write(*,*) " FILTERS I COLUMN OFDATA"Write(*,*)Write(*,*) "Type filename of input time domain data file (.csv)"Read(*,'(a)') )GILE\Yrite(*,*) "Type filename for filæred data output (.csv)"Read(*,'(a)') OFILEWrite(*,*) "Type input daø time increment (secs)"Read(*,*) delWriæ(*,*) "Type bottom band pass filter frequency"Read(*,*) botdWrite(*,*) "Type top band pass filter frequency (Displacemens)"Read(*,*) topdOpen(30,file=XFILE,staülrs='old',err= I 10)no=0

CC Here the data array is read from external file )GILE

Do 20 i=I,8read(*,*) TEXTwrite(*,*) TEXT

20 ContinueDo I k=1,16384

Read(30,*,END=2) temP, a(k)ai(k)=a(k)no=noll

I ContinueC

Close(30)2 Continue

n=l3 Continue

If(no.gt.n)thenn=2*ngoto 3

end if

243

APPENDX (A) - Band Pass Filær Forrran Program

C Arrays are augmented with zeros to get a function of 2Do 4 k=noll, n

a(k)=0.0ai(k){.0

4 ContinueC Transform to frequency domain completed giving data(n) array

isign=lcall realft(a,n,isign)Do 5 k=l,n

afdu(k)=¿(ft)5 Continue

C Frequencies are calculatedDo 6 j-l,nl2Freq()=j(n*del)

6 ContinueC Frequency domain data is filæredC acceleration band pass filter frequencies

call genfil(a,freq,n,botd,topd)Do 7 k=l,n

afdf(k)=¿1¡¡7 Continue

C Realft is called to perform the inverseC hansform of the filtered data

isign = -1call realft(a,n,isigrr)Do 8 k=l,ndell(k)del*ka(k)=2*¿1¡¡¡n

8 ContinueC Data ouÞut

Open(35,fiIe=OFILE,stah¡s='new',err= I 20)Write(35,*) "INPUT FILENAME : ",XFILEWriæ(35,9) del

9 Format ('SAMPll RATE USED IS =',F6.3,'seconds')Vfriþ(35, l0) botd, topd

10 Format (tsand pass frlter range',Fí.2,'Hz -'+,F5.2,TI2',)Wriæ(35,*)'"Write(35,+) "FREQIJENCY DOMAIN,,,,,TIME DOMAIN"Write(35, *) "No.,Frequency,Data,Data,,Time,Daa,Daø"Write(35,*) ",,unfilt filt,,,unfilt filt"Write(35, l2) afdu(l),afdf(l ),dell(l ),ai( l),a(l)

l2 Format ('1,0,'¡l 5.3,',',Fl 5.3,',,',F15.3,',',Fl 5.3,',',Fl 5.3)Write(35,13)freq(nl2),afdu(2),af df (2)dell(2),ai(2),a(2)

l3 Format (2,',F15.3,',',F15.3,','"F15.3,',,',F15.3,',',F15.3+,""F11.3)Do 14 k=3,n-1,2

Write(35, I 5) k,frq(H2-l 12),afdu(k),afdf(k),dell(k),ai(k),a(k)Write(35, l5) k+l,freq(lc/2- l/2),afdu(k+l ),afdf(k+l ),dell(k+ I )

+ ,ai(k+l),a(k+l)l5 Format (I4,',',F15.3,',',F15.3,',',F15.3,',,',F15.3,',',F15.3,',

+ ',F15.3)14 Continue

Wriæ1*'*¡ " "Wriæ(*,16) no

16 Format('Number of input data lines =',I10)

244

APPENDD( (A) - Band Pass Filær Fortran Program

Write(*,17) n17 Format('Number of ouþut data lines =',I10)

Write(*,*) "PROGRAM RUN COMPLETED"100 Stopll0 rWrite(*,*) "ERROR OPENING INPUT FILE"105 Stopl20Write(*,*) "ERROR OPENING OUTPUT FILE'

END

SIJBROUTINE genfilt(data,freq,n,bot"top)INTEGER nREAL daø(n), freq(n/2)

C Data in the frequency domain is filteredDo22i=3,¡-1,2

IF (Freq(i2- I /2).LT.bot- 1.0) TmNdata(i)=0.0daø(i+1)=0.0

ELSEIF (keq(l2-I l2).LT.bot-0.5) THENdata(i)=(2.0* (Freq(tl2- U2)-bot+ 1.0) * *2) *data(i)data(i+l )=(2.0*(Freq(i/2- l/2)-bot+1.0)**2)*data(i+1)

ELSEIF (Freq(tl2-I lZ).LT.bot) TI{ENd ata(i)=((-2.0* (Fteq(il2- I l2)-boÐ * *2)+ I )*data(Ðdata(i+ I )=((-2.O*(Freq(i/2 - | l2)-bot)**2)+ I )*data(i+l )

ELSEIF (Frcq(il2-l lL).LT.top) TmNdata(i)=data(i)data(i+1)dara(i+1)

ELSEIF (Fteq(rl2-l l2).LT.top+0.5) TIIENdata(i)=((-2.0*(Frcq(rl2- I l2)-top)**2)+1 )*data(Ðdata(i+ I )=((- 2.0* (Freq(il2- I 12) -top)**2)+ 1 )

*data(i+ I )ELSEIF (Freq(ú2-l l2)IT.topr 1.0) TIIEN

data(i)=(2.0* (Frcqbfz- il2)-toÞ 1.0)* *2)*data(i)data(i+l )=(2.0*(Freq(i/2- 1/2)+op- 1.0)**2)*data(i+l )

ELSEdata(i)=0.0data(i+l)=0.0

ENDIFData(l)=0.0Data(2){.0

22 ContinueEND

245

APPENDD( (A) - Band Pass Filter Fortran Program

SUBROUTINE realf(daø,n,isþ)INTEGER isign,nREAL data(n)

CU USES fourlINTEGER i,it,i2,i3,i4,n2p3REAL cl,c2,hli,hlr,h2i,h2r,wis,wrsDOUBTE PRECISION theta,wi,\4,pi,r4,pr,wr,wremprhera=3. 1 4 I 5 9 265 3 5897 93 dO/dble(n/2)c1{.5if (isign.eq.l) then

c2=-0.5call four I (daø,n12,+ l)

elsec2=0.5theta=-theta

endifwpr=-2.0d0*sin(O.5d0*the6)* *fwpi=sin(theta)wr=l.OdGrwprwi=wpin2p3=n+3do ll i=2,n14i1=2*i-1i2=il+1i3=n2p3-i2i4=i3+1wfs=sngl(wr)wis=sngl(wi)h lr+ I *(dara(i1 Þdata(i3))h 1 i+ I *(data(i2)-data(i4))h2r =- c2* (data(i2lrd ata(i4 ) )h2i<,2+ (daø(i I )- data(i3 ))data(i I )=h I r+wrs *h2r-wis *h2idata(i2)=h I i+wrs*h2i+wis *h2rdata(i3 )=h I r-wrs *h2r+wis *h2idata(i4)=-h I i+wrs*h2i+wis*h2rwtÊmP=wrwewr*wpr-wi*wpi+wrwi=wi*wpr+wtemp *wpi+wi

1l continueif (isign.eq.l) thenhlrdaa(l)data(l)=hlr+data(2)data(2)=hl¡-¿¿¡¿12¡

elsehlrdaø(1)data( I )=c I *(h lr+daa(2))daø(2)=c I *(h lr-daø(2))call four I (data,nn,- l)

endiffeturnEND

C (C) Copr. 1986-92 Numerical Recþs Softn'are 5lP.

246

APPENDX (B): Representative DPC ConnectionTest Results

Direction of Shaking:Normal Stress at Slip Face:

Out-of-plane0.164MPa (31.9k1.I)

o'EÉoEaåÉÞoo€=

v

MiGheigÞt Dirylacement (m)

a(slÞ) Jûst Añer Flrst S[p Ys TlmeFlftcrcd ave amax (after first slþ) = kv = Q.{.{g

ào

EOoE

0.ó

0.4

0.2

0

4.2

4.4

4.6Ilme (secs)

æoq

ôl+cl

clq{Næ\}oo¡r; ç;o¡êì

\o clnìô.¡ ô¡

çôON\o\C'ô¡ ôl

\oa\oôl

ô¡æqì9\o \ool ôl

\oIçd

Figure B I - Stândsrd DPC Connection One Layer of Standard Alcor

qÉ

eo\o

Hystercdc Bebavlourf,Ilte¡ed Ff(mx) = 14kì¡

Rebtlve Jolnt Dbpl¡cement (mm)

20

215gËt0o<f¡.åoçt)

-5

-10

-15:20

247

APPENDD( (B) - Representative DPC Connection Test Resuks

Direction of Shaking:Normal Stress at Slip Face:

Outof-plane0.164MPa (31.9kN)

aÉc)E6)C)GI

Èøâè0c)rtà

0.08

0.06

0.04

0.02

0

-0.02

-0.04-0.06-0.08

-0.1

- u(m)

MWD

rô ìn

Time(secs)

¡(sllp) Jûst After Flrst Slp V'r TlmeIlltcrcd

ave amax (afr€r 6rs¡ sùp) = kv - 0.a7g0.ó

0.4

e o.zêEooE

0

4.2

4.4

{.6Thc (secs)

ú09€

þdìrN(ìæ

æIFF-

úñ\o(' Ëæ

êl\\o oc!rr

Eysteredc BehavlourFllt¿rcd

15 kN

Rehlve Jol¡t Dbplacement (mm)

20

15

102é5o!olzo-5ô

_10

-15

:20

Figure B 2 - Ståndard DPC Connection One Layer of Super Alcor

248

APPENDD( (B) - Representative DPIC Connection Test Results

Direction of Shaking:Normal Stress at Slip Face:

Out-of-plane0.164MPa (31.9k1Ð

Absolute DlsplacerentsBebwC.mnectim

tAboveCm€ctionFirst slip bas ocorcd at ll.7

socs

50,10

î30;20oEr0oËoÉlX -lo

-20

-30

40

Thc (secs)

æ!i \oo\ \oY;ó

æIçq

a(slþ) Jus .lfter trlrst Sllp Y's TlmeItttercd ave amx (after frst sùp) = kv - 0.37g

eéêfooI

0.5

040.3

o.2

0.1

0

4.34.4{.5

The (secs)

Eystereüc BehavlourIllte¡ed

Ff(mx) = 12UV

zëoqê

f¡(Êì.

aÀ

Relalve Jolnt Dþlacement (mn)

Figure B 3 - Standard DPC Connection One Layer of Polyfiash

249

APPENDD( (B) - Represenrarive DPC Connection Test Results

Direction of Shaking:Normal Stess at Slip Face:

Out-of-plane0.164MPa (31.9k1Ð

Abeoluúe ltlsplacementstBelowCo¡neciolt Above Connection

qâ20€oËÊ -zooa940-ãâ{0

{0-100

Tlme (secs)

tct

æ\Éô¡eó

First slip has ooored at 16.4

o6)*\oq

socs

tI

a(slþ) Just mer X'lrct S[p Y's llmeIlltercd

ave arnx (afrer first slip) = þy - 9.36*Aryliur& of actntor c¡as d€€r€asdfu these cycles

19ê

Eo

r

0.5

0.40.3

0.20.1

0{.14.2{.34.44.5

llme (secs)

ët- g€

ô¡nræIÉ

€!.1\o

E¡rtereüc BebavlourIlltered = 12kN

l5

10

z5,¡a

oÊnfaÈ=-5cÀ

-10

-15

Rehüve Jolnt Dþlacement (mm)

Figure B 4 - standard DPC connection one Layer of Dry-cor (Embossed polythene)

250

APPENDIX (C): Representative Slip JointConnection Test Results

Direction of Shaking:Normal Stress at Slip Face:

In-Plane0.18 MPa (N=17.81ò[)

Absolute Dlsplacements tbelow cmnection

aboveænædion40

à20goÉ

Ê¿o340Êt

ã60-80

I¡me (secs)

First slip bas ocqrcd at 24.5 secs

c-dæ

ôl

ocì*NoclN

/

a(sllp) Jost Aftcr trlrst Sllp Y's TlreX'lltered

(aft€r first slip) = kv = 0.,169

3É

EOoE

0.6

o.4

0.2

0

4.2

4.4

4.6Tlme (secs)

c¡a\ocì

\f,o\c;cl

\otl(;c¡

æqscì

Hystereüc Bebavlourtr'lltered Ftuax=7.7kN=amax N

Rel¡lve Jotnt Dbpl¡cement (mm)

10

7.5

5zé 2.soËoèI -r(É!çt -5

:7.5

_10

nrN

Figure C 1- Slip Joint Two layers of Standard Alcor

25t

APPENDD( (C) - Representative Slip Joint Connection Test Results

Direction of Shaking:Normal Stress at Slip Face:

Out-of-Plane0.18 MPa (N=17.8k19

Figure C 2 Slip Jt¡int One layer of Standard Alcor

Absolute Dþlæements tBelowComectimtAboveCmrection

40

30

Ãn€roËoE -tott

È -20Ê -30

40-50

the (cccs)

First stip oq¡¡red at 1255 smnds I

ooq oeo

ofo it o!tñoeN

o09t

s(slþ) Ju6t After Ftrst Sllp V's TlmeFtlt€r€d ave amx (afrer firs slip) - kv - 0.439

úEÀo6ooE

0.5

040.3

0.20.r

0

4.14.2{.34.44.5

Ilme (secs)

æÕ¡

e oIoooge Eç

o\os û\f

o ccl ee\oæ

Hystercdc BehavlourXïltercd

F(mx) = 7.7 kll

Relaüve Jol¡t Dbplacement (rm)

10

8

Ãzé4o?,2oþ_v(À :¿

44-8

_10

252

zv oË'

IJO ÞÉ

.a9 ãs 8u

)E

lrz

t î.

t,oa

¡I1 "

Þ ô eFÉ |! fll z U X o I F o E (l a o Þ r, o v) Þ o Þ ô o E

I Þ ô () q, o ¡l o q F ô 2 ø

æE <g ¡úo sl z il -¡ 'æ tl z

20.8

0

21.2

0

21.8

0

ll a I E Èt e g FI 8. É N)

!..) fi

19.8

0

23.2

0

g = EL 6 I 6 E È o ã ô

Dis

plac

emen

t (m

m)

8üåü

ot,ä

tts

I YY

,84

gH EE FT 88 åB 98

â, €, n Þ EI

Fø &l g E ø c ri

ä Þ E ð q Elì ø ø I il ã' il F

(Ð I Sp

Acc

eler

adon

Ò^Þ

e^

95bì

5 ñõ

Hu(

fr(¡O

liu

È ¡l rÉ g

23.7

6

22.3

2

22.8

0

23.2

8

22.9

6

23.0

4

23.1

2

23.4

4

23.5

2

23.6

0

23.9

2

22.4

8

22.5

6

22.6

4

22.0

8

22.1

\

lJr

äãR E

F 1 I t B ð il b, E,

Sltp

For

ce ft

N)

E å 6 g I * Ë E E * I {9

rtt m \ ô o (¡ a v) E tr 9. È d o Þ ô ã q o o ã ô Þ ø (! À o Ë È a ô È v) .D aà

N)

L,I (,

APPENDD( (C) - Representative Slip Joint Connection Test Results

Direction of Shaking:Normal Stress at Slip Face:

Out-of-Plane0.18 MPa (N=17.8kN)

AhohcDl$æm r{boræCæcimBehn,Crrecio

30

ÉnË106)

EUð.â -10â -n

-30 sqt Th

{slip) Jr¡st After flrst Sllp \Is llræfflter€d

aæ amax (aftef frst dip) = kv = Q.{,{g

èo

E

olc)d)è¡(,)

0.6

0.4

0.2

0

4.2

{.4

4.6Ilnrc (secs)

o(ic¡

nûN

ooiôl

F-.no\ôl

Eo\c.l

ryrmx)=14k|¡HysferUflcBehvirur

Illtcred

2!û)IEê?Èv)

Reldive Joiú Dþhernt (m)

-5

l0{.5 0.5

Figure C 4- Slip Joint Orrc layer of Embossed Polythene (Dry-Cor)

254

APPENDIX (D): Rigid F-A - Various BoundaryConditions

o

R1

Ht4

w4

w4

co kN/m

O+W

Figure D 1 - Concrete Slab with DPC Connection Above

Taking moments about (A) to determine horizontal reaction forces

^

w12

IO+W12

255

APPENDX (D) - Rigid P-Á - Va¡ious Top C-onnection Types

o=ùh -wlr-Al-^"02 [2 2) ¿

R" =ry-Yú-¡)'22h')

n, =4*w lr-¡)'22h"Taking moments about (B) top free body

Rearranging

08

Maximum resistance occurs when Å=0

ah2 o(, - t)+\(t i) :(i -*n- ^,

,=#(o.T\,.o,

8rf'^* = lrll

w2

O+

)

\ryith the rigid body assumption static instability occurs at a mid height displacement

which causes the mid height reaction to move outside of the thickness of the wall. At this

point or=0

O+ w2

Rearranging

^

o+Y2 _T

o+Y2

t -Âr^)

,ß

256

APPENDX (D)- Rigid P-Å - Various Top Connection Types

CONCRETE SLAB \ryITH DPC CONNECTION ABOVE - STATIC INSTABILITY

STATIC FORCE-DISPLACEMENT RELATIONSHIP

8ra^ =f, w2

O+

zJ¿

!(goے)P

=-o¡r(t)

â

Bi-linea¡ rigid force - displacement

{ relationship

Real non-linear semi-rigid forcedisplacement relationship

Mid-height displacement, ÂAi^ = f

Figure D 2 - Rigid F-A Relationship Top Vertical Reaction at Leeward Face

(50-907o) ro"-.Depending on wallmaterial and conditionof rotation joints

257

APPENDX (D)- Rigid P-Å - Various Top Connection Types

o

R1

ol kN/m (A) R2

Figure D 3 - Tlmber Top Plate Above

)(B

^

w4

Hl4

w4

Hl4

O+W12

w

258

APPENDX (D) - Rigid P-A - Various Top Connection Types

Taking moments about (A) to determine horizontal reaction forces

o=ùh -o' -w22(Ðlt Ot W

(i-+)-.*R2

À1

(r-¡)2 2h2h(Dh Ot W, .\=_+_+_(r_^,12 2h 2h'

Taking moments about (B) top free body

o = @h2 * o( !-- ol*{11 - Al-¿8 [2 ) 212 2) 2

Rearranging

,=þl*r'-^) +o(T+2^)]

Maximum resistance occurs when A=0

eth _Ot _W2 2h2h (r-¡)

0-* =#l*.,},ofWith the rigid body assumption static instability occurs at a mid height displacement

which causes the mid height reaction to move outside of the thickness of the wall. At this

point co=O

o = þl*rt - L,^) + o(T+ za,^ l]

Rearranging

w+92Â,^ = (w -2o)

259

APPENDD( (D) - Rigid P-Â - Various Top Connection T¡res

TMBER TOP PLATE - STATIC INSTABILITYSTATIC FORCE-DISPLACEMENT RELATIONSHIP

@-* = #lrur,.orT',f

z.\4€(!o€c)

-oE.t)A

Bi-linea¡ rigid force - displacementrelationship

Real non-linear semi-rigid forcedi splacement relationship

(w -2o)Mid-height displacement, Â

^ IA

Figure D 4 - Rigid F-a Relationship Top vertical Reaction at centerline

(50-907o) ol,,--depends on wallmaterial andcondition

2

260

APPENDIX (E): Material Test Results

zâoFl

450

400

350

300

250

200

150

100

50

0OOOOOOOoooooÕoc.ìs\ooooc.ì$

MICRO STRAIN

aJ't

LOAD = 0.3372 MICRO STRAIN /-r_{

/S/f/'

á'

Figure E I - Bond \ilrench Calibration Plot 110mm Brick Specinren Bond \ilrench

Figure E 2- Bond Wrench Calibration Plot 50mmBrick Specimen Bond Wrench

z

225

200

175

150

125

100

75

50

25

0

âoÈ

OOOOOOOOO\nOl.)O\nO\nOlnri Ê C.ì C.ì C.¡ C.¡ É sl'MICRO STRAIN

LOAD -- 0.46II MICRO STRAIN -¿å

áÃ

-tF

4/F

261

APPENDD( (E) - Maærial Test Results

RESULTS OF BOND WRENCH TESTS

llOmm TwO BRICK PRISMS TESTED MARCH 1998 (SERIES l)

Brick thickressBrick lengthMass bond wrenchMass at lever armBrick and mortar mass above interfaceFront brick face to center of gravityFront brick face to notchElastic modulusBedded a¡eaTotal compressive force on bedded area

F"o =9.81(m"r+ fth+ %)

ll02304.043

2s300

mmmmkg

mmmm

1Illm-mm2

250't65

463833

lT;l Bending moment about rhe cenrroid of the bedded a¡ea

trt

oVERALL AVERAGE F.p FOR N-r- 4 BATCI{ESOVERALL ST DEV FOR ALL 4 BATCITESLOWEST BOND VALI.JEHIG}IEST BOND VALI.]E

¡rI "r =o.zw,(a,-'/)*n tt^(a,-'ú)

Flexural sEength of the specimen

f*=*'/o-'"ú,

0.37D.08

0.220.48

SpecimenNo.

TESTNO.

IIucrostrain

m"kg

m"ke

fspN

MPNmm

f"pMPa

AveMPa

StDevMPa

I I 23.5 3.3 302.57 t7t4t3.9t 0.362 14.3 3.17 ztt.o4 to't334.99 0.22 0.28 0.073 17.t 3.62 242.93 126837.27 o.26

2 I 27.2 3.09 336.81 t97184.78 0.412 24.4 3.05 308.95 177682.50 o.37 0.36 0.063 19.7 3.11 269.31 1M946.53 0.30

3 I 19.3 3 258.42 t42160.49 0.302 32.1 3.06 384.58 231313.77 0.48 0.40 0.103 28 2.99 343.67 202756.86 o.42

4 I 22.9 3.14 295.|t 167234.85 0.3s2 28.8 3.5 356.52 208328.94 0.44 o.42 o.o73 32.1t 3.54 389.39 231383.42 0.48

262

APPENDD( (E) - Maærial TestResults

l10mm PRE-DYNAMICALLY TESTED WALLS TESTED MARCH 1998 (SERIES 1)

I1102304.M3

2$AOfsp

F"o =9.81(mr+ nb+m!)

lT;l Bending moment about the centroid of the bedded a¡ea

Brick thickressBrick lengthMass bond wrenchMass at lever armBrick and mortar mass above inærfaceFront brick face to center of gravþFront brick face to notchElastic modulusBedded areaTotal compressive force on bedded area

250765

Illmmtnkg

mmmm

1mm-mm'

463833

M,p = ssm,(a, -' ú). o .z rrn,(a, -' ú)lTl Flexural süength of the specimen

Í,0=M'/,0-F"o//Ao

SpecimenNo.

TESTNO.

microsÍain

m2ke

lll3ke

FspN

[rfspNmm

fPMPa

AveMPa

St DevMPa

I I 48.01 3.8 347.92 342128.51 0.722 35.17 3.64 420.39 252696.62 0.53 o.g 0.103 44.34 3.18 505.90 316566.59 0.66

2 1 25.99 3.8 331.90 188757.01 0.392 31.09 3.5 378.99 224279.02 0.47 0.47 0.073 36.19 4.O3 434.22 259801.03 0.54

3 I 35.t',l 3.5 419.01 252696.62 0.532 28.03 3.t4 345.44 202965.81 o.42 0.47 0.053 31.09 3.97 383.60 224279.02 o.47

4 I 56.57 3.763 631.53 401749.76 0.842 40.27 3.72 471.20 288218.63 0.60 0.6r 0.223 25.99 3.925 333.r3 188757.01 0.39

OVERALL AVERAGE F"P FOR ALL 4 BATCIIESOVERALL ST DEV FOR ALL 4 BATCTIES

LOWEST BOND VALUEHIGIIEST BOND VALI]E

0.550.14

0.39

D.E4

263

APPENDX (E) - Material Tesr Results

l lOmm TWO BRICK PRISMS TESTED JUNE 1998 (SERIES 2)

Brick thicknessBrick lengthMass bond wrenchMass at lever armBrick and mofar mass above interfaceFrontbrick face to center ofgravityFront brick face to notchElastic modulusBedded areaTotal compressive force on bedded a¡ea

F"r=9.9I(mr+m2+m3)

1102305.36

25300

0.52J.t2ù.37D.7t

fllmfltmkg

mmflrmmm'mm2

2W765463833

li4-;l Bending moment about the centroid of the bedded area

t-_l Flexural strength of the specimen

¡'I "r =o.um,(a,-'/)*, tt (0,-'ú)

r,o=*'/,0-''/n

OVERALL AVERAGE F,P FOR ALL 4 BATC}IESOVERALL STDEV FOR ALL4 BATCI{ESLO\ryESTBOND VALI.JEHIGITEST BOND VALI]E

SpecimenNo.

TESTNO.

nucfosEain

m"kq

m'ke

FspN

MpNmm

fPMPa

AveMPa

StDevMPa

5 I 750 25.78 2.984 334.75 187183.33 0.392 1260 43.31 3.058 507.45 309283.45 0.65 0.s8 0.163 1360 46.75 3.551 546.01 333224.65 o.70

6 I 770 26.47 2.982 341.48 t9r9'n.57 0.402 770 26.47 2.985 341.51 191971.57 0.40 0.42 0.oÍ3 900 30.94 2.974 385.24 223095-13 o.47

7 I t200 41.2s 2.982 486.48 294918.73 o.62) 1300 44.69 2.984 520.21 318859.93 o.67 0.59 0.093 950 32.65 35W 407.28 23565.73 o.49

8 I 700 24.06 2.977 317.83 175212.73 o.372 1050 36.09 3.546 ut.43 259m6..93 0.54 0.44 0.093 800 27.50 3.013 351.90 199153.93 o.42

264

APPENDD( (E) - Material Test Results

tI

lIlllll2IIì3

drdz

Z¿

A'd

l10mm PRE-DYNAMICALLY TESTED TWALLS TESTED JUNE 1998 (SERIES 2)

Brick thicknessBrick lengthMass bond wrenchMass at lever armBrick and mortar mÍrss above interfaceFront brick face to center of gravityFront brick face to notchElastic modulusBedded areaTotal compressive force on bedded area

ll02305.36

2N765

fllmmmkg

IIlmmmmm3

mm2

46383325300

Fsp

F,o =9.81(mr+ mr+ m.)

l-ìrf-;l Bending moment about the centroid of the bedded a¡ea

t--ç-l

OVERALL AVERAGE FspFOR AJ-L4 BATCIIESOVERALL ST DEV FOR ALL 4 BATCTMSLOWEST BOND VALIJEHIGI{EST BOND VALUE

¡1,'I "r = o .zw"(a, -' /)*, rr^(0, -''/)

Flexural sfrength of the specimen

f ,o=*'o/o '"/o,

D.57

t. l7D.27

0.99

SpecimenNo.

TESTNO.

microstrain

m'ke

m'ke

fspN

MpNmm

f"pMPa

AveMPa

StDevMPa

5 I 1050 36.91 2.984 443.92 2@693.30 0.552 1100 38.67 3.058 461.89 276934.68 0.58 0.71 o-25

3 1900 66.79 3.551 742.59 472796.75 0.99

6 1 1000 35.15 2.982 426.66 252451-92 o.532 1300 45.70 2.985 530.14 325W.t9 0.68 0.s6 0.11

3 900 3r.64 2.974 392.tO 227969.16 0.48

7 I 800 28.12 2.982 357.70 203486.40 0.42., 500 17.58 2.984 254.27 130038.13 o.n 0.41 0.133 1000 35.15 3.502 43t.76 25245r.92 0.53

8 1 1000 35.15 2.977 426.61 2s245t.92 0.s32 1200 42.18 3.546 501.16 301417.44 0.63 0.59 0.053 I 150 40.42 3.013 478.69 289t76.06 0.ó0

265

APPENDIX (E) - Material Test Results

1l0mm TWO BRICK PRISMS TESTED SEPTEMBER 1998

Brick thiclnessBrick lengthMass bond wrenchMass at lever armBrick and mortar mass above interfaceFront brick face to notchFront brick face to center of gravityElastic modulusBedded a¡eaTotal compressive force on bedded area

F"o =9.81(mr+ nb+ m3)

Flexural strength of the specimen

ll02305.36

mmlItmkg

2OO mm765 mm463833 mm3

253W mm2

f-M--l

l--r'"-l

Bending moment about the centroid of the bedded area

¡vI "e =o.tua(a,-'/)., rt^(a,-'ú)

r* M "o//ZoF"o '//Ao

SpecimenNo.

TESTNO.

nucrostrain

m'kg

m'kg

psp

NMsp

NmmfrP

MPaAveMPa

StDevMPa

ll I 300 10.55 2.984 185.30 8to72.61 o.l72 1050 36.91 3.058 444.65 264693.30 0.55 0.32 0.203 450 15.82 3.551 242.59 ltj't96.75 o.24

t2 I 600 2r.o9 2S82 288.73 154520.88 o.32I 500 17.58 2.985 254.28 130038.13 0.27 0.30 0.033 550 19.33 2.974 271.41 142279.50 0.30

l4 I 750 26.36 2.982 340.46 t9lu5.o2 0.402 450 t5.82 2.984 237.03 rt1796.75 o.24 0.29 0.103 400 14.06 3.052 220.45 10s555.37 o.22

II

I

rII I

I r IIIrI

OVERALL AVERAGE Fsp FOR 3 BATCIIESOVERALL ST DEV FOR 3 BATCTIESLOWESTBONDVALUEHIGIIEST BOND VALI.]E

0.30).1 I0.tr0.55

266

APPENDIX (E) - Material Test Results

50mm TV/O BRICK PRISMS TESTED SEPTEMBER 1998

Brick thicknessBrick lengthMass bond wrenchMass at lever armBrick and mortår mass above interfaceFront brick face to notchFront brick face to center of gravityElastic modulusBedded areaTotal compressive force on bedded area

F,o =9.81(mr+ nh+ m))

502303.5

nìmmmkg

1925929583311500

mmnìmmm'mm2

l-Çl Bending moment about the centroid of the bedded area

t-?-t¡r

"n = s.tw,(a, -' /)*, rt^(a, -' ú)Flexural stength of the specimen

r,o=*'/o-''/n

fIl3kg

Fsp

N1ylsp

Nmmf"p

MPaAveMPa

St DevMPa

SpecimenNo.

TESTNO

TruCfO

sfrainIIl2kg

0.9 184.16 85680.95 0.8810 I 300 14.3'.1

0.9 184.16 85680.95 0.88 0.70 0.302 300 14.3735047.85 0.363 ll0 5.27 0.9 94.86

55034.60 0.56t3 1 185 8.86 0.9 130.11o.r714.r3 0.9 181.81 84348.50 0.86 0.762 295

295 t4.13 0.9 181.81 84348.50 0.863

OVERALL AVERAGE F,P FOR 2 BATCTIESOVERALL ST DEV FOR 2 BATCIIESLOWEST BOND VALUEHIGTIEST BOND VALUE

0.730.22

0.36D.88

267

APPENDIX (E) - Material Test Results

RESULTS OF MODULUS TESTS

SPECMEN No. (2) - 110mm THICK TESTED MARCH 1998

Estimate Modulus

SPECIMEN No. (3) - 110mm THICK TESTED MARCH 1998

15,000 MPa

3,300 MPa

STRESSMPa

00.99l.982.963.954.945.930.664.37

COMBSTRAIN

00.00000720.00013980.00016880.000203

0.00029110.0003982

Â(comb)

00.Nr24570.0240570.0290400.0349410.0500840.0ó8554

L(2)brick/morta¡

00.0020320.0264t60.034s440.0467360.0650240.o87376

^(1)brick0

0.001280.003840.008960.0192

0.024320.03072

NN

STRATN (2)brick/mortar

00.000010.00013.0.0w17)0.000230.000320.00043

16,600l10,556

STRATN (l)brick

00.00002520.00007s60.00017640.000378

0.00047880.0006048

57o ULTMATE337o ULTIMATE

DEMEC (2)bricl/morta¡

943942930926920911900

DEMEC (1)brick7827817'.|9

775767763758

T]LTIMATE

LOAD(N)0

25000

7s000100000125000150000332000

STRESSMPa

00.991.982.963.954.945.930.664.42

COMBSTRAIN

00.00069350.00079530.00101520.0012560.00r5380.00r697

A(comb)

00.1t92950.1367970.1746190.2161780.2646190.29t954

L(2)bricl/morta¡

00.1137920.13208

0.1706880.2153920.2661920.296672

^(l)brick0

-0.00896-0.00768-0.0064

-0.001280.002560.00768

NN

STRATN (2)briclc/mortar

00.000560.000650.0@840.00,1010.001310.00146

16,80011 1 ,888

STRATN (1)brick

0-0.0n01764-0.0001512-0.000126

-0.00002520.00005040.0001512

SVoIJLTG,ÃATE33VoULTIMATE

DEMEC (2)bricl/morø¡

911855846827805780765

DEMEC (I)brick988995994993989986982

ULTIMATE

LOAD(N)0

25000

100000125000150000336000

Estimate Modulus

268

5.930.664.38

STRESSMPa

00.991.982.963.954.94

COMBSTRAIN

00.00033800.00060510.00086770.0011020.0013600.001684

0.14925490. l 895680.23394520.289728

Â(comb)

00.05814170.1040914

L(2)bricl/mortar

00.0589280.105664

0.15240.1950720.2418080.300736

00.001280.002560.005120.008960.0128o.0r792

NN

A(1)brick

0.001190.00148

16,650110,889

STRATN (2)bricl/mortar

00.000290.000520.000750.000960.0001764

0.w2520.0003528

STRAIN (1)brick

00.00002520.00005040.0001008

843820791

5VoULTIJ'VIATE33VaULTIMATE

DEMEC (2)brick/mortar

939910887864

789786782

LILTIMATE

DEMEC (1)brick79679579479275000

100000125000150000333000

(N)LOAD

02500050000

SPECIMEN No. (a) - 110mm THICK TESTED MARCH 1998

Estimate Modulus

SPECMEN No. (5) - 110mm THICK TESTED JUNE 1998

Estimate

MPa

16,000 MPa

STRESSMPa0.000.991.982.963.9s4.945.936.927.91o.7t4.74

COMBSTRAIN

01.90565E-053.81131E-056.441228-050.000166r660.0001821940.w02793770.00038113 r0.000490128

Â(comb)

0o.æ32777260.0065554510.0110789030.0285806290.03t3373370.0480527890.0655545150.084301966

L(2)brick/mortar

00.0040640.0081280.0142240.0325120.0M7040.0629920.081280.10r6

0.00510.00640.02180.02430.02560.0282

NN

A(l)brick

00.00130.0026

18,000

STRAIN (2)brick/morør

00.000020.000040.000070.000160.ñ0220.000310.00040.m05

119,880

0.0005040.000554

STRAIN (1)brick

02.528-055.04E-050.0001010.0001260.0004280.000479

57o ULTIMATE337o ULTMATE

DEMEC (2)bricl/mortar

812810808805796790781772762

777775

T.JLTIMATE

DEMEC (I)brick797796795793792780778150000

175000200000

360000

(N)LOAD

0250005000075000100000r25000

269

APPENDIX (E) - Maærial Test Results

SPECMEN No. (6) - 110mm THICK TESTED JUNE 1998

Estimaæ Modulus

SPECIMEN No. (7) - 110mm THICK TESTED JUNE 1998

Unreliable Data No Estimate

13,900 MPa

STRESSMPa0.000.991.982.963.954.945.930.674.45

COMBSTRAIN

0-3.6571E-05-1.7514E-05-5.8657E-0s-0.000r0437-0.00051312-0.00043577

Â(comb)

0-0.00629019-0.m.301247-0.01008894-0.01795168-0.08825691-0.07495182

L(2)brick/mortar

00

0.0040640.0040640.0040640.0060960.016256

^(l)brick0

0.01020.01150.023

0.03580.15360.1485

NN

STRATN (2)brick/mortar

00

0.000020.000020.000020.000030.00008

16,9001t2,554

STRATN (l)brick

00.0æ2020.0æ2270.0004540.000706o.æ30240.002923

5VoIULTIJvIATE33VoULTIJvIAT]E

DEMEC (2)bricl/mortar

9189189169r6916915910

DEMEC (l)brick911903902

88379t795

ULTIMATE

LOAD(N)0

250005000075000100000125000150000

338,000

STRESSMPa0.000.991.982.963.9s4.945.936.927.9t0.624.12

COMBSTRAIN

04.725588-055.25983E-050.0001070970.0001897940.0002469640.w03Mt470.0004603860.000569383

Â(comb)

00.008128

0.0090469030.0184206290.0326446290.0424778060.0591932570.0791864340.097933886

L(2)brick/mortar

00.0081280.0t21920.0223520.0365760.0487680.0670560.0894080.109728

^(1)brick00

0.00510.00640.00640.01020.01280.01660.0192

NN

STRAIN (2)brick/morør

00.000040.000060.000r I0.000180.000240.000330.000440.00054

15,650t04,229

STRATN (r)brick

00

0.00010r0.0001260.0001260.0002020.0002520.0003280.000378

57o IJLTIMATE337o ULTMATE

DEMEC (2)bricl/mortar

95r94'.1

945940933927918907897

DEMEC (1)brick8r2812808807807804802799797

ULTIMATE

LOAD(N)0

5000075000100000125000150000175000200000

313000

Estimate Modulus

2',to

SPECIMEN No. (8) - 110mm THICK TESTED JUNE 1998

Estimaæ Modulus 5,400 MPa

SPECIMEN No. (10) - 50mm THICK TESTED SEPTEMBER 1998

Average Modulus 9,800 MPa

STRESSMPa0.000.991.982.963.954.945.936.927.91

0.483.22

COMBSTRAIN

00.0001070970.000254207o.ooo4032r70.0005640410.0007557350.w09756290.0012100080.o01463443

Â(comb)

00.0184206290.043723532o.0693532570.0970149830.1299864340.16780816

0.2081213370.25t71224

L(2)briclc/morta¡

00.022352

0.0508o.o772160.1056640.1402080.1788160.22t488o.268224

^(l)brick0

0.00640.01l50.01280.01410.0r660.01790.02180.0269

NN

STRAIN (2)briclc/monar

00.000110.000250.000380.000520.000690.000880.001090.00132

t2,25081,585

STRAIN (I)brick

00.0001260.@0227o.o0f252o.æ02770.0003280.0003530.0004280.000529

57o ULTMATE3370 ULTMATE

DEMEC (2)brick/mortar

9r8907893880866849830809786

DEMEC (l)brick84083s831830829827826823819

ULTIMATE

LOAD(N)0

250005000075000100000125000150000175000200000

245000

StressMPa0.001.302.6r3.9rs.226.527.83

1.338.89

STRAIN (1)brick/mortar

0.0000000.0000760.0402270.0004030.0005290.0007560.000857

9,l00MPa

DEMEC (I)briclJmortar

898895889882877868864

Test 4 ModulusEstimate

STRAIN (1)bricl:/mortar

0.0000000.0001760.0002770.0003280.0005800.0007560.000756

10,400MPa

895888884882872865865

Test 3 ModulusEstimate

DEMEC (1)brick/mortar

NN

STRAIN (I)brick/mortar

00.00007560.00022680.000378

0.000s7960.00070560.0009324

8,400MPa

15,350toz,23r

864Iest 2 ModulusEstimate

DEMEC (1)brick/mortar

901898892886878873

0.000693

57o ULTIMATE33% ULTIMATE

STRATN (l)brick/morør

00.0000r260.00020160.00035280.00045360.0006048

11,300MPa

880874

870.5Iest I ModulusEstimate

DEMEC (1)brick/mortar

898897.5890884

ULTIMATE

(N)LOAD

0150003000045000600007500090000

307000I I

271

APPENDIX (E) - Material Test Results

SPECMEN No. (11) - 110mm THICK TESTED SEPTEMBER 1998

Estimate Modulus 6,600 MPa

SPECMEN No. (12) - 110mm THICK TESTED SEPTEMBER 1998

11,600 MPa

STRESSMPa0.000.991.982.963.954.945.930.7r4.73

COMBSTRAIN0.0000000.00016r0.0003430.0005020.0006460.0007950.000909

Â(comb)

0.0000000.0276620.0589940.0862630.1 1 1 1060.1367360.156336

L(2)brick/mortar

0.0000000.0284480.0609600.0894080.115824o.t422400.164592

^(l)brick0.0000000.0012800.0032000.0051210.0076810.0089610.013442

NN

STRAIN (2)bricl/mortar

00.000140.0003

0.000440.000570.0007

0.0008117,950

119,547

STRATN (r)brick

00.0m,02520.000063

0.00010080.00015120.00017640.w2646

5% ULTIMATES3ToIJLTIMATE

DEMEC (2)bricVmorør

901887871

857844831820

DEMEC (I)brick812811

809.5808806805

801.5I.JLTIMATE

LOAD(N)0

25000

100000125000r50000359000

STRESSMPa0.000.991.982.963.954.945.930.785.23

COMBSTRAIN0.0000000.0000540.0001370.0ú2260.00031r0.0003940.000478

Â(comb)

0.0000000.0092100.0235010.0388070.0535s70.0678470.082204

L(2)briclc/mortar

0.0000000.0r r 1760.027432o.ou7040.0629920.0792480.097536

^(1)brick0.0000000.0032000.0064010.00960r0.0153620.0185620.024963

NN

STRATN (2)bricl/morør

00.0000550.0001350.0nn.220.000310.000390.00048

19,8s0132,200

STRATN (t)brick

00.0000630.0001260.0001890.ñ030u0.00036540.0004914

57o ULTMATE33/oULTIJvLAI]E

DEMEC (2)briclc/mortar

914908.5900.5892883875866

DEMEC (l)brick807.5805

802.5800

795.5793788

ULTIMATE

LOAD(N)0

250005000075000II150000397000

Estimate Modulus

).7)

SPECIMEN No. (13) - 110mm THICK TESTED SEPTEMBER 1998

Estimate Modulus Unreliable Data No Estimate

SPECIMEN No. (10) - 50mm THICK TESTED SEPTEMBER 1998

Average Modulus 6,700 MPa

STRESSMPa0.000.991.982.963.954.940.785.23

COMBSTRAIN0.000000-0.000027-0.000045-0.0000260.0000050.000060

À(comb)

0.000000-0.004718-0.007796-o.oo44s20.M9240.010364

L(2)brick/mortar

0.0000000.0000000.0020320.0081280.016256o.028448

^(1)brick0.0000000.0076810.0160020.0204830.0249630.029444

NN

srRArN (2)brick/mortar

00

0.000010.000040.000080.00014

19,850r32,2@

STRATN (1)brick

00.00015120.000315

0.00040320.00049140.0005796

57o ULTIMATE33ToIJLTIvIATE

DEMEC (2)brick/mortar

9t69t6915912908902

DEMEC (I)brick900894

887.5884

880.5877

ULTIMATE

LOAD(N)0

25000500007s000100000125000397000

StressMPa0.001.302.613.915.226.527.839.1310.43

1.328.77

STRATN (1)brick/mortar

0.0000000.0000250.0000500.0001510.0cp2270.0003280.0004030.0004540.000529

UnreliableData

DEMEC (1)bricL/mort¿r

803802801

797794790787785782

Iest 4 ModulusEstimate

STRATN (1)brick/mortar

0.0000000.0005540.0010580.0013360.0016380.0018140.0019910.a023690.002621

4,000MPa

DBMEC (1)bricL/mort¿r

867845825814802795788773763

Test 3 ModulusEstimateNN

STRAIN (1)brick/mort¿r

00.00007560.04022680.04030240.0004158

0.000630.00073080.00078120.00088211,800MPa

r5,150100,900

DEMEC (I)brick/mortar

811808802799

794.5786782780776

Test 2 ModulusEstimate

5VoIJLTNIATE33VoUI-TIIúATE

STRAIN (1)bricVmortar

00.000378

0.00073080.00120960.001386o.oot56240.00171360.00199080.0023688

4,400MPa

DEMEC (I)briclc/mortar

873858844825818811805794779

Test 1 ModulusEstimateULTIMATE

LOADN)0

150003000045000600007500090000105000120000

303000

273

APPENDX (E) - Maærial Test Results

RESULTS OF COMPRESSTVE MORTAR CI]BE TESTS

Series SpecimenNo.

SpecimenThickness

(mm)

Cube Number(l00xl00x100mm)

CompressiveStrength(MPa)

Marchl998 1 ll0 I 5.202 5.02J 6.82

Marchl998 2 110 I 5.882 6.183 5.62

Marchl998 J 110 I 7.161 6.84J 6.42

March1998 4 ll0 I 7.162 6.343 6.r4

June 1998 5 ll0 1 6.022 4.30

June 1998 6 110 I 6.062 4.O4

June 1998 7 ll0 I 4.022 4.98

June 1998 8 110 I 5.062 4.323 4.16

September 1998 l0 50 I 5.002 5.203 s.48

September 1998 l1 ll0 I 4.682 4.223 4.90

Sept€mber 1998 t2 lt0 I 5.282 4.943 5.08

Sepæmber 1998 t3 ll0 I 3.762 4.M3 3.84

September 1998 t4 50 I 4.082 3.563 4.44

AVERAGE 5.17

274

APPENDIX (F): Simply Supported \ü/all Test Results

MARCH 98SPECIMEN 3

JUNE 98SPECIMEN t

Figure F 1- Static Push Test - Un-cracked, 110mn¡ No Overburden

Height t.485tmIhiclness 110bnmLensttr 95rlmmDensity I80?t/r;ghl¡i

'Figure F 2- Static Push Test - Un-cracked, L10mrn' 0.15MPa Overburden

Applied Overburden 0 MPa460 kPaFlexural Tensile Süength, f,

Linear Elastic Analysis Prediction 2.ø4 KN

0.406 KNRieid Bodv Analysis P¡ediction

1.485[mHeightfhiclmess I10hr,m

9501l¡,¡ÍtLængttrDensity 1800

STATIC PUSH TEST _ MID HEIGTIT FOINT IOAD

35

3I 3.18

---i

-FEXPERTMENTAL rcRCE (kN)

'#RIGIDBoDY (kl.t)

- 'tr - LINEAR ELA.STIC ßN)

! r.tE9,Þ.1

É3 r.sdFìIrJ

0.5

0

0 20 Q 60 80 100MIDHEIGHT DEFI-ECTION (lvilvÍ)

Applied Overburden 0.15lMPaFlexural Tensile SEength, f, 46|kPaLinea¡ Elastic Analysis Prediction 4.S212lkr{Risid Bodv Analvsis Prediction 5.3Iólkl.I

STATIC PUSH TEST. MID HEIGHT POINT LOAD

1

6

2ðF5zf¡lúF.Ø¡¿l¡l

I

5

4

3

1

0

0 20 44 60 80 100MID.HEIGHT DBFLECTION (MM)

FORCE (kN)'-TRIGIDBODY (kÐ- Ð _ LINEAR ELASTIC (KN)I

ADDITIONAL II IERAL STRENGTF ABOVETHATOFruUU UUÞ IV üOVERBT]RDEN SlhD rt^--úr^T

!¡@ùÐ ùIAITLIRINGS FOUND TCtc

utrELlrvlì urBE SICNIFICANT

2t5

APPENDD( F : Out-of-plane Simply &tpported WaIl Test Results

ÉIeight l.485lmIhickness lI0lr.urrænsth 950Density 1800[rslm'

JUNE 98SPECIMEN 8

SEPIEMBER9SSPECIMEN 10

Figure F 3. Static Push Test - Cracked, 110mm,O.l5Mpa (Þerbu¡den

Figure F 4- Static Push Test - Cracked" 50mnD No Overburden

Applied Overburden 0.15 MPaFlexural Tensile Stengú" f, 0 kPaLinea¡ Elastic An¿¡lysis Pr,ediction 2.322 KNRigid Body Analysis P¡ediction 5.it6 KN

STATIC PUSH TEST - MID HEIGIIT FOINT LOAI)

6

5

2è9*üzt¡l&FU)¡dHf

4

3

2

I

0 20 40 60 80 100 120

MID-HEIGIIT DEFLECTION (MM)

EXPERJMENTAL K)RCE (KN).+RIGIDBODY (kN)

ADDITIONI/

LLATERAL STRI NGTTIABOVEt-I

rlut vrÃDEFLECTICFOTJNDTO

JIU DUE TL' IIìL]!¡OFOVERBIIRX¡ESIGNIFICANT

ENÐùIÂIIL]N SPRINGS0R f lOnm

WALLS

HeiehtIhichess 50Lengtlr

2300

Applied Overburden 0lMPaFlexural Tensile SEength, f, 0[rPaLinear El¿stic Analysis Prediction 0.07[lkNlieid Body Analysis Prediction 0.1071kr{

STATIC PUSH TEST.MID HEIGITT FOINTI,OAD

l5

0.r2

0.1

0.08

0.06

0.04

0.o2

0

2t9FozB]úF6-lúl¡lFf

0 5 l0 20 25 30 35MIDHEIGIIT DEFLECTTON (MM)

q 45

,/ FORG (kN)

RIGIDBODY (IN)\,

276

APPENDIX F: Out-of-plane Simply Supponed Woll Test Results

Heisht 1.485 mrnmThiclness 50

Lænsth 950 mmks/ÍfDensity n0a

SEPIEMBER9SSPECIMEN 10

SEPTEMBER93SPECIMEN 10

Figure F 5 - Static Push Test - Urcracked, 50mnu 0.Û75MPa Overburden

Figure F G Static Push Test - Cracked, 50mq 0.075 Overburden

Applied Overburden 0.075llvlPaFlexural Tensile Stensth, f, 750kPaLinear Elastic Analysis Prediction I.07Ilkl.IRisid Bodv Analysis Prediction Ø.587lklr

STATIC PUSHTEST - MID MIGI{T POINT LOAD

zJhzlI]úFU)JúlaFJ

1.1

1

0.90.80.7

0.60.5

0.40.3o.20.1

0

0510152025 30 35 40 45

MID-MIGI{T DEFLECTION50

F--- --i.! 0.9s ÐGERIMENTALFORCE (KN)

+RIGIDBODY (KN)_ I _ LINEAR ELASTTC (KN)

.-a\

L

Heieht 1.485 mIhiclness 50 mm

mmLeneth 950ÞnsiW 2300 ks/n:

Aoolied Overburden 0.075lMPaFlexural Tensile Srength, f, 0[rPaLineár Elastic Analvsis Prediction Ø.28ólkl.IRigid Bodv Analysis Prediction 0.órSlktI

STATIC PUSH TEST - MID HEIGIIT POINT IJOAD

0.7

0.6

2g o.sF

V o.+úF(t)c 0'3

fi< 0.2J

0.1

00 5 t0 l5 20 25 30 35 40 45 50

MID.HEIGTIT DEFLECTION (MM)

L

F -tsEXPERIMENTAL FORG (kl.I)

-+RTGTDBODY (kl.t)f $\.

fr¡

277

APPENDIX F: Out-of-plane Simply Supponed Wall Test Results

Height 1.48s mThickness 1r0 mmængth 950 nm

DensiW 1800 ks/m'

SEPTEMBER93SPECIMEN 11

SEPTEMBER93SPECIMEN 11

Figure F 7- Static Push Test - Cracked, lfOmnr, No Overburden

Figure F E - Static Push Test - Urrcracked, 110mnr, 0.l5Mpa Overburden

Applied Overburden 0lMPaFlexural Tensile Sfrength, f, 0[PaLinear Elastic Analysis Prediction o.27rlkl.lRigid Body Analysis Prediction 0.4061k1:{

STATIC PUSH TEST - MID HEIGIIT POINT I]OAD0.45

0.4

^ 0.35z,4I 0.3FoÁ o.zsúF

fr o.rs

Fl o.l

0.05

00 20 40 60 E0 100

MID-ITEIGHT DEFLECTION (MM)

-{tsEXPERIMENTAL FORCE (H{)

--+RIGIDBODY (kN)

r/ \* -\

\-\MORTARDREFFECTTVB \

)POUTREDUCIN(.IDTHOFTHE RIC

THEDBODY

ÉIeieht 1.485 mIhiclness 110 mmlæneth 950 filmDensity I 800 ks/m'

Applied Overburden 0.IíllvfPaFlexural Tensile Strength, f, 460lWaLinea¡ Elastic Analysis Prediction 4.82121kt{Rigid Bodv Analysis Prediction 5.3rólkt¡

STATIC PUSH TEST - MID IIEIGIIT POINT LOAD6

5

2F

zf¡ìÉØFI

útÐFs

4

J

I

0 20 40 60 80 100

MID-HEIGHT DEFLECTION (MM)

-$r:!.-:.Hh\¡r

FORCE (kN)--#RTGTDBODY (kN)

r' - LINEAR ELASTIC

\ÏTIAT OF RIGtrDEFLECTION C

DUE TO INCREAS]FOVERBT]RDEN SI

D STATICRINGS FOTJND

I

278

APPENDIX F : Out- of-plnne Simply Supported Wall Test Results

Heisht t.48slmThickress 110k¡l'mtænsttl 950hnmDensity 18007ù;s,lm

SEPIEMBER98SPECIMEN 12

Figure F 9 - Static Push Test- UN-cracke{ 110mm' No Overburden

SEPTEMBER9SSPECIMEN 12

Figure F 10- Static Push Test - Cracked, llûmrn, No Overburden

0 MPaepplied OverburdenFlexural Tensile Srength, f, 460 kPaLinear Elastic Analysis Prediction 2.ø4 KNRieid Bodv Analysis hediction 0.406 KN

STATIC PUSH TEST - MID HEIGTIT POINT LOAD

t.5

3

l-----' ---l

-ì-E)GERJMENTAL FORCE (kN)

---{-RTGTDBODY (kN)

- € - LINEAR ELASTTC (kÐI

t-ù--L*

2€ 2.sEFZJt¡.]ÉFa)¡ 1.5útqt-<

J

0.5

00 20 40 ó0 80 100

MID-HBIGHI DEFLECTION G/rvf)

Heisht 1.485Ihicloess lIlln¡rî

9501l¡¡ÍtLængthI

Aoolied Overburden a MPakPaFlexural Tensile Strength, f, a

Linear Elastic Analysis Prediction 0.271 KN

Risid Bodv AnalYsis Prediction 0.40ó KN

STATIC PUSH TEST - MID HEIGÍIT POINT LOAD

2út-(,zt¡¡dFro,ldt¡tif

0.45

o.4

0.35

0.3

o.25

o.2

0.15

0.1

0.05

0

0 20 40 60 80 100

MID-TIEIGTIT DEFLECTION (MM)

\-, -^:I-Ð0ERIMENTAL FORCE (kN)

--!-RTGTDBODY (kÐ

I

279

APPENDIX F : Out- of-plane Simply Supponed WaII Test Results

Heieht l.485lmfhickress ll?h¡tmængth 950Density I80Ìks,lm'

SEPTEMBER93SPECIMEN 13

SEPTEMBER93SPECIMEN 13

Figure F 11- Static Push Test - Uncracked, f10mn, No Overburden

Figure F 12- Static Push Test (Hysteretic) - Cracked, ll0rrun, No Overburden

Applied Overburden 0lMPaFlexural Tensile Srengú, f, 460WaLinea¡ Flestic Analysis Prediction 2.64418NRigid Body Analysis P¡ediction 0.'l06lkl-I

STATIC PTJSH TEST - MID HEIGTTT FOINT T.OAI)

5

2.5

2éF<(Jzl¡JÍ r.saâ-.¡

É,f0.5

F------

l : TEST (I) - I]NCRACKED E}PERIMENTAL FoRG (kN)

-{I-RIGIDBODY (kN)

- rr - LINEAR EIASTTC (kN)

=ÞH--

00 2A 4 60 80 100

MIDHEIGTIT DEFLECTION (MM)

HeightIhichess 110L,engtlr 950Density I

0lMPaFlexural Tensile Strengü, ft 0[rPaLinear Elastic Analysis P¡ediction 0.27lkl:{Rigid Body Analysis Prediction 0.4MlkÌ,t

STATIC PUSH TEST - MID HEIGÍTT POINT LOAI)0.5

0.45

o.4

2 o.tsTJ

H o,2po.zsFØc 0.2dH o.rsI

0

0.05

0

0 20 40 60 80 100MII}HEIGHT DEFT.ECTION (MM)

-ôTEST (l) 90úm TIYSTERESIS EKPERIMENTAL FORCE (KÐ+TEST (2) TOmm IIYSTERESIS ÐPBRIMENTAL FORCE (kN)'+TEST (3) sonm I{YSTERESIS Ð{PERIMENTAL FORCE (kN)

(4) 3onn HYSTERESIS EXPERIMENTAL FoRCE (kN)o TEST(5) 10m IIÍSTERESISEXPERIMENTALFORCE (kÐ

+.RIGIDBODY

oa

i ,f-rbì

ñ.ÌI -.\."tìiìl

280

EuzE¿

A

ÀrF"rÇnEro

Pti

AP PENDIX F : Out- of-plane Simply Supp oned Wall Te st Re s ults

SEPIEMBER9E SPECIMEN 13 - RF,SONANT ENERGY LOSS PER CYCLE

INPUTDATA

ENERGY DTSIPATED IN HAIF CYCLE OF ACTUAL STRUCTUREENERGY DISIPATED IN FULL CYCLE OF ACTUAL STRUCTLIREACTUAL MAX VIBRATION AMPLITIJDE

DEFIN]TION OF EFFECTTVE STIFFNESS

EFFECTTVE MAX YIBRATIONAL AMPLITUDEEFFECTIVE MAX RESISTANCE FORCEEFFECTTVE CYCLE STIFFNESSSTRAINENERGYDAMPING RATIO FORMAX VIBRATIONAL AMPLITUDE

Figure F 13- September9S Specirnen 13 - Resonant Energy Loss Per Cycle

DESCRIPTION E¿¡2 E¿ 4n Fn IÇn E- P*i AN N IItm N N/mm Nmm mm

MAXDISP.90 8213.61 16ø'27.23 40.00 220.4O 5.50 44{n.00 29.717o 90MAXDISP. TO 4026.40 wsz.79 35.00 2110.00 6.57 402s.00 15.X27o 70MAXDISP.50 2946.6 5893.32 32.00 2s0.00 7.8r 4{n0.00 l!.72?o 50MAXDISP.30 t761.6 3523.3t 18.50 285.00 15.41 2ß6.?,5 10.Ø7o 30MAXDISP.lO 68835 1376.70 6.00 3z).00 53.33 960.00 ll^.4lVo l0

DAMPING RATIO USING RESONANCE ENERGY LOSS PER CYCLE METHOD

ÀoFú(5zF*H

35.07o

30.O7o

25.01o

2O.07o

15.0%

10.0%

5.0%

0.07o

,/_/

0 l0 20 30 40 50 ó0 70 80 90 r00MÆ(MIJM CYCLE DISPLACEMENT (nm)

281

APPENDIX F : Out of-plane Simply Supported Wall Test Results

Heieht 1.485 mIhickness 50 mm.eneth 950 nm

Density x0a kslm'

SEPITMBER9SSPECIMEN 14

SEPTEMBER9ESPECIMEN 14

Figure F 14 - Static Push Test- Un-cracked, 110mn, No Overburden

Figure F 15 - Static Push Test - Cracked, 50mrq 0.15MP¡ Overburden

Applied Overburden 0lMPaFlexural Tensile Strensth, f, 0kPaLinear Elastic Analysis Prediction 0.0711k1.1Rigid BodV Analysis Prediction 0.t07lkt'I

SÎATIC PUSH TEST. MID HEIGTIT POINT I-OAI)

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0.11

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0

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-. - AI.TEtrI DINAII,ÍIC E,PERIMENTAL FIoRcE (kÐ+FRIGIDBODY (KÐ

TO DYNAMIC TESTING

0 5 10 15 20 25 30 35û4550MID,HEIGIIT DEFLECTION (MM)

Heisht L485 mlhiclness 50 mmængth 950 mm

Density 2300 ksÍn'

Applied Overburden 0.15lMPaFlexural Tensile SEength, f, o[<PaLinear Elastic Analvsis Prediction 0.47rlkl:{Rigid Bodv Analysis Prediction 1.M^kl,I

STATIC PUSH TEST - MID IIEIGTIT POINT LOAD

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0

0 5 10 l5 20 25 30 35 40 45 50

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_ FORCE (kN)?-RIGIDBODY (kN

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f -\

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282

APPENDIX F : Out- of-planc Simply S upported Wall Te st Re sults

MIDIIEIGHT RESPONSE DISPLACEMENT

50

40

30

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40-50

60

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SIMPLY STJPPORTED URM WALL RELEASE ÏEST RESTJLT PLOTS

SEPIEMBER 98 -Specimen (10) - Release Test (1)

MIDHEIGTIT }IYSTERESIS

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Figure F 16 - Release Test (1) - 50mnu No Overburden

MII>HEIGHT RESPONSE ACCELERATION

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APPENDIX F : Out-of-plnnz Simply Supported WaII Test Results

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SEPTEMBER 98 -Soecimen (1) - Release Test (2)

Figure F 17 - Release Test (2) - 50run, No Overburden

284

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APPENDIX F : Out- of-plane Simply Stryported WaII Test Results

MIDHEIGIIT RESPONSE DISPLACEMENT

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SEPTEMBER 9E -'Snecimen (1ì - Release Test (3)

Figure F 18 - Release Test (3) - 50mn,0.t75MPa Overburden

MIDHEIGHT RESPONSE ACCELERATION

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APPENDD( F : Out of-plnne S imply Supp orted WaIl Te s t Re s ults

SEPfEMBER 98 - Specimen (111 - Release Test (4)

Figure F 19 - Release Test (4) - 110mn, No Overburden

MIDHETGHT RESPONSE DISPLACEMENT

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APPENDIX F: Out-of-planc Simply Supported Wall Test Results

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APPEND IX F : Out- of-plane Simply Supp oned Wøll Te s t Re sults

-INSTRON

DISPLACEMENTS

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WALL ACCELERATIONS BWA

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APPENDIX F : Out- of-plane Simply Supported Wall Test Results

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SEPTEMBER 98 - specimen (101 - 05Hz Hatf sine Dispracement pulse

Figure F 25 - 05Hz Half sirc Displacenrent pulse,50mnu 0.û75Mpa overburden

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APPENDIX F : Out- of-plane Simply Supp orted WaIl Te st Re sults

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BWAWALL ACCELERATIONS

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AP PEND IX F : Out- of-p Inne Simply Supp oned WaIl Te st Re sults

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294

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APPENDIX F: Out-of-planc Simply SupportedWall Test Results

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SEPTEMBER 98 - specimen (101 - L.0H2 Hatf sine Displacement pulse

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BWAWALL ACCELERATIONS

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APPENDIX F : Out- of-plnne Simply Supp orted Wall Te st Re sults

SEPIEMBER 98 - Specimen (1.01 - 1.0H2 llalf Sine Displacement Pulse

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SEPTEMBER 98 - specimen (10ì - 2.0H2 Half sine Dispracement putse

DISPLACEMENTS

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298

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SEPTEMBER 98 - specimen (11) - 1.0H2 Hatf sine Displacement Pulse

Figure F 34- 1.0H2 Half Sirrc Displacenænt Pulse, 110mn, No Overburden

301

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APPENDDI F : Outof-plane Simply Supported Wall Test Results

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-0.1

4.2

{.34.4

ozI3áfIlJt¡lUU

INPTJT ACCEIÆRATIONS

-TI\BLEAg -FRAMEAg0.3

0.25

0.2

0.15

0.1

0.05

0

4.054.1

4.r54.2

à0

zot-dÍ¡l¡t¡ìUU

I I

rl Ill

1

tl'lü' .ì ñ ì l&; + .r r;' --r di oil HF(I

lllTIME(SECS)

300

AP PENDIX F : Out- of-plnne Simply Supp orted Wøll Te st Re sults

DISPI-ACEMENTS

-MWDm -INSTRONrm -- .. -TWDmn

Àt<zf¡làl¡,¡C)

JÀ(t)H

15

10

5

0

-5

-10

-15

-20

-25

-30

:35

-40

Âll iili fiit ,A

elhæ 1l oc.l9qóoo ¿I -1 Aì\oGlnnh\o vl0q

rrl/

ll

t I

I:. TIME (SECS)

SEPTEMBER 98 - specimen (10) - 2.0H2 Hatf sine Displacement pulse

Figure ß 32- z.OHz Half Sine Dis¡¡lacenrcnt Pulse, sùrun, 0.l5Mpa Overburden

WALL ACCELERATIONS

-TWAg -MWAg BWAg

¡fl¡Å il t

næ d!9qooo

I'I

t-ld

lr1¡ì\o noqrr

I f I ¡

ìj UI r I T

TIME (SECS)

15

O129 o.sF

áf{0t!(J?¿s

I

-15

INPUT ACCELERATIONS

-TABLEAg -FRAMEAg

è0

zo,kúslJt¡)QC)

I0.80.6

0.4

0.2

04.24.44.6-0.8

-1

-1.2

I¡l I

I¡r l1 t rlìA¡4,¡.¡"rÀ I m ¡1'1À.4 .-.- ^"Â flt ¡r-aÅo .^ --..¡.i f,.|\ .n ¡ ,iY ï_\'ïg ; ;-"JTI Jtt",rl'¡i'; oO

I a Nr N ! Ì1 ç \Ô l, p r r r

ì ITIME (SECS)

299

AP PENDD( F : Out- of-plane Simply Supp orted WøII Te s t Re sult s

-MWDmm -INSTRONm *--=-TWDrmDISPLACEMENTS

25

20

^15äroF2f¡¡ 5ar¡l?0JÀØ-)â

_10

-15

-20

-25

I

IilI t tlh i

æT aÉ d \cit- oqçq

iNO

flI

!l

}

¡

TIME(SECS)

SEPIEMBER 98 - Specimen (1.3) - 1.0IIz Gaussian Displacement Pulse

Figure F 36- 1.0H2 Gaussian Displacenrcnt Pulse, 110nur¡ No Overburden

-TWAg -MWAg Bv/AgWAII ACCELERATIONS

II I

¡

F-

Iôl

t:r Ilft, l,

l. Ër| 1'.

lr \lô¡ ñ

Iil I

rnm, lsncs¡r'Il¡

0.5

0.4

O o.¡

é o.zL¡< 0.1ú5of¡ìI ¡.r4' 4.2

4.3

4.4

-TABLEAg -FRAÀ,IEAg

0

4.05{).1

4.154.2

4.254.3

{.35

'l I Ih¡^--. JIl{l: o\e{É ;-i lrll"r

f -!ñFt

OræO\ç.-elóçn\oc- 000\È ÈÈôìclclc ô{ (\ e.l

TIME(SECS)

INPUT ACCELERATIONS

vFiúBÍllU(J

0.r5

0.1

@ o.os

303

APPENDIX F : Out- of-plane S imply Supported WalI Te st Re s ults

-MWDmm -INSTRONm -----TWDm

45û3530

â25À¿nF15ãroã53:Fr -J

F -roH

-15-m_25

-30_35

445

SEPTTDMBER 98 - specimen (131 - 1.0H2 Gaussian Displacement pulse

Figure F 37- 1.0H2 Gaussian Displacenrent Pulse, 110mrr, No Overburden

\ryALL ACCELERATIONS

-TWAg -MWAgBV/Ag

0.5

0.4

0.3

o.2

0.1

04.14.24.34.44.5

èo

2oFF&3f¡lc)(-)

Irl ,. II II rl

I I-^.i1.'i tf

I NôIeìôINI

ll ' ln' Ir"' I lr ' I TIME (srcs)

INPUT ACCELER,A^TIONSC

-FRAMEAg0.2

o 0.1z9oFd 4.13I ¡.2U< 4.3

4.4

{.5

¡l ¡l tlI l¿^,

{r¡\o 'l tr.r r 1 r

O\OÊ ôì¡ l^.1 / lL^.

^-, Õçn\ocl c.¡ ô¡ N

TTME(SECS)

304

APPEND IX F : Out of-plnne Simply Supp orted WaIl Te st Re sult s

_M.WDmn _INSTRONnn -____TWDmm

706560555045

È40e35F. 30Z1<q2ññ15Yl0J5àoã-s- -10

-15-20-25-30-354045-50

SEPTEMBER 98 - Soecimen (13) - 1.0IIz Gaussian Displacement Pulse

Figure F 38' 1.0H2 Gaussian Displacenænt Pulse, 110mÍL No Overburden

-TWAg -MWAgBWAgV/AII ACGT.ERATIONS

0.4

0.3oz 0.2oE o.t

ßo,lt¡lg {.r'n.2

{.34.4

t l[' trl Ilr

t I I I

I

I

III

I

€ \o

I

TIME(SECS)

INPUT ACCEI.ERATIONS

-TABLEAg -FRAMEAC0.3

0.2

0.r

0

4.1

4.2

4.3

4.4

{.5{.6

4ztrúsr¡lc)O

I

I ¡I I i

TFc- il t i-l "

!-..rlT {re.,¡o{nFæ O\ÈÊÈid e{ ôì e.l cì c.¡ ê.¡ cl o d

I

I

ìTIME(SECS)

305

APPENDIX F : Out- of-plane Simply Supp orted WalI Te st Re sults

-MWDmm

_INSTRONmm ____-_T.WDmm

6055504540

^35ãroázss20zt5Erof¡l JOOd -ro? -tsÅ -20

_25-30-354045-50-5550

SEPTEMBER 98 - specimen (13) - 1.0H2 Gaussian Disolacement Pulse

X'igure F 39- 1.0H2 Gaussian Displacenænt Pulse, llùûr¡ No Overburden

WALL ACCELERATIONS

-TWAg -MWAgBWAg

e9zoFúf¡l'-.1fJl(J(J

0.5

0.4

0.3

0.2

0.1

0

{.14.24.34.4{).5

¡ t" rl I L

F-

so\

'l lllJl' rl

II U t', it liUI I

TIME(SECS)

INPUT ACCELERATIONS

-TABLEAg -FRAIT,EAg0.6

o0¿á 0.,tr¿o3E o.zU<4t

4.6

4.8

I I ,J t

o\ tr- T 91..

c- o\

ïïME (SECS)

306

APPENDIX F : Out- of-plane Simply Supported WalI Test Re sults

_MWD mm

-INSTRON

mm -.- -TlyD mm

I

IIl I

.1ilf11". ,, . ,lilth. i. t.l¡. lllflhr

cìtq---1---F IK f9d

:t n æ'¡{t'; o{ ;;I9:Srr) ñ

lHll'; ød rl illñ r æ o r. þlhr d d o o Ì1

I

I

60

5040

e30âto2togoE -roÍ -zoctr2 -c¡â--

_40

-50

{0:70

-80-90

DISPLACEMENTS

TIME

SEPIEMBER 98 - Soecimen (1.3) - 05Hz Gaussian Displacement Pulse

Figure F 40- 0.5H2 Gaussian Displacenænt Pulse, 11ùûn' No Overburden

WAIIACCEI-ERATIONS

-TWAg -MWAgBWAg

0.4

0.36Z o.z

F 0.1

*oFl

I ¡.rO< 4.2

{.34.4

rl I i

I II I

ì¡ì

Io o\

il' ô.t cì ôlfl"'

rnrlSnCS¡l Ill

-T'ABI.EAC -FRAMEAg

III

,{tr,,F ü"o".;io*'^\o el sfr-.'9

'llr!l-.....''.''.''',.'Èho!+o-i--..:Èi,

ôt€o/i -.,: cì F-æeìv

fI

TIME(SECS)

0.3

0.26á o.toÈ-O

E o.tt¡l8 {.2

4.3

4.4

4.5

INPUT ACCELERATIONS

307

AP PEND IX F : Out- of-planc Simply Supported Wall Te s t Re s ults

-MWD mm

-INSTRON

mm ---'--TWD mm1009080't0

^60Ès03n230Ërot¡¡ l0Vod -roâ -ro

-3040-50{0:7O

-80-90

SEPTEMBER 98 - specimen (13) - 05Hz Gaussian Displacement pulse

Figure F 4f- 05IIz Gaussian Displacenænt Pulse, llùrun, No Overburden

-TWAg -MlgBV/Ag

WAII ACCELERATIONS

lrr rlI ¡, I

F-

ll I I

I I q ì{ I trr l,

0.5

0.4

0.3

0.2

0.1

0

4.14.2{).34.44.5

€9zoH

ú3t¡lOO

INPUT ACCELEKA*TIONS

-TABLEAg -FRAMEAg0.3

0.2

ô 0.1zotsúf4Èt¡lUU

0

4.14.24.34.4{.54.64.7

I

¡ ¡ ,lå.\1a., ,, ,J

R' 09sc¡9c¡ æ ¡- È-

I E¡Lh,¡¡ . .lil

H K''äi' =Êc¡ol¡-' ,r'lf-.F.r'' . 'çtn\o

el(îr\oræ Èôlelô¡e ô¡c¡e.¡ct

I

I f

TItr4E (SECS)

308

APPENDD( F : Out-of-plane Simply Supported WalI Test Results

-MWDmn -INSTRONmn

-__TWDmm

r

9080706050403020l00

-r0-20-3040-50{0-70-80-90

-100-r r0

eÉãztrl(J

Jo"9H

SEPIT,MBER 9E - Specimen (13) - 05Hz Gaussian Displacement Pulse

V/ALL ACCELERATIONS

-TWAg -lvIWAg BWAg

TIt\tE (SECS)

o.4

0.3

0.2

0.1

0

{.14.2{.34.44.54.6

€9zoFr

d5E¡C)(J

lrl.I tutI

i,ì1 i.l! t:,1

I i ,.11. ü

c- æo\

Figure f 42- O.sHz Gaussian Displacenrent Pulse, 110nnn, No Overburden

INPUT ACCEI-ERATIONS

-TABI-EA FRAMEAg

0.40.3

6 0.2zotsút¡lÞlrdO(J

0.1

04.14.24.34.44.54.64.7

I I Irl it J rl,tut ¡.L-L ù-tl.

o¡ \o æÈ( F+ N I qv r ^aÈdosn9ricìaìddôldôl(

I I

TIME (SECS)

309

APPENDIX F : Out- of-plane Simply Supported WalI Test Results

SIMPLY SUPPORTTD IIRM WALL TRANSIENT EXCITATION TEST S

Figure F 4! Transient Excitation Test - 667o E;lcentro, 110nrn, No overburden

-MWDmm -INSTRONnn

_--_-TWDmn

STJPPORT.INSTABILITYWALLMID-IIEIGI{T HIT

t20ll0100908070605040302010

0-10-20-3040-50-60-70-80-90

-r00-1 10

âÉ,t<zt¡¡

Ë(J.ltuØ

-TIVA g

-MWA g BWAg

WALL ACCELERATIONS

0.8

0.6

0.4

0.2

0

4.24.44.64.8

-1

ezEúr¡lÈt¡JU(J

TIME (SECS)

ACCELERATIONS

0.3

0.25

O o.z

Z o:sã o.rdI¡t 0.05JBo? o.os

4.14.154.2

-TABIÆAg -FRAMEAgI

I lr r tl¡ tl f I lt I t h ¡ ¡ I t.

ol-i { í ìf -{lI r

It TIME (SECS)

310

DISPLACEMENTS

-ìr[WD mm

-INSTRON

mm

-TWD

mm

eáFzf¡ì(J

JÀ?H

t2.5

l0

7.5

5

2.5

0

-2.5

-5

-7.5

-10

i

t il {r

ç I{ ô€dErìoq

\(/

TIME (SECS)

APPENDIX F: Out-of-plane Simply Supported WaIl Test Results

X'igure F 44 - Transient Excitation Test - 1ü)7o Nahanni' 110mrrD No Overburden

WALL ACCELERATIONS

-TWAg -MWAgBWAg

6zoF¿3t¡¡O(J

0.4

0.3

0.2

0.1

0

4.14.24.34.44.54.6

I

¡

ÈrrlLi

oo t- c- F-II

ITIME(SECS)

INPUT ACCELERATIONS

-TARr F Ag

-FRAlvfE Ag

0.4

0.3

0.2

0.1

0

{).1

4.2

4.3

4.4

{.5

.:9zFdSfr¡Q(J

II. .it l¡ I

Sh\Ot'.€O\ÉÊçno\hc)È

|ll'lI

TTME(SECS)I

311

APPENDD( F : Out- of-pluc Simply Supported Wall Test Results

WAIIACCELERATTONS

-TVlAg -MWAgBWAg

0.6

o 0.4

0.2

0

4.2

4.4

4.6

c)È

TIME(SECS)

INPUT ACCELERATIONS

-TABLEAg --FRAIvfEAg0.8

0.6

0.4

0.2

0

4.2

4.4

4.6

{.8

ezIt-d3EI()(J

I

I I ll. ilr ì llll-'r,,À^..Jì *... n. Jl¡1. ^ a -,slsrK lll Ého\ho\ËæmF.c.¡

dir¡ç^'::jj^irl, 'v r rl llf h ó hl¡-i æ çi È-l

tuF¿\.t' hi\oo cì I ÈÈÉÉ-s v I tr æ o\I

I

TrME(SECS)

Figure F 45- Transient Excit¡tion Test- 2NVo Nahonn¡, lllhrrnr, No Overburden

_MWDmm _INSTRONnn ___..TWDm

IF.zgf¡¡UJo.?H

2522.5

20L7.5

15

12.5r0

1.55

2.50

-2.5-5

-7.5-10

-r2.5-15

-17.5

I

/¡t ^./\&-prci ¡(}

I

ITIME (SECS)

312

APPENDIX F : Out- of-pløne Simply Supported WølI Test Results

WALL ACCF'I FRATIONS

-TWAg -MWAg BWAg

oo

zot-ú5r¡lC)c)

0.8

0.6

0.4

0.2

0

4.2

4.4

{).6

4.8

eìo¡o\

TIME(SECS)

Figure F 46 - Transient Excitation Tæt - 3û07o Nahanni, 110mn, No Overburden

mm _INSTRONnn -"_-_TWDmm

30

25

20

9ts3rof-Ásño(J

S-so.

É -to-15

-20

_25

-30

-35

[, l1 ¡ fi

ilft

ì +v,

Jo

oôÊÈ 'iI ,xn ls

\/o1, lo\t-\/¡

r r æ Ø q

ITrME (SECS)

INPUT ACCELERATIONS

-TABLEAg -FRAMEAg0.8

^ 0.6€9

é o-qFFS o.zf4!E0c.)< 4.2

4.4

{.6

I

ll,I il

. ^nilllO\næodl-j ur

I

Ill' TIME(SECS)

313

APPENDIX F : Out- of-pløne Simply Supp orte d Wall Te st Re sults

Figure F 47 - Transient Excitation TesJ - 4007o Naharmi, 110mn, No Overburden

_MWDmm _INSTRONnm .. '-_,TWD-m30

25

20

^15äroFãsfrol-sor

É-r0-15

-20

-25

-30

-35

llI iT l

{1, \ t / \ A I:'j'' ''-lll'ifl I

" "l/"il ,høhæ ,lr I ø rd ',f+ .U

llv

I TIME (SECS)

-TWAg -M\ryAg BWAg

WALL ACCELERATIONS

0.6

o 0'4

z9 o.zFú140Jt¡¡U? o.z

{).4

4.6TIME (SECS)

-TABLEAg -FRAMEAg

It

I ,l¡

i, À¡r.,-, MO\hO\rf,æo r c.¡ï rl) r æ q" lt,lïl

TIME (SECS)

0.8

0.66¿0AF o.zd30i:J

8 4.2

4.4

{.6{.8

INPUT ACCELERATIONS

374

DISPLACEMENTS

130120ll01009080706050403020l00

-10-20-3040-50{0-70-80-90

-100

G.

ÊãzE2r¡l(J

,¡ÉLØo

-MWDmm -INSTRONnn --TVfDmm

l.

il it

¡l i

a( ¡\ l@ l\-U-'

APPENDIX F: Outof-plane Simply Supported Wall Test Results

Figure F ¿|8 - Traruient Excitation Test - 67o E;lCentro, 110mn¡ No Overburden

WALL ACCEIÈR,ATIONS

-TV/Ag -MWAgBWAg

€9zts

dÍÐJt¡lU(J

0.6

0.4

0.2

0

4.2

4.4

4.6

4.8

-l

trL,- ,hrl ttär, lt,..lÅ., ¡l I

TIME (SECS)

INPUTACCELERATIONS

-TABLEAC -FRAMEAg0.3

^ 0.219z9 o.rF

Éof¡l(.)

? o.r

4.2

{.3

I

I

I

[' 'ltll

ITTME (SECS)

315

APPENDD( F : Out- of-plnne Simply Supported Wall Te st Re s ults

-MWDmm -INSTRONñm -TWDmm80

70

60

50È¿oè-302H202Broloâ¡

É -t0-20

-30

-40

-50-60

-70

11il

¡. rA il

I Il/

I {t AJ 1,1iltÀrN,rf æ d þ ;t t¿¡l lllil{I'.ä\*^ä';/'' oq r'\.¡ p -,.{q -\Þ /Êdo* t{il/ fllFì : = = = = : F Ft--6Fã -' ñ K r-" Ë 3

I I

v

TIME (SECS)

Figure F 49- Transient Excitation Tæt - 667o Pacoirm Daq 110mnU No Overburden

WALL ACCELERATIONS

-TWAg -MWAgBWAg

0.4

0.3

0.2

0.1

0

{.1

4.2

{.34.4

ozoFút¡ldU(J

I tt¡Jl I

it I rllllI

I |l

i I s N õ

\ tl'I I

f Til i,II

TIME (SECS)

-TABLEAg -FRAMEAg

INPUT ACCELERATIONS

0.4

0.3

0.2

0.1

0

{.14.2{.34.44.5

€9zoH

drllJr¡(J

?

I

ilt ù.¡<æôl\o

c.ìmtç m

rI

TIME(SECS)

3t6

APPENDIX F : Out- of-plnne Simply Supponed Vlall Te st Results

-MWD

mm

-INSTRON

mm

-TWD

mm

¡ A

,t I t/1 t¡I ill ït

lt/t ilt ht lh,\Þ1 Fll+ì : 16= Y F ì.TuÞffi tì Ë ëì- àà ¡iÊNo{

lvv

TIME (SECS)

80

70

60

50403020

10

0-10-20-30-40-50-60

-70

å2

ãz¡¡lUsÞrØo

Figure F 50- Transient Excitation Test - 807o Pacclirm Darn, 110mn¡, No Overburden

-TWAg -MWAg BWAs

WALL ACCELERATIONS

I I

¡l il¡I

I

ilII

TIME(SECS)

0¿

0.3

o o.zzv 0.1F-fof¡¡d ¿.r(J

? ¡.2{.34.44.5

trNPIJT ACCELERATIONS

-TABIß Ag

-FRAME Ag

LQzot-árqJEU

0.3

o.2

0.1

0

4.1

4.2

4.3

4.4

I

j

1r \oêì o

I

TIME (SECS)

317

APPENDIX F : Out-of-plane Simply Supported WqlI Test Results

-MWD mm

-INSTRON

mm

-ÎYy'D mm

100

90

80

70

9ooã50ã¿ol'ì 30

iroc.iÉLO!

0

-10_20

-30

40-50

í\WALLMID-IIEIGI{T TIIT STJPPORT - INSTABILITY

tA

rì

I Iil I illl

It/ I |+{t Itl, . \ .\t9Qer_E iJ lq-q "t - 4 ç "q -\. ç'L'ö/-''bi;"/'i";iNñç tþl r ; J\r¡l\zãv/?r = ñ \.r

^r-.,è- N a \L/ àì ¡ä

t

yv

TIME (SECS)

Figure F 51 - Traruient Excitation Test - 1fi)7o Pacoinra Dan¡ 110mn¡ No Overburden

-TWAg -MWAgBWAg

WALL ACCELERATIONS

0.5

0.4

o 0.3

6 o.zFI 0.1drq0!E ¡.r(J< 4.2

-0.3

4.44.5

'l llrI tl

lll'

TIME (SECS)

INPLTT ACCELERATIONS

0.4

0.3

I o.zzI o.tFSoñEl 4.1(J

2 4.24.3

4.44.5

-TABLE Ag

I

¡ lrI

nhhh

1 ddN ddd

TIME (SECS)

318

APPENDIX (G): Non-linear Time History AnalysisROWMANRY FortranTT Code

Program rowrnanryc lilriüen February 1999c Program "ROWMANRY" was derived from the original progr¿ìm "romain"c to determine the rocking behaviour of both rigid and semi rigidc objects making allowance for various support conditionsc The main program drive subroutine is "Row-ray" whichc determines the displ. time-history of a rocking modelc using a tri-linear dynamic force displacement profile approximationc Rayleigh damping is assumed with an iterative half cycle process usedc to ensure the proportional damping assumed at the start of each half cycle is appropriatec at the end of the half cycle (where the instantaneous frequency is known)c An initial damping coefficient of 3 is adopted however with the iterative processc generally is not critical to the successful running of the programc Uniform wall properties are assumedc The acceleration data filename ACTIVE, time-step dt and the analysis timec segment ta are required as input.c The program will produce time-history arrays of the relativec displacement u, relative velocity v, and total acceleration atc at the top of a free standing object or mid height of a propped cantilever.c Maximum u, v and at will be displayed on screen at run time.c There is an option to writ€ the time-history series to a new filec with the filename designaæd by the user (char variable ofile)-

character *50 ACTIVE,TEXT,ofile,typecharacter *1 yesnocharacter *60 codeinteger NN,NTP,NT,NK,kinæger IOS,ERL,X,Y,Lreal ts(O: I 2000),as(0: I 2000)real alpha, dt, ta, ag(0:16384)real u(0: 16384), v(0: 16384), at(O: 16384)real agmax,umax,vmax, aÍnaxreal ke(-l: l), re(-1: l),ulirnit(-l: l),uy(-2:2),pi,greal scalereal h,t,mreal HEFFR,ÌIEFFS, gam,PCreal a0, al, aOm, alm

c real EM,rdreal PCFreal PDMreal ulim¡bparameter(pi=3.1 41 59265 4)paramet€r(g=g.806)

c Rocking is independent of the mass of the object. Thus, ac unit mass (l.Okg) has been assumed in subroutine roïvray.

m=I.0c

writel*,*¡"*********************tc************r.*t<t *r.r.******r<*****rrwritel*,*¡" hogram ROTWMANRY"wriæ1*,x¡" For time history rocking analysis of'

3r9

APPENDD( G: N0n-linear Time History Arutysis ROWMANRy FortranTT Code

write(*,*)" Free Standing or Simply Supporæd Objecs"write(*,*)" LatestVersion: FEBRUARy1999"wfitel*,*¡******************************************************nwriæ1*,*¡" Units in length - rL time - secs, "write(*,*)" Force - N, Density - kd^t "write(*,*)" Stress - MPa unless shown otherwise "write(*,*¡" "

c Inpuaing accelerogram daø into ag(t) arraywrite(*,*)"fype filename for accel. data [<= 8 Characters]:"read (*,'(a)')ACTIVEL=INDEX(ACTIVE,')ACTIVE(L:L+4)='.csv'

c wrir€(*,2000) ACTIVE(1:L+4)write(*,*¡ " "write(*,*)" --- FORDEFAIJLT VALUES I I TYPE 0 ---"writelr',*¡ " "write(*,*)"Type scaling factor for ground accel. [1.0]:"read(*,*)scaleif(scale .eq.0.O)then

scale=1.0writel*'x¡ " "writelx,*¡"-- DEFAIJLT SCALINGFACTOR [1.0] ADOPTED -- "writel*,*¡ " '

end if5 write(*,*)"Type time step interval dt [0.01]:"

read(*,*þtif(dt.eq.0.O)then

dt{.01write(*,*) " "write(*,*) "-- DEFAIJLT TIME INCREMENT [0.01] SECS ADOPTED --"wriæ1*'*¡ " "

end ifopen(25,file=ACTIVE,staü¡s='old',iostaFIOS,ere I 000)

c Go passed 8 header lines in datafileERL=ldo l0 k=I,8

read(25,'(a)',iostat=IOS,err= I 0 I O)TEXTERL=ERL+1

l0 continuec read (25,*,iostat=IOS,en=101O)NNc ERL=ERL+I

NN=Odo 20 k=0,16384

read(25, *,iostat=Ios,er=l 0l 0,END=3) ts(k),as(k)NN=NN+las(k)=5salls*asg¡ERI=ERL+l

20 continue3 continue

close(25)wriæ1*'*¡ " "wriæ(*,45) NN

45 format("NUMBER OF DATA POINTS IN INPUT prI F = ",lJ)writel*,*¡ " "

c Data inærpolationcall linter(NN, ts,as,dt"NTP,ag)

320

APPENDIX G: Nùn-Iinear Time History Analysis ROWMANRY FortanTT Code

write(*, *) "Record time is ",rea(NTP)*dt, " seconds"wriæ(*,*)"Type analysis time [Record time]:"read(*,*)taif(ta.eq.0.0)then

ta=eal(NTP)*dtwriæ(*,2010) tawritel*,*¡ " "

2010 forma('-- DEFAULT : IRECORD TIME',F6.3,'secs] ADOPTED -')writelx,x¡ " "

end ifNT=in(taldt)if (NT.gr16384)then

write(*,x)"Required no. of time steps exceed limit of 16384"write(*,*)"Retype longer time step or shorter analysis time"goto 5

elseend ifif(NT.gt.NTP)then

c Augment ag(k>=NTP) with zerosdo 30 k=NTP,NT-l

ag(k)=030 continue

elseend if

4l continuewritel*,*¡"---wriæ1*',*¡" OBJECTRIGIDITYCLASSIFICATION"write(*,*)' Is the object to be analysed either :"writc(*,*)" (Typecorrespondingnumber)"write(x,*¡" "writ€(*,*)"(l) RIGID eg steel library bookshelves"write(*,*)"(2) SEMI RIGID eg simply supported URM wall"wriæ(*,*)" parapetURM wall"writelx,*¡"---read(*,*) Xif(X.ne. 1.AND.X.ne.2)goto 4 1

4 continuec Definition of support conditions

wriæ1*,x¡"WTitC(*,*)" DEFINTTION OFVERTICAL SI.JPPORT CONDITIONS"wriæ1*,*¡" V/hat support conditions exist:"write(*,*)" (Type corresponding number)"writel*,*¡" "write(*,*)"(l) Free standing object, base reaction at LF"write(*,*)"(2) SS non loadbearing, base reaction at LF"write(*,*)"(l) SS loadbearing, top & bottom reactions at CL"wriæ(*,*)"(4) SS loadbearing, top reaction at CL, bottom reaction

+ atthe LF"write(*,*)"(5) SS loadbearing, top & bottom reaction at LF"writel*,*¡" "write(*,*)"where SS = simply supported"write(*,*)" LF = leeward face of object"wriæ1*,*¡" CL = center line of object"

read(*,*) Yif(Y.ne. l.AND.Y.ne.2.AND.Y.ne.3.AND.Y.ne.4.AND.Y.ne.5)goto 4

32t

APPENDIX G: Nùn-linear Time History Anatysis RowMANRy FortranT7 code

cc

c

Inputing structural parametersgam=O.0

wriæ(*,*)"Type total height of the object (m) :"read(*,*)hwriæ(*,*¡"Type total thickness of the object (mm) :"read(*,*)tt=t/1m0.0

cif(Y.ge.3)then

c Loadbearing simply supported requires overburden sfress and densitywriæ(*,*)"Type the overburden stress at top of object (Mpa),'read(*,*)PC

write(*,*)"Type object densiry [1800 kg/m3] :"write(+,x)"[Masonry density approximarely 1500 - 2500 kg/m3]"

read(*,*) gamif(gam.eq.0.0)then

gam=1800.0wriûe1x,x¡ ' "

writelx,*¡"-- DEFAIJLT OBJECT DENSITY [l800kg/m3] ADOPTED --"wriæ1*'*¡ " "

end ifc Calculation ofoverburden stress facûo¡

pCF=2.0*pC* lE6(h*gam+g)else

PC{.0PCF{.0

end ifc

if(Y.eq.1)thentype="Free standing object base reaction at LF"

c Stiffness and resistance acceleration conversion factorsÍIEFFS=1.0HEFFR=I.0writel*,x¡ " "write(*,1)HEFFSwrite(*,2)ruFFRwritelr"*¡ " "

I forma(" Stiffness coefficient (IIEFFS) = ",fl 3)2 forma(" Resistance coefficient (IIEFFR) - ",n 3)

end ifif(Y.eq.2)then

type="Ss non loadbearing G,F)"ÍIEFFS=4.0HEFFR=4.0write(*'r'¡ " "write(*,1)IIEFFSwrite(*,2)IIEFFRwritel*'*¡ " "

end ifif(Y.eq.3)then

type="Ss loadbearing top & bocom (CL)"ÍIEFFS=4.0*(t+pCF)IßFFR=2.0*(1+PCF)wriæ1*'*¡ " "

322

APPENDIX G: N)n-linearTime History Analysis ROWMANRY Fortøn77 Code

write(*,1)HEFFSwriæ(*,2)IIEFFRwritelx,x¡ " "

end ifif(Y.eq.4)then

type="Ss loadbearing top (CL) bouom (LF)"IIEFFS=4.O*(l+PCF)I{EFFR=4.0*( 1+0.7 5 *PCF)write(*'*¡ " "write(*,1)IIEFFSwrite(*,2)HEFFRwriæ1*'x¡ " "

end ifif(Y.eq.5)thentype=" SS loadbearinC top & bottom (LF)"

IIEFFS=4.0*(l+PCF)ffiFFR=4.0*(1+PCF)wriæ1*'x¡ " "wriæ(*,1)IIEFFSwrito(*,2)I{EFFRwritelx'*¡ " "

end ifc Apply SDOF conversion fac0or to ag which does not include the factor

do 60 k=O,NTP-1ag(k)=1'5x¿t1¡¡

60 continuec3000 Continuec Set first half cycle iteration approx proportional damping

alpha=3.0c Set the propofional damping experimental to SDOF conversion factor

PDM=2.0ß.0write(*, +) "Type mass proportional damping coefficienl : "read(*,*)a0

c Modify a0 to fit SDOF modelaOm=PDM*a0write(*, *) "Type stiffnes s proportional damping coefficient. : "read(*,*)al

c Modify al to frt SDOF modelalm=PDM*al

Rigid body complete instability displacement (mm)ulimrb=t* 1 000.0*IIEFFR/I{EFFSSide eccenEicities are t/2 as uniform properties assumedCalculation of the rigid body resistance accelerationre( I )= I . 5 *[IEFFR* g*t/ttre(- 1)=- 1.O*re(1 )Calculation of the rigid body negative stiffnesske(1)=- 1.5*tfrFFS*c/hke(-l)=ke(1)

Completely rigid objecsif(X.eq.1)thenSetting the rocking displacements to a nominally small value (>0)

uY(l)=l.E-4

cc

cc

c

ccc

c

323

APPENDIX G: N0n-linearTirne History Analysis RowMANRy FortanTT code

cc

uy(-l)=l.E-4uY(2)=t.f,-4uy(-2)=l.E-4ulimi(l)=ulimrbulimi(- I )=- | *ulimit( I )

end if

Semi rigid objoctsif(X.eq.2)tben

wriæ1*'*¡ " "write(*,*)"Type disp.rocking expected to commence (mm)"writ€(*,*)"(This disp. dictates the initial rocking stiffness"writelx,*¡" and must be greîrur than zero)"read(+,*)uy(l)uy(l)=uy(1)/1000'0uy(-l)=-1.O*uy(l)write(*'*¡ " "wriæ(*,*)"Type disp. at start negative stiffness (mm)"wriæ(*,*)"(1his disp. dictates the peak rocking resistance',

wriæ(*,*)" plateau as it is the point of inærsection of'wriæ1*,*¡" the semi rigid and rigid body force disp profiles)"read(*,*)uy(2)uY(2)=uY(2)/1000.0uY(-2)=- I .0*uY(2)write(*,*)"Type complere insøbiliry disp (mm) IRIGIDI"u'dte(*,71) ulimrb

Format("I-ess than or equal to 'f6.2," (mm) - RIGID -")read(*,*) ulimi(l)if(ulimit( I ).eq.0.O)thenulimit(l)=ulimrbwriæ1x,*¡ " "\4,rite(*,72) ulimrb

forma('--DEFAULT INSTABILITY DISP|,F6.2,'I mml ADOPTED--')wriæ1*,*¡ " "

end ifulimi( I )=ulimi( I Yl 000.0ulimi(- I )=- | *ulimit( I )

end if

Doing the achral computationscall rowray( l .0, alpha,re, uy,ke,ulimit NTdÇ ag,u, v,at code, aOm+,alm)Finding the maximum out of each arraycall fndmax(NT, I 6384,ag,agmax)call fndmax(NT, I 63 84,u, umax)call fndmax(NT, I 6384,v,vmax)call fndmax(NT, I 6384,at,aunax)

Oupuning the key results ûo screen(system output)write(*,*¡' "wnte(*,22þúeformat("ANALYSIS CONCLUSION : ",a60)

If the code message does not begin with "M" for "Model"go straight to the end of the program.if(icha(code(l : l)).ne.77)goûo I 100write(*,*)"Analysis results summary: "

7l

72

22

cc

c

cc

cc

324

APPENDIX G: N0n-linear Time History Arulysis ROWMANRY FonranTT Code

cc

write(*,21)"Max. rel. displ. = ",umaxwrite(*,21)"Max. rel. velocity = ",\'maxwrite(x,21¡"tax. total accel. = ",atmax

2l format(a21,1x,f9.6)

Setting effective parameters back to originaluy(1)=1000.0*uy(1)uy(2)=1000.0*uY(2)t=t*1000.0

I7

Reporting the time-history ouÞutwriæ(*,*)"Time-history results can be written to a file"write(*,*)"Type y/n to indicaæ if hle is wanûed:"read(*,'(a)')yesnoif(ichar(yesno).eq. 1 1O)goto 30 10write(*,*)"Specify output filename [<= 8 characters]:"read(*,'(a)')OFTÍ FÞINDEX(OFil-E,' ')OFILE(L:L+4)='.csv'wdte(*, *) OFILE( 1 :L+4)

open( I 5,file=ofile,iostat=IOS,ERR=l 020)write(*,*)"Type no. of time steps for every reported results"read(*,*)NKwrite(15,*)'***t *4c**********ll****r<*****'F**************d'**t'********¡** ***** * ** **** * *r. ** * n

write(ls,*)" ProgramROWMANRY"*,rite(15,*)" For ti¡ne hisûory rocking analysis of'wriÞ(I5,*)" Free Sønding or Simply Supported Objects"wriæ(15,*)" Latest Version : FEBRUARY 1999"wriæ115,*¡"*t t<*** ****t<*******r<****t*****************t<****t *r.***1.1c

¡****** **i<* ** * ** * rc * * *rr

wriæ(15,+)"Ouþut filename : ",ofilewriæ( 15, l7)"Accelerogram data from : ",ACTIVEformat(a23,lx,al3)

wriæ(15,18)scaleformat("Accelerogram scaling factor selected - ',f7.3)

write(15,t)'"Echo input datawrite(15,*)"INPUT DATA SUMMARY FOR: "write(15,*)typewrite(Is,*)" "write(15,11)h

format("Height of object = ",f7.3," m")wriæ(15,13)t

format("Object width = ",f7.3," mrn")write(15,9)PCforma("Overburden sEess at top of objec¡ = " ,f7 .3," MPa")write(15,*)" "write( I 5, *) "Tri-linear force disp profile data"wriæ(15,16)uy(l)

format("Disp I selected for initial stiffness = ",f5.2," mm")write(15,26)uy(2)format("Disp 2 selecæd for maximum force plateau = ",f5.2," mm")

wriæ(15,1)HEFFSwrite(15,2)IIEFFRwrite(15,*) " "

18

cc

c

c

lll3

9

l6

26

325

APPENDIX G: N0n-linearTime History Analysis ROWMANRY Fortran7T Code

wriæ( I 5, *) "Proportional damping data"wriæ(15,27)a0

27 format(" Mass proportional damping coeff. = ",f7.4)write(15,28)a1

28 format(" Stiffness proportional damping coeff. = ",17.4)wriæ1t5,*¡" "write(15,*)" "wrire(15,22þodewriæ(15,12) ø, dt

12 forma('Analysis time =',f7.4,'secs time inc =',f5.4,'secs')write( 1 5, *) "Iæ gend :, ag = input ground acceleration "write( I 5, *) ",u = relative displacement"write(I 5,*)",v = relative velocity"write( I 5, *) ",at = total acceleration"write(15,*)" "write( I 5, *)"Time,ag(m/s/s)

+,u(m),v(m/s),at(m/s/s)"c Printing the maximum out of each array

wriæ( 15,42)"Maxim :",agmax,umax,vmax,aÍnax42 format(a6,',',f7 .3,',',f9 .6,',',fl .3,',',f8.4)

write( I 5, *) "Tirne, ag(m/s/s)+,u(m),v(m/s),a(m/s/s),experimental u(m)"

c Printing the time-history ¡uraysdo 40 k{,NT-l,NKwriæ( I 5,5 1 )rea(k) *dt"ag(k),u(k),v(k), at(k)

5 I forma(f6.3,',',f7.3,',',f9.6,',',f7.3,',',f8.4)40 continue

close(15)3010 write(+,*)"Type y/n to continue analysis:"

read(*,'(a)')yesnoif(ichar(yesno).eq. 1 I O)then

goro 100else

c Re-Setting effective parameterst=t/1000.0goto 3000

end if100 wdte(*,*)"Program completed"

stop

Error messages0O0 write(*,1001)"opening file ",ACTWE

l00l format("Error in ",al3,al2)goro ll00

I 0 I 0 wriæ(*, I OO2)"reading fiIe",ACTIVE,ERLgoto I100

1002 format("Error in ",al3,al2,"atline ", i5)1020 wriæ(*,I001)"opening hle ",ofile

goto ll00I 100 \r,rite(*,*)"Program aborted"

stopend

cc1

326

APPENDIX G: N0n-Iinear Time History Analysis ROWMANRY FortranTT Code

cccccccccccc

ccc

Subroutine rowray(mrpcrreruyrkerulimrNTrdtragrufrvratrcoderaOm+,alm)Rowray was originally derived from Rotha including atrilinear static force displacement relationshipIterative half cycle procedure to determine Rayleigh dampingcoefficient for current instantaneous frequencyuy(1) is the initial positive rocking displacementuy(-l) is the initial negative rocking displacementuy(2) is the secondary positive rocking displacementuy(-2) is the secondary negative rocking displacementre(l) is the completely rigid positive rocking resistancere(-1) is the completely rigid negative rocking resistanceke(l) is the rigid body stiffness for +ve rockingke(-l) is the rigid body stiffness for -ve rockingulim(l) is the +ve ultimate displacementulim(-l) is the -ve ultimate displacement

Declaration of parameterscharacter*60 codeinteger NTreal m, pcreal ke(-l:1), re(-1:1), W(2:2), ulim(-l:l)real ag(0:16384),dtreal u(0: 16384), uf(O:16384)real v(0: ló384),at(O: I 6384)Decla¡ation of local variablesinteger Jevenq k, j, p, e, d, X, Yinæger f, I, I, pxreal ry(-1:1)real du, dv, da, a, dag, dpsreal ktsl, ktsp, kts2real fl,f2,f3rcal t0,tl,AJj,t4real pi, plreal alm, aOmreal dpsx, dpsy, nc, jx, jyreal ay, axparameter(pi=3 . I 41 59265 4)

c

cc Initialise conditions

u(0)=0.uf(0)=0.v(0)=0.a{.ag(O)=0.at(O)=0.Jevent=0UYY=O.0tO=O.0tl=0.0t2=0.Oß=0.0t4d).0j{e=0d=0

327

APPENDIX G: NÙn-linear Time History Analysis ROWMANRY FortranT7 Code

c5

c

P=Oxd)y{f{I=1px=Ocode="Model did not rock"

continueif(e.eq.l)thenReset time st€p at start of iteration

I=yend ifif(d.eq.l)thenReset time step at start of iteration

I=xend if

open(unit= l,file='out. dat',status='new')write(I,*) "NT I(=x) pc"write(I,*) NT, I, pc

u(k) is the displ. obtained at the end of each time sæp, anduyy is the displ. calculated and updated within the time step.Time history computation do-loop

do 10 k=I,NT-lif(f.ne.l)then

c Determine pseudo-static force for each time-step exceptc on iteration where returned ûo previous zeroed conditions

dag=¿g1¡¡- ag(k-l)fl = m*dagf2 = m*((4.*v(k-l)/dt)+2.*a)f3 =2. * pc * v(k-l)dps = f2+f3-f1uyy=u(k-l)

elsec Reset flag for refurned ûo previous zeroed conditions

f{end if

Time sæp counter for time between zero crossingst0=0+dtif(dps.eq.0.0)then

u(k)=uYYgoto 25

end ifBEGINEVENT ITERATION:

Determine the dynamic stiffness profile for theparticular proportional damping coefficient

Determine pseudo-static stiffness (Jevent I rocking stiffness)ktsp=(4. *nr(d t* * 2.))+ (2.* pc I dt)

Rocking threshold accelerationry( I )=re( I )+ke( I )*uy(2)+kæp*uy( I )ry(-l)=re( l)+ke(- I )*uy(-2)+ktsp*uy(- l)

Determine Jevent 0 rocking stiffness

c

cccccccc

c

cccccc

c

c

328

APPENDIX G: N0n-Iinear Time History Anølysis ROWMANRY FortranTT Code

cktsl=ry(l)/uy(1)

Determine Jevent 2 rocking stiffnesskts2=ktsprke(1)

write( l,*)"kts 1 ktsp kts2"wriæ(1,*) ktsl, ktsp,kts2

continueNON ROCKING (DISP INCREASING ORDECREASING)

if(Jevent.eq.0)thendu=dps/ktslUYY=uyy+du

POSITIVE DIRECTIONif(dps.gt.0.0)then

ROCKING NOT COMMENCED-NO EVENTif(uyy.lt.uy( I ))then

u(k)=r¡YYSTAGE I ROCKING LEVEL REAC}IED-WITH EVENT

elsedps=kts1*(uyy-uy(l))uyy=uy(1)Jevent=1code="Model rocked within limits"goto 15

end ifNEGATIVE DIRECTION

elseROCKING NOT COMMENCED-NO EVENT

if(uyy. gt.uy(- 1 ))thenu(k)=uYY

STAGE I ROCKING I-EVEL REACMD-ìWITH EVENTelse

dps=kts I *(uyy-uy(- I ))uyy=uy(-l)Jevent=-1code="Model rocked within limits"goto 15

end ifend if

elsePOSITTVE STAGE 1 ROCKING

if(Jevenleq.l)thendudps/ktspuYY=uYY+du

INCREASING DISPLACEMENTif(dps.gt.0.0)then

STAGE 2 ROCKING LEVEL NOT YET REACMDif(uyy.lt.uy(2))then

u(k)=¡Ytelse

STAGE 2 ROCKIN LEVEL REAC}IEDdps=ktsp*(uyy-uy(2))uyy=uy(2)Ievent=2code="Model rocked within limits"goto 15

end if

ccc15c

c

c

c

c

U

c

c

c

c

c

329

APPENDIX G: N0n-linearTirne Hístory Analysis ROWMANRY FortranTT Code

cc

elseDECREASING DISPLACEMENTNOEVENT

if(uyy.gt.uy(l))thenu(k)=uYY

elseWTTH EVENT

dps=ktsp*(uyy-uy(l))uyy=uy(l)Jevent{code="Model rocked within limits"goto 15

end ifend if

end ifNEGATIVE STAGE I ROCKING

if(Jevent.eq.- 1)thendu_Jps/ktspuYY=uYY+du

INCREASING DISPLACEMENTif(dps.lr0.0)then

STAGE 2 ROCKING I.EVEL NOT YET REACTIEDif(uyy.gt.uy(-2))then

u(k)=¡Ytelse

STAGE 2 ROCKING LEVEL REACMDdps=ktsp*(uyy-uy(- 2))uyy=uy(-2)Jevent=-2code="Model rocked within limis"goto 15

end ifelse

DECREASING DISPLACEMENTNOEVENT

if(uyy.ltuy(-l))thenu(k)=¡YY

else\ryTTH EYENT

dps=ktsp*(uyy-uy(- I ))uyy=uy(-l)Jevent=Ocode="Model rocked within limits"goto 15

end ifend if

end ifPOSITIVE STAGE 2 ROCKING

if(Jeventeq.2)thenif(kts2.le.0.0)goro I 000dudps/kts2uYY=uYY+du

INCREASING DISPLACEMENTif(dps.gt.0.0)then

COMPI-ETE INSTABILITY NOT REACHEDif(uyy.lt.ulim( 1))then

c

c

c

c

c

cc

c

c

c

c

330

APPENDIX G: N)n-IinearTime History Analysis ROWMANRY FortranTT Code

u(k)=uYtelse

c COMPLETE INSTABILITY REACÍIEDc Update pc and return to initial conditions

if(px.eq.0)thenpl=pc

end ifc Vary proponional damping to try and achieve convergence

if(px.lt.5O)thenpç=pl -real(px)*O.02+p1

end ifif(px.eq.50)thenpc=pl

end ifif(px.gt.50)thenpc=pl +(real(px)-50.0) *0.02*p I

end ifif(px.eq.101)then

write(*, *) " Iteration limit reached- NO CONVERGENGE "

u(k)=uYYv(k)=O'0at(k)=0'0do 38 l=I'kuf(l)=u(l)

38 continuec Set remaining final displacement store to zero

do 41 l=k+l,NT-luf(l)=0'0v(l)=0'0a(Ð=0'0

4l continuegoto 1000

end ifdps=dpsxj=jxa=axuYY=o'0jevent=Opx=px*1d=1f=1

c write(1,*)"dpsx initial cond at"s write(I,*) dpsx, xc Resta¡t iteration with new predicted proportional damping coefficient

goto 5end if

c DECREASING DISPLACEMENTelse

c NOEVENTif(uyy.gt.uy(2))then

u(k)=uYYc WTTHEVENT

elsedps=kts2*(uyy-uy(2))uyy=uy(2)Jevent=l

331

APPENDIX G: N)n-linear Tíme History Analysis RowMANRy Fortran7T code

code="Model rocked within limits"goto 15

end ifend if

end ifc NEGATWE STAGE 2 ROCKING

if(Jevent.eq.-2)thenif(ks2.Ie.0.0)goro I 000dudps/kts2uyy=uyy+du

c INCREASINGDISPLACEMENTif(dps.lt.0.0)then

c COMPLETE INSTABILITY NOT REACIIEDif(uyy.gt.ulim(- I ))then

u(k)=uYYelse

c COMPI-ETE INSTABILITY REACTIEDc Update pc and return to initial conditions

if(px.eq.0)thenpl=pc

end ifif(px.lt.5O)then

pç=p1 -real(px)*0.02 *p Iend ifif(px.eq.5O)rhenpc=p1

end ifif(px.gt.50)thenpç=p 1+(real(px)-50.0)*0.02*pl

end ifc write(1,*)"Complete instability"

if(px.eq.l0l )thenwrire(*,*)"Ireration limit reached-NO CONVERGENGE"u(k)=uYYv(k){.0at(k)=O'0do 35 l=I,kuf(l)=r¡(l¡

35 continuec Set remaining final displacement store to zero

do 42I=k+l,NT-luf(l)=Q'9v(l)=O'0a(l){.0

42 continuegoto 1000

end ifdps=dpsyj=jva=ayuyy{.0jeventd)px=px+le=lf=1

c write(1,*)"dpsy initial cond at"

332

APPENDIX G: Nln-Iinear Time History Analysis ROWMANRY Fortrøn77 Code

ccccc

c write(l,*) dpsy, yc Restart iteration with new predicted proportional damping coefficient

goto 5end if

c DECREASINGDISPLACEMENTelse

c NOEVENTif(uyy.lt. uy(- 2))then

u(k)-uyyc WITHEVENT

elsedps=ks2*(uyy-uy(-2))uyy=uy(-2)Jevent=-lcode="Model rocked within limits"goto 15

end ifend if

end ifend if

Zero crossings, instantaneous frequency andRayleigh damping

Identify zero crossing from neg to posif(tO.ne.t2)thenif(u(k).gt.0.0.AND.u(k- I ).1e.0.0)then

write(1,*) "neg pos zero cross"tl =dt*u(k- I )(u(k- I )-u(k))t2dt*u(k)/(u(k)-u(k- 1 ))tO=t0-dt+tlj=j+lif(.gt.l)then

if(d.ne.1)thenProvided not prior to first half cycle or reiteration determinesRayleigh damping of compleæd half cycle response

nc=(aOm+a I m*pi*pil(tO* *2))Setting the maximum proportional damping coefficient forFrequency range of interest

if(nc .gt. 10.0)thennc=10.0

end ifwriæ(1,*) "period outcome predicted iteration k"wriæ(1,*) t0, nc, pc, p, k

if(nc.gt. 1. I *pc.OR.nc.lt.0.9*pc.AND.p.lt. 1O(Ð)thenLimit on iterations t0 1000Compares Rayleigh damping with initial predictionff out of the specified bounds a reiteration is requiredwith new predicæd proportional damping coefficient predicted below

wriæ(I,*) "REITERATE - new pc"pc=0.5*nc+0.5*pc

write(1,*) pcReset the initial conditions to the start of the current cycle

dps=dpsyj=jya=ay

c

cc

cc

cc

ccccc

cc

333

APPENDIX G: Nhn-linear Time History Anolysis RowMANRy FortranTT code

c write(1,*)"dps j a"c wrire(l,*) dps, j, a

uyy=O'0jevent{

c Iteration numberp=plle=lf=l

c Restart iteration with new predicæd proportional damping coefficientgoto 5

elsec write(I,*) "PC-NC within limis"

if(p.gt.99)thenc write(*,*)"Iteration limit exceeded"

end ifP=0px=0e=0

c Setting the predicted proportional damping for the next half cyclec to the successful proportional damping of the current half cycle

pc=3.0c Transfer successful iteration to final displacement store

do 20I=I,k-luf(l)=r¡11¡

20 continueend if

end ifelse

c Transfer displacements prior to first half cycle to final disp storedo 2l l=I,k-l

uf(l)=¡1¡¡2l continue

end ifû=A

c Set the initial conditions for the next half cyclec The zero value for the dps depend on the new u(k) location

if(u(k).lt.uy( I ))thendps=ktsl*u(k)

elseif(u(k). lt. uy(2)) then

dps=uy( I )*krs t+(u(k)-uy( I ))*ktspelse

dps=uy( I )*kts I +(uy(2)-uy( I ))*ktspr(u(k)-uy(2))end if

end ifuyy=O'0Jevent=0

c Store the initial conditions for the next half cycledpsx=dpsjx=j-lax=ax=k

c write(l,*) "dpsx jx x k u(k)"c write(I,*) dpsx, jx, x, k, u(k)

goto 15end if

334

APPENDIX G: N0n-linearTime History Analysis ROWMANRY FortanT7 Code

cc

end if

Identify zero crossings from pos to negif(t0.ne.t4)thenif(u(k).lt.0.0.AND.u(k- I ).ge.0.O)then

write(1,*) "pos neg zero crossing"t3dt*u(k- 1)(u(k- 1)-u(k))t4{r*u(k)(u(k)-u(k- 1 ))t0=t0-dt+Bj=j+1if(.gt.l)thenif(e.ne.l)then

Provided not prior to fftst half cycle or reiteration determinesRayleigh damping of compleûed half cycle response

nc=(a0m+a I m*pi*pi(t0* *2))if(nc.gt.10.O)then

nc=10.0end if

write(1,*)"t0 nc pc p k"write(l,*) t0, nc, pc, p, k

if(nc. gt. I . I *pc.OR.nc.lt.0.9 *pc.AND.p.lt. I 000)thenLimit on iterations to 1000Compares Rayleigh damping with initial predictionIf out of the specified bounds a reiteration is requiredwith new predicæd proportional damping coefficient predicæd below

wriæ(l,*) "REITERATE - new pc"pc=0.5*nc+O.5*pc

write(1,*) pcReset the initial conditions to the start of the current cycle

dps=dpsxjjxa=ax

write(1,*)"dps j a"write(l,*) dps, j, a

uyy{.0jevent=O

Iteration numberp=pt_ld=lf=1

write(1,*) "new dps j x d f"write(1,*) dps, j, x, d, f

Resørt iæration with new predicted proportional damping coefficientgoto 5

elsewrite(1,*) "PC-NC within limits"

if(p.eq.100)then, w¡iæ(*,*)"Iteration li¡nit exceeded"

end ifP=0px4d{

The successful predicted proportional damping for the current halfcyclebecomes the fnst approximation for the next haH cycle

pc=3.0Transfer successful iteration to final displacement store

c

cc

cc

cccçc

cc

cc

c

ccc

c

cc

c

335

APPENDIY G: N)n-linearTime History Analysis RowMANRy FortranT7 code

do22l-\k-luf(l)=u0)

22 continueend if

end ifelse

c Transfer displacements prior to first half cycle to final disp storedo 23 l=I,k-l

uf(l)=u(l)23 continue

end ift0=t4

c Set the initial conditions for the next half cyclec The zero value for the dps depend on the new u(k) location

if(u(k).gt.uy(- I ))thendps=ktsl*u(k)

elseif(u(k). gt.uy(-2))rhen

dps=uy(- I )*lfs I +(u(k)-uy(- I ))*ktspelse

dps=uy(- I )*kts 1 +(uy(-2)-uy(- I ))*ktspr(u(k)-uyC2))end if

end ifuyy=o'0Jevent=0

c Store the initial conditions for the next half cycledPsY=dPsjy=j-lîY=aY=kgoto 15

end ifend if

Sub-step iteration endsdu =u(k)-u(k-l)

dv = 2.*(du/dt) - 2.*v(k-l)v(k)=v1¡-1¡*¿'ttda=-2.*a+(2.*dv/dt)a =a+daat(k)= ¿g(lç¡ .r u

if(k.lt.NT)thenwrite(1,*)'Jpku(k)"wrire(I,*) j, p, k, u(k)

end if

10 continuereturn

1000 code="Model beyond timits - possible iterative instability"feturn

I100 code="Invalid results, dtûoo large"feturnend

cc25

cccccc

336

APPENDIX G: N)n-linearTirne History Analysis ROWMANRY FortranT7 Code

cccc

subroutine frrdnnx(Nrdin¡x,max)c Subroutine to hnd the absolute max. value of ac single dimension ilray xc decla¡ation of parameters

inæger N,dimreal x(O:dim),max

c decla¡ation of local va¡iablesinteger Imaxd).do l0 I=0,N-l

if(ab s(x(I)). ge.abs(max))thenmax=abs(x(t))

elseend if

10 continuereturnend

subroutine linter(NNTTTA,DT,NG'G)This subroutine interpolates linearly between uneven sample points.The interpolated data are then generated at a specified sample inærval

declaration of parametersinægerNN,NGreal T(0: 1 2000),4(0: 12000),DT,G(0: 163 84)declaration of local variablesinteger J,Kreal S

NG=int((T(NN- 1 )-T(0))/DT)+ IG(0)=A(0)J{do 50 K=l,NG-1

55 if(K*DT.lt.T(J+1))thens=K*DT_T(J)G(K)=A(J)+S*(A(J+ I )-A(J))(T(J+ 1 )-T(J))elseJd+lgoto55end if

50 continuerehlfnend

c

JJI

338

-u(m)_MWD

o o

v \yTime(secs)

0.02

0.015

0.01

0.005

0

-0.00s

-0.01

-0 015

-0.02

ooodè

t-¡

èooÊ€À

4

3

Ot

l¿1O^^Qd<È u

.$ -lo€-t

= -J

-4

t\Á

-at(trì/VÐ-MWA

óN

Time(secs)V

-J_

I

\

I

;doooo,

ôdÐo^!t ñ'ã<EVè0o¡JÀ

rr

Mid Height Displacement (m)

+-at(m/Js)_+MrilA

/

APPENDIX (H): Non-linear Time History Analysis Experimental Confirmationt *t(**********{c*r!*t ***t :ß:ß********{.**********************

Program ROWMANRY .

For time history rocking analysis ofFree Standing or Simply Supported ObjectsLatest Version : FEBRUARY 1999

***********r<**:1.:t<***********t *********************1.***r<*Accelerogram data from I Hz 16mm Amplitude PulseAccelerogram scaling factor selected = 1.000INPUT DATA SUMMARY FOR:SS non- loadbearing base reaction at LFHeight ofobject = 1.500 mObject width = 110.000 mmOverburden stress at top of object = 0.000 MPa

Trilinear force disp profile dataÂ(1) selecæd for initial stiffness = 7.00 mmÂ(2) selected for mædmum force plateau = 33.00 mm

Stiffness coefficient (IIEI'FS) =Resistance coefficient (ÌIEFFR) =

Prooortional damping dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

I-egend:aB = input ground accelerationv = relative velocity

1.50000.0050

u = relative displacementat = total acceleration

v(t) (m/s) a(t) (m/s2)0.471 3.6385

4.04.0

ANALYSIS CONCLUSION : Model rocked within limitsAnalysis time = 4.0l00secs time inc =.0100secs

Time q(t) (m/s2) ^(t)

(m)Maximum 3.545 0.038978

339

AP PENDIX H : N on- Iine ar Time History Analy sis Exp erime ntal C onfirmation

*** *** * **** **** ***** ******* ***d< **** *** ** **** *** ****** **

Program ROWMANRYFor time history rocking analysis ofFree Standing or Simply Supported ObjectsLatest Version : FEBRUARY 1999

*********+****:ß********+***********t ********+t***{.*t(***Accelerogram data from I Hz 24mm Amplitude PulseAccelerogram scaling factor selected = 1.000INPUT DATA SUMMARY FOR:SS non- loadbearing base reaction at LFHeightofobject= 1.500mObject widrh = 110.000 mmOverburden stress at ûop of object = 0.000 MPa

Trilinear force disp orofilé dataÂ(1) selected for initial stiffness = 7.00 mmÀ(2) selecæd for maximum force plateau = 33.00 mm

Stiffness coefficient (IIE¡PS) =Resistance coefficient (IIEI,¡'R) =

Proportional damoine dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

Iægend:aB = input ground accelerationv = relative velocity

1.40000.0040

u = relative displacementat = ùotal acceleration

v(t) (m/Ð a(Ð (m/s2)0.471 3.638s

4.04.0

ANALYSIS CONCLUSION : Model rocked within limitsAnalysis time = 4.0l00secs time inc =.0100secs

Time ar(t) (m/s2)Maximum 3.545 ^(t)

(m)0.038978

-u(m)_MWD

omel

Time(secs)

0.05

0.040.03

0.02

0.01

0

-0.01

-0.02

-0.03

-0.04

ëooodo.

H2è¡)

à

5

4ÔJ

EoALõ^8gl;sdo -l-=>-L

-3

-4

- ar(Íilvs)

-MWA

lmooomom

vJv Time(secs)

¡clN(Ôì

3V>h

^,

3hbn

Á/\

)hohoh

.5doõ-!ì ?.¡'<*

Ávè¡!o

troooo(oooo(-iâ-iA

MidHeight Displacement (m'

+at(m/Vs)+MWA

340

*****************:ß******:le*****d.**'r*************+*i.{.**t {.

Program ROWMANRYFor time history rocking analysis ofFree Sønding or Simply Supported ObjectsLatest Version : FEBRUARY 1999

**'r **** * *** ** *** * **** *** * **** * *** ********* ***{c *<*{.** **t<:1.

Accelerogram data from I Hz37nm Amplitude PulseAccelerogram scaling factor selected = 1.000INPUT DATA SUMMARY FOR:SS non- loadbearing base reaction at LFHeightofobject= 1.500mObject width = 110.000 mmOverburden sEess at top of object = 0.000 MPa

Trilinear force diso orofile dataÂ(1) selected for initial stiffness = J.50 mmÂ(2) selecæd for maximum force plateau = 25.00 mm

Stiffness coefficient (IIEFFS) =Resistance coefficient (IIEFFR) =

4.04.0

Prooonional dampine dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

Legend:ag = input ground accelerationv = relative velocity

1.50000.00s0

u = relative displacementat = total acceleration

ANALYSIS CONCLUSION: Model rocked within limitsAnalysis time = 4.0100secs time inc =.0100secs

Time ar(t) (m/s2)Maximum 7.516

) a(Ð (m/s2)4.0328^(t)

(m)0.073902

(m/sv(r)0.613

oo(gÞ.

f-l

Ò0o

À

0.08

0.06

0.04

0.02

0

-0.02

-0,04

-0.06

-0.08

-0.1

ÊÊ ÉelClô.¡Ncleloomóooo;JðèèÌr"f\\/

-¡(m)-MV|/D

Time(secs)

54

OJd1BLo^lONåÉ 0Ëë -t4'õ -)

-4-5

-

at(mj/si/s)

-MWAtt I

Tl.¿)o\ì

t\

döo^!ì ñ'ì*JÈ¡

ot)o¡

i

MidHeigbt Dsplacement (m)

+at(m/ds)----+-M\ilA

I

34r

APPENDIX H: Non-linear Time History Analysis Experimental Confirmation

*** ***** *** * *************+*** ***:r:ß******+* **** **** *****Program ROWMANRYFor time history rocking analysis ofFree Standing or Simply Supported ObjectsLatest Version : FEBRUARY 1999

*'ß* *t<.** ********:ß**************t* ****** ** ***** **** **** **

Accelerogram data from YzHz 4Ùmm Amplitude PulseAccelerogram scaling factor selected = 1.000INPUT DATA SUMMARY FOR:SS loadbearing top & bottom reaction at LFHeight of object = 1.500 mObject width = 50.000 mrnOverburden stress at úop of object = 0.075 MPa

Trilinear force diso profile dataÂ(1) selecæd for initial stiffness = 5.00 mrnÂ(2) selected for mærimum force plateau = 15.00 mm

Stiffness coefficient(IlE¡fs) = 21.735Resistance coefficient (HEFFR) = 21.735

Proportional damoine dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

Iægend:ag = input ground accelerationv = relative velocity

3.00000.0060

u = relative displacementat = total acceleration

AÀIALYSIS CONCLUSION : Model rscked within limitsAnalysis time = 3.0l00secs time inc =.0100secs

Time as(t) (m/s2)Maximum 4.78

v(t) (m/s) a(t) (m/s2)0.202 7.6747^(t)

(m)0.005211

gts

eo

-éà0o

5

0.0060.0050.0040.0030.0020.00r

0-0.00r-0.002-0.003-0.004-0.00s-0.006

-(m)_ MWD

.r l\

v

nllÍ\ ^

-lr v- I

10

8

8oË¿Ea oo6-iËlìo¡)'Þ -2

È-4-6

-8

il\t l

elel

\AA..A

- at(m/srs)

-MWA

Time(secs)v

éo€oo^qd9u)

c¡o

ÀMid-heigþt Displacement (m)

142

*********{.*******{c***'1.************1.*,1.{.*******{<*t<t **1.*r.d.

Program ROWMANRYFor time history rocking analysis ofFree Standing or Simply Suppoted ObjectsLatest Version : FEBRUARY 1999

**¡lc*¡lc**t(******t *********rl.**+*****{.******{<*{<*1!***1 1.****:tc

Accelerogram data from r/zHz 60mm Amplitude PulseAccelerogram scaling factor selected = 1.000INPUT DATA SUMMARY FOR:SS loadbearing top & bottom reaction at LFHeightofobject= 1.500mObject width = 50.000 mmOverburden sEess at top of object = 0.075 MPa

Trilinear force disp Eofile dataÅ(1) selecæd for initial stiffness = J.00 mmÂ(2) selecæd for maximum force plaûeau = 15.00 mrn

Stiffness coefficient (HEFFS) =Resistance coefficient (HEffR) =

Prooortional dampine dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

2r.73521.735

3.00000.0060

: Model rocked within limits' time inc =.0100secs

u = relative displacementat = total acceleration

^(t) (m) v(r) (m/s) a(t) (m/s2)

0.007558 0.285 8.3396

Analysis time = 3.5100secs

Legend:aB = input ground accelerationv = relative velocity

Time ar(Ð (m/s2)Maximum 6.398

343

0.0080.0060.0040.002

0-0.002-0.004-0.00ó-0.008

-0.01

-o.012

1'o

eo&d)o,éÀ

_(m)

-MWDÂ rrr--qF (r Y q¡ r--ieiõiÕiõiõiñú;riri

{

Time(secs)

\1,ì\ÉvuJIA

ooo

l08

É€6db4Ec 2

Íè od.É

-8_10

-at(m/Ys)-MWAA

IññÀñi¡ñã¿à¡

rr Time(secs)

II

t/

f\ ,r

ilYU

l

oôoo

É'5doO^od<èË.,11oùoÉ

Mid-height Dsplacement (m)

APPENDIX H: Non-linear Time History Analysis Eryerimental Confirmation

'1.**********1ê**************t **{<*************************Program ROWMANRYFor time history rocking analysis ofFreæ Sønding or Simply Supported ObjectsLatest Version : FEBRUARY 1999

*** ***** *** **:N.** ******** ********* +**X:N.* *** ******** *****Accelerogram data from I Hz 30mrn Amplitude PulseAccelerogram scaling factor selected = 1.000INPUTDATA SUMMARYFOR:SS loadbea¡ing top & bottom reaction at LFHeightofobject= t.500mObject width = 50.000 mmOverburden shess at top of object = 0.075 MPa

Trilinea¡ force disp orofile dataÂ(1) selected for initial stiffness = 415 nrnrtÂ(2) selected for maximum force plateau = 14.00 mm

Stiffness coefficient (IIEFPS) =Resistance coefficient (I{EFFR) =

Proportional damoine dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

Iægend:ag = input ground accelerationv = relative velocity

3.00000.0060

u = relative displacementat = ûotal acceleration

v(t) (m/s) a(Ð (m/s2)0.283 9.4s62

2t.73521.735

ANALYSIS CONCLUSION : Model rocked within limitsAnalysis time = 2.0100secs time inc =.0100secs

TimeMaximum

ae(t) (rn/s2)5.839 ^(t)

(m)0.0087r8

0.010.0080.0060.0040.002

0-0.002-0.004-0.00ó-0.008

-0.01

Þc(l)Eo)()(úo-.ao.9)q)

p

-u(m)-

fvfvvD

^

r - \¿r-;

Tine(secs)

rOoo

)tl //\ I

rb// å,&ð"¡

^ ocI

l()

o

108

q6'ã4s^ 28g 0

Íè'2B-4€-6Ë-8

_10

-12

- at(mirs/s)

_MWA

V

VTime(secs)

I

lll r

Å[^.

5dÐ

8ñåçÞeEà

14¿.

******t **1.*******+******t *+t<************t<******'F*têrêt ***Program ROWMANRYFor time history rocking analysis ofFree Standing or Simply Supported ObjectsLatest Version : FEBRUARY 1999

,1.'1.***t(********{.**d<***{<**t<**t *******'1.***r!*{<*******1.*****

Accelerogram data from I Hz 50mm Amplitude PulseAccelerogram scaling factor selected = 1.000INPUT DATA SIJMMARY FOR:SS loadbearing top & bottom reaction at LFHeightofobject= 1.500mObject width = 50.000 mmOverburden stress at top of object = O.075 MPa

Trilinear force disp orofile dataÀ(1) selected for initial stiffness = 4.75 mmÂ(2) selecæd for maximum force plateau = 13.50 mm

Stiffness coefficient (HEFFS) =Resistance coefficient (IIEfpR) =

Prooortional damoine dataMass propofional damping coeff. =Stiffness proportional damping coeff. =

Iægend:aB = input ground accelerationv = relative velocity

3.00000.0025

u = relative displacementat = total acceleration

^(Ð (m) v(Ð (m/s) a(t) (m/s2)

0.030496 0.575 9.2466

21.73521.735

ANALYSIS CONCLUSION : Model rocked within limitsAnalysis time = 3.9400secs time inc =.0l00secs

Time ar(Ð (m/s2)Maximum 8.531

-(m)-MWD

À n, ^,-æ

Time(secs)

0.04

ë 0.03ËÊ o.o2ooE o.ol

äoÁèoÐ -0.01

= -0.02

-0.03

l08

c65(̂€'-ÞzO^8g 0<l'-ë -¿

B-4€-6E-8

-10-12

-at(m/Ys)-MWA

tl\

ñLrl1

V

a__]NI'j,

illt

â.l,

Ëës+

od{)o^ONa) .ò

èDoÉÀ

345

APPEN DIX H : Non- linear Tirne History Analy sis Exp e rtmcntal C onfirmation

*** **** *+** ************* ********* ***** +*** **** **** *****Program ROTWMANRYFor time history rocking analysis ofFree Standing or Simply Supported ObjectsLatest Version : FEBRUARY 1999

*** ****:t*** *** ** ** ** ***+ ***** ******** *******'ßi. **** * ****Accelerogram data from 2Hz l5mm Amplitude PulseAccelerogram scaling factor selected = 1.000INPUT DATA SUMMARY FOR:SS loadbearing top & bottom reaction at LFHeightofobject = 1.500 mObject width = 50.000 mmOverburden stress at top of object = 0.075 MPa

Trilinear force disp profile dataÂ(1) selected for initial stiffness = {.75 mmÂ(2) selected for manimum force plateau = 13.50 mm

Prooortional damoing dataMass proportional damping coeff. = 3.0000Stiffness proportional damping coeff. = 0.0060

ANALYSIS CONCLUSION : Model rocked within limitsAnalysis time = 2.2100secs time inc =.0100secs

Stiffness coefficient (IIEFFS) =Resistance coefficient (IIEnfR) =

Iægend:aB = input ground accelerationv = relative velocity

Time ar(t) (m/s2) ^(t)

(m)Maximum 6.972 0.023191

21.73521.735

u = relative displacementat = ûotal acceleration

v(t) (m/s) a(Ð (m/s2)0.479 10.1605

-(n)-MWD

c-l

vTime(secs)

t

o

0.020.0r50.01

0.0050

-0.005-0.0r

-0.0r5-0 02

-0.025-0.03

âøoooGÈâ2è¡)o

108

a6'iã46b?O^8S 0<t.30 -4o€-6

=-8 -10-12

-at(m/Vs)_MWA

I ime(secs)

IE\I

A.*.\

Ðo^AN9u)

c)oãtÀ

?46

*** **{r* ***{. * *{<** *** * **{. *1.*r<** +*** ** ** ***** **** *ts:lc * ***ic*

Program ROWMANRYFor time history rocking analysis ofFree Standing or Simply Supported ObjectsLatest Version : FEBRUARY 1999

**********:*:1.**:1.:1.*rß**t(**********¡1.*r¡**t ,1.*****+********r<t *Accelerogram data from I Hz 30mm Amplitude PulseAccelerogram scaling factor selected = 1.000INPUT DATA SUMMARY FOR:SS loadbearing top & bottom reaction at LFHeightofobject= 1.500mObject width = 50.000 mmOverburden shess at top of object = 0.15 MPa

Trilinear force diso nrofile dataÂ(1) selecæd for initial stiffness = 7 mmÂ(2) selecæd for maximwn force plateau = 2l mm

Stiffness coefficient (HEFFS) =Resistance coefficient (IIEFFR) =

Propgrtional dampine dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

Iægend:aB = input ground accelerationv = relative velocity

2.00000.00s0

u = relative displacementat = total acceleration

^(Ð (m) v(t) (m/s) a(t) (m/s2)

0.008301 0.306 12.0173

39.47t39.47r

ANALYSIS CONCLUSION : Model rocked within limitsAnalysis time = 1.6600secs time inc =.0l00secs

Time ar(Ð (m/s2)Maximum 6.266

0.010.0080.0060.0040.002

0-0.002-0.004-0.006-0.008

-0.01

ooodo.

è0o

À

-(m)_MWD

Time(secs)

tJ/ u\)3I

\\/\\ /ltoo

V !

.l3ä\\

t4l2r088'Ë6

b4O^()d t

d'õ -1¿= -OÈ-BÁ -lo

-12-14

- at(m/s/s)

-MWA

ô

oO^a ô^¡<ìàt)o

fmlid-heidit Llisolacemen

zI

347

AP P EN D IX H : N on- line ør Time H i s t ory Analy s i s Exp e rime nt al C onfi rmat ion

*1.t ************{.********************:F******************Program ROWMANRYFor time history rocking analysis ofFree Standing or Sirnply Supported ObjectsLatest Version: FEBRUARY 1999

************:F************:¡:t i.***************+***{.***,tc*,ß*Accelerogram data from I Hz 50mm Amplitude PulseAccelerogram scaling factor selected = 1.000IMUT DATA SUMMARY FOR:SS loadbearing top & bottom reaction at LFHeightofobject= 1.500mobject width = 50.000 mmOverburden shess at top of object = 0.15 MPa

Trilinea¡ force diso profile dataÂ(l) selecæd for initial stiffness = 8 mmÂ(2) selected for maximum force plateau = 23 nrn

Stiffness coefficient (IIEFFS) =Resistance coefficient (IIEFFR) =

39.47139.471

ANALYSIS CONCLUSION : Model rocked within limitsAnalysis time = 2.0500secs time inc =.0100secs

Proportional damoine datåMass proportional damping coeff. =Stiffness proportional damping coeff. =

Iægend:aB = input ground accelerationv = relative velocity

2.00000.0050

u = relative displacementat = total acceleration

^(t) (m) v(Ð (m/s) a(0 (m/s2)

0.020974 0.535 12.966Time ag(t) (m/s')Maximum 7.487

gÉtsoo6tè

H

clo

0.02

0.015

0.0r0.005

0

-0.00s

-0.01

-0.015

-0.02

-0.02s

-u(m)-MWD

I

Time(secs)

)

o l-l (rÍèl;/At

; c;\/d v¿

o'!doO^9N<tc)o,4€À

12.5l0

7.55

2.50

-2.5-5

-7.5-10

-12.5-15

- ar(m/Vs)

_MWA

V

Ãt

-Jt,Jl \L

\I

t*\

Y\\

GoO^a c.¡<l.$C)

ÀMid-heigþt Displacement (m--Fos:ËÈJf+tÚz

?4R

****{.*!.1.'**{<r.*************t ******************************Program ROV/MANRYFor time hisory rocking analysis ofFree Standing or Simply Supporæd ObjectsLatest Version : FEBRUARY 1999

********:t ***********{.r.************dc*****ds****:1.*¡lc***t :k**

Accelerogram data from 2Hzã0rll.n Amplitude PulseAccelerogram scaling factor selected = 1.000INPUT DATA SUMMARY FOR:SS loadbea¡ing top & bottom reaction at LFHeight ofobject = 1.500 mObject widrh = 50.000 mmOverburden súess at top of object = 0.15 MPa

Trilinear force disp profile dataÂ(1) selecæd for initial stiffness = 7.2 mmÂ(2) selected for maximum force plateau = 23 mm

Stiffness coefficient (IIEFFS) =Resistance coefficient (IIEFFR) =

hooortional dampine dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

Iægend:aB = input grouqd accelerationv = relative velocity

2.00000.0060

u = relative displacementat = total acceleration

39.47139.47t

v(t) (m/s) a(Ð (m/s'?)0.567 12.532

ANALYSIS CONCLUSION: Model rocked within lirnitsAnalysis time = 1.7600secs time inc =.0100secs

Time ae(t) (m/st)Maximum 7.605 ^(t)

(m)0.020093

oõodÀA¡o0o

0.0250.02

0.0150.01

0.0050

-0.005-0.0r

-0.0r5-0.02

-0.025

-¡(m)-MWD

É

doO^oñOøi<è.9o-éEÀ

1512.5

107.5

52.5

0-2.5

-5-'7.5-10

-12.5-15

-

at(rrils/s)

-MWA

T

II

^U

doO^8g<èE-c)o,é€À

349

APPENDIX H: Non-linear Time History Analysis Eryerimental Confinnntion

*************************r.*'*:t *:t *********1.**'F****+*t****Program ROWMANRYFor time history rocking analysis ofFree Standing or Simply Supporæd ObjectsLatest Version : FEBRUARY 1999

{.****¡ß*+********************************:**.***t<**t t *****Accelerogram data from 807o Pacioma Dam E/QAccelerogram scaling factor selected = 1.000INPUT DATA STJMMARY FOR:SS non- loadbearing base reaction at LFHeightofobject= 1.500mObject width = 110.000 mmOverburden stress at top of object = 0.000 MPa

Trilinear force diso nrofile dataÂ(1) selecæd for initial stiffness = 15.00 mmÂ(2) selecæd for maximum force plateau = 35.00 mm

Stiffness coefficient (HEFFS) =Resistance coefficient (IIEFFR) =

4.04.0

hoportional damoine daøMass proportional damping coeff. =Stiffness proportional damping coeff. =

lægend:aB = input ground accelerationv = relative velocity

1.0000.0030

u = relative displacementat = total acceleration

ANALYSIS CONCLUSION : Model rocked within limitsAnalysis tirne = 34.9600secs tirne inc =.0l00secs

Time ag(t) (m/s2)Maximum 3.545 ^(t)

(m) v(t) (m/s)0.038978 0.471

a(t) (m/s2)3.6385

0.08

0.06

0.04

0.02

0

-0.02

-0.04

-0.06

-0.08

goÁooñ=H

è¡)o€À

omçra¡È-æe.¡ (\ Cl C^l€ÀÉÈelcî iô

-(m)-MWD

I

Time(secs)

4

3Éo1dblO^8S n<è -:s-1à0O^

-4-5

- at(m.i/Vs)

-MWA

T

é'.ÉdÐo^!ì ñ'<*

!vc)oãÀ

t,

(

Mid Height Displacement (m.

a(n/Vs)---r-MWA

?sfl

******.i;ffiiåüffiåi*++' ***1'*"'F{<*¡

For time history rocking analysis ofFree Standing or Simply Supponed ObjectsLatest Version : FEBRUARY 1999

*,1ê******{<*****,1.*******{<**:*:N<{.***********{<**t rlÊ*******'tr(X{<

Accelerogram data from 507o Pacioma Dam E/QAccelerogram scaling factor selected = 1.000INPUT DATA SIJMMARY FOR:SS non- loadbearing base reaction at LFHeightofobject= 1.500mObject width = 110.000 mmOverburden sfress at top of object = 0.000 MPa

Trilinear force disp profile dat¿A(1) selected for initial stiffness = 12.00 mmÂ(2) selected for maximum force plateau = 35.00 mm

Stiffness coefficient (IIEFFS) =Resistance coefficient (HEFFR) =

4.04.0

ANALYSIS CONCLUSION : Model rocked within limitsAnalysis time = 34.9600secs time inc =.0100secs

Prooortional damoins dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

Legend:ag = input ground accelerationv = relative velocity

1.5000.0050

u = relative displacementat = total acceleration

^(t) (m) v(t) (n/s) a(t) (m/s2)

0.044787 0.453 3.52rTime ar(t) (m/s2)Maximum 3.059

Time(secs)

-u(m)-M\ryD

0.050.040.030.020.01

0-0.01-0.02-0.03-0.04-0.05-0.06

oÉoodot-l-éqf)oÉ

-43

oadÐlO^

åÉ o

d-toErJ _,,à

-3

-4

-at(m/Vs)-MWA

ómt-ôlFAicì

Time(secs)

oË*oe^üçl<É¡vc)oÉ

À

l=oooo (

MidHeight Displacement (m,

+at(n¡lJs)_r-MWA

351

APPENDIX H: Non-linear Time History Analysis Experimentøl Confirmation

*** ******* ***** {< **** *{.*********** **** *****:ß*** *********

hogram RO\ryMANRYFor time history rocking analysis ofFree Standing or Simply Supported ObjectsLatest Version : FEBRUARY 1999

*** ******** ************* ***.*:t **** **** ***** **t(* *********Accelerogram data from 667o ElCentro E/QAccelerogram scaling factor.selected = ' 1.000INPUT DATA SUMMARYFOR:SS non- loadbearing base reaction at LFHeightofobject= 1.500mObject widrh = 110.000 rnmOverburden súess at top of object = 0.000 MPa

*Trilinear force diso orofile dataÂ(l) selected for initial stiffness = 15.00 mmÂ(2) selected for maximum force plateau = 35.00 mm

Stiffness coefficient (HEffS) =Resistance coefficient (IIEFFR) =

hooortional dampine dataMass proportional damping coeff. =Stiffness p,roportional damping coeff. =

Iægend:48 = input ground accelerationv = relative velocity

1.7500.0060

u = relative displacementat = total acceleration

4.04.O

ANALYSIS CONCLUSION : Model rocked beyond limitsAnalysis time = 22.4600sæ,s time inc =.0100secs

Time ag(t) (n/s2)Maximum 3.986 ^(t)

(m)Failed

v(t) (m/s)0.706

a(t) (m/s2)4.0053

?Éooodô.oèooÉÀ

0.t20.1

0.080.060.040.02

0-0.02-0.04-0.06-0.08

-0.1-0.12

-u(m)_MU¡D

ñ

v-

r rme(socs,

t^

Specimen Failure

I ll a ^ - r

t._

^l ucl l?

Ê5dÒooo

E,1¡oÉÀ

6

4

2

ñ0Lz

-4

-6

-8

. at(m/vs)_MWA

7 Tr,rf ll|rï *|fl = fsvf! : 3r:'= 3 R N

I Time(secs)

Itô-u,.1

tt..

IIIrl

ìI

T

((

r

.lir-Trdrc

Ê

6oe^EçI<*¡vèoo

-1Å

I

Mid Heigþt Displacement (m)

)

J.

+at(n/Vs)--¡-MWA

tfr

a\t

*t<***{e*************:***t :***:1.******{<*******************rc*

Program ROWMANRYFor time history rocking analysis ofFree Standing or Simply Supported ObjectsLatest Version : FEBRUARY 1999

**rr***1.*:{ê*:1.***rs***t t {.*******r<r<******t+**{<*r<t!**********+Accelerogram data from 1007o Nahanni AftershockAccelerogram scaling factor selected = 1.000INPUT DATA SUMMARY FOR:SS non- loadbearing base reaction at LFHeightofobject= 1.500mObject width = 110.000 mmOverburden stress at top of object = 0.000 MPa

Trilinear force diso orofile dataÅ(1) selected for initial stiffness = J.00 mmÂ(2) selecæd for maximum force plateau = 25.00 mm

Stiffness coefficient (IIEITS) =Resistance coefficient (HEffR) =

4.04.0

Proportional damoine dataMass proportional damping coeff. =Stiffness proportional damping coeff. =

Iægend:aB = input ground accelerationv = relative velocity

4.0000.0060

u = relative displacementat = total acceleration

ANALYSIS CONCLUSION: Model rocked within limitsAnalysis time = 12.4200secs time inc =.0100secs

Time ae(t) (Ír/s2) ^(t)

(m) v(r) (m/s) a(t) (m/s2)Maximum 6.413 0.012088 0.248 4.6692

5oEoo(Ë

H¡èf)oÉÀ

0.0r20.01

0.0080.0060.0040.002

0-0.002-0.004-0.006-0.008

-0.01

I

-(m)-M\IrD

I Time(secs)

IrJü

4

3é^aL

ËrEç o

Íè-r.9a-L

E-3-4

-5

ô[,r -¡r¡ -

f--F-

[iI¡.Il$llrt ra¡¡ lf -at(Inj/Vs)-MWA

til

É.5ñoHal*!vdoÉJ

D

Mid Heigþt Displacement (m)

at(m/Vs)--r-MWA

353

354