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DmEjlBILITY h\rD LOAD TRANSFER CHA.?WmFUSTICS OF VIBRO-DRWEN PILES

A Dissertation

Presented to

The Faculty of the Department of Clvil and Environmental Engineering

University of Houston

In Partial Fulfillment

of the Rtquircments for the Degree

Doclor of Philosophy

By

Daniel 0. IVong

Decanber. 1988

DR.NEABILlTY AhD LOAD TFbIiUSFER CHARACTERISTICS OF 1qBRO-DRNEN PILES

An Abstract

Presented to

The Faculty of the Department of Civil and Environmental Engineering

University of Houston

In Partial Fulfillment

of the Requirements for the Degree

Doctor of Philosophy

BY

Daniel 0. Wong

December, 1988

Abstract

Piles installed by vtbration have been a foundation practice since the early

1930's. The method has not galned wide acceptance in the U.S. because of limited

understanding on driveability and load transfer mechanisms. Restr- vibro-drlven

piles is very often required for analysis. A large scale laboratory study on the basic

behavior of displacement piles installed with vibratory drivers compared to t rpac t

l~nmmers and rhe influence of various soil and driver parameters on the behavior of

piles was undertaken.

In order to achieve the desfred goais, a model testlng system consisting of a long

sand column capable of slmulating deep sand deposits. instrumented 4-in.-diameter

closed-ended pLle. vibratory driver and impact harmer was designed and built. Among

the driver parameters investigated are frequency, bias mass and dynamic force

(cccentric moment) and sand parameters such a s grain size. relative density i65 and

90%) and in-sltu elfective stress (10 and 20 psi].

The optimum frequency for the testing condltions. selected based on the

maximum rate of penetralion, was 20 Hz and was lndependent of bias mass ~ q d soil

condilions. Among the varlables investigated, the reiative density of sand had the

greatest elfect on the rate of penetration during vibro-driving. Penetratlon rate also

increased with increasing bias mass and decreasing in-s1:u horizontal stress. impact-

driven piles in sand with 85% relatlve density developed hlgher resistance in

compression Ulan I h e vibro-driven piles. but vibro-drivcn plies exhibited better statlc

performance in sand wlth 90% relative density. Restriking of vibro-driven piles In

sand does not signilicantly change the compression capacity.

Four design methods to predict the bearing capacity of a vibro-driven yile have

been propcsed and a procedure to select a vlbro-driver for given sol1 conditions Is

recommended. A computer program has also been developed !o model vibratory

driving.

The study reported herein was sponsored by the National Cooperative Highway

Research Program of the National Research Councll. The completion of thls study was

made possible by many individuals and organhations who contributed dlrectiy and

indirectly. The authcr is grateful to Dr. Cumaraswamy Vipulanandan. the author's

graduate ad~ l so r and the principal project co-investigator and Dr. Michael W. O'Neill.

the principal project co-investigator for their advice and guidance throughout this

study. Appreciation 1s also expressed to Drs. Sheng Taur Mau, Willlam E. Vanksdale

and Carl E. N o r m a n for serving in ihe author's dissertation co~nmittee and for offering

valuable suggestions.

The author is thankful to Maurfcio Oshoa and Oscar Ugaz. fellow graduate

students. and to Daniel Mofar, Mike McClellan and John Brown. fellow undergraduate

students. for their experimenthl a^~d theoretical help Ln ~s study. Recognflfon is also

given to Roy Henson. Martin Kowls and Brad Cana. Ckil Engineering Technicians. for

their technical asistance. to Will Rainey and Charles Deckert cf Ralmond Technical

Facilities, Inc. for designing the vibro-driver. and to the Waterways Experiment Station

of the U.S. An-ny Corps of Engineers fcr sharing Fnibrmation relative to parallel studies

of the behavior of piles installed by vibro-driving.

ABSTRACT

AC~'O~vL.EDCEME?.Ts

LIST OF TABLES

LIST OF FIGURES

CHAPTER

1. Ii\lTRODUCTION

1.1 OBTECTNES

1.2 RESE4XCH APPROACH

2. BACKGROUXD

2.1 IhrnODUCnON

2.2 DFUVING FORMUIAE

2.3 SUhlMAI?Y

3. DESCRIPTION OF TESTING SYSTEM

3.1 TEST CHAVBER

3.2 TEST PILE

3.3 V i B R O - D r n R

3.4 IMPACT HAMMER

3.5 DATA ACQUISITION SYSTEMS

Dynamic Data Acquisition System

Static Data Acquisltton System

3.6 SAND PLACEAMENT

3.7 CALIBRATION PROCEDURES

AxiaI Strahi Gage and F'icssure Eansducer Bridges

Amplitude of Tce Acceleration

Phase: Between Eead and Toe Accelerations

Phase Between Velocity and Force at Head or Toe

4. SA.XrD PROPERTIES A'iD TEST FESTJLTS

4.1 %\'D

Craln-Slze Distribution

Mtnfmum and Maximum Density

Permeability

Triaxial Compression

Interface Shear

Resonant Column

4.2 VIBRO-DRMSC PARAVETERS TESTS

Typical Force and Velocity Time Histories

Typical Lateral Pressure-Time Histories

Rate of Penetration

4.4 IMPACT AND XSTFUKE TESTS

Qplcal Force and Velocity Time Histories

Penetration Resistance

4.5 WATER EXPULSION

4.6 COMPRESSION AND UPLIFT TESTS

5. ANALYSISOFTESTRESULTS

5.1 PERFORU4.VCE REWTIONSHIP B-EN DRO-DRIVER AND IMPACT HAMMER

5.2 POWER AND ENERGY TRPLFiSMISSION

Energy

Power

5.3 RATE OF PENETRATION AND ACCELERATION

5.4 WAVE-EQ UAT?ON PARILMETERS

5.5 LOAD-MOVEMENT RELATIONSHIPS

5.6 STATIC UNrr LOAD TRANSFER RELATIONSHIPS

5.7 DYNAMIC LOAD TRANSFER RELATIONSHIPS

5.8 PHASE RELATIONSHIPS 176

6. ESTIMAnON OF B W N G CAPACrrY A\?3 SELECTION OF 186 VIBRO-DWTR

6.1 LOAD-MOVEMENT REMTIONSHP 190

Two-Parameter Model 192

Three- Parametzr Model 1 93

Four-Parameter Model

Static Load-Movement I?esbonse

6.2 E W N G CAPACrrY RELATIONSHIP

Power Transfer Mzthod 20 1

Normallzed Capacity method 2 10

Ultimate Resistance Method 2 12

6.3 SUMMAXI' OF METHODS TO ESTIMATE BFSLRINC CAPACI?Y 2 13

6.4 SELECTION OF VIBRO-DRIVER 215

7. MODELING OF VIBRATORY D R M N C 2 17

7.1 THEOREnCAL DEVELOPMEhT 2 19

7.2 PROPOSED V I B R O - D m C hlODEL 222

Modelfng of Vibro-Driver and Driving Force 224

Radlaljon Damping 225

Sol1 Model 23 1

7.3 NUMERICAL SOLUl7CN 243

7.4 AWYSIS OF W R O - D m N G BY WAVE EQUATION 25 1

8. CONCLUSIONS AND RECOhlMEXDAnONS 253

Vlbm-Driver and Pile Parameters 255

Effect of SoLl Parameters on Vibro-DriveablUty 257

Modeling of Statlc Unft Load ?kansfer Characteristics 257

Load Transfer Durlng Vibro-Drlving 258

Rtsldud Suesses 258

v i i i

Effect of R e s t n k h g the Vibro-Driven Pile

Estlrnation of Bearlng Capacity

Modeling of Vibratory Drivtng

8.2 RECOMMENDATIONS

REFERENCES

APPENDIX

A. COMPUTATION OF THEORETICAL W V E R

B. TIME HISTORIES AT FULL PILE PEhElTATlON FOR VIBRO- D R M N G TESTS

C. TAME HISTORIES AT FULL PENETRATION FOR IMPACT AVD RESTRIKING TESTS

D. OSE-DIMENSIONAL WAVE EQUATION AYALYSIS

TOPDFUVE ALGORITHM

SENSITIVITY ANALYSIS

E. STAnCLOADTESTINGLWDFAILURELOADS

TESTING PROCEDURES

INTERPRETATION O F FAILURE LOAD

F. USER'S MANUAL AND LISTING OF PROGRAM UH-ViBRO

LIST OF TA3LES

Table

1.1

1.2

1.3

3.1

Page

Test Program for Vibro-Driver with San Jacinto Rver Sand 7

Test Prograni for Vibro-Driver with Blasting Sand 8

Impact Hammer Test Program 9

Measured Values of Relatlve Density ('36) of Dry Sand Xs Placed 57 in the LVLPSC; Tests on San Jacinto River (Fine) Sand

hfeasured Values of Relatke Density (%I of Dry Sand As Placed 58 in the LVLPSC: Tests on B1asLh-g (Coarse) Sand

Summary of Permeability Test Results 72

Darnping Ratios of Medlum Dense Sands 85

Blow-Counts for Restrike Events 110

S u r r m q or Total Amount of Water Expelled from Chamber 1 i2

Su imary of Pile-Head and Pile-Toe Parameters lor Vibratory Tests 128

Summary of Pile-Head and Pile-Toe P a r a ~ e t e r s for An Impact 129 Test [Test 19: Blastlng Sand: Relattve Density Wh: Chamber Pressure 10 psi1

Sunlmaq of Pile-Head and Pile-Toe Parameters for An Impact 129 Test Uest 20; San Jadnto Rfver Sand: Relz.Uve Density 65%: Chamber Pressure 10 psl)

Summary of Pile-Head and Pile-Toe Parameters for .4n Impact 130 Test (Test 21: San Jacinto Rlver Sand: Relative Denslty 90%; Chamber Pressure 20 psi)

Summary of Plle-Head and Pile-Toe Parameters for h Impact 13 1 Test (Test 22: San Jacinto Rfver Sand: RclaUvt Density 90%; Chamber Pressure : 20 psi vulical: 10 psi horlzontall

Summary of We-Head and Pile-Toe Parameters for Tests with Restrike

Summary of Total Energy Dcllvtred lo the Pile Head

Sunrnary of OptLmum Parameters from TQPDRJVE Analyses

Comparison of Fallun Loads In Kips for Compression Load Tests

Comparison of Failure Loads m Klps for U p U Load Tests

Summay of Least-Squares Coelllcients for Selected Compression and Uplift Loads

Residual Slrcsses Developed After InstalbUon

Summary of Tests for Development of Dynamic Unit Load Transfer Curves

Energy Loss Per Cycle to Find Penetratior!

Measured Phase Relationships Between Plle-Head and Pile-Toe Acceleration

Summary of Methods to Obiatn f-w and q-w Curves for Sand

Bearing Capacity Rat!o lor Various Prediction Methods

Summary of Proposed Theoretical Solutions (After Rodger and Littlejohn (36))

Summary of Radiation Damping Coefficients

Parameters for M a 1 Solutions Using TOPDRIVE: Test 9

Parameters for Rial Solutions Using TOP3RIVE: Test 17

Parameters for Trial Solullons Using TOP3RIVE: Test 2 1

Parameters lor Trial Soiutior,~ Using TOPIiRNE: Test 22

Summary of Optimum TOPDRIVE Parameters

Variables in TOPDm SensiUvity Study (Test 91

LIST OF FICUPES

Figure

1.1 Schemztic of Vibro-Driver and Pile

3.1 General Schematic of The Testing System

3.2 Detailed Schematic of LVLPSC, Showtng Laterd and Vertical Pressure Membrane System

3.3 Schematic Longituainal View of Reusable Test Pile

3.4 Toe Load/Accelerometer Cell Detail

3.5 Schematic 01 Laboratory Vibro-Drive

3.6 Detail 01 Articulated Swivel Connection Between Vibro-Driver and Pile

3.7 Theoretical Periormance Cuntes for Laboratory Vibro-Driver

3.8 Schematic 01 Impact Hammer

3.9 Schematic of Data Acquisition System for Driving Tests

3.10 Schematic of Data Acquisition Syslem lor Statlc Load Tests

3.1 1 Model Ralners lor Sands : (a) for San Jacinto River Sand: (b) for Blasting Sand

3.12 Schematic Diagram of Full-Scale Rainer Used for San Jacinlo FUver Sand and Dense Blasting Sand

3.13. Schemz?tic Diagram of Full-Scale Rainer Used for Medium Dense Blasting Sar.d

3.14 Location of Gravlmetric Sampling Points in Chamber

3.15 Schematic of Calibration Test for Toe Accelerometer

3.16 Time Histories 01 Pfle Wall and Toe Lozd Cell Acceleratlon: (a) Uncorrected; (bl Corrected

3.17 Schematic of Callbratlon Test for Phase Lag Between Indicated Head and Toe AcceleraUons

3.18 Phase Callbratlon Test; I'yplcal Tlme Histories for Acceleratlon : (a) Pile Head (Average): (b) Pile Toe

3.19 Spectral Magnitude and Phase Rdatlonships Between Head (Average] and Toe Accelerometers: Phase Callbration Test

4.1 Graln Size DistribuUon for Sands Selected for The Study

4.2 Results of Consolidated-Drained Maxial Compression Tests for San Jacinto River Sand at 60% Relative Density

Page

2

26

28

Results of Consolidated-Drained Triaxlal C:ompression Tests for San Jacinlo River Sand at 85% Relative Density

Results of Consolidated-Dnlned Triaxial Compression Tests for Blasting Sand at 60°h Relative Density

Results of Consolidated-Drained Maxizl Compresslon Tests for Blasting Sand at 85% Relative Densiiy

Failure Envelopes for Triaxial Compression Tests on p'-q Diagram

Results of Direct Interface Shear Tests for San Jacinto Rlver Sand at 60% Relatlve Density

Results of Direct Interface Shear Tests for San Jacinto River Sand at 85% Relative Density

Results of Direct Interface Shear Tests for Blasting Sand at 60% Relative Density

Results of Direct Interface Shear Tests for 3lasting Sand at 85% Relaiive Density

Failure Envelopes for Direct Interface Shear Tests

Dynamlc Shear Modull Vs. Shear Strain Amplitude (Single) a s Functions of Sand Type and C o n f i r ? Pressure from Torsional Resonant Column Tests

Rate of Penelration Vs. Frequency for San Jacinto River Sand

Rate of Penetralion Vs. Frequency for Blasting Sand

Pile-Head Veloclty and Force Vs. Tlme: Test 1 la/13a (Relatlve Density = 65%; Chanlber F'ressure = 10 psi)

Plle-Toe Velocity and Force Vs. m e : Test 1 l a / 13a (Relative Density = 65%~: Chamber Pressure = 10 psi1

Pile-Head Velocity and Force Vs. Time: Test 17 (Relative Density = 90%; Chamber Pressure = 20 psi)

Pile-Toe Velocity and Force Vs. Tlme: Test 17 (RelaUve Density = 90%: Chamber Pressure .: 20 psi1

Total Pressure and Pore Water Pressure Time Histories for Test 1 la/ 13a (Rtlattve Density = 65%; Chamber Pressure = 10 psi)

4.20 Total Pressure and Pore Water Pressure Tlme Hlstorles for Test 9 ln Shallow Penetration ( Ftelative Denslty = 90%; Chamber Pressure = 20 psi): Pile Penetrating

4 2 1 Total Pressure and Pore Pressure Time Histories for Tesl 9 at Large Penetration ( Rehtive Density = 9%: Chamber Pressure = 20 psi); Pile Penetrating

Total Pressure and Pore Pressure %ie Histor!es for Test 9 at Large Penetration ( !?elalive Density = 9Wh; Chamber Pressure = 20 psi); Pile Stationary

a t e of Penetration Vs. Toe Depth- to-Dfameter Ratio (D/B); SJR Sand at 900/6 Relatfve Density

Rate of Penetraticn Vs. Toe Depth-Lo-Diameter iiatio (D/B): BLS Sand at 90% Relative Density

Rate of PenetnUon 'Js. Toe Depth-to-Diameter Ratlo (D/B); Comparison of Tests a t f3S0h Relatlve Density and 10 psi Chamber Prssure

Rate of Penetration Vs. Toe Depth-to-Dfameter Patio (D/B): Comparison of Tests a1 900m Fklatlve Density and 20 psi Chamber Pressure

Driving Records for Impact Tests

Results of Compression Tests: VlSro-Driven Piles with Reslrike: ElTectfve Chamber Pressure = 10 psi

Results of Compression Tests: Vlbro-Driven Piles with Restrike; EITectlve Chamber Pressure = 20 psi (Test 9 Synthesized to Full Penetration by Program APILE)

Results of Compression Tests: Comparison of Behavior of Vibro-Driven Piles and Restruck Vlbro-Driven Piles: EITective Chamber Pressure = 10 psi

Results of Compression Tests: Comparison of Behavior of Piles Tested Under & = 0.5 with Piles Tested Under & =1.0; Effectlvc Chamber Pressur? = 10 psi

Results of Compressfon Tests: Compariscn of Pfies !-?stalled by Vibratlon, VibraUon wiUl Restriking and by Impact: SJR Sand: 90% Relative Density: 10 psl ECTective Chamber Prtssure

Results of Compression Tests: Comparison of Piles Installed by Vibration. VibraUon with Rcstrikfng and 3y Impact: BLS Sand: 90% Eklative Density; 10 psi Efleclive Chamber Pressure

Results of Compression Tests: Cornparisoil of Pfles I~lstalled by VlbraUon with ResWLiig and Impact; SJR Sand: 65% Relative Density; 20 psi EfI'ecUve Chamber Pressure

Results of Compression Tests: Comparison of PLles Installed by Vibration with Restriking aad Impact; SJR Sand: 90% Relative Density; 20 psi Efrective Chamber Pressure

Results of Uplift Tests: Vibro-Dtfven Piles with Restrike; EfT'eWe Chamber Pressure = 10 psi

e s u l t s of Uplift Tests: Vibro-Driver? Pees with Restrike; Effecllve Chamber P re - sun = 20 psi [rest 9 Synthesized to Full PenelraUon by Program APILE)

Results of UpliftTests: Comparison of Behavior of Vibro-Driven Piles and Restruck Vibro-Drlver, Piles; EfIective Chamber Pressure = 10 psi

Results of UpllfiTests: Corngarison of Behavior of Piles Tested Under KO = 0.5 with Ples Tested Under KO = 1.0; EffecWe Chamber Pressure = 10 psi

Results of Uplift Tests: Comparison of Pfles Installed by Vibration. Vibration with Restrlktng and by Impact; SJR Sand; 90% Relative Density; 10 psi Effective Chamber Pressure

Results of UpliftTests: Comparison of Pfles Installed by Vibration, Vibration with Restriking and by Impact: BLS Sand:

assure 90% Relative Density: 10 psi Effective Chamber Pr-

Results of Uplift Tests: Comparison of Piles Installed by Vibration wllh RestrFkLng and Impact; SJR Sand: 65% Relative Dens!ty; 20 psi Effective Chamber Pressure

Results of Uplift Tests: Comparison of Pfles Installed by Vibration with Restriking and Impact; SJR Sand; 90?h Relauve Density; 20 psi Effective Chamber Pressure

Relationship Between Penetration Velocity for Vibro-Driven Piles and Drivlng Resistance for Impact-Drlven Piles

Relationshfp Between Power Ratio and Peak Pile-Head Accelerationfor Vibro-Driven Piles

Pfle Penetraion Velocity (vp) Vs. Peak Plle-Head Acceleration (ah): Sand Relative Density = 65%; MectIvc Chamber Pressure = 10 psi

Pile Penetraion Velocity (vp) Vs. Peak P!Je-Head Acceleration (ah); Sand Relative Density = 90%; ElTective Chamber Pressure = 10 psi

Pile Penetraion Velocity (vp) Vs. Peak Pile-Head Acceleration (ah); Sand Relative Density = 90%; EfTectfve Chamber Pressure = 20 psi

Cornparfson of compression Capacities of Vlbro-Driven Piles and Impact- Driven Pi!es

Load Distribution for Test 17; Compression

Load DistribuUon for Test 17; Upli[t

f-w Relationships for Tests 5. 6 and 7

f-w Relationships for Tests 8.9 and 1 l a / 13a

5.11 f-w FWatlonsNps for T e s l 14. 15 and 16

5.12 f-w Relationships for Tests 17, 18 and 19

5.13 f-w Relationsh!ps for Tests 20. 2 1 and 22

5.14 q-w Ftelationships for Tests 5. 6. 7. 8. 9 and 1 1 a/ 13a

q-w Relationships for T e s l 14. 15, 16. 17, 18 and 19

q-w Relationships for Tests 20. 2 ! and 22

Summary Noxmal!.zed f-w Relatlon for Pile Driven by Impact and Vibrated into SJR Sand at 65Oh Relative Density

Summary Normaked f-w Relation for Pfle Driven by Impact lnto S J R Sand at 9G?! Relative Density

Summary Normalized f-w Relation for Pfle Vibrated into SJR Sand at 90% Relative Density

Summary Normalized f-w Relation for Pile Vibrated (nto BLS Sand at 65% Relative Density

Summary Normallzed f-w Relation for We Drlven by Impact into BLS Sand at 90076 Relative Density

Summary Normalized f-w Relation for Plle Vibrated into BLS Sand at 90% Relatlve Denslty

Summary Normalized q-w Relation for Pile Drlven by Impact and Vibrated into SJR Sand at 65% Relative Density

Summary Normalized q-w Relation for Pile Driven by Impact into S J R Sand at 9096 Relative Density

Summary Normalized q-w Relation for Pile Vibrated into S I R Sand at 90% Relathe Density

Summary h'onnalfied q-w Relatlon for PCe Vibrated lnto BLS Sand at 65% Rtlatlve Denslty

Summary Normallzed q-w Rtlatlon for Pfle Driven by Impact into BLS Sand at W! Relatlve Density

Summary Normallzed q-w Rclati~n for Pfle Vibrated into BLS Sand at 90% Relatlvt Density

Dynamic Unit b a d Transfer Curves: Test 5

Dynamic Unit lxMd Transfer Curves; Test 7

Dynamic Unit Load Transfer Curves: Test 9

Dynamic Unit Load Tnnsfer Curves; Test 1 1 a/ 13a

Dynamic Unit Load Transfer Curves; Test 14

Dqnamic Unit Load Trarsfer Cun7es for Pfle fn Motion and at Rdusal; Test 17

Comparison of Dynamic and Static Urilt Load Transfer Curves: Test 5

xv!

Comparison of Dynamic and Static Unit Load Transfer Curves; Test 7

Comparison of Dymmic and Static Un i t Lead Transfer Curves; Test 9

Comparison of Dynarnlc and Static Unit Load Transfer Curves; Test 1 la / 13a

Comparison of Dhnanlfc and StaUc Unit Load Transfer Curves; Test 14

Comparison of Dynamic and StaUc Unit L9ad Transfer Curves; Test 17

Comparison of Dynamlc (PUe at Rdusal) and Static Unit Load Trarder Curves: Test 17

Comparison of Experimental and Predicted Bearing Capacily Vs. Blow Count

Comparison of Experimental and Predlcted Bearing Capacity Vs. Rate of Penetration

Experimental and Predlcted f-w and q-w Curves: Tests 5.6 and 7

Experimental and Predlcted f-w and q-w Curves: Tesls 9. 1 la / 13a and 14

Eh-perlmental and Predlcted f-w and q-w Curves: Tests 15. 16 and 17

Experimental and Predicted f-w and q-w Curves: Tests 18, 19 and 20

Experimental and Predicted 1-w and q-w Curves; Tests 2 1 and 22

Measured and Predicted bad-Movement Culves: Tests 5 and 7

Measured and Predicted bad-Movement Curves: Tests 9 and 1 la/ 13a

Measured and Prcdrcted Load-Movemerit Curves; Tests 14 and 17

Measured and Predicted Laad-llla.ernent Curves; Tests 19 and 21

Frequency Histogram of Number of Laboratory Tests Vs. Ratio of Measured to Computed Normalized Static Compresstve Ple Capacity

Relationship of Normalized Capacity and Rate of Penetration

Vibro-Driving Model

Measured and Predlcted Pile Hesd Forces: Tests 5 and 7

Measured and Predicted PLie Head Forces; Tests 9 and 1 l a / 13a

Measured and Predicted We Head Forces; Tests 14 and 17

Reloading and Unloadhg Paths of Soil Msdel

Proposed Soil Model and Expermental Dynamic Unit Load Transfer Curves: Test 5

Proposed Soil Model and Expermental Dwarnlc Unlt Load Transfer Curves: Test 7

Proposed Sofl Model and r!3permental Dynamic Unit Load Transfer Curves; Test 3

Proposed Soil Model and Expermental Dynmdc Unit Load Transfer Curves: Test 1 1 a / 13a

Proposed Soil Model and Expermental Dynamic Unit Load Transfer Curves; Test 14

Proposed Soil Model and Expermental Dlnarnic Unit Load Transfer Curves: Test 17

Measured and Predicted Displacement Time Hbtories of Vibro-Driven Pile; Tesls 5 and 7

Measured and Predicted I)lsplacement Time Histories of Vibro-Drfven Pile: Tests 9 and 1 la/ 13a

Measured and Predicted Displacement Time Histories of Vibro-Driven Ptle; Tests 14 and 17

Measured and Predicted Rate of Penetration X's. Depth-to-Diameter RaUo (D/B); Tests 5 anti 7

Measured and Predicted Rate of Penetration Vs. Depth-to-Dlameter Ratio (D/B); Tesls 9 2nd 1 !a/ 13a

Measured and Predicted Rate of PenetraLion Vs. Depth-to-Diameter Ratlo D/B); Tests 14 and 17

Measured and Predicted Displacnlent Tlrne Histories of Vlbro-Driven Pile by UH-VlBRO and TOPDRNE

A1.

A2.

B. la.

Si.ng!e-Degree-of-Freedom System Model ~f Vibro-Driver

Fret-Body Diagram of the System

Pile-Head and Toe Acceleration Vs. m e : PenemUon=75 Inches; Test 5

B. lb.

9. lc.

B. ld.

B.2a

B.2b.

B.2c.

B.2d

B.3a.

8.35.

B.3c.

B.3d.

B.4a

B.4b.

B.4c

B.4d

B.5a

5.32.

8%

B.5d

Pile-Head Velocity and Force Vs. Time: Penetration=75 Inches; Test 5

Pile-Toe Velocity and Force Vs. Tlme: Penetration=75 Inches; Test 5

Totd and Pore Water Pressure Vs. Time a) Bottom of Pile Shalt: PenetraUon=75 Inches; Test 5

Pile-Head and Toe Acceleration Vs. Time; Penetration=7 1 Inches; Test 7

Pile-Head Velccily and Force Vs. Time; Penetration=7 1 Inches: Test 7

Pile-Toe Velwity and Force Vs. Time: Penetration=7 1 Inches; Test 7

Total and Pore Water Pressure Vs. Time at Bottom of Pile Shdt : Penetration=7 1 Inches; Test 7

Pile-Head and Toe Acceleration Vs. Time: Penetratfon=53 Inches: Test 9

Pile-Head Velocity and Force Vs. Time: Penctration=53 Inches: Test 9

Pilr-Toe Velocity and Force Vs. Time: Penetration=53 Inches: Test 9

Total and Pore Water Pressure Vs. Time at Bottom of Pile Shdt ; Penetntion=53 Inches; Test 9

Pile-Head and Toe Acceleration Vs. Time: Penetration=55 Inches: Test 9 (Refusd)

Pile-Head Velocily and Force Vs. TLme: Penetratlon=55 Inches; Test 9 (Refusal)

Pile-Toe Velocity and Force Vs. Time: Penetntion=55 Inches; Test 9 (Refusal)

Total and Pore Water Pressure Vs. Tlrne a? Bottom of Pile Shaft: Penetration=55 Inches: Test 9 (Rdusal)

Pile-Head and Toe Acceleration Vs. Tlrne: PenetraUon=75 Inches: Test 1 l a / 1%

Pile-Head Velocity and Force Vs. T h e : PenetraUon=75 Inches; Test 1 la/ 13a

Ptle-Toe Velocity and Force Vs. Tlrne: PenetraUon=75 Inches: Test 1 1 a/ 13a

Total and Pore Water Pressure Vs. Time at Bottom of Pile Shaft: PenetraEon=75 inches; Test 1 1 a/ 13a

Pile-Head and Toe Acceleration Vs. T h e : Penetration='i?, Inches: Test 14

Pile-Head 'Je!a-i!y and Force Vs. Time: Penetratlor,=72 Inches: Test 14

Pile-Toe Velocity and Force Vs. Time: Penetration=72 Inches: Test 14

Total and Pore Water Pressure Vs. Time at Bottom of PUe Shall; Pene tration=72 Inches: Test 14

Pile-Head and Toe Acceleration Vs. Time; Penetration=72 Inches; Test 17

Pile-Head Velocity and Force Vs. Time; Penetrallon=72 Inches: Test 17

PUe-Toe Velocity and Force Vs. Time: Penetration=72 Inches: Test 17

Total and Pore Water Pressure Vs. Time at Bottom of Pile Shaft; Penetration=72 Inches: Test 17

Pile-Head and Toe Acceleratlcn Vs. Time: Penetration=74 Inches: Test 17 (Refusal)

Pfle-Head Velocity and Force Vs. Time: Penetntion=74 Inches: Test 17 (Refusal)

Pile-Toe Velocity and Force Vs. Tlme; Pene tration=74 Inches; Test 17 (Refusall

Total and Pore Warer Pressure Vs. Time at Bottom of Pile Shaft: Penet~iaUon=74 !nches: Test 17 [Refusal)

Measured Head and Toe Force and Velocity-Impedance Time Histories; Restrike at Full Penetration; Test 6

Measured Head arld Toe Force and Veiocity-Impedance Time Hlstories; Restrike at Full Penetration; Test 7

Measured Head and Toe Force and Velocity-!npedar,ce i'lrne Hlstories; Restrike at Full Penetration; Test 8

Measured iiead mc! Toe Force and Velocity-Impedance Time Histories; Restrikt at Full Penetration: Test 9

Measured Head and Toe Force and Velocl@-Impedance Time Hlstories: Restr!!!e at Full Penetration; Test 15

Measured Head and Toe Force and Velocity-Impedance Tlme Histories: ResUike at Full Penetration; Test 16

Measured Head and Toe Force and Velocity-Impedance Time Histories; Restrike at Full Penetration: Test 17

Measured Head and Toe Force and Velccitjr-Impedance Time Hls!ories; Impact-Driving at Full Penetration: Test 19

Measured Head and Toe Force and Velocity-Impedance Time Histories; Impact-Driving at Full Penetration; Test 20

Measured Head and Toe Force and Velocity-Impedance Time Histories; Impact-Driving at Full PenetraUon; Test 2 1

Measured Head and Toe Force and Velocity-Impedance Time Histories: Impact-DrlvLng at Full Penetration: Test 22

Measured and Computed Pile-Head Velocities and Forces; Test 9

Measured and Computed Pile-Toe Velocities and Forces: Test 9

Measured and Computed Pile-Head Velwll_ies and Forces: Test 17

Measured and Computed Pile-Toe VelociUes and Forces: Test 17

Measured and Computed Pile-Head VelociUes and Forces: Test 2 1

Measured and Computed Pile-Toe Velocities and Forces: Test 2 1

Measured and Computed Pile-Head Velocities and Forces: Test 22

Measured and Computed Pile-Toe VeloclUes and Forces: Test 22

TOPDRIVE Analysis oTTest 9: Increased Toe Weight: VeIocilfes

TOPDRNE Analysis of Test 9; Increased Tce Weight; Forces

TOPDRIVE Analysis of Test 9: Variable Shaft Resistance: Velwitles

'IY>PDFUVE Anaiysls of Test 8: Variable Shaft Resistance: Forces

TOPDRNE Analysis of Tcst 9; Increased ?@e Weight and Variable Shaft Resistance: VelocfUes

TOPDRNE Analysis of Test 9; Increased Toe Weight and Variable Shaft Eieslslance: Forces

TOPDRIVE Ana'ysis of Test 9; Increased Toe Wefght. Variable Shaft Resistance and Decreased Ttme Step: Velocities

TOPDRNE Analysis of Test 9: Increased Toe Welght. Variable Shaft Resistance and Decreased Tlme Step; Forces

WEAP 86 Analysis of Test 9 Using Optlmum Parameters from TOPDRNE Analysis with Dmerent Cushion SWness

Elevation Schematic of StaUc Compression Testing Arrangement

ElevaUon Schemallc of StaUc U p U TestLng Arrangement

INTRODUCTION

Piles are usually stalled by impact driving or by the use of a vibrator affixed to

the head of the pile. A vibrator, or "vibro-driver." depicted schematical!y in Flg. 1.1.

produces a sinusoidal vert:cal forcing function at frequencies ranging from as low as 5

Hz lo a s high as 1 4 0 Hz. A vibratory driver typically consists of a vibrating element

(eccentric moments produced by unbalanced counterrotatlng masses snown in Fig. 1.1).

b!as mass. isolation springs between the bias mass and a connection to the pile. The

bias mass performs the function of producing a near-static compression force on the

pl,le that assists the vertical forcing function to drive the pile. This mass is prevented

from vibrating along with the vibrating element by means of the isolation springs,

which are of such a stillness to assure that the resonance frequency of the bias mass-

isolation spring system is considerably below the operating frequency of the vibrator.

The pile-vibrator coanection is usually a chuck-type or pinned connecticn. whose

detailed design is irnporta~t 111 the prevention of damage to the pile dufing aeving.

Vibratory drivers have been used for installing piles in many parts of the world

since the early 1930's a s a3 alternative to the more conventional impact hammers. In

recent years vibratory pile drivers have gained popularity with contractors reiative to

impact drivers because they produce less nolse and less damage to piles during driving

and permit signlflcantly faster rates of penetration In favorable soil co~dl t ions

(generally, cohesionless scfls). Vlbro-drivers are generally grouped as low-frequency

drivers ( u p to 4 0 i-iz). which operate mainly by reducing soil resistance !hrough

excitation of the soil particles and, perhaps, simultaneous bulldup of excess Fcre water

Fig. 1.1. Schematic o i Vibro-Driver and Pllt

BIAS MASS

ISOLATION SPfilNGS

SOlL

PILE

I SHAFT RESISTANCE

7 TOE RESISTANCE

pressure, and high-frequency drivers !-between 40 Iiz and 140 Hz). which often pera ate at

the free natural frequency or second harmonic frequency of the plle. which in turn

provides slgruficant ampltCication of the forcing function and more rzpid penetration.

Neither type of dnver Is considzred generallqr effective Fn deposits of cohesive soil. and

such soil 1s therefore excluded from the laboratory study. The most popular drivers in

operation are the low-frequency type, because they are easier to maintain

mechanically. whose operatlig frequencies arc from about 5 Hz to 40 Hz. Vibratory pile

dnvers have not gamed wmde acceptznce in the United States, except for the installation

and ejrlraclion of non-bearing piles such as sheet piles. because the engineering

community is generally unfamiliar wilh this method of installation and because there

i;re uncertahtles regarding the estimation of ultimate bearing capacity. Due to these

uncertainties. restriking a vibro-driven pfle with an Impact hammer is often required

to assure that a pile has developed a design bearing capacity. but this process greatly

reduces the economic beneflts of using vibratory drivers.

A limited number of laboratory model studies and full-scale studies on vlbro-

driven plles have been reported In the Ilterature. as summarked In Chapter 2. These

sludles relate vibratory driver parameters. such as dynamic force, displacement

amplitude. frequency and bias mass to the drivcabflity (rate oi penetration) and the

static bearing capaclty of the pile. Although ?ast studies are important. wry little has

been done to Lrlvestlgatt the iriluence or the soil parameters (particle size, volume

change characteristics, strength) and tn-situ stress conditions on the performance of

vibro-driven piles. In order to develop more accurate predictive methods for the

ultfmate bearing capac~ty and load-movement behavior of vlbro-driven plles. induced

residuzl stresses and +he magnitudes and dhtrlbutlon of shaft reslstanee along the ptle

and toe resistance (Fig. 1.1) must be u~lderstood in the context of the properties of the

soli. As a step toward developing a better understanding of the behavior oivlbro-dnven

piles in saturated cohesionltss soil, a detsiled. large-scale laborztory experfmental

study was undertaken. This laboratory study wzs limited to LmTestigaiing the

perforni'=ince of low-frequency vi5ro-drivers because of the predominance of their .

.&a1 sys

details re[

chamber. 7 2 s --

acquisitior

?ratcl?c .rverall objective of this study is to evaluate the load-deformation behavior

of piles installed in the laboratory with vibratory drivers. Specific objectives include

the following: (1) the identification of driver parameters and soil parameters that

significantly affect driveability and load-deformatfon b?rha:-ior of piles installed with

vibratory drivers; (2) a comparison of load-deformation behavior of piles tnsta!led

with vibratory drivers and impact hammers; (31 a comparison of load-deformation

behavior of piles installed with vibratory drivers wd'h and without restriking using an

impact hammer. to evaluate the effect of restriking; (4) the development of predictive

methods to estimate the bearlng capacity of vibm-dwen pUes and a procedure to select

a suitable vibro-driver for given driving condltlons: (5) the development of a computer

program to model vlbro-driving.

1.2 RESEARCH APPROACH

In order to achieve the desired goals. a model tesUng system was designed. built

and appropriately instrumented. The testlng system included a long sand column. pile.

vibratory W e r . impact hammer and data acqulsitlon equipment. The sand column

was formed in a containment vessel 30 inches in diameter and 1 0 0 inches in height.

The contafnment vessel was designed to apply confining pressures ln any selective

manner to simulate various in-sltu stress conditions and to submerge the sand. A

reusable, Instrumented. closed-ended steel pipe ('displacement pile") with 3 4-inch

diameter and 0.185-tnch wsl! thickness was used a s the model plle for the entire study.

Soil particle sue, volume change charac~erfstlcs (contraction and dilation u ~ r l e r shear]

and tnternal ar,d interface (soil-steel) frictlcn angles and in-situ stress r penetr+s .we

considered to exelt the stror?gest incluellce on vtbratory pile drivingsfve Sou. ~!?,o

u d o r m sFllceous sands with ef:ec?ive grain sizes of 0.2 mm (fine Sa:i'lar drivers ler

Sarld, or "SJR8 Sand) and 1.2 rm (coarse BlasUng Sand, or '73~s''' Sand] wrtO mainta lor

testing. To represent contractlon and dilation condltions. these sails wrre'Prat0-?,*i . n

the test chamber at relative dens!ties of 65% and 90°h. This range of relativc 2ia~1slty is

one of practical interest. since values of less than about 50 - 55% are rarely found in

natural deposits, and values exceeding 90% are representative of d e ~ o s l t s that

normally would not require pile foundations. Since most plles that support

transportation structures in submerged granular soils will be driven to depths in the

nnge of 50 to 100 feet. it was decid$;d to simulate the mean elrecuve stresses that occur

in soil masses between the ground surface and these depths tn the test chamber.

installation and loading tests were therefore conducted at ellecthre confining pressures

of 10 psi (simulating a pile with a 50-foot penetraticn: i. e.. 25 feet to the middepth of the

pile Umes a buoyant unit sol1 weight of 57.6 pcf = 1440 psf. or 10 psi) and 20 psi

(slmulatfng a ptle with a 100-foot penetration) under an isotropic stress state and under

condiUons ol KO = 0.5 in the test chamber to du;llicate typical in-situ vertical and

hofmntal stresses.

From past studlts It has been suggested that the dynamic fom. displacement

amplitude. frequency and static bias weight are the most important drlver parameters.

A hydraulically operated. rotating-type model vibratory driver with operating

hquency between 5 Hz and 50 Hz was desfgned =ii burlt to apply a rnaxfrnum dynamic

force amplftude of 13,000 lb and a m-um eccentric moment of 300 in-lb with a bias

weight of 2000 lb. A single-acting impact hammer with a maximum rated energy of

I I 50 12-15. per blow at fuU stroke was used for Im?act drivk~g and restriking of the

vibro-dnven pde. and the hammer was operated at 69 to 7Z0h of full stroke dur?ng this

study. A2 analog data acqulsilion system was used for collecting dynamic data. and a

digital system was used for static compression and tenston loading tests. Furiher

details regarding the experimental arrangements, including details of the test pile,

chamber. vfbro-driver and lmpact hammer. descriptions of the Lnstruments. data

acquisition systems and calibration procedures, da;a reduction techniques, results of

laboratory soil properiy tests. and descriptions of sand deposition techniques. are

given in Chapters 3 and 4.

A total of 22 model tests were performed to zchieve the stated objectives. The

testing program, as outlined in Tables 1.1, 1.2 and 1.3. lncluded d r l m g the closed-

ended plpe pfle to a penetration of about 78 inches into the pressurized chamber with

both the vibro-driver m d the impact hammer. Init ial tests were parametric studies to

ldentliy and quantify the driver and soil parameters that exert the strongest influence

on the rate of penetration of the pile. These tests. identified a s "parameter" tests in

Tables 1.1 and 1.2. were driving tests only. and no corresponding static loading tests

were conducted. The remaining tests, identified a s "capacity" tests, were tests in which

the pile was installed either with the vibro-driver using optimum driver parameters

obtained from the parameter tests or with the Impact hammer. In selected tests the

vibrated pfle was restruck with the impact hammer to investigate the effect of

restrFkLng on vibro-driven piles. During each restrike event the p!le was drlven a

distance equal to one-half of Its diameter.

Compression Ioadlng tests. followed by uplift loading tests. were conducted to

compare performance of t'lc vibro-driven pile to that of the lmpact-driven pile. As a

fundamental means of maldng compzrisons between the behavior of Ule pLle installed

by the vibro-drfver, with and without restrike, and the impact driver. unit shaft and toe

load transfer reiatlonships were determined for all of the static loading tests. To better

undersland the pattern of s o l resistance durfrg vftro-driving, shaft and toe unft load

Table 1.1. Test Program for Vlbro-Drfvcr wtth San Jaclnto Rlver Sand

Wave Equaeon Analysis Conc!l;ctcd: \'lbrat=ry E w e r = V: !mpact Harnrr,cr = 1 : P = Parameter trst : C = Capacity test

Xotc: "a" and "b" suffLxes lndlcate that eEectlvc chamber pres?;re was changed during a test , so that one installation could be considered a s a test of two chamber pressure conditlans. Tests l a znc! lb. 2a and 25.3a and 3b. and 4a and 4 b wen: each cocducted durlrg a single pile LnstaIIaUon.

5

C

4b

P

6

C

X X S

S

2b

P

) ; > ; X X X X X X

2a

P

Rst NQ Variables

X 1

\ “ X ~ k

Soil - J I O = ~ : m i h

Pcr1:cle S u e

D1O=i 2mm

65% Relattue

7

x

i

X

31

P

vemmp~ct

~ e s t P r a m ' P I P

Vibro-Driver cb-lsmt

ryequency \'anable

~ZSGi i

2,as \;US

la

' : I S

X

D e n s ~ l y 93%

la!!&%rStress 10 Fst

C'7g0fVl

a@ %=aj

I3sBs

Log& Test

lb

X

.Y

X s

S

8

i

X

x

I

S

3b

P

X

I

S

9

C I C

X X X X S

4a

v v v v v v v v v v v v V

P

I i x

X

C

x

X

X

Y

:<

I x x x x

X X x X X

X ( X i

G ,

L&9

X

X

X

I

I X

X

i I

. I Z

! S

X

I X I X I

x

X

X

S

x

I

Table 1.2. Test Program for Vlbro-Drivcr wtth Blasting Sand

IVclve Equation Analysis Conducted Vibratory Driver = V: Impact Hammer = I : P = P m e t e r test ; C = Capacity Lest

Test No. Varla bi ts

Vfbm/lmp.d

Tcst Natan

Vlbm-Driver CcrrstarP

Requency Variable

CarSara Bias .Ifass

Sotc: "a" and "b" suU"cs indlcatc that effecuvc chamber p ~ s s u r t was changed durlng a test. so that one tnstallatlon could be Consldercd as a test of two chamber pressure conditions. Tests 10a and 12a. lob and 12b. I l a and 13a. and 1 lb and 13b we= each conducted dumg a single pile hs~allallon. Test 1 la/ 13a was an e.<cepUon. In that It was ofiglnaliy tntended to be a dud ppar;lmeter test but was charged d u m g the course of tcsung lo be a capacity test.

10a 1% l l a l l b 12a 1% 133. 13b

v V v v v v v v v v v v

P P C P P P C P T P P P

X

X X X x x x X

X

\:mk I 3Q!.!

D 10=0.2mx, 1 / I

?anic!e Size

D l o = 1 . 2 m X .

65'1'0 Relati~~e

-4 rnh

Ln Situ Strcsg io pd

c-fi Gr0-

3-

%=a

xT-j?(IS,---

14

x

.y

r pg

Bs!!s

15

X X X X

X X X X

x s

Y. X X ,Y

S X x

: < x x s

x

X

I

16

x

17'

I X

,Y

X x

I

X

)(

X

.-

x

X X X X

X S S

Table 1.3. Impact Harrhmer Test Program

Wave EquaUon A . i U Conducted: Vibratory Driver x V: Impact Hammer = I

22'

m=L

sot1 -

21' 20

1 I : I I

Frequenql

19 T d NO.

Variables

mm/Lmpact

Tcst Nature

Vlbro-Driver m53,';I

lfj

traisfer relatlonships were deterrntned from the dynamic data for the v ibra t l r~ pile for

selected condilions. In addition. wave equatlon st dies were conducted ~n mpact-

driven and vibro-driven/restrike pfles in order to understand whether Smith-type

wave equatlon parameters (quake. damplng and dlstributlon of resistance) that are

used in the analysis of Fmpact-driven pries can also be used for the evaluation of the

behavior of piles that are vibrated Inlo place and later restruck with an impact

hammer. Complete analysis of the test results were given in Chapter 5.

In Chapter 6, various methods for estimating the bearing capacity of a

displacement-type, vtbro-driven laboratory pile iq submerged. granular soil from

known driver and sol1 parameters are described. Several constitutive relationships

were used to model the static load transfer relationships of vibro-driven piles. A

procedure ls reommended for the selecuon of v!bro-driver to lnstall displacement piles

cf desired statlc capaclly for a given set of sou conditions.

In Chapter 7. a nonlinear soil model using static load transfer relationships

wilh appropriate degradation factors and hystersis is presensted. A one-dlmenslonal

rigid body model is also dexrlbed which predlcts the driveabllity of vibro-driven piles

using predicted forcing functions and an appropriate soil model. lncludlng both

radiation and hysteretic damping. A computer program has been developed for the

analysis. Selxted data were also a n d p e d uslng the wave equation computer program.

When compared to wave equatlon analysis, the rigid body steady state model predicts

the observed phenomena reasonably well.

Finally. Chapter 8 sumrnarlzes the conclus!ons Ulat can be deduced from this

study and provides ncmsnendatlons for further research.

CHAFTER 2

BACKGROUND

Research into vibratory driving of piles began Ln 1930 in Germany. and the firs:

cornrnercfai application was carried out in 1932. At. the same time, studies on vibration

of foundat io~s were carried out in the USSR. Pavyluk began his work on footing

vibrations in 1931, and Barkan in 1934 demonstrated that th: vertical vibration of a

pile markedly decreased the shalt shearing resistance between the pile and the soil (36).

In 1946, Rusakov and Khokhevich studied the mechanisms of low-frequency vibratory

drivers and observed lmpact between the pile and the soll. Commercial application of

low-frequency vibratory drivers in the USSR was demonstrated at the Gordy

hydroelectric development project, where a vibratory driver operating between 38 and

45 Hz. drove a total of 3700 sheet plles to depths ranging fro= 29.5 to 39.4 feet in

saturated sand and taking about 2 t o 3 minutes per pile. The vibratory driver drove

more sheets and consumed only 25% of the power compared to a pneumatic impact

hammer (191.

In 1953. high-frequency vibratory drivers with resiliently mounted surcharge

(bias masses1 were used to drive piles weighing 2.2 tons to depths of 65 feet in saturated

sand (191. In 1955. Tatarnfkov was able to apply the vibratory method to piles having

large toe resistance uslng low-lrequency dilvers (7- 16 Hz) (36). It was found that at !ow-

frequency of vibration, penetration ls enhanced by a large displacement amplitude and

the repeated impacts which occur due to the separation of the pile toe 2nd the soil. In

1956, a vibrocorer workiiig at 42 Hz with a 0. I-inch displacement. amplltcde and a 35

IGV electric motor was used to install casings for exploratory boreholes.

In 1957. Barkan 13) investigated many parameters that influence the vibratory

pile driving method. These include oscillator peak acceleration. displaceme~t

amplitude. frequency. noninertia load (bias mass). pile cross-sectional area. soil grain

size and angle of internal friction. and shaft resistance. This study concluded that. at

constant amplitude and frequency, penetration speed decreased with increasing pile

cross-sectional area, while the toe resistance increases and hence limits pezetration

and thereby the practical appllcatlon of the vibration method of pile driving. The

inertial and noninertial loads acting on the driver element influence the speed of

penetration and maximum driving depth. The toe resistance of the pile increases in

direct proportion to vibratory frequency. and hence driving at a high frequency is not

recommended by Barkan. There is a n optimum value of the driving force at which

penetration speed and penetration depth reach a maxlmum. and the nonfnertial loads

help in increasmg both the speed and maxlmum penetration. Th,k study also concluded

that linear oscillation theory may be used for the calculation of necessary vibratory

parameters when the amplitudes are less than 0.4 lnch. This observation agrees wlth

the conclusion of Shekhter (41). When the driving is carried out with large eccentric

moments on the vibrator and lf the vibrator displacement amplitudes are greater than

0.4 inch, linear oscillation theory is inadmissible.

In a follow-up discussion to Barkan's paper (3). Mao (25) described successes with

vibratory drivers in fine. coarse and gravelly sand and wen clays. Vibrators were very

eirectlve in sinking pfles Into more than 33 feet of sou. Various vibrators had vibrating

forces of 17.5 to 120 tons, frequencies of 6.7 to 16.7 Hz. unbalanced moments of 720 to

2740 ft-lb. and staUc weights of 4.5 to 11.25 tons. Durlng the construction (1955 to 1957)

of the Yantzu Rfver brldge at i-Iankow. Chlna. vibratory drivers were used to drive-16-

foot-dlameter hoilow concrete caissons though soft material to a depth of 1000 ft (26).

In 1959. Barkan attempted to lncrease the capacity of vibratory driven plles by

using the concept of soil-pile resonance. At the same time. Albert G . Bodine. Jr . ,

developed the sonic pile driver. which vibrates the pile near the pile's second harmontc

frequency. In 1961. the C.L. Guild Co. of h-ovidence, RI., demonstrated that the sonic

(resonant) pile S iver could drive a closed-end plle 71 ft. whfle an adjacent steam

hammer drove an identical pile only 3 lnches in the same time period. Furthermore,

Bodine's sonic driver was found to be successful in driving piles into permafrost. whfle

conventlonal impact driving often led to excess!ve pile damage (16). Meanwhfle.

German and French engineers were encouraged by the success of high-frequency

machines and designed thelr own new generation of dxlvers. However, the high rates of

wear ~ I I motors and bearings reduced the desgn frequency to 25 Hz (36).

From model tests Szechy (44) obtalned valuable data describing the effects of

vibratory driving and impact driving on the porosity of granular solls surrounding a

pile. Fine sand with a coefficient of unlfonnity of 2.5. internal friction angle of 3S0.

porosity of 0.34 and density of 1.75 t/m3 was used. The frequency of the vibrator varied

from 47 to 50 Hz. and the vibrator weighed 42 lb. The diameter of the seamless steel

tubes used to model pipe piles varied from 1.0 inch to 3.5 inches. Changes in void ratio

were measured to determine the change in relative density and the angle of Internal

friction of the soil. These results could be conceivably be used to include the effects of

vibratory drivlng in the static formulae to be used to find the bearing capacity of the

pile. Szechy's observations concerning the changes in void ratio can be summarized a s

follows. The change in porosity around vibrated open-bottom tubes dfifers

considerably compared to the drlver? tubes. There is only one common phenomenon ln

both. 1.e. the porosity just below the ground surface undergoes a cons!dexable reductton

A d e h i t e lmsenlng can be found to be about the mld-height outside the vibrated tubes.

whereas no practfcal changes occurs for the driven tubes. The greatest difference In the

change in porosity occurs below the plle. where .:ompaction occurs In the case of

vibrated tubes. and where slight loosening occurs III the case of driven tubes. Based on

these observations and assumirii that the degree cl compaction may be regarded a s a

measure of tne internal stress conditlons. it was concluded that the b e a ? ! resistance

will be derived mainly from point-resistance for vibrated tubes and from shaft friction

for driven tubes. Szechy theri compared the volume of soil lntruded int:, the tube, which

was much greater due to vibration than impact drivlng. In the case of vibrated tubes. he

observed that the height of the sou plug within the pile is on the average at the same

level a s the original ground surface and stands even hlgher in the tubes of larger

dlameter. The avenge reduction in porosity ol this inner soil core ranged from 2.5 to 11

percent. On the other hand, the ievel of the plug was always lower in drlven tubes, the

daerence Increasing with the reduction In the tnsido diameter of the tube at a generic

penetration. The reduction of the origlnal porosity was observed to be about 6 to I4

percent. The study also compared the bearing capacity of the vibrated tubes with that of

the driven tuSes. for various diameters. and it was concluded that vibrated piles are

inferior to driven plles. This fnferio13ty was most evident for small vibration tlmes to

force the plle to the required penetration depth. Thls lnferforlty nearly disappeared

when the vibration time exceeded one minute (the usual vlbratlon time was only about

20 to 40 seconds].

Hunter and Davlsson (17) studied the load transfer mechanisms of full-scale

piles in medium-dense and medium-fine sand. The angle of Lnternal friction of the s a ~ l d

varied from 32 to 35 degrees. and the steel-to-sand sLidlng friction angle was 25 degrees.

Thls study concluded that significant residual loads are developed in pflts driven with

conventional Impact h a n n e r s but that the residual loads from vibratory drivers did

not exceed the weight of the driver. It was also shown that the load transfer

. measurements made assumlng zero residual loads arc likely to bc tn emor with respect

to division of load Setwecn frict!on and polnt bearing. It was recommended that

instrumented pile tests should be organized so as to obtain the complete stress htstory

for the pfle. They also observed that +he shaft friction during compression loadlng was

about 30 percent higher than that during tension loadlng and that the avenge value of

the earth pressure coefficient was 1.1 for piles driven ulth a ~lbrator.

Bernhard (4) studied the effect of soil moistgre content on model piles vibro-

driven into Ottawa sand and Princeton red c!ay. Based on these experimental results a

dynamic formula for the estimation of bearing capacity of vibro-driven piles was

deve!oped. Schrnid (38) also studied the driving resistance and bearing capacity of

vibro-driven laboratory model piles. Cylindrical brass tubes of 3/4-inch diameter and

lengths varylng up to 36 inches were used a s pi!es. A variable-frequency

e1ectron:agnetic vibrator with a maximum dynamic force of 50 1b was ~ s e d in this

study. and the tests were I5uizrl to a uniform dry sand (Ottawa 30-40 sand at 0.44 void

ratio). I t was concluded that the peak force transmitted to the pile toe is a direct linear

function of frequency and non-inertial load and that for closed-end pipe piles there

appears to be a good correlation between maxlmum d p a m i c resistance and static

bearing capacity. It was also obsemed that the maxlmum penetration ve!oc!ty occurred

only at speciric oplimum frequencies and that the effect of skin friction during

7enetration was practically cegllgfble. Larnach and Al-Showof (22) conducted model

tests on pfles driven into sand by vibrators and developed a dimensional analysis that

resulted in a relationship between bearing capacity, penetration depth. d p m f c force

and total weight of the pile-vibrator system

Although these studies provide important Insights into the performance of

vibm-driven pffes. there are severa3 limitations to that preclude their direct adaptation

to the field. Most important m.ong the llmltatlons are scale ef ic ts (38) and inaccurate

modelling of in-situ effective stresses in the soil.

Based on a labcratary study on vibratory driving in granular soLls. Rodger and

Littlejohn (36) have identtned iwo types of vibratory pile driving. termed "slow" and

"fast." The occurrence of slow or fast motion is d e h e d by the mt!al sou density, pile

diameter. displacement ampiitude and acceleration of vibratlon. with slol.v vibro-

drivmg being the most common method. This stady also concluded that the two

parameters normally used ln deflnlng the range of 2pplication of ~dbratory dnvers are

the displacement amplitude and frequency of vibral!on and that the cho!ce of

frequency should be related to soil type: coarse grained sand 4-10 Ez; fine to medium

sand 10-40 Hz. They have also recommended ranges of values for frequency, peak

displacement and peak acceleration for dlITerent pile-soil condftlons. The amplitude of

vibrational acceleration has been accepted a s the parameter controlhg the occurrerice

of fluidization (shear strength reduction). With reference to the eEect of thls parameter

on the shearing strength of cohesionless soil. three distinct physical states Ln the sol!

are described a s sub-threshold (elastic response). trans-threshold (compaction

response) and fluidized response. During elastic response (acceleration < 0.6g). the shear

strength has not been found to decrease by more than 5%. In the trans-threshold state

(0.72 c accelerat!on < 1.5d the decrease in shear s t r e q h is governed by the exponential

function of acceleration of vibration, and the parameters oi this exponential are

determined by the grain she, shape and magnitude of static normal enective pressure.

During th: fluidized response state (acceleration > 1.5 g). shear strength reduction

reaches a maxlmum. According to the authors, this reduction should be achieved

theoretically at a n amplitude of acceleration equal to that of gravity; however. Fn

practice. due to the presence of inter-particle friction the amp1:tude of vibrat!on

required is approximately 1.5g. A theory has bee11 developed for slow vlbro-driving

based on rigid body motion. viscous-Coulomb shaft resistance and elasto-plastic toe

r e s i s t a ~ c t under combined sinusoidal excitation a ~ l d static surcharge force.

Experimental vexlficatlon of this theory has been acconplfshed by means of driving a

h~l ly instrumented 1.5-inch-outside-dianeter. closed-ended steel pfle into a bed of

dense untform sand (CU = 1.2. d l 0 = 0.29 mm) at a relailve density of 71.5% and havrng

an angle of internal fricuon cf 4 1 degrees (36).

A lull-scale field study was u~de r t aken by the L'. S. Naval Civil Engifieeri~g

Laboratory using 20-inch-diameter (0.5-inch wall thickness) open-ended pipe plles

and a vibro-driver with a 35-ton driving force (131. The soil at the test site consisted of

very dense sand with an average total unlt weight of about 127 pcf. m e piles were viSro-

driven in 4-loot lncrernents. and the dynamic resistance at these depths were

detemiined by using a diesel impact hammer. The maximum penetration that the piles

were able to attain was 13 feet, and the bearing capacity varied from 40 to 53 tons lor the

four piles tested. The rate of penetration varied from 0.03 to 0.30 feet/rnLnute near llnal

penetration. A Limited amount of tests were conducted using 8.63-hch-dlameter closed

and open ended plpe plles, but the extremely dense sand condltlons in the test area

limited both the type a n d quantity of data collected (13).

In 1986. a f!eld study was sponsored by the U.S. Army Corps of Engineers. Lower

Mississlppl Valley Dlvis:on, to compare the performance of vibro-driven pUes to

impact driven piles. In this study six H piles were driven using vibratory drivers to a

depth of about 35 it at the Hunter's Point shipyard in San Francisco. California. Two

borings at the 40 foot x 40 Coot site lndlcated 5 to 6 fezt of dense silty sand and gravel fill

underiain by medium-dense fine-to-medium sand. The bearing capacity of the vibro-

driven piles varied from 180 to 200 kips. except for one pUe which had only 135 Ups

capacity (32). The Deep FoundaUons Institute also sponsored a study to lnvestlgate the

performance of sllt vibratory drivers in drlvlng a 33 it long instrumented H-plle (HP

14x73) at t he same site. The six vibrators selected for thls study. had "free-air"

frequency, amplitude and acceleration varying between 22-26 1-h. 0.12-0.19 inches and

7.7g-11.6g. respecttvely. The maximum rate of pene'.ratlon during driving varied from 5

feet/-. to 2 1 feet/min, depending on the t - e of vibratory driver (47).

In another study performed by the U.S. Arm,? Corps of Engineers (28). the

performance of vibro-driven piles was compared to that of impact drive,? piles at

dlfTerent field sites. In the report five testir,g prograrrs have been discussed. induding

17

two Arkansas Wver Locks and D m (No. 4 and No. 3). a Crane Rail Track. Geochern:c;ll

Building (Harvard C'nlversity) and Wall No. 7 on 1-95. Providence, Rhode Island. At

Lock and Dam No.4 (also the source of some of the data of Hunter and Da~lsson). a

double-acting steam hammer and a Bodine sonic drhrer were used to drive 12- to 20-

inch-diameter pipe piles. 16-inch concrete piles and H piles. Comparing the load

carried by 16-inch pipe piles, impact-driven piles exhibited about 25OA greater toe

resistance and 2% higher shaft resistance than the vibro-driven $le. The H pile driven

by the Bodine sonic driver had 11% higher bearing capacity than the impact-driven

pile, with 23% higher shaft resistance but 55Yo lower toe resistance. Although the

impact-driven, 16-inch pipe pile showed an 8Oh higher compression capaclty. the ratio

of uplift to compression capacity of 0.48 remained almost a constant between the

impact-driven and vibro-driven piles. At the Arkansas River Lock and Dam No. 3 a

low-frequency vibratory driver and a steam impact hammer were used. The H pUes (14

BP73) driven with the impact hammer had hlgher capacities than the vibratory driven

piles by an average of 32 tons in compression and 5 tons in uplift. The uplift to

compression ratio varied from 0.25 to 0.31 for both impact- and vibro-driven piles. In

another study (pile foundation for a crane rail track]. prestressed concrete piles with 13

inch diameter were driven using a drop hammer with a 5-ton weight and a fret fall

distance of 15.8-inches, and a vibratory driver with frequency, amplitude and weight of

18.3 Hz. 0.39 inch and 5.6 tons. respectively. was also used. The bearing capacity ratio of

vibro-drlven to impact-driven varied between 0.25 to 0.88. It was also shown that when

vibro-driven piles had their last 9 feet of penetration produced by drMng with a drop

hammer. the bearing capacity reaches the failure load of a n Impact-driven pile.

2.2 DRIVING FOR?.TLUE

There are in existence a few static and dynamic formulae for determining the

bearing capacity of piles installed with vibratory drivers. In the static fomu!ae the

internal friction angle for sand beneath the pile toe and along the pile shaft are

generally modfied to account for the effect, of vibration. There are four pile driving

'iormulae that were specilIc3lly derived for vibratory drivers. These relationships are

summarized below.

(a) S ~ J D ( 19681

This empirical formula was originally published in Russian in 1968 (19).

According to this formula. we have

where

P = bearing capadty of p!Je in ki,

N = power used by vibratory driver to drive the pile. in Kw,

& = vibration ampiitude of pile in crn,

n = rotation frequency of vibrator eccentric weight in Hz.

Q = total weight of pfle and vibratory hammer in kN.

h = coefficient considering the influence of vibratory driving on the soil

properties.

Stefanoff and Boshlnov (421 proposed the following expression to find N far

elcctrfcally powered vibratory hammers,

N = Tj (3)0-5 !IV cos 0/1000) - 0 . 2 5 ~ ~ .

where ?l = efficiency of vibration hammer.

N ~ = rated power ofvibration hammer.

I = current intensity.

Cos Q = power factor, derived from three-phase electric current theory.

V = voltage.

('3) Bernhard (1968)

Based on a dimensional analysis on the results of laboratory tests. Bemhard (4)

proposed the following formula.

Fstat = I I l m a K ~ ~ / ~ p a v e p ,

where

Fstat = static bearing capacity,

n 1 "'" = maximum eITiciency factor (suggested value is 0.1).

P = power lnput mlnus the losses due to the driving mechanism.

L = length of the pile.

vpave= average penetntion velocity, and

p = total penetration.

The losses due to the dfivfng mechanism must be predetermined by operating the force

generator at the pile driving frequency on a very rigid or very soft support, having a

natural frequency well above or below the operating frequency of the hammer.

(c) Davisson (1970)

Davisson (101 proposed a dynamic formula for pfles driven by the Bodlne

resonant driver. In deriving his lormula, he began with a simple relation for energy

conservation. which is energy supplied = energy used + losses. This simple relation fs

a!so tke basis for practically all inpact pile-driving formulae. If the resistance to

driving Is denoted as R,, then the abcve relationship can be expressed as

where E = hamiier energy.

s = h a 1 permanent set of the pile per blow,

sL = an empirically determined set that represents all losses.

Assuming that the static bearing capacity of the pile is equal to the resistance to

driving, then the static bearing capacity wffl be equal to Ej[s+sI). This expressim is

applicable only for impact hammers. Davisson has extended this relation to vibratory

drivers by developing an equivalence of one cycle of oscfllation to one blow of impact

driving. eaergy (E) to horsepower (Hpl divided by the frequency If) and set (s) to rate of

penetration (rp) divided by the frequency. Since one horsepower equals 550 ioot-

lb/sccond. RU can be wressed a s follows.

where R, is in !b, rp i s in feet/sec, s~ is in feet and fin Hz. If the pile capacity is low and

the rate of penetra!ion is high, then another power term shouid be added to the

numerator to account for the kinetic energy of the driver. equal to 22,000 rp. The loss

factor. SL, varfcs with soll condition and the power tr?.nsmission characteristics of the

pile.

(dl Schmid (19701

Schmid (401 uses an lmpulsivc approach to the pr~blem by considering the force

acting on the ?ile tw as an m~rlpolstve force and tntegnting it cver one vtbratory cycle.

For a one-system oscfllator 0.e. one pair of eccentric masses rotating in opposite

directions). the dynamic forces integrated over an entire cycle ts zero. The remaining

terms in the impulse equation yield

(Bt E + Q ) T = R d t = a R T c I 0

where R = penetration resistance.

B = weight o l the bias mass,

E = weight of the vibrator.

Q = weight of the pDe,

T = period of vibration.

Tc = contact tmle between the soil and the pfle tip.

a = a coelficient hetween 0.5 and 1.0 and genenlly assumed to be 2/3.

The only unknown term in the above expression Is Tc, and it is calculated a s

follows. To drive the pfle into the ground, a rninlmum acceleration amin is required.

a m can be established in a drivlng test a s acceleration of pile when refusai is reached.

Therefore, only the acceleration in excess of amin is used to achieve the penetration

velocity. Vp. Representing the average excess acceleration over the threshold

acceleration a m h by ao, which is equal to (a - amin) averaged over the contact period.

the follouing expression can be written for the contact period, Tc .

where x is the penetratton per cycle given by the penetrauon rate Vp divided by the

frequency. Heme. penetrat!on resistance R can be represented by

More recen:!y. Chua et al. (S! applied the one-dlmenslonal wave equatior,, which

is a widely accepted mathematical model for impact-driven piles. to :he majysis of the

behaeor of vibro-driven piles. By replacing the impacting ram. cushion and capblcck

with a forckg functlon from a simple harmonic osciilator and the spring-mass syst:m

to represent bias mass above the vibrator. the authors claimed that gznera! agreement

was found between measured force-time hlstories along a full-scale pile that w a s

vibrated into a sand deposit (13) and those that were computed by means of the wave

equation, and the mathematical model provided a reasonable prediction of rate of plle

penetration. Although the authors did not publish the wave equation parameters

needed to obtain the correlations, they concluded that the wave equation can be adapted

to predlct the behavior of piles durFng vibratory installarion. -

2 .3 SC?A .VARY

A number of laboratory and full-scale studies on the behavior of vfbro-driven

piles have been published since commercial application of vibrztoxy pile driving began

ln the early 1930's. Vlbnting the pLle at i t s flrst or second harmonic frequency was

found to be a feasible and effect!ve way GI installation of pfles under certain soil

conditions. The laboratory studies have rcvealed that parameters influencing the

driveability and load transfer characteristics of vibro-driven piles are the acceleration,

displacement amplitude and frequency of the vibro-driver as well as soil grain stze and

. soil strength. However, these hboratory tests have f ' e d to simulate any in-siiu stress

effects and thus application of test results to full scale test data 1s questfonr;ble. A

handful of wel!-instrumented, full-scale tests have been reported where the bearing

capacity of vibro-driven piles are compared to impact-driven piles. In full-sca;s tests

there is very llttle contiol ii-~ the test variables such a s soil properties.

Four equations to predict the bearing capzcfty of vfbro-driven piles are reported

in the literature. Verification of wave equatlon analysis to study the vibratory pile

driving problem is in its prilininary stages. Howover. further verification of these

predictive methods from controlled tests are w-nted belore widely applying them in

the field.

CHAPTER 3

D E S C ~ I O N OF TESTING sysmrd

The complete testing system described in this chapter includes the test chamber.

t e s t pile, vibro-driver, impact hammer and data acquisition system. The calibrzition

procedure for the instrumentation and the sand placement devices are also discussed.

3.1 TEST CHAVBER

The test chamber is termed the "long variable lateral pressure sand column"

(LVLPSC). A conceptual schematic of the LVLPSC and the test arrangement is shown in

Fig. 3.1. The sand column was 30.0 inches in diameter by 100.0 inches high. The

boundaries of the sand column consisted of waffle-type . neoprene energy absorbers (2.0

lnches thick) at the base of the column. which made the base seml-rigid. and rubber air

pressure membranes at. the top and lateral boundaries. which made those boundaries

flexlb!e (constant. ccntrolled pressure boundaries:. An impermeable rubber membrane

was placed between the sand column and the boundaries to provide watertightness to

the sand column and permit it to be saturated. The pressure membrane at the top of the

LVLPSC was affixed to the underside of a steel plate that formed the top of the chamber.

The top membrane was flat.with three holes passing through i:: One for the pile port

and two drainage ports for passage of water that was expelled from the chamber during

insertion of the pile that allowed for free drainage of the soil.

Pulley System To Lift DriverIHamrner Driver1 Hammer

/

'\ I o u v e

Crane

\ T - n -rhea3

, : ] Supaart And '., I Guide Frame (Brace not shown for I I I c l a r i t y )

Fig. 3.1. General Schematic of The TestLng System

A more detailed cross-section of the L1,IPSC is shown in Fig . 3.2. The chamber

cons~sted of four 25-in.-high stee! contaiAmlent cylinders bolted end to end through

flanges. This design was necessitated by the need to disassemble the long, slender

chamber to remove the sand after each test and to facilitate deposition of sand In a

controlled manner. There were eight lateral pressure memkranes. each 12.5 inches

high. cf tomidal shape. and 33 inches in outside diameter.

The sand was first flushed with carbon dioxide to displace mtrogen. which tends

to form air bubbles in the soil pores. Then the sand was saturated using a perforated

metal diffusion ring at the base of the sand column and allowing the dealred water flow

under a small head of water to rise through t3e column. A three to four hour saturation

period was necessary. Eight slotted vertical tubes were placed at equal in!ervals around

the perimeter of the sand column. inside the rubber membrane. to collect water Ulat was

flowing away from the penetrating pile. so as to produce radial drainage during pile

driving and load testing.

The pressure in each of the eight lateral pressure membranes was controlled

independently in order to producc a known, unlform lateral effecuve pressure In the

sand at the lateral boundary of the sand column. An important detafl is that the

varlous lateral pressure membranes were all separated by steel rings. so that one

membrane did not impinge upon another membrane that was pressurized to a different

pressure and cause t-ertical distorllon of the membranes. Since the pressure in the top

Ivertlcal) membrane can be varied independently of the lateral pressures, it was

possible to vary the coemcient of lateral earth pressure (horizontal to vertical effective

prlnclpal stress ratlc) in the sand column.

Plastic Jackets (lapped sections of sheet plastic] were placed inside the

impermeable membrane to contain the sand Curing placement an? prohlblt Iatera!

strains that would be accompanied by changes Ln denslty of the sand. These jackets

were supported 1a:erally by the separation rlngs between the lateral pressure

?lLE PORT

S C ~ E E N E C ) PQESSURE RELIEF m a 1 rGFtnvEL PACKED). tSHOWN ROTA-iEO 80 OEG.1 , I 10 a 20 PSI

I I I I 3ESSURE RELIEF PORT ( S m W N

ROTATED 90 DEG.)

VESSEL o.:s.IN..THICK FLAT STEEL 6 In PLATE

CONF lNEM t n ~ % P S l * u .

CEWRLE

SEGMENT tr FA FOR

s q Lateral and Vertlcal Pcssurz 3.2. Detailed SchemaUc of LVLPSC. Shc !ilernbranc Systera

membranes. This procedure wzs necessitate:! because of the fact that during fillL?g L?,

lateral pressure membranes were not pressurized in order to ensure that pass:ve

conditions dld not e'xist at any point the sand. which would have also produced

density changes. Once the chamber was filled. It was pressurfied in steps so as to

minimize the differential pressuye between adjacent membranes, u p to the desired

values of total pressures. Soll deposition ar,d density control procedures are descrtbed

later in this chapter.

During filling, the forming jackets supported outward-directed radial normal

siresses from the sand (assumed approximately equal to at-rest eflective stresses). Once

the chamber was filled and lateral stresses from the bladders were applied. the lateral

body stresses were transferred to the air bladders, since the forming jackets were not

capable of supporting compressive hoop stresses. Therefore the total lateral stresses in

the sand at the boundary of the chamber were equal to the pressures in the bladders.

These values of pressure were maintained constant throughout the remainder of a test.

Because the bladder pressure was calculated to be equal to the desired lateral eirective

pressure plus the hydro stat!^ pore water pressure produced by a free water surface at the

top of the sand column, :he lateral eflective stresses remained constant in the sand

column at the boundary throughout a test. except possibly for brief periods af transient

pore water pressure. The vertical efTecUve stress at any point in the sand column was

theoretically equai to the vertical stress applied by the top membrane plus the body

stress produced by the buoyant soll within the column. However, Li the analysis of data

it was assumed that the vertlcal effective stress anywhere in the chamber is e q u d to the

pressure in the top membrane.

3.2 TEST PILE

This section describes !he reusable test pile that was employed during the study.

The choice of the diameter of the pile and chamber represented a compromise between

minimizing scale effects between m&um sand particle size (which was 2 rnrn In the

case of the coarse sand) and pile size. by utilizing a minimum pile diameter-to-soil

particle size ratio of 50 to avoid any scale effects. which resulted In ;he choice of the 4.0-

inch-diameter pile. The diameter of the sand column was set at 7.5 times the dian~eter

of the pile, which resulted in the 30-inch sand column diameter. With this calumn-to-

pile diameter ratio, some boundary effects may have occurred in the chamber (49).

although they would have been minimbed with the flexible boundary that was

employed. A longitudinal view of the p!le is shown in Fig. 3.3. The pfle was a 4.00 in.-

diameter steel lube with a 0.188-in.-thick wa!l. To mitigate the possibility of fatigue of

the pile head. vertical reinforcing strips were welded to the to;, of the pile as shown in

Fig. 3.3, and coupling the pfle to the driver was achieved by the introduction of an

articulated coupling between the pile head and the drlver.

Except for the accelerometers. the pile instrumentatfon was in place

permanently on the pile prior to the first trial test and remained on the pile throughout

the study. Seven levels of strain gages were placed in the pile wall. a s shown

schematically in Fg. 3.3. Each level was a full-bridge circuit. The levels are denoted by

the numerals "1-7." and the lwel marked "1" served as a force transducer during

vibration and Impact driving. The remaining six levels were read during the static load

tests to develop load transfer wms but were not read during driving. At each gage level

a linear strain gage was epoxy-bonded to the pLle wall in each of two slots machined

into the adernal side af the pLle wall, situated 180" apart on the perimeter of the pfle.

The two gages were wired as active gages in a Wheatstone brfdge. permitting the

cancellation of any bending stresses that d g h l have been Lnadvertently applied to the

TOE 3.00 HEAD

46 .00 / 12.00 IN. /F16.00 IN.--/+--- 20.00 IN.-*- 20.00 IN.--+ 7.00 /r- 1.0 X 1.0 X 1.2 IN.

2 @ 180 ( 7 PAIRS) 3.5 IN. WELD TOE LOAD/ PLASTIC BLOCKS (2) NECK FLANGE

ACCEL. CELL

"e 45.00 IN. PENETRATION

C H A M ~ E R / 1 ';kbo~~~. PILE MATERIAL: SEAMLESS CARBON STEEL TUBING

GRADE 1018

FLANGE: FORGED STEEL

/ LOW-G 4 IN. x

OR HIGH -G 0.2 IN. x

8.5 IN. 0.0. -- ACCELEROMETERS 0.2 IN. 0.038 IN. THICK LIP (2)(BOLT- REINFORCIt.(G

MOUNTED) STRIPS (FD1,CET TOTAL WEIGHT = 78.8 LEI. (INCL. FLANGE) WELDED)( 16

P. TOTAL PRESSURE CELL 0 PORE WATER PRESSURE CELL

pile and sLmultaneously doubling the sensitit<@ of the circuit to axial stresses. The

dummies for this bridge were precision resistors placed directly outside the test

chamber to avoid difierences in temperature with that of the active gages on the pUe.

Lead wires for the active gages were carried through the Fnside of the pile to a conneciion

strip mated to the inside surface of the pile near the pile head, from which the leads

were gathered and soldered into a plug that could be connected with a mating plug from

the data acquisition system. The brldge circuits were completed outside the pile using

external dummy resistors.

Two miniature total pressure cells were constructed and embedded in the wall of

the test pile. with their sensing faces normal to the wall. as shown in Fig. 3.3. 'fie

primary purpose of these cells was to measure lateral stresses against the side of the pile

near the toe and near the mid-depth during the static load tests, when the pore water

pressures could be closely approxinlated a s hydrostatic. thus providing also a measure

of the elrectrve normal stresses on the pile shaft during static loading. The bottommost

of these cells was also read during installation, both impact and vibratory. to obtain an

indication of the time-dependent total lateral stresses against the side of the pile during

the installation processes, and together with the pore water pressure cell situated near

the pile toe. a measure of effective stress during installation. The cell operated on a

membrane principle. in which the membrane was a 0.600-in.-diameter by 0.008-h.-

thick steel plate that was integrally tied to a rigld ring at its boundary. The membrane

was instrumented with a single llnear strafn gage oriented so that its primary sensing

direction was perpendicular to the direction of propagation of the stress wave in the

pfle. This procedure was successful ln lsolaUng the cell from the low-magnitude stress

waves produced by vibratory driving, but some efiec! of the passage of stress waves

produced by impact driving was registered by the cells. Therefore. the data from thc

bottom-lwei total pressure! cell were not analyzed ex?ensively for impact Criving.

The total pressure cells were also read a s luil-bridges, with precision resistors

mounted a s described for the plle wall strain gages used in the adJacent arms and

opposite arm of the bridge to complete the circuit. The dSO size of the San Jacinto

River sand was approximately 0.4 mm. giving a ser~sitlve-membrane-diameter-to-sotl-

graln-diameter ratio of about 38. Correspondlngly. the dS0 size of the Blasting sand

was approximately 1.15 rnrn. gftmg a ratio of about :3 . These ratios afiect, to some

extent. the quality of the data. .Kith the better-quallty data expected ior the larger ratio.

A pore water pressure cell was mounted with its face normal to the wall of the

test ptle at the level of the lower total pressure cell, a s shown fn Flg. 3.3. The primary

purpose of this celI was to confLrm that the pore water pressure agafnst the pUe was

hydrostatic during laad testing. It was also read during vibratory driving to gain

inforination on the variation of pore water pressures during installation and the role of

pore water pressure development on dynamic soil resistance. Its design and operation

were Identical to the total pressure cells except that the sensing face [membrane) was

located below a small free-water saturation chamber !hat communicated with the pores

of the soil through two flnely perforated plastic disks separated by a segment of coarse

f i ter fabric. The cell was saturated by passing dealred water under pressure through a

tubular saturztlon line into t h e free-water chamber. which was vented to the

atmosphere though the perforated disks. Flow of water though the disk openings

indicted saturatlon of the cell, after whlch the saturation line was plugged. No

desaturation of the cell was observed during vibration. It was ilot possible to observe

whether desaturatlon occm-rcci durlng impact driving; however. the pfle was placed into

the chamber such a marmer that the pore water pressure cell was submerged before

driving c m u r c e d . such that dcsaturatlon was unll'iely.

A load cell was designed =d constructed to pennit direct measurement of the

load at the toe of the pile. The decision to use this load cell had a major impact on the

test program. because i ts use forced the clcsure of the pile !o and p r e d u d d the testing of

non-displacement pdes However, the fundamentzl Fnformatlon gamed from its use

(such a s measuremznt of dynamic load transfer :urves) was considered sulficlent

justification to warrant testing of closed-toed pUes. The toe load cell was attached to

the end of the test pde through a threaded connecti~n. A detail of this cell is shown ln

Fig. 3.4. Load was measured using the electronic resistance straln gage principle. with

eight gages bonded wtlh epoxy to a machined section of the cell mred In a full-bndgf:

configuration. Four of the gages were mounted vertically and served a s active gagcs:

four were mounted horizontally and acted a s temperature compensation gages. Thus .

the Wheatstone bridge schematic required no external dummy resistors. Wire

management and connection schemes were similar to those for the pile-wall strain

gages.

Mounted on the top of the toe load cell. lns:de the pile, were two piezoelectric

accelerometers. One was a low-g accelercmeter (range, 0-50 Q For use In the vibratory

tests. and one was a high-g Accelerometer (range. 0-2500 g) for use in the inpact tests or

during restnke events after installation by the vtbro-driver. The low-g accelerometer

was protected 10 2000 g and so was not damaged during impact events. The purposes of

the accelerometers were to provide a means of measuring power and energy at the toe of

the pile. and velocity and displacement of the toe sf the pile during dynamic events.

Energ. and power evaluation required simultaneous evaluation of the force and

acceleration time histories a t the toe. Thls informa',!on was useful in caliSratlng wave

equation models. as explained in Chapter 5 . ana In evaluating energy and power

transmission through the pLle to the pile toe in various sou conditions.

The complex geometry of the toe load cell cast some doubt on whether the

accelerations measured by the accelerometers mounted atop the cell were

representative of the acceierations on the pile wall. Thls concern prompted the

calibration that is described laler in this chapter.

0.125-IN (8 PORT FOR STRAIN G A G E WIRES

v LOW-G ACCELEROMETER

STRAIN G A G E

TOP VIEW LGW-G ACCELEROMETER

ALL. S T E E L

SOFT CALKING

ALTERNATildQ WRENCH HOLES (HI ORIENTATIONS)

Fig. 3.4. Toe Load/Mcelerometer Cell Detail

Piezoelectric pile-head accelerometers were mounted on plastic blocks. as

s h o w in Fig. 3.3, to permit measurement of acceleration at the head of the pile in order

to determine energy or power being accepted at the piie head and to determine pile-head

velocities. Low-g accelerometers were used during vibration tests. These

accelerometers were exchanged for high-g (5000-5) accelerometers during restrike

events and full-depth impact drit-ing.

A schematic of the laboratory vibro-driver is shown in Flg. 3.5. Thls device.

which operates on Ihe principle of counterrotattng masses that produce additive

slnusoidal, vertical forces and that cancel (in theory) all horizontal forces. was

designed by Raymond Technical Facilities. Inc.. of Houston, Texas. and manufactured

under contract by Hydradyne Hydraulics. Inc.. also of Houston. Texas. The dy;lamic

force is provided by unbalanced weights d k e d to flywheels on the shafts of two self-

synchronizing motors. The motors are powered by flowing hydraullc fluid provided by

a 15 gpm hydraullc pump, also manufactured for this project by Hydradyne Hydraulics,

Inc. The pump capacity was designed to prwide a flow rzte sufficient to produce a

maximum frequency of 50 Hz in the driver. but the drhrer was not operated above about

35 Hz because it was found that the actual pump power requirements w e n higher than

those assumed in design. This did not im?act the objectives of the study. since

optlrnum driving frequencies for the test pile were always found to be below 30 Hz.

The housing for the countemtatlng masses was connected to sllde ratls that slid

freely against mating rails in the senqce (guide) frame. The outer surface of the siide

ralls on the driver were teflon-caated and the mating surface on the guide frame was

greased to reduce friction while the driver was in operation A set of removable blas

weights was placed directly above Ule vibrator to place a static bhsed compression force

on the pile during vibro-driving. In order for *.is force to be essentially independe~t of

the blbrational motion of the .ribrator casing. the blas weights werc Isolated from the

vibrator by a series of springs. Part of the purpose of the research was to assess the

effect of the magnitude of bias weight on the ?erformance of the dnver and bearing

capacity. which required varying these weights from zero to the maxlmum value of

1620 lb. As the magnitude of blas weqht was varied. so was the number of isolation

springs between the vibrator and bias weights, so as to keep the natural frequency of the

bias weight/spmg system I = ( I / ~ ~ ) [ K / M ~ ) ~ . ~ . where M~ is the mass of the bias wcight

and K is the combined constant of the spri-rigs in position] at less than 3 Hz.

A swivel-head (pinned) connection was used to connect the driver and the plle.

This connection is shown in schematic form in Fig. 3.6. It is bolted between the flange

on the pile head and.the center of the base plate on the driver. provides for free rotation

about an axis parallel to the axes on the driver motors and operates with less than

0.001 in. double amplitude axial slack.

The system was designed so that the two hydraulic motors would be self-

spchronfzfng. In operation they were found to be dllficult to synchronize inftially and

lo frequently desynchronfie durlng operation. This was unacceptable performance for

the study being conducted, and Raymond Technical Facflltles redesigned the vibro-

driver to synchronize fuIIy a: all times. This was accompllsfied by rebufldlng the two

&wheels so that they interconnected through a system of gears. a: their outer edges,

which meshed to a very low to1erar.c~.

The theoretical performance curves for the vibro-driver is shown ln Fig. 3.7.

.Four d f i r e n t sets of unbalanced weights were constructed that permitted the

appUcation of the four discrete values of eccentric moment. The theoret!cal force

(single arnplltude) generated by the countenotallng masses . Fc. !s ghen by

V I E R 0 1 DRIVER v

0,375 IN. BOLTS (4/Rlf3 @ 1.0 IN.)

(MACHINED

SURFACE)

0.5-IN. BOLT

(3/R18 @ 1.5 IN.) REINFORCEMENT

TEST PILE u SIDE VIEW OF TYPICAL RIB + (BOTTOM RIS SHOWN)

Fig. 3.6. Dctui of Articulated Swivel Connection Between Vlbro-Drtvtr and Pile

Frequency (Hz)

Fig. 3.7. Theoretical Periorrnance Curves for Laboratory Vibro-Driver

where Moe is the comblned eccentric moment produced by the pair of unba!anced

masses, f i s the operating frequency In Hz and g is the acceleratlon 3f gravity (386

Li/sec/sec). The vziues of bias weight. eccentric moment and frequency were varied

durir?g the "parmeter" ' tests (Tables 1.1 and 1.2) and the best combination of these

parameters were selected based on the rate of penetration. All of the "capacity" tests

(Tables i.1 and 1.2: were conducted with full biased weight (1620 Ibs. plus 380 Ibs.

carriage weight). 100 in-lb eccentric moment, 780 Ib vibratory body weght and f = 20

Hz. m e combination of the eccentric moment and frequency produced (theoretically)

a n unbalanced vertical force a t the axes of the motors Fc of 4.1 Ir. Structurally, the

driver could not operate with Fc > 13 k.

The driver and pump were connected through ordinary fle.dble hydraulic hoses:

one pressurized hose and one unpressurlzed (return-lne) hose per hydraulic motor. A

flow divider was employed at the point of connection of the pressurized hoses with the

pump to produce a s nearly equal fluid flow through each of the two motors a s possible.

3.4 IMPACT HAVMER

A st~gle-acting air hammer was used for the impact tests and restriking the

piles dr!ven with the vibro-driver. A schematic of this impact hammer is shown L? Fig.

3.6. The hammer operates as follows:

a. The solenoid vahre is dwed Sy an actuator mounted on the valve upon

command from a controller operated by electronic signal. The a& is allowed to flow

under regulated pressure of 20 psi from a reservoir into the chamber of the hammer.

lifting the ram. The pressure above the ram remains atmospheric throughout the cycle

because the top of the hammer cylinder is open.

b. At the full 1st height of the ram (set accordhg to the Lnpact energ.) a

tube f l i e d to the ram breaks a light beam at tl-:: top of the cylinder caslng. which sends

10.25 In. I. 0. Honed Steel Shell With 0.375 In. Wall (@en al Top)

To Trigger Circut

Removable Aluminum Tube /(Beam Breaker) for 21 In. Drop)

Valve Aduator

Close in 0.05 Sec.)

3 In. Flexible H ~ s e (20 psi)

Top of Pile: /

Baited to Anvil

0.75 In. Cia. Air Inlet Line (10 - 20 Psi)

Mist Lubricator (SAE 90 Weight Oil)

' Teflon bushings to prevenl metal drag

Fig. 3.8. Schematic of Impact Hanr .er

a tr!!er signal to the actuator on t h e solerAoid v&e to opec the valve and to reduce the

air pressure in !he Wet line, m d n a k l r the 3-m. hcse an exhaust h e .

c. The ram then falls freely. t ~ p a c t l ~ g a harnrner cushion (2.5 in. of

plywood sheets) that is sitcaled on top of the a n d at the base of the cylinder. The anvu

of the impact hammer was bolted to the flange on the head of the test pile.

The beam-breaker tube was set to produce a 21-in. actual drop (20-in. nomLnal

drop) during this study. Since the ram welghs 460 15.. this resulted in a theoretical

energy of 0.805 it-k per blow. Fluid mechanics studies of the air compression in the

cylinder indicated that compression 01 atr produced only a 3Oh loss of energy. The

machhed lnside surface 01 the cyllnder is lubricated on every blow through an i n - h e

mister, and the ram has tenon bushings on its perimeter to prevent metal drag. To

nlinimize transmission of energy of tmpact Lnto the hammer casing and thus maximLze

the transmission of energy into the plle. the anvil at the base of the cylinder is not

rigidly connected to the cyiinder caslng but is connected by means of sprlngs located

around the perimeter of the caslng.

The controller can be operated autornarically. in which the rate of driving is

controlled by a prescribed time lag between the receipt of the trigger signal to open the

valve and the generation of a new signal to dose it. During the impact tests, the rate

was set at apprauimately 23 blows per mlnute. The controller can also be operated

manually. which was the mode d operation during the restrike tests. The time between

restrike blows was set at 30 to 60 seconds to allow observation of accelerometer and

straL.1 gage signals between blows and thus verify correct operation of the

instrumentation.

A nenv cushion was used for each hnpact test. although very little visible damage

was observed in the retired cushions. A reusable cushion was employed for the restrike

tests because relatively few total blows were involved.

3 .5 DATA ACQUISITION S Y S T E X S

Two separate data acquisition systems were used for the "capacity" test series:

One for acquisition of dynamic data during pile installation (vibration. impact and

restrike) and one for the static compression and uplift tests.

Dvnamic Data Acoutsttion System,

The dynamic data acquisition system is shown in schematlc form ln Fig. 3.9.

During an installation event, the following data were recorded on an eight-channel

analog magnetic tape recorder: Pile-head acceleratfcn. pile-toe acceleration, pile-head

force, pile-toe force. total pressure (bottom cell location), pore water pressure (bottom

cell location] and rate of penetration (on the voice channel) . -4coustlc time marks were

p!aced on the yoice channel. on which an observer indicated the passage of various

depth marks past the top of the top plate ol the LVLPSC, which allowed for accurate

delerrninatlon of the rate of penetration and which tied the data on the other channels

to a ?articular penetration into the chamber. Tke eighth channel on the tape was used

for flutter control and was therefore not available for data. The tape recorder was run

continuously during the period of pfle installation for any given capacity test.

The resulting data tapes are recordings of voltage outputs for the various

instruments on the channels that are indicated in Fig. 3.9 ar.d are valid for a tape speed

of 7.5 inches per second. ?he voltages that arc recorded on those tapes were multfplied

by the appropriate instrument calibration factor found by the calibration procedure

described ln the next section to obtaln englneerlng units.

Wave forms from fmpac! tests were expected to be very complex because !he test

pfle was very short. permitt% rapid r e t ~ m of rellected waves from the pile toe and (of

lesser magnitude) from the boundaries of the chamber during impact tests and restrlke

events. Since h!gh-speed. real-time dlg!tking equipment was not available, it was

Averaging I 1 Pass F i l t ~

Accelorom.' 1 , ' 161 F o m

Load Cdl

(Piezoelectric Component)

I Ruzer CcnW (Ulan. 5)

I Time Mark

r \

Analog Oscilloscope Iwl 'Switched to Hishog or Low-0, As Appropriate

" Voice Channel Used to Record Rate of Penetnoon and Other Events

High-Speed Magnetrc (Ta? s& = 7.5 Ips] Analog Tape Remrder

Microcomputer m a I (Data Reducoon I &

and Analysis) Spectrum Analyzer C@td OsoUoscope

(SpocUl Digilizad T i m Historirs)

Flg. 3.9. Schematic of Data Acquisition S y s t m for Driving Tests

decided to record the b~r,amic data on analog tage 2nd to dfgitize olf llm at a rate that

was appropriate to replicate the analog slgnals. Thk was accomplished two channels at

a time by the digitizmg circuits contat?ed by an A/D converUcg unit that was coupled to

a spectrum anaiizer (Flg. 3.9). Digitized data were stored in the memory of the spectrum

analyzer for further processing by the spectrum analyzer (either Fourier analyses or

simple multiplication by callbration factors) after which they were output to z pen

plotter or to a microcorr.puter for further reduction and/or analysis.

Immediately after a test. digitized data were rwiewed for apparent correctness

using the digital oscilloscope. The digital oscilloscope was also used to monitor the

frequency of the acceleration of the vibratory driver in real time during vibratory

driving alter the output of an accelerometer placed on the caslng of the vibrator had

been converted to its fasi Fourier transform (FFT). This monitoring system permitted

accurate determination of driviiig frequency acd additionally gave information

regarding the synchronization of the motors on the vibratory driver (through

observation of the harmonics of the driving frequency and the decay of their

magnitudes with increasmg frequency).

Filtering was employed to remove the effects of frequency components of any

signals that are of no importance in the analysls of the tests. Low-pass fllters were

employed on all of the instruments. using a 2 KHz rolloff for the accelerometers and a 1

KHz rolloff for the circuits for the pfle-wall slraln gages. pressure cell and load cell.

The tape recorder itself had a nominal 5 KHz uprer h l t frequency response. Any

signals with frequency components higher than the rolloIT levels described above have

been discounted In the presentation and analysis of the data.

Phase shifts produced by the piezoelectric devices (accelerometers). as weU as by

components of the data acquisition system (an averaging circuit that was u.sed with the

pile-head accelerometers and the various fi1ters)was a concern. The dynamic

calibrations of the accelerometers r ep~r t ed in next section were therefore conducted

with the averaging ch-cuit &?d fFlters Ln the configuration used in the m ~ d e l tests. A

d!scussion of obsemed phase shlfts LS given In the next section.

Although not explic~tly shown In Fig. 3.9. each electrical resistance strain gage -

type circuit (including pUe-wall strain gages. pressure cells and toe load cell] was a full

XVheatstcne bridge that was connected to a shunting resistor to balance each circuit

individually prior to each tests. All instruments on the pile were zeroed by balancing

the circufts while the pile was resting vertically on the surface of the sand at the top of

the LVLPSC. without the harnmer/drtver restlng on its head. Therefare. the readrngs

that were taken during installation are readings relatlve the fnitially unstressed state

of the pile.

Static Data Acauisitlon Svstern,

The data acquisilion system that was used during the static load tests Is shown

schematically in Fig. 3.10. Data from 12 channels (plus the power supply) were

acquired on command from the microcomputer, which was manually controlled.

Readings of amplified data from all channels were made at intervals of pile head

movement of 0.01 inch (prior to a pile-head displacement of about 0.25 inch) and at

intervals of about 0.02 inches of penetration thereafter. resulting in 60 readlngs during

the loading phase of a test. Keying the computer sent a command to the scanner to read

each channel serially (requiring about 0.5 second). The clig!tal voltmeter used with the

scanner permitted acquisition of five digits of significant data. The digltfzed voltages

were sent to a buffer from which +hey were read immediately by the microcomputer.

Physically, all of the system shown within the dashed boundary in Fig. 3.10 was

contalned in one unit. I

The computer thee performed simple mathematical operations (multiplying the

voltage on each channel by the appropriate calibration factor) and wrote the resulting 1

output (in engineering units) to both paper tape and a magnetic tape cassette. The hard

copies (paper tapes1 have been =chived a s permanent records of the static tests. The

Fa. 3.10. Schematic of Data AcquLsltIon System for Stat!s Load Tests

10-V Power Supply I LVOT A

- - - - - - _ - _ _ _ _ I

I

Strain 4

Sua~n I i I

Stram I I - Gage

Circuit 4 200:l Amp:~l~er

Stram

i' 1: [ 200:. *mp, l f ,~ 1 I I

I

1

I i I

I

I I I

I

I f I

I Microcomputer I

MiCCepln I I (lndusion of Calibration - Tc:al Press. ' , a Factors and Writing 13

S ~ I ! , I Storage Un~ts) 2CC:l Amplrfier I

1 L I

I I

I

1 i Hard Copy Casseno Tace

LVCT a I

(LVOTs hava built-in POWW tupplior)

! - - - - - - - - , - 4

a I

I

1

t

4

4 I

4

I

I

cassettes were re-read In delayed t m e by the rnicrwornputer and transferred to a second

microcomputer (the one used with the dynamic data 3.cquisition system] for

development of load transfer curves and load-movzment cu~rves.

As with the dynamic data acquisition system. the various strain gage circuits in

thc stztic system were ba ia~ced while the pile was stress free (sitting vertically on the

top of the chamber). These zero conditions were used for the static load tests (1. e.. no

rebalancing was done once pile installation started). so that the stresses reported for

the static load tests contain the efiecls of any residual stresses that were induced in the

pile during installation.

'3.6 SAYD PWCELIEhT

I t wasjudged that the sand densities of greatest practical interest would be those

in the medium dense to very dense range (relative density of approximately 6046 to

90%). since naturally occurring sands are relatively rare at relative densities of less

than 50 to 60336. and pile foundations would not normally be needed +a soils with

relative densities exceeding 90%. Experience indicated that the ~nos t appropriate

means of preparing specimens of approximately 40 cubic feet in volume (to flll the test

chamber) w s to place them ln!o the chamber by raining through air ("pluviatile

compaction").

Initially. small-scale model rairlers Gig. 3.111 were tested for producing sands at

600/6 and 90% relame density. They consisted of a funnel. a pair d # 10 sieves placed at

various distances below the mouth of the funnel and at various distances from each

. other, and a sheath. which directed the falling sand and which excluded currents of

from passing through the fallag colun?n of sand. These ralners were also used in the

preparation of specfmens for strength tests.

F u n n e l

Funnel \ /

+ 6 S i e v e s

Sieves

+ I 0 <- +10

Sieves

,

- - -

- -

L A

(For D e n s e Sand) (For Medium Sand)

( a 1

t---i 1.54'

, Funnel

(For Dsnse Sand) (For Medium Sand)

(b)

Fig. 3.1 1. Model Rakers for Sands: la1 for San Jacinto Riwr Sand; (b) for Blasting Sand

Full-scale rahers were then d ~ e l o p e d from t'le designs shown on Fig. 3.1 1. A

schematic diagram of the full-scale rair,er that was developed for deposition of both

sands in all states (except for the medium dense Blasting Sand) is shown in Fig 3.12. 1

In place of the funnel on the laboratory rainers, a pan hopper with a bottom-discharge

shutter was used in the full-scale rainer. The shut ter consisted of matching metal %

sheets with ccrrespondlng hole patterns, a s shown in Fig. 3.12. The top sheet was

designed so *ha? !t could slide laterally. As tke hopper was filled the holes in the top c

sheet were ou t of line with those on the bottom (staticnary1 sheet. To deposit the sand,

the top sheet was slid laterally until the holes aligned and the sand fell onto the top

sieve. The holes In the stationary sheet were machined in such a way a s to produce :

minimum turbulence of the falung sand particles a s they exited the shutter.

Attainment of the medium dense state (60-65% relative density) by pluviatile

compaction with Blastlng Sand could not be accomplished wlth the ralner shown in

Fig. 3.12;' therefore, it was necessary to construct another rainer for depositing sand

under those cond1Uons. That rafner is shown schematically in Fig. 3.13. li consisted of

a shutter. a s shown, whlch was activated by torsional motlon. No sieves were used. and

the sand was dropped through a distance of three inches directly from the shutter to the

surface of the newly deposited sand.

Us- the raL..g dev!ces described Fn the preceding section. each of the four

cells in the LVLPSC was filled wit! dry sand, beginning with the bottom cell and

concluding with the top cell. At the base of the bottom cell were placed the energy

absorbers described b d o n . followed by the water dilfusion ring and riser. prior to

beginning the ralnlng process. Plastlc forming jackets tha t could not resist

compress!ve hoop stresses werc used to provide lateral cordinemeat to the sand and

w e n put into place in a given ceU just prlor to b e p n i n g !he illling of that cell. Once the

topmost cell had been filled with dry sand, the top x p of the chamber was bolted into

?lace. The &amber was then piessurized to the required levels of total stress to

4 Braces Equally Spaced

To Overhead 1.0" 0 Pipe Pulley To Stop Shutter

/

Sand Pan Hopper (Sheet Metal)

Shutter

2 Sieves in Locations Depending Upon the Desired Densi ty

Sheet Metal S k i r t

Sand Column Containment Vessel

lmpermeabie Inner Liner

Flexible Plastic Sheet

4 Holes of 46 Holes of 0.5" 0 18 Holes of 0.25" 0

Same Pattern of Holes on Shutter and Bottom of Sand Pan

Shutter

F!g. 3.12. Schernatlc Di~!gran of Full-Scale Rainer Used f3r San Jaclnto Wer Sand and Dense BlasUng Sand

Elevation

Turning Bar L t

0 Holes

128)

Plan

I U p p e r Plate

Sand Pan Hopper

Ffg . 3.13. Schematic D l a g a m isf FuU-Scale ~ainc-r Used for Medium Dense Blasting Sand

L I 1

C= 28'

- S p a c e r Block

J

produce the effectiv~ stiesses required for the ~artlcular rest for which Ihe chamber was

being prepared. That is. the vertical total stress applied at the top of the chamber was

equal to the target effective stress. but the total stresses. in the lateral pressure

membranes were set equal to the target effective stress pius the pressure pmduced by the

head of water in the pores of the sofl ln the chamber. The pores of the dry sand were

then purged with carbon dio.xlde; finally, the chamber was saturated with deaired

water, through !.he Mus ton ring.

?The instrumented test plle was then placed into the top of the chamber through

the plle port to the elevation of the bottom of the pLle-port guide tube (Fig. 3.2). and the

test was conducted.

Following the ~ o ~ ~ l e t l o n of a given test, the free pore water was drained back

through the diffuser ring into the tank. The: chamber was then depressurized and the

pile exlncted vertically. The top cap of the chamber was then removed . and :he moist

sand was removed from the top cell by vacuuming or by shovelling. This process was

repeated with the remaining cells a s the sand was removed from the chamber in the

reverse sequence from which it was placed. The moist sand was then placed in a forced-

air convection oven for drybg. The oven-dry sand was then placed back tnto the

stockpile bin for reuse in future tests. The drying process. wkich occurred in a small

bakery-type oven, required about two days for 40 cubic feet of the Blasting Sand and

about three days for the 40 cubic feet of San Jacinto W e r Sand.

The grain-size distribution of the sand was checked against the initial

distrlbuuons (Fig. 4.1) periodlcaily during the test!ng program to observe whether reuse

resulted in degradation of the sand particles. None co-Ad be observed.

Preliminary studies with the full-sized rainers indicated that they give slightly

higher densjtfes in the chamber than the corrcsponciing laboratory rainers (Flg. 3.21.

Therefore. while the sofls were deposited at relatlve densities of approximately 6096

and 85% for small scale testing. the cornsponding relative densities attained In the

chamber were approximately 6596 and 90%. Since the process of isotropic

pressurization m the triaxial tests r a s e d the relative densities of the looser specimens

from about 60% to about 65Oh. the deposited relative densiLjr of 65Oh in the chamber to

represent the medium dense case is probably more representative of the actual relathe

density after pressurkalion of the chamber. Cravirnetric checks were also made of the

densities of the sands a s they were placed Ln the chamber ior every test. This was

accomplished through the follow'bg process:

a. Twelve sarngllng points were established within the chamber, a s indicated In

Fig. 3.14:

b. After placcrnent ol the fourth lift in each cell. c~luminurn sampling cans

(standard 1at;oralory molsiure sample cans). two inches in diameter and 1.5 lnches in

height, were placed on the sand surface and Ule next ltrt placed;

c. A thin-walled tube (longer than the height of can) was then pushed into the

sand isol~tlng each sampling can. The overburden sou was removed bdore recovering

the sample can;

d. me votd within the tube was filled with sand using the appropriate

labcratory rainer. and the tube was withdrawn;

e. The weight of the d;y soil wlthin the sampling can (whlch had a known

volume) was measured, t 5 e dry unit weight calcujated and the relative density

deterrnhed based on the h o w maimurn and macbnurn Index densities (chapter 4).

Results of the gravfmetric tests on the density samples u e given LTI Tables 3.1

a ~ d 3.2.

Depth in Chamber (In.)

I Note: All Sampling Points in an Em. West Plane

Flg, 3.14. Location of Cra-etric Sampling P o h t s in Chvnber

Tablc 3.2. Measured Values of Relnllvc Der~slly (%) of I)ry Sand As Placed In the LV1,I'SC; Tests on Dlnst~ng (Conrsc) S;lli(l

M,?xlmum dry unll welght = 102.6 pcf Mlrlln~urn dry unll weight = W. 17 pcf

Each vnlut Is an average of three gravlrnctrlc snnlples.

-. ~%-pli~ 1 n Chanrber (In.)

12.5

37.5

62.5

87.5

Avg,

Tnrget J Value

'l'cst Nu. v

1m/ IOU/ l ihl 11111 14 15 16 17 19 1 2 ~ 1213 13A 1313

97.1 96.3 72.0 59.5 9 G . 6 98.2 67.5 93.9 05.1

99.8 99.6 70. G 61.0 94.1 96.2 6.1.1 95.5 91.2

97.1 98.4 69.8 64.5 96.1 97.2 67.0 98.0 92.1

98.8 96.6 72.3 70.6 95.G 08.2 62.3 96.0 98.6

98.2 97.7 71.2 63.9 95.6 97.5 65.4 96.6 94.8

$HI 90 65 65 90 (90 65 90 90

-

Axial Strain Gape and Pressvre Transducer B r l d m .

The plle was calibrated in compression to a load of 41 kips on three separate

occasions: prior to the first test. during the testing program and after all the tests were

completed.

Tne calibration process was as follows: The plle was placed in a compression

loading dellce la wide-flange steel section configured to rest on the tips of its flanges on

the floor. with reaction plates welded on its ends). A hydraulic jack situated at the head

of the pi!e then applied a compression load of 4 5 kips, which was then released. This

process was repeated from three to five tlmes. in order to exercise the pile and mitigate

the effects of residual stresses from manufacture and welding. The pfle was then loaded i

in increments to 41 kips. and each strain gage bridge was read uslng the static data

acquisition system and bridge completion circuit that was used In the chamber tests.

along with a calibrated Lebow load cell, which was placed a t the head of the pile,

between the plle and the jack, and the power supply. A swivel-head device was placed 4

between the jack and the load ceil to minimize moments applied to the pfle during

calibration. The pile was not calibrated in tension. It was assumed that the

calibration constants determined from compression loadlng also applied to tension

(uplift) loading.

T h e pore water and t o t d pressure transducers were also calibrated statically.

whfle the pile was urJcaded. The callbration consisted of a fluid pressure test, in which

a small cylindrical water reservofr was clamped to the pfle dlrectly over the transducer

being tested. 'Pie water in !he calibration cylinder communicated directly with the

s e n s h g face of each traxsducer. {The pore water pressure transducers had been

saturated prior to this time.] Pressure was applied to the water column by a n air-over-

water devfce in a triaxial test panel and read by means o i a calibrated pressure

transducer in the tria>ual panel. The calibratlon procedure consisled of exercising the

pressure transducer three to five tlrnes to a pressure of 60 psi and releasing the pressure.

Records of pressure vs. plle transducer output were then n a d e tncremenially during

loading and unloading of the transducer.

Essentially no zero shift or hysteresis was observed In either the pile axial

strain gage or lateral pressure transducer output during any of the calibrations. The

calibration constants of the strain gages. the lateral pressur? transducer and the toe

load cell were thus obtained and well-documented (30).

Am~litude of Toe Acceleration.

Some doubt Wsted regarding the correspondence of the acceleration indicated

by the toe accelerometer during driving to the true acceleration of the pile toe because

the toe load cell Itself is flexible and can polentially magnify pLle accelerations. In

order to verify this effect, the test pile was freely sxspended In a horizontal position.

and the plle-head accelerometers were remounted on the wall of the plle at the level of

the toe accelerometer. The pile was then struck lightly at the head. a s indlcated In Fig.

3.15. to study the output signals under dynamfc conditions. This test produced a

standing wave ln the pile havtng a frequency of appioxlmately 500 Hz. A comparison

of the Urne history records of the two types of accelerometers is shown in Fig. 3.16a.

The hlgh-g toe accelerometer. as mounted, gave peak acceierations that were

consistently higher than the average of those measured on the put wall. A calibratlon

factor (multiplier) of 0.76 for the toe accelerometer was found to be necessary to bring

that accelerometer into .approximate compliance with the wall accelerometers. a s

indlcated in Flg. 3.16b. That factor was used to correct of the toe acceleratfon data

for th6 impact, restrike and vibro-driving tests.

Phase Between Head and Toe Acceleralfons,

Because piezoelectric accelerometer circuits can experience phase shuts.

particularly when employed usi..g e1ectrcjn.k averagbg circuils. as was done in the tests

4 C.25-In. P!ywcoc' Cushion

Toe Accgieroce:er ' 1 Mounted on Tce Lctd Cell

Pi le-Held Accelercmeters Attached 13 Wall of Pile

Fig. 3.15. Schematic of Calibration Test for Toe Acce!erometer

4 0 0 ~ n Toe &el-

CALIBRATION FACTOR APPLIED roo ,

Flg. 3.16. T i n e Htstories cf P i e wall &?ti T G ~ Load Ce!! Arcclcratlon: (a) IJr,corrt~:ci: (b) Corrrded

reported here. it was also decided to detenrzne the phase between the !ow-g pile-head

accelerometers and the low-g pile-toe accelerometer that were acquired dur ing

vibratory installation. This particular phase shlft is mponan t because the toe and

head acceleration (and force) information was used to determine unit load transfer

relationships during vibrational installation. .The calculated phase between head and

toe is appra-dmately 2.9" at 20 Hz for a wavespeed of 16.300 ft/sec Ln steel. !n the data

reduction procedures the t ine history for the toe acceleration was then shlfted re!ative

to the head acceleration by 2.9".

The testing arrangement i s shown in Fig. 3.17. In which an available 4 Hz

(nominal] vibrator was used to excite the pile. Time historles of both the pile-head

(average) and pile-toe accelerometers are shown in Fig. 3.18. and the corresponding

phase and magnitude spectra and coherence function are shown in Fig. 3.19 (Note : the

cross power spectrum is a measure of mutyal power between two signals at each

frequency and the coherence function shows the degree of causality between the two

signals). At 3.9 Hz, the phase is 5". At 20 Hz the phase is then 25.6" (eaect due to

electrical circuit and size of pflel, such that the tee accelerometer data must be shsted

forward in Ume 22.7" relative to the recorded position in the time domain at 2

frequency of 20 Hz (that is. 3.15 msec).

No formal assessment was made of the phase shlft in acceleration at the toe

during impact drfvlng, since such shifts were not needed in the data analysis.

Phase Between Velocity and Force at Head or Toe.

No formal calibrations were made of the phase between force and acceleration at

either the head or the toe. When the velocity (integrated acceleration) acquired dur ing

each of the chamber tests was mu!tiplled by pile impedance at the head (or the toe1 and

the resulting time historles compared with the corresponding measured force-time

hlstorfes during the initial part of an impact blow: however, the resulttng curvfs did not

exactly match, indicating that a small electronic phase shill existed between force and

I Suspended from Ceii~ng

I Pile-Head Accelerome:ers Attached to Wall of Pile

4 Hz Vi3ra:cr

1 ;-

Fig. 3.17. Schematic of Callbration Test for Phase Lag &tween Indicated Head and Toe Acctleratlons

Test Pile I.. i .. . 4-+

Toe Accelercme!er Mounted on Toe Load Cell

-

Flg. 3.18. Phase Calibraaon Test: 7'ypical Time Hlstcrles for AweleraUon : (a) Pile Head (Average): @I Pile Toe

1. e m

E. 9 9 8

13. B 20. eaa

Fig. 3.19. Spectral bfzgnitude and Phase Relauonships Between Head (Average) and Toe Accelerometers; Phase Calibration Test

acceleration at the head (or toe) level. This shut was accounted for in the development

of pile force and velocity relations a n d for comparisons with the wave equation

solutions for the impact and restrike tests, a s stress wave theory require% This shlft, m

terms of time, was noted. and a corresponding shlft was made in the liitegrated

acceleration records h r purposes of computing energy (which requires that velocity and

force be nultip!!ed together timewise and integrated across time). N o corresponding

shu t s were made in th? vtbratory test data because of the low frequencies lnvolved

(approximately 20 Hz).

CHAFTER 4

SAND PROPERTIES AND TEST RESULTS

This chapter presents the properties o l the two sands and the results of all

driving tests.

Index. triaxial compression. interface shear . permeability and torsional

resonant column tests were conducted to characterize the San Jaclnto River Sand (SJR)

and Blasting Sand (BLS). Although these tests do not necessarily represent the stress

paths to which the sand wcs subjected in the LVLPSC during pile driving. they provide

info;matlon on the mechanical properties of the sacds. Past studies have ldentSied

that the grain slze cf sands were more important than the grading. Hence the efrect of

the effective grain size. d 10, was investigated but distribution was not.

The penetrations of piles of lnterest to transportation facility designers is in the

order of 50 to 100 feet. In selecting effective pressures ln the chamber, it was assumed

that the ground stresses for such penetrations could be simulated wtthtn a reasonable

approximation by a p p l y i ~ g an isotropic effective stress withln the chamber eqcal to

the ground stress that would occur at the middepth of the pfle IfKo in the deposit being

simulated were 1 .O. Hence, the in-situ lsotroplc effective stress levels of interest are tn

the range of 10 to 20 psi. Most of the pfle tests in thc chamber were conducted with

initial isotropic eflectfve pressures of 10 and 20 psi. However. the mean effective stress

ln !he soll mass during installation and static loadlng could tncrease'the level of mean

ellective stress around the pile considerably aba te the initial. ln-situ value. Therefore.

laboratory strength tests were conducted with confining stresses varying from 10 to 50

psi.

X fe;v piie dilving tes:s were conducted ln the LVLPSC with KO = 0.5 (anisotropic,

initial. in-sltu stresses in the scil), In which the 10 psi pressure range was maintained

for the horizontal effective pressures; however, no corresponding strength tests were

conducted under this inftial effective stress condition.

The grain size was the maln concern in this study and hence two uniform sands

were selected.

Grain-Size Distribution.

The averages of three grain-size distribution tests for the two test sands are

s h o u n in Fig. 4.1. For the San Jacinto a v e r Sand (SJN the effective g r a b size. d l O , is

0.2 rnm. and the coefficient of uniformity CU Is 1.74. From viscal observations the

typical shape of the grains was subrocnded, and the SJR is classified according to the

Unified Soil Classtfication System a s "SP." or a poorly graded fine sand. For the

Blastlng Sand ( B E ) dlC, and C, are 1.2 mrn and 1.42. respectively. The grain shapes

were angular lo subangular. and the Unified classFficat1on is "SP," or a poorly graded

coarse to medium saxd. Both sands were siliceous in mineralogy with no organics or

soil finer than the No. 200 sieve slze.

Minimum and Mzimum Denstty.

Volume-change characttristics of the sand are considered to be one of the factors

innuenclng the driveability and the behavior of the pile-soil system under load. The

volume-change characteristics are complex functions of the effective stresses and

initial density of the sand. Since the relative density of most m t u r a l sand deposlts

into which piles will be vlbrated will exceed 500h. it was decided to deposit the test soils

in the LLZPSC at target relative densities of 60 and 8S0h. In order to determine the

actual density required for the attainment of these values of relative density, it was

necessa7 to cmduct tests for ml rmum and maximum densities as defined by A S n f

standards D 4253 and D 4254 (1). Each density was obtained a s an average oi three test

results on sarmples taken randomly from the stockpiles of the sands. The mean values

of the maximum and rninlmum index densities for the SJR were 110.4 pcf (standard

deviation was 0.13 pcl) and 94.2 pci (standard deviation was 0.76 pcl), respectively,

(corresponding to a mhirnuln void ratio of 0.50 and a maximurn void ratio of 0.76). and

the corresponding index dexsities for BlasUng Sand were 102.6 pcf (standard devtat!on

was 0.02 pcfJ and 90.2 pcf (standard deviation was 0.57 p d . respectively (corresponding

to a minimum void ratio of 0.61 and a maximum void ratio of 0.83).

During triaxial testing the sample dlameter was established at 1.5 inches. When

SJR and BLS were deposited at a relative density of 60% and consolidated at hydrostatic

pressures of 10 and 20 psi, relative density was increased by about 5%. Therefore. while

the sands were deposited. both in the chamber and in trlaxial cells. at a relative densily

very near 60%. changes in relative densities could be expected during pressurization.

and some of the results are sumrnerkd in Tables 3.1 and 3.2.

Permeability.

Constant-head permeablllty tests were conducted on both solls deposited in the

relative density range of interest. Tests were ccnducted by depositing oven-dry soil by

raining through air into cylinders 3 inches in diameter by 6 inches high and then

saturating the samples very slowly with deaired water by gravity to simulate

approximately the procedures that were used to deposit and saturate the sand in the

LVLPSC. Flow during the permeability test was from top to bottom of the specimens,

parallel to the dlrecUon of the particle velocity vector during deposition. The results

are summarized in Table 4.1. I t is obsented that the Blasting Sand (the coarser of the

two test sands) is about twice as permeable as the San Jaciiito River Sand.

Table 4.1. Summary of Permeability Tes t R e s u l t s

Trtaulal Comnressloq.

Consolidated-dralned triaxial compression tests were conducted on saturated

samples of dense (85% nominal relatlve density) and medium dense (60°/6 nominal

relative density) S J R and BLS Sands. These tests were conducted to provide

infomation on stress-straln properties and shear strength, a s characterized by the

angle of internal friction. of both sands. The samples were prepared by raining or A oven-

dry sand, a s per the permeablllty tests. Aiter gravity saturation (and verification of

saturation by measurement of the B-parameter). the 1.5-inch-dlameter by 3.0-fnch-

high specimens were consolidated lsotroplcally and then loaded to failure by

increasing the major (vertical) princ!pal stress at a constant displacement rate of 0.23

rnm/mlnutc. During ihe appllcaUon of load, volume change was measured by recording

.A

the amount of water that flowed into or out of the specimen from a calibrattd burette

that cornmurdcated with the pores of the specimen.

- Sand

San Jacinto RIver

Blasting

RelaLVe Density (%)

9 1

a

88

a3

Coeflicierlt of

Permeability (cm/sec)

0.9 X

1.0 X 10-2

2.1 X lo-2

2.3 X loa2

The s t ress -s t ra in and volume-strain curves are shown in Figs. 4 . 2 - .I.s,

Volumetric changes are expressed a s volumetric s!raln (change in volume / hi t la ]

volume. a s a per cent). The dense ELS Sand wlth efiective confining pressun, of 20 psi

was subjected to two unloading cycies to delennine the plastic s t ra ln and re!oadi~g

modulus (Fg. 4.5) . While the s p e c m e n had only a small s t rain recovery, the reload

stress-straln relationship i s h e a r and the modulus exceeds by a factor of about two t ? e

nlodulus obtained upon initial loading. The same specimen was also tested to 15?6

axial s train to determine the large-srrain residuzl shea r s t rength , and the peak

strength was four-ld to be reduced by 15Oh at this value of major principal s train. A

sirriilar high-straln test was conducted on a dense specimen of S J R Sand wlth eflective

conlining pressure of 30 ps i (Fig. 4.3), a n d greater high-strain degradation (peak

strength reduced by 38%0 a t 15% srrztn) was observed than fn the BLS Sand. Both s ands

a re seen to dilate consistently in the dense state under triaxial compression loading

conditions.

The results for t he medium dense s a n d s ( re l~ t lve density of 60%. Figs. 4.2 and

4.4) hdica te that the solls contract Wtial ly upon shearing, with b e magnitude of

contraction depending on the value of t he codLnLng pressure. and then dflate after

- shearing failure begins. The specimens of S I R Sand tended to d a t e more than BLS

Sand a1 this density state.

Plots of m e a n effective normal s t r e s s versus maximum shea r stress ("p'-q

diagrams") are presented in Fig. 4.6, 141e angle of Fntcrnal friction (l can be derived

from the slopes of Lhese relations as

- 1 Q = sin [ tan 5 1 ,

Axial Strain, ca (%)

Fig. 4.2 . Results of Consoilda!ed-Drained %axial Compression Tcsts ior San Jacinto River Sand at 60% Relative Density

Axial Strain, r , (%)

'18. 4.3. ILsults of Consc1lda:cd-Dmcl 7Max!al Comprcsslon Tcsts for San Jaclrita Rvc; Sand at 35% Rrhciauve Density

Axia l Strain, 6, (%)

Flg. 4.4. Results o l ConsoUdated-DmL?~d Maxlal Compress;on Tests for Blasting Sand at 60% Relative Density

Axial Strain, c, (%)

Fig. 4.5 . Rtsults of Consolidated-Dralned Triaxial Compression Teats for Blasting Sand at 85% Rrlatfvt Density

where : is thz s!ous ol the lppropriate 1:ne 111 Fig 4 6 Tllz angle of ~nterna l friction

v m e d from 33 5" to 43 6 "

Interface Shear

It was also considered lrnportant to investigate the interface shear strength

properties of Lhe sand 2nd the material comprismg the ou:er wall of the plle In order to

s tudy Lhls efI'ect. interface shear tests were conducted ?n a dkect shear apparatus Sand

was deposited by nlnlng the sol1 in a dry s ta te at yelalive densities of 60% and 850/6

onro a prepared flat steel pls:e Ln the bottom half of a clrcular dlrect shear box 3 inches

~n d~arneier , follow4ag whlch the top of the sand surface b a s vibrated lightry to ensure

that the relative density at the sand-sleel interface was equivalent to that m the sand

m a s s ~v i thm the shear box. In order to represent th: the pile surface closely, the steel

?late was made of the same m a t e n d a s the pile and was p e n the same fWsh a s that on

the p ~ l e by lightly machhlr ig it wiLh a n end mill and r ~ b b r g it with a n emery cloth

pllor to depositing the sand Aiter placement, the sand was saturated and tested in a

consolidated-draLned mode under normal interface stresses of 10. 30 arid SO psi. Both

shea r stress-displacement and vefiicd-horizontal-displacement relations, are glven In

Flgs 4 7 - 4 10 The .SJR Sand contracts at the interface at 60046 relative dersit-4 but

dllates ar 85% relative density (Figs. 4.7 and 4 8). wt.lle the BLS Sand contracts at 60%

relatlve demlty but rindergoes relztfvely mF?or volume change at 8.5% relative density,

except at the 50 psl normal s tress , where It contracts slightly. This type of interface

behavior suggests tha t the test plle will exhlblt somewhat M e r e n t load transfer

characteristics when installed in the two types of sand ln the LVLPSC.

Interface frictional failure envelopes are s h 9 w in Fig. 4.11. Tine interface

frictlon angle Is seen to be largest for dense SJR Sand (30") a?d smallest for rnedlum

d e r s e BLS Sand (25") It is noted that these values d e all considerabiy lower t3an :he

angles of h t e rna l frlctlon obtained from rrlzclal cor?presslon tests for peak pm-clpd

s t x s s d d e x n c e s ar,d are also somewhat lower tha? angles 9f internal friction that can

Hor izon ta l Deformation, x 7 o - ~ in.

Fig. 4.7. b u l t s of Bkcct Interface Shear Tests for Sari Jaclnto ,%a Sand at 60% RcIaUvc Density

Horizontal Deformation, x 1 Q - ~ in.

Fig. 4.8. Results of D b x t Interface Shear Tests far San Jacinto River Sand at 85% Rrh.Uve De=ity

4 0 80 120

Dilat ion

Horizontal Deformation, x 1 o - ~ in.

F!g. 4.9. Results of D 4 n c t Intcrfacc Shear Tests for Blasting Sand at 6095 Szlativt Density

-10 - ' f I 1 I i 0

I 40 80 120

Horlrontal Deformation, x 1 o - ~ in.

Fig. 4.10. Rislilts of DLmt lnterfacc She= Tcsis icr B k s l l n g Sand at 85% -9rlaUvc Density

be inferred for high-str;:n soil-on-soil res!dual stiengtfl conditions in the triaxial

compression tests.

Resonant Column.

Several tors!onal resonant column tests were perf3rmed on samples of S J R and

BLS Sands at the n o r m ~ a l relative density of 65%. The results of these tests provide an

indication of the stiffness a n d material damping of the s a n d at very low strain

amplitudes [for example, near the boundaries of the test chamber). The test specimens

were similar in size to the triaxial compression samples and were also prepared by

raining. However, they were tested in the dry condition to preclude the bulldup of pore

water p re s su res dur ing application of the vibratory torsional momen t s to the

specimens. Variations in the shear modulus of the sand with shear strain amplitude

are shown in Fig. 4.12. and the measured equivalent single-degree-of-[reedom damping

ratlos are t,abulated m Table 4 .2 .

Table 4.2. Damplng Ratios of Meditirn Dense Sands

Cordhing Pressure (psi)

an Jacinto River

y = 7x10-3 - 1 . ~ 1 0 - 2 y= %lo-3 - 1 .5~10-2 y = 6x10-3 - 1.2~10-2

D = 2.2 - 3.3 D = 1.0 - 1.8 D = 1.0 - 2.5

y = =lo-2 - 1 . 9 ~ 1 0 - ~ Y = 9x10-3 - 1 . 7 ~ 1 0 - ~ y = l X 1 0 - ~ - 2.2X10-~

Notes: y = shear strah amplitude ln percent; D = damping ratlo Ln percent of critical

Shear Strain (%)

r I

Fig. 4.12. Dynamic Shcar Modull v ~ . Shear StraJn Amplltudc (Slnglel as Functiom of Sand Type and ConfhLng Pressure from Torsional Resonant Column Tests

4 0

3 0

-

- 50

I Conf in tng P r e s s u r e = 30

- 3 0 a,

-& %

2-4 - ".a

20

70

- %. 10

--. - 10

==--=-.

- . s q -. ..&-. , "L 1 1 I I l I l l 1 1 I I I ! I I ,

1 o - ~ 4 Q - ~ l o - '

At eqi?.iva!e::t cordinlng pressures and shear strairi ampli tudes the shea r

mcdulus of the ELS Sand :s much iower :ha11 :hat of :he S J R Sand. with dilTerences

lncreaslng with lnc reashg confining 7ressure. Th: damping ratios for both sands

appcar to be similar fcr equivalent ranges of shear s train amplitude a n d conlining

pressure. For both sands the d a m p i ~ g ratio tends to decrease slightly with hcreasing

conlining pressure.

The purpose oi the 'parameter " tests (Tables 1 1 and 1 2) was to assess the eflects

of bias mass , mean ellectlve chamber pressure, effective grain size and relatlve d e n s ~ t y

of the so11 on the penetration rate of the pile dur:ng vibratory driving. Data from all

paranleter tests with the vibro-driver a re summar'zed graphicalIy in the fonn of

pcnetratlon rate versus dnver frequency and are presenled in FIGS. 4.13 - 4 14

F1g 4 13a tnd~ca te s that 50 ir,-lb of unbalanced moment IS inadequate to drive

the test pile ID S J R Sand at 90°h relative density and 20 psi effective chamber pressure.

A low rate of penetration was achieved at 10 psi effec!ive chamber pressure in the

Irequency range of 10 to 25 Hz. with an optlrnum rate occurring at a frequency of about

20 Hz The efkct of hcreaslng the unbalanced moment to 100 hi-lb and increasing the

bias mass a re addressed In Fig. 4 13b. which provides data for SJR Sand in the "dense"

s tate (relative density = 90%) and at high (20 psi) effective chamber pressure. With a

minimum b k s m a s s a low rate of penetration was achieved by increasing the

unbalanced moment to 100 in-lb: however, the optimum rate of penetration of about

0.15 ips Is probably too low for rapid drlviiig app!icatlans. Increasing the welght of the

bias mass from the m n i m u m value of 380 lb (!he permanent carriage weight) to 2000 lb

[by adding 1620 Ib of bias msss) caused the rat: of penetratlon to trlple at the optimum

Dense S J 2 S a n d

Danse SJii Sand

!,.(edium Derse SJR Sand

ttbq. (Hz)

Flg. 4.13. Rate of Penetration Vs. Frequescy lor San daciiito Fiiver Sand

Dense Blasting Sand

Dei lse 2Ias:i:g Sand

Frrq. (HI)

fAedium Dense 8las:ing Sznd

Fig. 4.14. Xatt o i Pcnttntion Vs. Frcqucnc] for Blast*!: S x , d

driving frequency. which was agaln very near 20 I k . ?'he magnitude of the t;ks mass

appeared to have relatively little effect on tiie optimum driving frequency.

I t was declded that, because of the failure of the driver w l t h 50 t7-lb unbalmced

moment to drib~e the piie under 20 psi chamber pressure. even for relatively shd!ow

penetrattons. an unbalanced moment of at least 100 in-lb was needed for future d-imfig

tests. Examination of thr: driver performance curve (FLg,. 3.10) reveals that the next

h g h e s i discrete unbalanced rnoment exceeding 100 n - l b was 3 0 0 Ln-lb; however. that

moment could not be used above 20 Hz, since it produced forces exceeding the design

capaciiy of the driver at such frequencies. SInce a frequency ln the range of 20 Hz

appeared to be the optimunl driving frequency . it was declded not to conduct tests with

300 Fn-lb unbalanced moment. but to consider 100 In-lb a s the optlmum value.

Successful Fnstallation was achieved using this unbalanced moment ln ald tests but two,

where refusal was n e t prior to achieving full peneiralion of the pile.

Figure 4 . 1 3 ~ further cod i rms an optlmum driving frequency ol near 20 Hz for

S J R S,md, even at 65% relative density, regardless of the magnitude of bias mass. I t

also re idorces the conclusion d r a m previously f ~ r the dense sand condltion that

increasing the bias mass increases rate of penetrati3n signlr1cantly. Furthermore. it is

obvious in Fig. 4 . 1 3 that much higher rates of penetration were achieved under lower

ekc t ive chamber pressure (simulated mean sol1 pressure for 50-foot penetration) than

under the higher pressure (s f iu la ted 100-foot penetration).

Based on a review of Fig. 4.13 which applles to Srri Sand, it was concluded that a

driving frequency of 20 Hz, a maxLmum weight of bias m a s s of 2000 lbs and a n

unbalanced moment of 100 in-lb were the optimum parameters for the laboratory

testlng system ar,d that these parameters would be ~ s e d in future capacity-assessme~ts

tests u l th SJR Sand. Although the effects of' wave reflecttons from chamber b o u n d ~ ~ e s

and drainage conditions may have had some effecr. on optimum driving frequency in

the laboratory tests. there is no indication that the optimum frequency would have

byen signgicantly dflerenl from 29 Fiz In a full-scale field operation for the conditiors

that were simulated in the la'aorzitory.

Fig. 4 .14 ?resents the resul!s o i similar parameter tes t s using BLS Sand,

Identical conclus!ons with respect to optimum frequency, bias m a s s and e c c e n t r ; ~

mornent can be drawn a s were d ra~vn for S J R Sand. The one dflerence in BLS Sand

relative to SJR Sand is that for a given set of driver conditions and chamber pressures,

penetration was more rapid In the coarse BLS Sand in the medium-dense state than In

the fine S J R Sand in the medium-dense state , while very little difference was obsenred

in the dense state.

One significant efrect that iiras observed Fn the parameter tests that !s dlfllcult to

report quantitatively is that once tibro-drlving was s topped for a pile t ha t w a s

penetrating at a reasonable rale (as was necessary in some of the early tests !A order t o

synchronize the motors of the drlverl, tt was dLlllcult to relrLitiate positive penetration

with the same driver parameters that had successIully kept the pile penetrating prior to

the stoppage. This obsemation suggests that i t is important no: to stop driving the pLle

once a desirable rate of penetration h a s been reached, prior to achieving design

penetration.

4 .3 VIERO-DRWILrG CAF'.ACI?Y TESTS

Tmtcal Force and Velocltv TLme Hlstorle~.

Observation of the time histories of pile-head and plle-toe forces and velocities

provides further Fnslght h t o the mechanisms p rodwing penetratlon in vibro-drlven

plles. DetaLled force. \.,elocity, acceleration and lateral sofl pressure time Nstory data

for all vibro-capccity tests are provided in Appendix B. A few typical records a re also

presented in this chapter !n order to discuss some of the significant aspects of the

behavior of the plle-mil s;.stzz~ during LdSro-inst~llation. A few general t i ends that

are evident in the data ti^ AppendLx B are that accelzraiion signzls tended to be mcre

noisy with the coarse sand Ihan with Lhe flne s a d . perhaps due to more severe slipping

of gralns Fn the coxse r :and. hlagnlcudes of pezk acceleration were also greater Ln the

coarse sand under comparable testing cor,dittons, which may suggest that t h e coarser

s a n d requires somewhat hlgher accelerations to produce a rate of penetration

equivalent to that in fine sand. The range of accelerations (at plle head and pile toe)

that were found to produce penetration were 3 - 12 g. which Is In general agreement with

the work of Rodger and Littlejohn ( 3 6 ) ; however. !n Test 9 (hlgh density and high

pressure In fine sand) , in which refusal was met at a penetration of about 13 diameters.

peak accelerations at the head and toe were ln the xar$e oh 4 to 5 g. I t appears, therefore.

tha t the threshold acceleration required for penetration proposed by Rodger and

Littlejohn (1.5 g! is too low for the most severe zonditlons studred herein. I t is

speculated t h a t any threshold value Is probably alsz a function of conltrai~.lg pressure.

density and graLn slze characteristics m d was of the order o15 g for the conditions that

existed in Test 9.

Pile-head and pile-toe force and velocity time histories are presented for two

separate conditions In Figs. 4.15 - 4 .18 (velxity time histories were obtalned by

integrating the corresponding measured acceleration signals). In these figures positive

velocity corresponds to downward movement of the pile. and positive force corresponds

to compression. Figures 4.15 and 1.16 are data from nezr fuii p e n e h t f o n in Test

-ssu re 1 la/13a, which was conducted fn medium-dense BLS Sand at 10 psi confhi rg pr-

and represents the "easy drivir,g' end of Ule spectrum. In this test Lle histories of head

and toe velocities were very similar and were very nearly sfnusoidal. The head and ioe

forces exhibited near-sinusoldal behzvior, but with magnitudes skewed toward positlve

(compresstve) values cl force. NegaUve fclrce peaks of about 200 Ib in Test 1 l a / 13a (Flg.

4.16) are probably assxia ted with suction at the plle tw, but othenvtse the pile did not

develop significant negative reactions durlng driving. The magnitude of peak force a t

TEST 1 1 CI 8c 13a PEN. 75" PlLE HEAD VEL VS TIME

-0.9 f I 1 I 1

D Z O O roc9

TIME (meoc)

TEST I la & 13a PEN. 75'' PlLE HEAD FORCE V 3 TIWE

200

TlYf (mcrr)

Fig. 4.15. Pllc-h-cad Veloclq and Force Vs. Tlme: T a t 1 la/ 13a lfidatfn Density = 85%; Chvnbu i>rcssurr = 10 psi)

TEST I l a & 13a PEN. 75'' IPIU T O Y V T L V J T l u h

1.2 [ 1

I

-1.2 1 I I T 1 1

0 200 400

T l M E (mrec)

TEST 1 1 0 & 130 PEN. 75" PILE TOE FORCE VS T l M E

Fig. 4.16. Pile-Toc Vclcrlt-1 and Force Vs. Tlrnc; Test I 1 a/ 13a (fithtwe Density = 65%: Chamber hsstrrc = 10 pslJ

TEST 17 FEN. 72"

I I I 1 0 2 Q Q a80

TIME ( m a e a )

TEST "I PEN. 7'2"

Fig. 4.17. Pflt-Xead Velocity and F o m Vs. Tlme; 'Test 17 !Re!aUve Gensii)- = 9056: Chamber Ptssu r t = 20 ps!J

TEST 17 PEN. 72" PILE TOE vtt. VS TIME -

TEST 'I 7 PEN. 72" PILL: TOE FORCE VS T I M E

1 7 I

TlME (rn***)

Fig. 4.13, PCc-Tcc Ve!wity and Force VS. ?Li t : Test 17 (seiat!vc Density E 9W: ChaxTiScr F ~ s s z r e = 20 ;sU

the tce was about 6596 of iha l at tJh: head. Fqures 4.17 and 4.18 x e data from near full

penetration tn Test 17, which was ccnducted in dense coarse sand at 20 psi c o n i - m g

pressure and represents the "hard driving' end of the spectrum. The tkne history oI' toe

I'orce is quite dflerent in this test t han in Test 1 l a / 13a. First. while the ratio of toe

force arnpiitude to head force amul1ti;de remained at about 0.65 - 0.70 Ln Test 17, the

magnitudes of the respective p e a k are about 4 times those observed Ln Test 1 l a / 13a.

Second, while very minor r,egat!ve toe forces were observed Test 17, the negative

values persisted for over one-half of e2ch cycle. ; -~nich. along with the sha rp positive

(compressinn) peaks and general non-stnuso!dal na ture of the toe force tlme history,

suggests that . unllke the behavlor ln Test 1 l a / 13a. the pile toe was being Uted off the

underiying soil on the upstroke of the driver and thrus t back against i t on the

dournstroke. Driving t h u s simulated rapid Fmpact drfvLng in terms of to:: penetaatlon.

Cornparissn of the pile-head force-time histories for the mealurn-density/low pressure

conditions in Figs. 4.1.5 and 4 .16 with the head and !oe force time b~lstorles for the higii

density/high pressure conditions in Figs. 4 . 1 7 and 4.18 indicates that some shaft

resistance developed on the apstroke Ln the dense sand under hlgh presswe, as suggested

by the presence of appraximately 4 kips ~f negative force amplitude at the head in the

absence of a shnLlar amplitude at the toe, while esseniiaily none dweloped for the

medium der)se/low pressure conditlons, a s evidence by essentially zero amplitudes of

negative toe and head force. This n e g a t l ~ e shalt resktance appears to have Ilmited t he

negative velocity achieved on the upstroke to about one-half of that achleved o n the

downstrokt: at both the head and toe (Figs. 4.17 and 4.18). which would hat-e llndted the

amplitude of displacement of t h e pLle and t h u s the elfecthreness of the driver. (Soon

zRer the data reported in Fgs. 4.17 and 4.18 were recovered, the pfle reached refusal.]

This behavior is also viewed from the perspective of the soil response against

the shaft and toe of the in-motion pde in tke final mGjor sectlon of this chapter.

A review of the data irorn Appendix B indicates that the cf pile-head

and toe velocities had almost the same magnitude under equivalent test ccnd i t io~s .

Magnitudes of pile-head and pile-toe downward velocities tended to increase sightly

with lncreasing relative density and chamber pressure.

n p i c a l Lateral Pressure-Tlme Histor!es.

The relative ease of driving could conceivably be t-tewed in t e r n s of the buiidup

of pore water pressure at the pile-soil interface durlng driving and in terms of the

excursions in pore xvater pressure that occur with each cycle of lcadlng. F:g. 4.19a

shows pore water pressure-time relationship at the lower level o l the lateral pressure

transducers (1.4 diameters above the toe) during insertion of the pile in Test 1 l a / 13a. in

which the conditions were coarse sand at medium density and 10 psi confining

pressure. The sinusoldal pattern of pore water pressure in response to excitation is

evldent, but the excursions about Lhe mean are relative!^ small. On the other hand, the

mean (baseline) value Is see.] to be shLTting rapidly upward, indicating a n increase in

background pcre water pressure 01 about 0.3 psf in only about 8 cycles. At the tlrne Ln

which these data were acquired the sensors were only about 30 inches below the top of

the chamber (equivalent to the free water surface). so that the background pore water

pressure had been elwated from a geostatlc value of about 1.1 psi to a value of about 2.5

psi. While this induced excess pore water pressure was undoubtedly helpful in alTecting

pile penetration, it should be noted that. even ln the case of the looser soil a t low

pressure depicted by Fig. 4.19b. the maximum, instantaneous pore water pressures did

not approach the value of total pressure in the chamber. It also appears that they did

r!ot approach the value of total pressure at the pile-sol interface. measured at the same

level a s the pore water pressures. although, a s indicated by the nonperiodIc nature of

the total pressure data in Fig. 4.19a. the measurements of total pressure for thfs test are

somewhat questionable. In any event, the measured total pressures always exceeded

the measured pore water pressures by a considerable amount, which suggests the

TEST- 1 4 a & " 1 3 e PEN. 35" T O T L PWES9UP.E VS. P l U K

1 1 1

T I M & ( m e e a )

T E S T I I e & 1 Sa PEN. 35" P O R E W A T E R P R E S 3 b l R t '43. T I M E

2.8 ,

1.e - - I I I

a a00 COO

l l Y L (rnaar)

'!c. G . !?, Total P=sure and Pcr t Wa:e; .-ssurr FJ;~c !-IIS:OTJCS :or TCSI 1 l a / 133 Td~k:h.t r\~:&:Jy = 65%: (S2;~7\.Sti --~JIT = ;O p!!

maintenance of positive eflectlve stress at [he tnterfzce between the s n i t and the so11

and the exclusion of soil iiqutfaction around the pile shalt under these soil a n d

chamber conditions.

The more severe soil and chamber conditions (high density and high pressure)

are represented hi Fig. 4.20 (Test 9) . Here. i t can be secn that no buildup in backgr3ur:d

pore water prcssure appexed to occur but b a t excursions of about 0.5 psi occurred about

the mean. The total pressure data appeared to be more reliable In this test in flne sand

than ln Lhe test reported Fn Fig. 4.19 In coarse sand. The total s tress data are periodic.

and the excursions are much more pronounced than those in the pore water pressure

data . Xotably, however, the peak values of lateral total pressure are less than the

applied ellective chamber pressure plus pore water pressure, which suggests that a zone

of reduced lateral stress was generated around the pfle as the pile was belng blbrated.

Figures 4.21 and 4.22 compare the total and pore water pressure time histodes

[or the same test a s is documented in Fig. 4.20. F g u r e 4.21 shows data that were

recorded while the pile was still penetrating, whlle Fig. 4.22 shows data after the pile

had met refusal but continued to be vibrated. The most notable dflerences in the twc

ilgures are that pore water pressure excursions are reduced in the stationary pile and

the mean total lateral stres.vs are increased. The mean pore water pressure is slightly

higher in the stationary pfle probably because the sensor is sllghtty deeper.

It appears from analysis oi these data and corresponding data from other tests

documented in Appendh B that reductions In shaft resistance that occurred durlng

vfbro-drivfng was not primarily due to increased pore water pressure but was probably

.due to temporary decerases in effective stresses along the pile shaft due to the induced

dynamic motion of the sand g r a b s .

TEST 9 PEN. 38" TOTAL C R E S J L ' R L V3 TIME

1

TEST 9 P E N . 38" CORE WATISR PREf3UAE L J T I M E

Flg. 4.20. TotaJ P n s s u n and P o n Water F?-essure Time Histories for Test 9 at Shallow Ptnttrat ion (&iative Dcnsl!y = 90%; Chamber Prcssurt = 20 psO

c---

I t 3 1 9 PEN. 53" T O T A L P R E S I J U R L V 3 . T I M E

1 6 1

I r 1 8 200 roo

T I M E ( m s s c )

TEST 9 PEN. 53" PORE W A T E R PteCrSSUWC V3. T I M E

2.7

2. s

2.5

h 2.4 -

m a w 2.3 W K I3

2.2 W (L P

2.1

2

1.0

1 .8 0 200 a03

T I Y E (mrsr)

Fg. 4.21. Tctal b s u r c and Pore Water i2;wYureTL.ne His?orlcs .corTest 9 at Large Penctratlon (Relattve Density = 9096: Chambc FTessurc = 23 psi); Pllc Penctrattng

TEST S PEN. 55" TOTAL F'ffE53URIC M. TlUK

17

TEST 9 PEN. 55 ' " PORE WAT'IA PRESSURE VS. TIME

2.8 ,

-. : :g, 4.22. Total Pxssc;e and POR W a t a PrZs~ure Tlrne illstorles for Test 9 at Large

Penetration (P'latJvr Dcrslty = %; Ci.lmtcr Wssnrz = 223 psi); PUe Stationary

Rzte of P e n e t r ~ : i o ~ .

T'ne efTect of sod cond!tions oa rate of penetratlon of vibro-driven p;ies IS

shown i i ~ Figs. 4 .23 - 4.26. Note that the rate of penetratlon (vp) is plotted agalnsr

nondimensiornl penetration or depth (D/B). where D is the deptFl of the pile toe and B IS

the diameter of the ptle. The result clearly shows that the rate of penetration appears to

be controlled by lateral effective soil pressures rather than by vertical effective

pressures, since withL7 experimental errors the pattern of penetration rate for KO = 0.5

(vertical efIectl1.e stress = 20 psi; lateral eilective stress = 10 psl) in fine Sjii Sand in Fig.

4.23 more closely conforms to the patterns for othpr pile installations in S J R Sand

with 10 psi undorm chamber pressure (also in Fig. 4.23) than to the patterns defined h

Fig. 4.26 (20 psi isotropic chamber pressure). Figs. 4.23 (Tests 5 and 6 ) a d 4.24 show the

general scatter for rate of penetration with a vibro-dAver, a s the two tests reported in

each figure were conducted under a s nearly identica! conditions a s could be contrplled

in the laboratory.

Significantly higher penetration r a t e s occurred a t comparable depths of

penetration at 10 psi chamber pressure when the relative density was 65Oh compared to

equivalent conditions a t 90?h relative density. For example, it can be observed In Fig.

4.29 that penetration rates ranged from 2 Ips to 10 Ips for medium dense sand, while

penetralion rates were from 0.2 ips to 2.5 ips for d m s e sand (Figs. 4.24). Increashg

effective chamber pressures lrom 10 psi to 20 ?sl clearly decreased the rate of

penetration (Figs. 4.23, 4.24 and 4.261. although the eLTects were not a s prominent a s

those of relative denslty.

A reasonable definition of refusal Fn the laboratory tests Is a rate of penetration

of 0.1 ips. At values higher than 0.1 ips it was possible to malniafn a reasonably

uniform rate of penetration a s the pile penetrated more deeply, but once the rate was

reduced below zbout 0.1 ips. it rapidly came to a com?lete stop.

0 . 2 c . 5 : . 3 1.5 2 . 3 2 S 3 . 0 3 5 4 3 4 5 5.0

C

2

4

- - - Y e s : 5. SJA Sac:. 90%: . . - , ~ s l : V~b:a:c!ry

- Tes: 6 . SJR Sand. 33%.

CI . * . , 3s.: V S:;:=ry a?:! \

c3 F i g s : - ~ n e

' 2 -.-Tes: 8. SJA 534:: 32:0. doz: 5. V ;:a:zVy a-:: 7 2 s " rle I

Fig. 4.23. ~%:e of Penetration i's. Toe Depth-to-Diameter h t i o (D/B): S J R Sand at 90°/o Relalive Density

P ( i p s )

I i

0 -- - Tecf 14; Blast~ng Sand: 90%; 10 psi: Vibralcry

-Test 15; Blasting Saod: 90%; 10 psi; V~bratory and Rostnkr

Fig. 4.24. a t e of Penetratton Vs. Tot Depth-to-Diameter iiatio (D/B): BFS Sand at 90% Re1ath.c Drnslty

Fiq. 4.25. Rale of Penetration Vs. Toe Depth-to-Diameter Ratio (D/BI: Comparison of Tests at 659.0 Relative Denslty azd 10 psi Chamber Pressure

3 2 + 6 8 1 3 i 2 1 4 4 - . 3

,.

Fig. 4.26. Rate of Pcneiraticn Vs. Toe Depth-to-Diarr.ettr Ratio (D/B); Comparison of Tests at 90% FklaUve Density and 20 psi Chamber Pressure

2

4

6 @

' I

I -..- Tes: 7 . SJR Sacd; 65:;.

0 . 4

C3 . n

3 "

' 2

"2

. - -

. E

Res:.:lce

. sand GS?.. '; 2s. :

. - - -Test :6. E!:as:ly Sa-c :

'

, /

/ '

- - cl

m i c a 1 Focce and Ve!ocitv TPne Hist,=.

Plle-head and toe force a n d velocity time histories for lmpact and restrike

evznts a re given in Appendix C. To assis t in visual!zatlon. the velocity da ta are

presented in the form of !mpedance ( ~ p ~ l e / c o m p r e s s i o n wave velocity of the pile

material) times veloc!ty, ra ther t h a n velccity directly. At the initial force peaks the

velocity-impedance generally remains cons tant or increases slightly a s the force

decreases rapidly. This b e h z ~ l o r is opposite to that observed in impact-driven piles in

the field. in which velocity-impedance decreases more quickly than force once reflected

energy begins to re turn to the pile head. The behavior in the laboratory may be

explained by the apparent fact that reflected tenslon waves were returning from the toe

of the very short pile while the r a m was still decelerating agairist the pile head , causing

the s t r e s s to reduced while t he downward velocity of the pi!e head remained

temporarily high.

In general. larger departures in the velocity-impedance relatlons from the force

relations occurred at t h e intial peaks for the piles with low driving resistance (lower

soil density a n d lower soil pressure conditions) thar. for those with high driving

resistance (higher pressure and higher density]. suggesting larger magnitudes of tension

wave reflections, consistent with the development of lower toe resistance. The force

and velocity-tmpedance records usually exhibited a secondary peak at a tlme value (4 to

5 milliseconds after the initlal peak) that is consistent with the return of a reflected

compression wave from the base of the chamber. Tne time lapse between the Lnitia.1

peak a n d the second peak. representing the reflection of the wave frdtn the bottom of the

chamber, was generally consistent among all lrnpact and restrikz tests. except for those

t e s t s in wnich the pile was vibrated into position in medium-dense sand at low

c o d i n i n g pressure. fn which was the lapse period was longer. This increased lapse

period !s interpreted a s representing lower compression wave velocities in t h e so11

between the pile toe and the base of t5e chamber.

I t is notable that the peak compression forces at the pUe head tended to be about

twice a s large a s the corresponding peaks for vibro-dilving (30 - 35 k versus 6.5 - 2 1.5 k).

and the maximum tensile (negative) forces tended to be a n order or magnitude greater

for the impact-driven pile than for the vlbro-driven pile. (Compare data from Appendix

C with those from Appendix B.) It Is evident that vlbro-driving produced much lower

axial stresses in the pile than did impact driving. which would suggest that the vibro-

driver should be considered when stress conditlons in the pile during installation are of

major concern.

Penetration Resistance.

Penetration resistance records for all lrnpact driving tests are depicted in Fig.

4 .27 . The increase In penetration resistance appears more prominently affected by

doubling the effective chamber pressure from 10 psi to 2 0 psi than by increasing the

relative density from 65% to 90°/6. This statement can be venfied by comparing the

results of the various tests in Fig. 4.27 and then comparlng the results of Test 18 with

Test 2 1. In this respect the behavior of the impact-driven piles was dmerent from that

of the vfbro-driven pUes. However. by comparing Test 22 with Test 21 and Tests 18 and

19, it is seen that the penetration resistance of the impact-driven pile, like that of the

~lbro-driven pUe. was much more strongly controlled by lateral ezective soil presscres

than by vertical effective pressures.

Penetration resistance records for all restrike events are glven ln Table 4.5. The

general trends, ln terms of penetration resistance during restrike as a function of -

chamber pressure and relative density, are consistent for both fine and coarse sand and

are consistent uqih the trends established in the impzct-driving t e s t s relative to

effective chamber pressure and relauve density of the sand. The second Lnch of restrike

olfered less penetration resistance than the first inch for conditions of high density

B l o w s p e r i n c h

v I 2 3 4 5 6 7 8 9 : S

h u

P e n .

( I n . ) 4 3 - Tesl 19: 9:as:.r; S a n d .

B l o w s per I n c h

P e n . ( 1 n . 1 4 3

Te:: 21; S:a Sand; 5::;.

Fig. 4 . 2 7 . T3rfiimg Records for Impact Tzsts

Table 4.3 . Blow-Counts fcr R e s t r k Events

and high pressure. however. Fiestrike penetia!:ons were !Imited to one-haif

diameter.

4.5 WATER EAYPCZSION

The test chamber. which is descnbed in detail ln Chapter 3 , permitted the

measurement of the volume of water eupe!led from the pores of the saturated sofl during

installation of the pile. IVhile the pores of the soil were sa tura ted , water volume

e-xpelled during a test does not necessarLly represent precisely the volume change in the

soil produced by installing the pile. since the vertical and lateral boundaries of the

chamber could expand or contract in order to mzintain a constant total pressure on

those surfaces. However, the volume of water evpelled is believed to be arl appravtmate

measure of the volume change produced by Fnstallation and should serve a s a mehns of

assessing the relative volume change produced by vibro-driving =d by lrnyact driving.

The results of the water expulsion measurements are given in Table 4.4.

The vibro-driver and impact driver produced about equal amounts of water

expulsion for the soil at 65% re!ative density. Vibro-driving produced much more water

expulsion than impact driving when the soil was at 90% relative denisty and more than

for vibro-driving at a relative density ~f 65Oh . ThLs result, which Is contrary to

intuition, appears to indicate that volume change In t2e vibro-driven piie is strongly

associated with the time requlred to vibrate the pile lnto position, which increases with

increasing relative density, a s indicated In Table 4.4.

Table 4 . 4 . S u ~ r r n a q + ~ f T o ( 3 J , ' ~ o u ~ I oiIVa1er E q e l l e d [ram Ch2rnbt.r

Volume o i pile at 79-tnch penelrauon = 993 fn3 " S = SJR : B = BLS / RelaUve density I%) / EBtxtW chamber prvessun (psi! : I(o = 10 pw boa and 20 pst vcrt. 0..

No water expelled was recorded after venetratlon of 25 Inches.

*

Flnai Penetra t ion

(In.)

75

79

i-cst / C o n d ~ t j o n

7/[~/65/ 10)"

2 3 / ( 5 / 6 5 / 10)

! 12.5 133!5/65! 10)

I6/(3/65/ lo)

S,'(S/90/ 101

6/ (S/90/ 101

:8/(5/90/10)

6 /6 /9o / t6 ,

22/(s/9o/K&

13/(B/90/ 101

1 S / D / S o / 101

19/(B/90/ 101

9/(5/93/20t

2 1 /(s/90/20)

17/1B/90/201

iuTiotin~ o j Watsr Expellcd

(h3) 1% d Wc ~~7

1543 156%

! 101 11145

9'21 93Oh

1032 104%

1106 l! !OA

1570 15595

N A S A

1529 154%

w*'~ 56%

1055 106%

lOCO 101%

N A h' A

2 138 215%

627.- 63%

866'" 8 7%

78

77

r 3 - -

7 5

7 9

75

79

77

76

79

- 55

79

74 1

Total Tlmc o l V1brat:on

lsccf Sumbcr of

~ I G W S

26 scc

144

S3sa

17 ~r

217 s e ~

72 scc

1 96

105 SCZ:

176

177 sec

118scc

199

351 sec

336

391 scc

I

I

1

Graphical results cf the sta:!c comFression tests are shown Ln Figs. 3 . 2 8 - 4.35.

in the follou4ng groupings,

(a) dl tests of ~ S r o - d r i v e n piles with restrike a t an eflective chamber pressTJre

of 10 psi (Fig. 3.28) ;

(b) all tests of blbro-driven piles wlth restrFke at a n efiective chamber pressure

of 20 psi (Fiz. 3.29) . [in Test 9 (SdR Sand) i t was pgssible to drive the ~ i l e only to a

penetratfon of 55 inches with the ~ i b r a t o r . The pile was restruck to drive it to a final

penetration of 57 tnches. In order to compare the results of this test with Tcst 17 (BLS

Sand). a load-movement curve was synthesized for a penetration of 77 inches by uslng

comps t r r program APILE (46), which produczs load-seitiement relations from pile

stiffness and untt load transizr function inputs. The measured shaft unit load transfer

relations (f-w cufires, chapter 5) lor the top half of the pile and the bottom half of the

pile were applied, respec~lvely, to the top and bottom halves of a pile penetrating 77

inches, and the measured toe unit load transfer relation (q-w curve. Chapter 5) at the

actuai test penetration (57 Lnches) were used a s inputs to APILE to sjntheslze the load-

movement curve shown L-I Fig. 4.29.j

jc) a!! tests of vibro-driven piles compared with corresponding tests of piles

daven with vlbratlon with restbike a t a n efiective chamber pressure of 10 psi (Fig.

4.30):

(d) all tests (vibratory and impact) conducted under conditions of & = 0.5, with

corresponding tests l ~ n d e r KO = 1 (Fig. 4.31). ln which the lateral eTective chamber

pressurc was 10 psi In each test:

(e) corr,parison of individual tests of lmpact-driven ptles with tests of vtbro-

dr!ven pFles under conrespnding condl!ions (Fgs . 4.32 - 4.35).

Fig. 4.23. Resul ts of Compression Tests: Vibro-Drlven Piles with Restrike: EITectfve Chamber ?ressufie = 10 psi

Load ( k p s j

0 5 1 0 1 5 2 0 2 5 3 9 35 40 4 5 5 0 5 5

Flg. 4.29. Resul ts of Cornpression Tests: Vlbro-Driven P2es with Rrstrlke: E!Tec:ive C 3 a r b c r Pressure = 20 psi

(Test 9 S)r,:heslzed to Full Pcr.etratlr~n by Proprvn AIILE)

h a d ilrcl;Si

I r'O. Tes l 5 Sji? S a n e ~ $ 1 ;

13 psi. V1S:a:ory 0 5 1 0 1 5 2 0 2 5 3 0 - -

. Test 6; S J R Sand, SC?:; ! O DSl: V ~ b r a : o r j and

0.1 . fies:r;ke

c . 2 ,. - 'Om Test 7; Sd2 Sane: 655;:

0.3 - :3 PSI; V ~ b r a l o r y and 2es:r:;re

Tes; ' :a 5 :;a. 3:as: -s

,̂ 5 s a r c 559;: :: cs,: ' / lbra:3ry

C 6 - , . m a - 1 es: ' c , 2'as:.c9 Sa--J

n - r . " . I

9C96 : 2 p s ~ ; Vtb'a:c?y

*A- r.5: '5. S..r:.-; Sam.: - A : Y - e ' S 2 5 . . Vfc.a!=.y ;,.- - 7 2 5 : - < s i

cs* .: z 3:. - - c = - * - - - - . - - - :::. .. - - - - 2s - - - . - - * - = - , i i-c 2 ~ 5 : . < e i

Fig -1.30 R ~ S U I I S of Conipress1on fcs ls : Comparison of Behavior of Vibro-Driiven p p s and Restruck Vibro-Driven Piles: ElTective C h m b e r Pressure = 10 psi

Vibratory and Restrike

7 . 4.3 1. Results of Compress i~n Tests: C c r n p m y ~ n of Behavior of POes Tested Under Kc = 0.5 ulU1 Pries Tested Under & = 1.0; Effective C h m b e r RDSU~C = 10 psi

Fig. 4.32. Results of Compression Tes:s: Comparfson of Piles Installed by \'ibration. L'ibration with Restnkmg and t;v Impact: SJii Sand:

90')/0 Relative Density; 10 psi Egective Chamber Pressure

Sand; 90% 10 psi;

Test 1 5 ; Blast~ng Sand; 90°/.: 10 psi; Vibratory and Restrike

Test 19: Blasting Sand; 90%; 10 psi:

Fig. 4.33. Results of Compression Tests: Comparison of PCes LnstzEed by Vibration. Vibration with Rest1-g and by impact: ELS Sar.d:

9% i ic !a~vt Genslty; 10 psi EZICL!P Chamber Pressure

F . 4.4. Resulis o l Compression Tests: Comparison of Piles Installed by i'ibraiion \irith Restrikmg and Impact; S J R Sand: 65% Relative Density:

2 0 psi Eaective Chamber P r e s u r e

. - , A , ..- ,,, ( ' L V > l

Fig. 4.35. Results of Compression Tests: Comparison of Piles Installed by Vibration with Restriking and Impact: STR Sand: 90% Re1a:ive Density;

20 psi Effett&e Chamber Pressure

Figures 4.36 - 4.43 present the load-movement curves ::om the uplLrt ces:s in t h e

same groupings as above.

Sweral observatiorls can be made from the load-movement resuits:

(a) The static capacity of vibro-driven piles was much more dependent upon

relative density than upon effective grain size at a a n effective chamber pressure o i 10

psi (Fig. 4.28).

Ib) The errect of grain size is evident at a n elTectivr chamber pressure of 20 ps i , a s

the coarse-grained sand IBLS Sand) produced higher capacity than fine-grained sand

(SJR Sand) for the vlbro-driven pLle with restrike (Fig. C . 2 9 ) .

Ic) No conclusive evidence exists that restrike Increased the compress1011

capacity of vtbro-driven piles (Flg. 4.30).

(4) It appears that vibro-driven piles had very slightly greater compression

capacities than Impact-driven pfles under similar conditions at 90°h relathe density

(Figs. 4.31, 4.32. 4 .33 and 4.35). However, vibro-drlven piles yielded a lower capacity

than impact-driven pfles at 65% relative density (Fig. 4.34).

(5) The uplift load-movement results exlibited similar trends to those described

for the compression tests. Comparison of compression-test load-movement data at the

pile head with corresponding upW test da ta and analysis of the toe resistance-

movement data for the compression tests from Chapter 5 leads to the conclusion that

the dtiference in capacity a t 90?h relative density between vlbro- and impact-driven

ptles was due to increased toe capacity in the vlbro-driven piles, whFle at 65% relative

density the df i rence was due to somewhat decreased shaft reslstance ln the clbro-

driven piles (e.g.. compare Flgs. 4.31-3.35 with 4.39-4.43. respectively]

Fig. 4.36. Resu i t s of L'plift Tesis: Vibro-Driven Piles w ~ t h Res:rlke: Ef iec t~ve Chamber Pressure = 10 ps i

Restrike; 55'

Test 9; APILE Program

.a' Test 17; Blasting

Fig. 4.37. Results of Upllft Tests: Vlbro-Dmen Piles uqth Restrl.!!~: Effective Chamber Pressure = 'LO psi

(Test 9 Sqmthes.ized to Full Penetration by Program APILE)

0- Test 5. SJFi Sand. 13";. 1 . : 3 ;sl: V~bra:ory

Test 6 . S J R Sand: 409:: 10 psi; Vlara~ary and 1 R e s l r ~ k e I I

I Test 7; S J R Sana, 55%. , 10 pst; V ~ b r a : o r j and j R e s t r i k e I

Tes: :<; 3 ' a s r ; ~ ; Sa.0, 904;: 13 p i : . V5ra:a:y

I Tes! 1 5 , e!as:;?g Sane: i A " 3 1 3.r ... .,. . P S I ; VI>!a:sfy i

- - - - --.. sm .. rt.> k e I I

Fig. -1.36. R c s ~ l l s of L'pldtTests: Ccmpafison of Behavior of Vibro-Driven Piles and Xestruck \ '~t.ro-Driven Piles: Elfecti\.e Chamber Pressure = 10 psi

Fig. 4.39. Results of LpLftTests: Comparison of Beha*,-ior cf Piles Tested Under KO = 0.5 with Piles Tested Under KO = 1.0: EfTective Chamber Pressure = 10 psi

Fig. 4 . 4 0 . Xesulls of Cpldt Tests: Cornpanson or Piles Installed by iVlbration. Vibralion wilh Restnkinq and by Impacl; S J K Sand:

90?/0 Re!ati\le Defisity; 10 psi EfTective Chamber Pressure

Fig. 4.41. .%suits cf UplifUests: Cornpaison of Piles Installed by C'ibratioa. 'Jibration with Restriking ar,d by Impact: BLS Sand:

900h iielative Density: 10 psi Effective Chamber .F?essure

FIG. 4.42. Results o i Uplilt Tests: Comparison o i Piles Installed by Vibration u i t h Restrddng and Impact: SJR Sand; 65% Relative Density;

2 0 psi EITectlve Chamber Pressur?

Test 9; APILE Program

Fig. 4.43. Results of Uplift Tests: Cornparkun of Plles Instaxed by Vibration with Restriking and Impact: SJR Sand: 90% Relatlve Density:

20 psi Effective Cfizmber Pressure

CHAYJER 5

ANALYSTS OF TEST RESULTS

This chapter describes the analysis of relevant test data in order to develop

better understanding of vibro-driving and relationships of the following: (a) the

p e ~ o r m a n c e relationship between the model vibro-driver and the impact hammer. (b)

the power and ener&v transmissfon characteristics of the vibro-driver and impact

hammer, (c) the static capacity of vlbro-driven a n d impact-driven piles. (dl the

relationship between penetration rate and power transmission ratio of vibro-driven

piles. (e) the wave equetion parameters for restrike and Lrnpact events, (1) the static and

in-motion load transfer characteristics of vibro-driven piles and Ig) the phase

relationship between the plle head and toe of vibro-driven piles.

5 . 1 PERFORMANCE RELATIONSHIP BETWEEN VIBRO-DmR AND I M P A C T

HAMMER

A performance relationship between the model vibro-driver and model impact

hammer used in this study was established In terms of rate of penetration (vp) for the

vibro-driver and blow count @lows/lnch) for the tmpact hammer for tests where soil

conditions were identical. That relaUonship, shown in Fig. 5.1, denonstrates that for a

given pile, pair of drivers. pile cushioning, etc., it may be possible to convert rate of

vibro-drfver penetration h t o equivalent blow count for an Impact-driven pile. which

VIBRQ-DRIVER V S IMPACT HAbIMER

Blows l In,

Fig. 5.1. Relationship Eetween Penetration Velocity foi Vibro-Drlven Pfles and DrixW~g Resistance for Impact-Driven Pfles

m1g;r.t p s s i b l y be csed (9 verify pi!r capacity In granular soil. The re!atioriship is also

expressed a s

vp (ips) = 12.32 X -2.65 ,

where X = blow count of the hammer blow/in.).

h'ote that the particular relationship given m Eq. (5 .1) is only valid for drlver

and hammer in thls laboratory study.

This s ~ c t i o n describes certain procedures that were employed in reducing

d>-rlarnic data in cornpuling pile head and toe energy and power.

The following procedure was used in pi le-head a n d pile-toe energy

computations (impact events):

1. Digital time histories were developed from electronically filtered

analog records of head and toe force and acceleration for several consecutive blows (10.

if availble: less Lf 10 biows were not acqu!red, a s in some restrike events). u s b g a

dlgitizatlon time step of 78 p e c over a time window of 40 msec to ensure that the whole

biow was captured. The average records for these blows were then obtained by averaging

values for each time step.

2. A segment of each average digitized signal, containing the main

portion of the signal to be processed, was selected by first locating the peak value In the

strain gage (force) record and then including the previous 1.5 msec and the subsequent

20 rnsec, for a total of 2 1.5 rnsec. This wIndow ensures that adequate w o r d lengths are

utillzed for energy computations. S e ~ a r a t e windows were employed for the head and toe

records, and Identical windows were used for the force and acceleration data at one

location.

3 . Any zero offset % the pile-head ;;nu pile-toe s train gage signal was

removed by subtract ing the average of the 50 discrete force values immediately

preceding the time w i ~ d o w .

4. A correction was applied to the filterrd pile-head acceleration signal

ln order to ensure that the conditions of zero velocity and displacement equal to the

measured plle set are satisfied at the end of the tirne window of each blow considered in

?he analysis. This linear correction takes the form.

a,(t) = al0 - ( b + c t I , (5.2)

where

a,(t) = corrected acceleration signal:

a( t) = uncorrected acceleration signal;

b = aav - 0.5 c T (satisfymg veloc!ty condition):

c = 1 2 / ~ ~ ( S / T - vaV a 0.5 aav T 1 (satisfyiig displacement ccndition);

S = permanent pile set per blow in range of interest;

T = total period of the signal (2 1.5 miliisec I ;

-aav = average of acceleration signal over T and equal to

(1 /T 1 IoT a(t) dt: and

va, = average of velocity signal, obained from integration of original

signal over T and equal to ( 1 / T ) IoTv(t) dt, where v(t) = jot a(t) dt. A sFmllar correction

was made to the toe accelerometer signal.

5. Ned, the blow energy was computed a s follows, where am(t) ls the

corrected pile-head or toe acceleration signal and F,(t) is the corrected pile-head or toe

force signal:

(a) Compute velwity for each time step (time 1) by -

usir,q [he ;rapezaidal P~:;? for numerical integ;atloil. (Note: I?i;s s:ep leads ;o the

v e i w i t y tknr hfscories that h a v e been reported (Appen2tu Cl. The force tLrne hIstorles

are s~nlp ly d;e graphs of measured lorcr versus time.)

(b) Compute the product E(t) = viT,(1) F,(t).

(c) Compute pUc-head energy Er from Er - St Cover T Elt). where ~t is

cons:ant and is :he integration time s tep (normaily 78 psec).

Power.

Po\ver cornputatlons for vibratory pile tes ts were made In a slrnflar manner ,

except tha t uncorrected digitized force and acceleration time h l s t ~ r y records were used.

and a tLrne window (T) equi~raient to 10 cycles 06 head or toe force was used in the

computat ions. Xiatherr,atjca!ly, the power lor a. giver, time window?' c an be expressed

a s

where integration is conducted using the trapwoidal. rule uslng a time increment of 0.98

n x e c (512 data points per Lnlegr-ation).

The power measured at the plle head m d pfle toe In the laboratory study

for the vibro-driver tes ts Is tabulated for var ious values of toe per;etratlon in Table 5.1.

Correspondingly. the e n e ~ g y measu red on representative blows a t various discrete

penetrations is tabulated ior ' rests ;9 - 22 (h lpac t -hammer tests) tra Tables 5.2 - 5.5. I t

!s noted that data from Test 18 are not Lncluded because pile-head farce data were not

reasonable for that les t , apparently due: to t he fact tha t o m of the lead wires became

ir~termlttent!y grounded to the pile a s the pile was being Impac:cd. Table 5.6 also

summar~zes the ener-gy accepted by the pile for the varlous restrike e;ents that fcllowed

instaliat!on with t he v!bro-driver.

Table 5. I . S u ~ ~ r n a i y ol Pile-Head a n d Pile-'Toe ! ' a r m e t c r s :or Vibraior]: Tests

.a = hccelezatdan: v I. Velocity: F = Force -

Table 5.4. S u m m w j o i P.!e.He-d and Pile-Tw Paramelers for Xn Impact test

(Test 11: Ssn JacLqLo River Sand: RelaUvc Llenstty 9096: Chamber Pressure 20 ps11

Table 5.5. S u r r m , ~ ~ of pie-Head and P!lc-Tm P a r u n e t c r s lor An Irr,pact Test j rest 22: San Jacinto W c r Sand: Kclattvr: Density 90%;

Ct~amber Prrssurr : 20 psi vcfical : I0 psi hofizan~al)

t'lrc Toe 7

I

512 2 9 2

63 70 7 1 7 2 7 3

E s Enrrgy: a = Accclca:!on: v = V c i r l v : F F o r e

Table 5.6. Summary of PUe-Head and Rlc-Toe P=ametcrs for Tests ~ l t h Rcstrtke

The total energy del~vered during the !nstalla!ion of vlbro-driven and irnpuct-

driver, piles is summarked in Table 5.7. I t can be observed that for conditions or

medlum dense sand (relative drnsi ty = 65°/0) and simulated depth of 50 feet (10 psi

enective chamber pressure) vibro-drlving required only about 65% of the energy, on the

average, required by impact d r f v i ~ g . in t e r n s of energy reaching the plle head (first

segment of Table 5.7) . On the other hand. vibro-drixtrg was found to require 3 to 8

times the total pile-head energy to install the pfle for very dense sand [relative density

= 9096) and /o r for a sirnul3:ed depth of 100 feet (20 psi erective chamber pressure) , a s

can be determined by obsening the last twcl segments of Table 5.7. I t is also clear from

Table 5.7 that more total energy was required to drive the plle either by vibration or by

impact a s the effective chamber pressure was increased from 10 psl to 2 0 psi. The total

delivered energy In b o b methods of t?stal!ation for an efiectlve chamber pressure of 2 0

psi avenged appraxtiately twice Cle value observed at 10 psi.

I1 I s polntfd out that poBrer or energy delbered t c the pLle head is not equivalent

to power or energy beIng produced by the vibro-driver o r impact hammer . The

theoretlcal power Pt of a counterrotatlng-mass vibrator. the type of clhrator that was

used in this s tudy to represent the most common type of vlbro-driver that i s used In the

field. c a n be computed based upon principles of mechanics, a s described in detail in

Appendlx A. Such power is a functlon of the operatf ig frequency, 0 ( rad ians per

second). eccentric mass, m, eccentricity of the eccentric mass. e. vibrator body mass, M,

weight of the bias mass. W, and value of the constant of the b l a t i o n springs, k, located

between the bias mass and the body of the vibrator, a s s u m m r i z e d ln Eqs. (5.5a) and

(5.5bl. 2 2 P, = [3W + 2(rneto + MZO I 1 Z ( 0 / 2 K ) . (5.5a)

where

3 2 Z = (me to - ) /M[WM)-O 1.

Table 5.7. Summary of Tatal E ~ e r g y Dehvercd to the Plle kiead.

I i

= : = B~~ / &htwc dcmiv (I% ) /iTectlvc chamber p r c s s u ~ (psi) : k = 10 Psl honz. and 20 psi vcrt.

' " ~ s t ~ m a t t d from dynamlc data of Tcst 22. /

I t was found that the power delivered to the pile head was a l~vays less than [ h e

theoretical power developed by the driver. possibly because of rnechan!cal energy losses

in the driver and/or the dfiver-pile comector . energy losses in s1idir.g friction between

the vibrator and the guide frame. coupling of \dbrator energy into f lewrzl ener-gy ln t he

pile and other [actors. A reasonably consistent relationship was obsemed be*een the

ratio of delivered pile-head poj.vPr (Ph) and theoretical poxer (Ph /P t ) and peak pile-

head acceleration at the bot~orn of the downstroke [positive value of acceleration in the

grahps In Appendix B) (ah) close to f ind penetratlon for the labora tov study, a s shown

in Fg . 5.2. P h / P t . which can be viewed a s an eff!ci@ncy factor. I s seen to hakfe

h c r e a s e d a s maximum pile-head acceleration increased. For condi:ions of easy

drix-ing (the condillon most favorable for the vibro-driver in terms of pile-head energy

r ~ q u i r e d to install the pLle). the average value of Ph /P l was approximately 0.45 (four

da ta points in F!g.: 5.2 lor the lowest accelerations). For condltlons of hard dri~ring

(remaining points In Fig. 5 . 2 ) , the average ratio was 0.75. A llnear rzgression a ~ a l y s i s

of the da ta given in Fig. 23 Lndicatrs (shown by the solid lLne In that figure1 leads to the

followir,g equatlon,

I t is important to note tha t the cons tants tha t appear Ln thls relationship are

most probably vibrator-speclf!~, a n d quite possibly pfle-specific. so that Eq. (5.6)

should be reevaluated for a variety of vibro-drivers and pfles be:ore any des!gn method

developed from this laboratory study c a n be applled successfully In the f!eld. Further

use will be made of the observed relatlonshlp Lr, the developme~t of a design procedure.

The theoretical energy for the impact hammer (ram weight tlrnes drop height].

a s operated during the labontory study. was 810 ft-lb. The average ratlo of plle-head

e n e r a (Tables 5.2 - 5.6) to this theoretlcal energ l was conslstently apprcxdmately 0.46.

regardless of the conditions of the sou or the na tu re of the impact (continuous driving

Fig. 5.2. Relationship Between Power Ratlo znd Peak File-Head Acceleration for Vlbro-Driven Pges

or restrike). Since bo:h the vibraiory driver and impact hammer were operating ar

almost identical efficiencies for the conditicns of easy driving, one can conclude that

the ratio of mechanical driver energy required to operate the vibro-driver to that

r e q u t r ~ d to operate the Impact hammer was approximately equal to the ratio of ptle-

head energies ior that coildition. That is, the total energy requlred to operate the vibro-

driver was 65%0 of that required for the i m p c t h s n m e r for the case of medium dense

sand at a simuIated penetration of 50 feel. Kovrever, since the vibro-driver was

performiiig more efficie~tly than the lmpact hammer for the higher sol! density and

for the simulated penetration of 100 feet (0.75 versus 0.46). the actual ratio of vibro-

driver energy to impact hammer energy required to drive the pLle was in the order or 2

to 5, compared to the rat!o of 3 :o 8 for energies actually delivered to the pile head.

5.3 RATE OF PESETR\TTOX' A-YD ACCELERATION

The relationships for rate of penetration and the peak pile-head acceleration

are shown in Fgs . 5 .3 - 5.5 for medium derise s a d (65% relative density) at 10 psi, dense

sand (90% relative density) at 10 psi and dense sand at 20 psi. respectively. I t ls seen

that the v - ah relationships, which were obtained from the data for a pile penetration P

of 12 diameters or greater, depend primarily upon soil g r a b size (SJR Sand was fine

and Blasting Sand was coarse]. relative density and effective horizontal sou gressure.

A11 of these relationships can be expressed in one simple parametric equation, a s

follows.

where

F1g. 5 3 P ~ l e Penctraion \ 'eloc~ty (vp) Vs. P e a k W e - 3 e a d Ac:eisrat~on (ah): Sand Re1nt1i.e Denslcy = 6330: EKecr~ve C h m b e r 13cssure = 10 p s ~

1 c b 1 0 '

a

Fig. 5.4. Pile Penctraion Velocity (vp) Vs. Peak We-Head Acccleraucn (ah);

Sand RelaUve Density = 90%: Eficttvc Chamber Prrssurr = 10 psi

a JQ)

ng. 5.5. H e P e n t t r a c n Vc!ccity (vd Vs. Feak .We-H-d .kcdmt lon (ah): Sar.d RcLaUvt Dcnslty 1 LO%; ETeclfvc C S a n k r Pressure = 20 psi

v = velocity of pile penetration h h c h e s per second (Ips), P

ah = peak (single-amplitude) pile-head acceleration ln g's.

a l = relative density parameter

a2 = grain-slze parameter, and

Cr3 = ezectlve stress parameter.

The parameters a l . a2 and a3 si~rnmrlrized belo5A! are obtained from the test

data and are listed below :

a , = - 2.186 + 3.5-1 DJ%) . 65% r D, 5 w?:

% = 8.99 + 2.76 dlO(mm), 0.2mrn 5 d I 0 < 1 . 2 m

% = (1 . 7 l - 0 . 0 8 M ~ p s i ) ) - l o p s i d b h S 2 0 p s i .

where OSh = lateral effective chamber pressure.

Parametric s tudies were conducted on the impact d r i v i ~ g da ta for Tests 2 i and

22 and the restrike da t a for Tests 9 a n d 1'7 using program TOPDRIVE, a one-

dimensional wave equation analysis prcgram, which is described in Appendk D. T h e

wave equation program was used to attempt to reproduce measured pile-head ve!ocity

time histories and pile-toe force and velocity time hlstories using the pile-head force

time history as input , by o p t b ~ i z i n g Smith 's wave equatlon parameters . The primary

objective of th is exercise w a s to ascer ta in whether Smi th- type wave equat ion

parameters that have been shown to be acceptable for modelling the behavlor of

impact-drfven piles can also be used to model piles that are vibrated into place and then

restruck. A summary of the optimum values for all back-computedSmlth parameters

from the TOPDFUVE analyses is given in Table 5.8. Fur ther details, including

compafisons of computed time histories with measured tlme historbes. are given in

Appendtx D.

Fcr those tests, values ci quake a n d d a r n p i ~ g a re noi z tnhng ly di[rerent ~ h . , ~

the pile was driven by Lqbraticn and by ccntlnu.;bs i?lpact. fn?onfi the tests conducted

i? S a n Jacinto R ~ e r Sand , i k e z t i o of static !oe h r c e to to:d force is F.lghest for Test 9,

ttie resWce test, but i t c a i be a r ~ u r d that that ratio is high due to Uie fact that in Test g a

penetration of o d y 57 ir.c!les i i3.25 pile diemeters) was achizved. It estimated from

s m p i z proporlions that had the ?~!e been vibro-driver! to a penetration of 77 h?ches.

which 1s con?arable to the gene!r?,tion achieved for the lmpact dnven pges under the

s a m e rondiiions, [hat ratio tvould have been about 0.35, urh!ch LS generally coasistent

:vith t he 1-atios fro= the cont:ncous impact driving tests in the S a n J a c h t o Rve r Sand,

I t & also observed, t? compcir~!g Tests 2 1 and 22 in Table 5.8, that the effect of KO on the

Smi th pa rame te r s for impact-ciriiren piles w a s relativzly minor , a l thgugh solrle

dll^lerences, particularly In the rat!o of shaft darnpin,: to toe darnping and in the value

of shaft and toe qcake , are e\?i<ent.

In the test in coarse 2izs:iPig Sand (Test 17). dLCTerences with respect to the other

t e s t s in fine sand are evldeni. The ratio of s ta t ic toe resistance to total resistance was

relatwely hlgher t h a n Ln either the vlbrat ion/restr ike o r con t inuous impact driving

tes t s In S a n Jac in to Rve r Sand when the corrected resistance ratio of 0.35. desci-lbed

above. w a s assumed for Test 9. The quake values a r e also noticeably higher than for

the tes t s in San Jacinto River Sand.

The values of quake that appear ln Table 5.8 are consistently lower t h a n the

va lues t h a t a r e ordlnarfly recommended for analysis of ptle-driving ln the field, and

therefore thek d h c t use is not recommended. The shaft damping values are generally

consis tent wlth values that are recommended for analysis of full-scale piles. while the

average toe d m p i n g is about one-half of t he v d u e rmonmiended far field use. The low

quake values a re most proSab!y associated with t he efrects of geometrlc scale (pile

diameter cf 4 inches versus i'uy-scale ?Lie diameters of at least 2.5 tfrnes of tha t value!.

despite the mode!ling of soil eirective s t resses in this s tady . The presence of reflected

Table 5 .8 . S u i r i r z ? v o i 0 p t L n ~ l m P m r i l e t e r s from n ? D R b X r L d y s e s

.----.a-

---.-. = staUc capac

KO = tzmh p m u r c m d k i e n t in chamber.

- -- I 1

.- rty

e r , s r a from the base o i the rharnber could accouct for the low toe dampi_n.g, but no

analysis of this eflect was conducted. a l i h o ~ ~ h some discussion of the elfect I s provided

in AppendLx C.

Analyses using program JVEXP86, a FHWA standard wave equation prcgram

developed for the microcomputer, were also conducted for Tests 2 1 and 22 with the

opt imum yarameters developed from TOPDRIVE to a s ses s the effect of different

computat ional algorithms. Results from i K A P S 6 are compared with those from

TOPDRWE in A p ~ e n d i v D, along with the results of and a SensiCivity s tudy of cushion

stdfness in JVEAP 86.

5.5 LOAD-;\IOFl2?/IE\T EL4TIONSHIP

One cf the principal objectives of the s tudy was to de t e rmhe the relationship

between static bearing capacity achieved by impact driving and by vtbro-driving, ul th

and without restrike. Descriptions of procedures for conductkg the static load tests are

provided in Appendb E. S h c e plungfng failure (or the equivalent thereof for uplFft

loading) was r a r e b achieved, it was necessary to deflne failurz load by some consistent

method involving the pattern of deflection of the ptie. Five n e t h o d s were hvestigated

in this eflort. and the results are presented In Tables 5.9 (compression loadlngl and 5.10

(uplift l oad i r ?? . The methods are discussed in AppendLx E. Upon txarninatlon of all of

the load-movement curves and the summary data con tahed in Tables 5.9 and 5.10, it

was decided that failure load would be interpreted consistently among the various tests

for purposes of c ~ m p a r i s o n as the value of load corresponding to a movement of the pile

head of 1% of the plle diameter (0.4 inch for the model pile used in this study). I t is

tmmedfately obvious L? Tables 5.9 and 5.10 that the uplgt capacity of the pile was

always considerably jess thzn the compression capacity. Analysis of the load transfer

da:a. which are addressed the next subsection. lndicate that average unit side shear

Table 5.9. Camparison of y u u r e Loads Ln u p s for C G X ~ ~ ~ S S ! O ~ Load Tests

*' bad-Movcment cume determlntd by A P I E prcgrarn See Flg. 4.29.

Dawsson (OKseO

Sordiund (Sloue)

- 1 CSl .Mazur-

klcwtcz Co.?uil!on'

Table 5.13. Co.~?arLson of Fnllure Loads In iUps for Upiffl Load Tests

" S=SJR ; B=BLS/ Rrlatfvc Density (45) / ConfFnLng Prcssurc !psi) : KO = 10 psl horlz. and 20 psi vert. / V .r Vlbro-dr!vtn : R = b t r k : I r Impact-dfiwn

"" Laad-Mcmmcnt curve dctcrmlned by APEX p m g m Set flg. 4.37

A

that was developed in upU't was ccns!stenr!y less than that developed in compression

fc.r all methods of instal!ation.

The compression capacities of the vibro-driven pile i s comparzd w!th that of t l ;?

continuously myact-driven pile in Fig. 5.6 fcr all seven pairs of tests in the laboratory

study ~n which conditions were otherwise identical. and for which dh-ect comparisons

can therefore be made. Five of these palred tests involved vibro-driven piles that were

restruck and the other two pairs :nvolved \",bra-driven piles only. It appears that the

capacity of the vibro-driven pile, with or without restrike. was essentially equal to or

greater than that of the continuously impact-driven pile ln sand cf 90% relative density

(open data points in Fig. 5.6). Ho:vever, the capacity of the vibro-driven pile was not

greater than that of impact-driven pile in sand of 65% relative density (solid data point

In Fig. 5.6).

5.6 STATTC UXrT LOAD TFMSSFER RELATIONSHIPS

Relationships of static unlt shalt snearing resistance (0 to local pile movemerlt

(w) and unit toe bear-ng resistance (ql to toe movement (w) for all static load tests are

presented graphically In th is section. Such information is useful In visually

interpreting the maximum load transler in both shalt shear and toe bearing and the

shear and bearing s t f lness at the pile-sou interface, particulariy in terms of the

relative effects of the test parameters. Experimentally derived unlt load transfer

relationships will be used to synthesize the statlc axld behavior of piles of dlmenslons

. different from those employed in this s tudy, providing the effective stresses in the - system are scaled. which was done tn this study.

In order to develop the relationships o f f to w and q to w, It is necessary first to

dctermtne the load dlstribut1on relationships along the pile. This was acconpllshed

for every test by using the cahbrated output of the strzin gages mounted alcng tne !ength

Nok: V - Vibm: R - Rclbikc: and I - Impact

Fig. 5.6. Comparison of compresslon Capacities d Vibm-Drfvtn Piles and Impact -Driven Piles

of the pde. which are descnbed tr Chapter 3. Figs. 5.7 to 5.8 show the representative

load distnbution re la t io~ships lor compression and uplift for several selected values of

applied load for Test 17. In those figures. the load measured by the top lead cell is

recorded at the top of each column ln the figures. Negative values of load Lndicate

tension. while positive vaiues Indlcate compression. The weight of the pfle is not

explicitly included ln the results. since its effect was zeroed durtng the Fnitlal readings.

Therefore, the straln gage readlngs represent the effects of external forces acting on the

pfle durlng a static load test. I t is emphasized that the measured ioacis are based on zero

readings taken before the pile was driven. and :he unlt load transfer curves that were

developed from these load distributions contain the eEects of any residual stresses that

were developed during installation of the pile.

Since the load distributlon data are discrete, it is desirable to develop a n

analyticai expression to f i t the data. Thls was accomplished in this study by using a

series of second order polynomials to f l t the d k r e t e data points. The fltted load versus

depth relations were determined from the pxpression Qlzi = a + Bz + yz2. where Q(zl is

load distribution in the pile and z is depth below the chamber surface, measured from

the top of the top cap (Chapter 3). and a, P and y are l eas t - sq~ares coefncients. Table

5.11 presents these coefficients at selected values of compression and uplift loads lor

each test. The f-w relations were developed for two depths: 20 laches and 60 inches,

which represent the mid-point of the top and bottom halves of the pfle, respectively.

Unit shaft load transfer, f and q. was computed from the 812) f u n c t i ~ n uslng t h e

following expressions,

1 d f = - -

2rcB dZ QkI, and

Flg. 5.7. Load Distribution for Test 17; Compression

Fig. 5.6. Load DistribuUon for Test 17; Upllft

Table 5.1 1 . S c ~ m m a r y of Least-Squares Coefficients lor Selected Compress ion and Liplift Loads

Appl ied C c m p r e s s i o n Up l i f t

1 Load a I3 Y Load a 5 Y i ( k p s ) (k ips )

7

A = cross sectional area of pilz

The corresponding w value was calculnted by using the following relationship,

1 z

W = W O - dQ(z) dr . (5.13;

wo = measured pile head moveinent. and

A_E = product of Young's modulus and cross-sectional area of the pile.

This process was repeated for zach of the several functions to develop sets of

polnts defiriliig the f-w and q-w relatlons. Flgures 5.9 - 5.16 present the experimental f-

w and q-w relat ionsh~ps far each of the capacity tests . Negative values of w lndlcate

upward movement of the pile rela!l\.e to the soil, while positlve values represent

down*.vard movemen:. Corres?ondingly. negative values of f represent dow-nward-

dLtect shea r s tresses on the face of the p!le shaft . while positive values represent

upward-directed shear stresses. Positive q indicates compressive load on the pile toe.

The unit loads and movements from these re1ationsh:p.s were then normalJzed by the

eirective horizonla1 chamber pressure ( ~ ' h ) and pile diameter (B), respectively. and tests

were grouped tcgether zccordlng to sand graln s k e and method of installation, except

that tests conducted at 65% relative density were grouped in terms of grain size only.

Average relationships for smcra! groupings o l tes t s were produced. Those groupings

are, h order. (a) all tests conducted b SJR Sand at 65Oh relatfve density; (b) all tests on

impact-driven pilp SJR Sand at 900%~ relative density; (c) all tests on ~qbrc-driven pile

m SLQ Sand at 909.6 relative d e m i v , (dl all tests o a vibro-driven pile PA ELS Sand at

65% relative density (no impact tes t performed for th is condillon); (e) all tes t s on

impact-driven pUe at 9% relatfve density: and (0 all tests on vfbro-driyen pile at 90??

relat!ve density. Figures 5.17 - 5.22 present the f-w relatlons in this order, and Figs.

5 2 3 - 5.28 present the corresponding q-w reia!ions. Residua; s t resses after

ir?stallation a n mclu5ed in these graphs; kowever, the residual s tresses at the end of

TEST 5 TEST 5 63-IN DEPTH

TEST 6 23-IN DEPTH 3

2

t

0

-1

.2

. 3 1 . 0 -0.6 - B . I . B . O O . Z 0.) 1 . 0

TEST 7 22-tN: D E P M

UPLIFT

TEST 6 3

TEST 7 -IN. DEPTH

TEST 14 T,-IN. DE?;W TEST l A 6;-:N D E ? T i

w (In.)

TEST ' S ::.IN DE?TH

TEST 16 ?&tK DEQYU

TEST 15 65.1Y DEPTH

TEST. 16 60-M DE?TH

r"g. 5. ! 1. i-w ?.eiaUmxsh!ps for Tas 14, 15 and 16

w (In.)

TEST 20 €3-i!i GEPTH

T E S T 21 TEST 21 69.1~. DEPTH

Fig. 5.13. f-w &iationships for Tests 20, 2 1 and 22

TEST t TEST 8

0.0 0 . 2 0.4 3.6 J.1 I . O

w {In.)

TEST 7 TEST 8 t z l -T

TEST IlUlaA 6)

m

LO

sa

40

x1

M

1 a

0

0.0 0.2 0 . 1 3 . 4 4 . 8 1 . 9

w (m.)

F!g. 5.14. q-w XelaUonships for Tests 5, 6. 7 , 8. 9 and 1 la / 13a

I I I C t------7---~-- 0.0 9 . 2 8.6 0.6 5 . 1 1 . 3

w (In.)

TEST 15

='I I I I I I

TEST 16 T E S Y 11

h9 31:

Tc 2%

KJ 3

Q(Gr) 2 q ( s f 'J:

do 1 P

E 54

c z 0 . 0 0.2 0 . 4 0 . 0 0 . 8 9.0 3.0 0 .2 0.4 0.6 0 . 8 1.0

On.) **On)

~ i g . 5.15. q-w Pzlagonsldps for Tests 14. 15. 16. 17. 18 and 19

156

TEST 22

$ o(*o 4

0.G 6 . 2 6 . 4 $ . I 0.4 1 . 0

w (In)

Ti;. 5.36. q-w F-~!a'Jor,ch!ps fsrTmis 20. 21 &?ci 22

20-In (5B) Depth 60-In. ( 1 5 8 ) Depth

Fig. 5.17. Surnmary Xormallzed f-w Relation for Pile Driven by Impact and Vibrated into S J R Sand at 65Oh Rplathre Density

20-In. (5B) Ocplh 2

Fig. 5.18. Summary Normallzed f-w Relation for Pfle Driven Sy Impact lnto SJR Sand at 90% Relative Density

20-1% (35) OePlh 60-In. (158: Deplh

Fig. 5.19. Summary NomaLfitd f-w e la t Jon for Pile Vib=-._!ed i l t o S j R -d at -3% Pzlamo Ders i ty

Fig. 5.20. Summary Normallzed f-w Relation for Pile Vibrated Lqto BLS Sand at 65% Reiative Density

Fig. 5.21. Summary Normallzed f-w Relation for Pfle Driven by Impact into BLS Sand at 9W RelaUvc Densi ty

Fig. 5.22. Sc?mmsry h'oandiz,-d f-w Reht ion for FLlc Vibrated into Y S Siind a: YCCh Rclat'ic Demi?j

~ l g . 5 .23 . S u m m q Normallzed q-w Relatlon for Plle Driven by Impact and Vibrated into S J R Sand at 65% Relative Density

Fig. 5.24. Summary h'ormalized q-w Relation for Pile Driven by Impact lnto S J R Sand at 90% Relative Density

Fig. 5.25. Scrnmary Normallzed q-w Relatlcn for H e Vibrated tqto S T X Sand at 3CQh Rciattve Cersity

Fig. 5.26. Summary Normallzed q-w Relatlon for Pile Vibrated into ELS Sand at 6596 Relatlve Density

Fig. 5 .27 . S u r i i a r y rv'crmdlzed q-w Relation for Pile Driven by Impact Lnto BLS Sand a t 9G% Relative Density

Flg. 5.28. Summary : iormahd q-w iielaticn f ~ r Pile Vlbratcd lnto BLS Sand z! 9% ,%!auvc Derst ty

Installation were generally small. Valcrs are eupl!cirfy zoied on Flgs. 5.9 - 5.13 and are

summarized Ln Tabie 5.12.

Several observations from Fgs . 5 ! 7 - 5 23 can be made.

a. Ultimate unit shaft resistance in compression (positive w/B) was higher in

the lmpact-driven ptle than in the vibro-driven pile in medium-dense Sjfi Sand. (The

results for vtbro-driclng and impact-driving ior 6590 relative density are combined in

Fig. 5.17. so F g . 5.9 and Flg. 5.13 must be consdted tc; conflrm this statement.)

b. L'ltlmate unit toe resistance was higher for the vibro-drlven plle. with and

without restriking, for both sands at 90% relative density than for the Impact-driven

pile (Figs. 5.24 and 5.25; Figs. 5.27 and 5.28).

c. Maximum ultlmate values of unlt shaft resistance occurred ln the upper hall

of the pLle (depth of 20 inches'or 5 3 in Flgs. 5.17 - 5.22) when the pile was installed by

vibration or by blbratlon with restPAng. Xowever. the continuously lmpact-driven

pile produced the maximum u1tLma:e vdues of urdt shaft XsLtarice Lr. the lower half of

the plle (depth of 60 lnches or 15B in Fgs. 5.17 - 5.22). Thls suggests that the effect ol

the penetrauon of the toe past a given elevation may have degraded the shaft resistance

in the vibro-driven pile and that as the pfle penetrated deeper the shaft resistance at

that elevation was gradually restored by vibration of the sou. No such effect, or perhaps

the opposite eifect, occurred with the Impact-driven pCe.

d. The general tendency of the development of uitimate values o f f was for f in

compression loadfng to exceed f m upiLrt loading In the top half of the plle but not in the

bottom half of the plle. No particular trend with respect to method of installation could

be determined in this regard. Average ultimate f v d u e s divided by the mean effective

chamber pressure for all 1oadLr-g tests from Figs. 5.17 - 5.28 were

Compression Loading Uplllt Loading

Top Half of Pfle 1.12 0.52

3ottom Hall of Pile 1 .03 1.10.

These data suggest that a s ~ ~ r f a c e effect evisted during uplift loa&!g, whereby the free.

pressurized surface of the s a n d within the chamber permitted development cf shea r

planes a t a n angle to the interface, which possessed a lower shear strength than the

interface plane and whlch Lherefore pemlltted [allure to occur at a lower s h e a l n g stress

during uplift loading than during compressiorl loading. For this reason no attempt was

made to cornpare uplift capacities for various methods of lnsrallation in the way in

which compression czpacities were compared.

e. The ultlmate value of f was, on the average for all tests. 8GVo of the lateral

eflectfve chamber pressure for Dr of 65% and 120941 of the lateral effective chamber

pressure for Dr of 9096. Since the angle of interface shear varjed from 25" to 30" (Fig.

4.11). It can be demonstrated that the insertion of the pile into the chamber produced a n

increase in !he horizontal efrective s t r e s s !n the chamber at the pile-soil interface.

iissurring that f = o ' ~ 'an 8, where o ' ~ is the horizontal efTec!ive stress at rhe pde- m 5 ~

soil interface, and 8 is the angle of interface shear (average value of 27.5"). the average

horizontal efrective s tress at the pile-soil interface can be computed to be 0.8 / tan 27.5"

which is 1.5 times the simulated horizontal in-sltu (lateral effecrlve chamber) pressure

for Dr of 65% and 1.2 / tan 27.5" which is 2 . 3 times the simulated horizontal In-situ

pressure for Dr of 90%. The pile, whether vibrated or impacted Wito place, therefore

mus t have served to increase the efrective s tress In the sou Fmrnediately surrounding

the pfle.

f. The ultimate values of both f and q were generally about 80% fu!ly developed

a t a local dlsplamment of 5% of the pfle diameter but continued to increase slightly a t

larger displacements. Deformation softening behavior was not observed in either

shaft or toe resistance when ttle pl!e was installed either by vibro-drlvhg or by Impact-

driving.

Further insight &to the behavior of the test pile during vibratory d m . $ can be

gained by observing unit load t r a ~ s l e r relations (f-w and q -w curves) that developed

dur ing vibro-drlvlng and comparing [hose relations with the equivalent relations

developed during subsequent static load testing, as described in the preceding section.

The d lnamic unit load transfer curves were determined from the digitized time

histories of force and acceleratiofi. Three to f ~ u r cycles of load were selected from

analog records, and the pile-head and pile-toe force records a n d t h e pile-head

acceleration record were dlgftized (512 poin ts for each record). The pile-head

acceIcra!lon record w a s fntegrated once, a s described above. 1: necessary, the resulting

digitized velocity record was shifted one o r two time s teps so tha t the pile-head force

and velocity records began to rise on the first cycle a t the same time. The pile-head

velocity record was integrated again to obtain pile-head displacement record wm(t) by

using the trapezoidal rule for numerical evr!uation and 512 Ume steps.

Test dara hdica te that the plle. during vibratory lnstallatlon. behaved a s a

rigid body, so that the value of w,(t) was assumed to apply all along the pLle at any

given instant of t i m e . At this same ins tv l t af t lme the value of dlgltlzed toe force

divided by toe area (12.57 square inches) was taken to be qlt). Cor~es$ondlng values of

w,(t) and qlt) were then graphed a s unl t load transfer curves that occurred dxrlng

vibro-driving.

The value of unit shaft resistance f i t ) correspond!ng to w(t) was computed

from the digitized head and toe force records (Qhead(t) and Qtoe(t)!. respectlvely) and t h e

digitized head acceleration a,(t) record from

Q,(tIl/ As.

where IV is the weight of the pile and A, is the shaft area of penetrating part of pile. The

digitized functlon f [ t ) . which represents the mean unit shaft resistance along the pile at

time 1, was then plotted versus wmltl. The weight of the pile was small (0.080 d. and its

peak inertial force was typically only about 5 g X 0.080 k = 0.4 k (about 3% of the avenge

peak plle-head force), so that the effect of the inertial f o r e of the pile itseIf was

relatively srnall in this !aboratory study.

I f is noted that the djnamic f-w and q-w curves contain the efrects of qny

residual stresses that may have been developed during the period for which the cunres

were derived. The beginning polnt of a plot was selected to occur at a tfme near !he top of

a stroke (pile-head in upmost position during a vi5raUon cycle).

Dynamic f-w and q-w curves are shown for a penetration of about one diameter

less than full penetration for several tests in Figs. 5.29 - 5.34. The f-w curves are

average ~ I a U o n s h i p s for the entire penetrating portion of the pfle. Two to three cycles

of loading are shown. and each relation begins with an arbitrarily assumed w value of

zero, which was chosen to correspond a p p r m a t e l y to t h e beginning of a downstroke

of the driver. Posltlve values off or q correspond to upward-directed stresses on the

shaft or toe. while downward-directed stresses are represented by negative signs.

Figures 5.29 - 5.34 correspond to Tests 5. 7, 9, 1 l a /13a , 14 a i d 17~respectively. and

pertaln a wide variety of SOU conditions, which are sumrnaried ln Table 5.13. Effects of

instantaneous residual stresses are included In these figures, since !he zeroes for the

instruments were those acquired prlor to insertion GT the pile.

TEST 5 PEN. 70" DYNAMIC f -w CUPT(X

l o I 1

TEST 5 PEN. 70" DYNAMIC q -w CURVE

1.4 [

Flg. 5.29. 3yxunic 'Jnit Load m d c r C u m : Test 5

TEST 7 PEN. 75" D Y . W U l C I - w CURVE

10 , 1

Flg. 5.30. Dynamic Unit Load M e r Curvcs: Test 7

TEST 7 PEN. 75" DYNAMIC q -w CURVE

1 .* - 1.2 - -

1 -

I

7-7-P-

i I 9 PEN. 49'' O Y N A U l C I-w CURVE

I

F!g. 5.3 1. Dynamc Unit Load ?Yansfer Curves: Test 9

TEST 1 1 a/13a PEN. 77" OYKAMIC q-w cUWg

1.4

1.2

1

I

TEST 1 1 a/13a P E N . 77" QYNAUlC I - r r C U W f

' " a dB

d

4

2

0

- 2

I I -4 -i I

Fig. 5.32. Dynamic Unit Load h r e r Curves: Test 1 1 a/ 13a

- -4

I 1 I I I I I f

0 0.2 0.4 0. a 0.BI 1

TEST 1 4 PEPJ. 70" D Y N A M I C I -w CURVE

1 0 , I

Fig. 5.33. 3 j m c Umt L a d Trdn.fer Cumes: Test 14

TEST 14 P E E . 77" OYNAMIC q-w C U M

l.A -. - 1.2 -

-.

1 7

I I I

I

TEST 17 PEN. 7G" DYNAMIC 1-w CUR-

'O -?.---- I I 1 - I n M o t i o n I

.a (In)

F L ~ . 5 .34 . D y n a ~ J c Unit L a d Eansfer Curves for PUe Ln Motlon and at Rd&: Test 17

Takle 5.13 Sumary of Tests for Development of R ~ m i c TLnlt Load Transfer C :~n / e s

Table 5.14. E n e r a Loss Per Cycle Close to Final Penet ra t ion

- I ~ S I So .

5 7 9

1 lA/ 13A 14 17

Relarive. Densi ty

I O/o

90 65 90 65 90 90

Eir'ective G r a i n She

(mm)

0.2 0.2 0.2 1.2 1.2 1.2

Sand ? B e

SJR sJri S,T BLS ELS B LS

Euective Chamber Pressure

(pst )

10 10 2 0 10 10 20

The following obsen7at10ns can be made from F g s . 5.29 - 5.62:

la) In order tc Fnvestlgate the effect of relative d e n s ~ t y , Fig. 5.29 c a n be

compared with Fig. 5.30 ( S J F I s a n d ) , and Fig. 5.33 can be compared with Fig. 5.32 {BLS

S a n d ) . The maxlmum and minLmum va,ues of f were not strongly innuenced by

relative density Fn either soils, a!though the value of minimum f was somewhat larger -

(in absolute terms) for the higher relative density in both sands. In the Fix Sand the

peak value of q was also essentially independent of relative density, bu t Fn the EiLS

Sand the peak value of q almost doubled when the relative density increased from 65%

to 900h. The dmerenczs In effect oi relatlve density on toe capacity in the two solls may

be due either to grain shape effects or to the development of more efTicient drainage in

the coarser sand.

(5) The eflect of effect!ve chamber pressure (simulated depth) can be observed by

comparing Figs. 5.29 and 5.3 1 (SJR Sand) and Figs. 5.33 and 5.34 (BLS Sand) . The

eZective s tress h a s relat i~~ely little effect on the maximum or mintmum values of f in

S J R (fine) Sand but produces approximately a 50°/o imrease in the peak value o f f i n

3125 (coarse) sand. The effect of effective chamber pressure is more pronounced when

peak q values are compared. In SJR Sand the peak value of q was doubled, while

doubling the effective chamber pressure and in BLS Sand produced about a 30°!

increase In peak q. Hence, the increased resistance to penetration a t higher efTective

pressure occurred in both s h d t resistance and toe resistance for BLS Sand (coarse) and

toe resistance for SJR Sand (L?e).

(c) A comparison of pile in motfon vs. pLle in a refusal state in Fig. 5.34 reveals

no signlflcant changes in the shapes of the curves or the peak values for the two

conditions bu t indicates t h a t both the f-w and q-w curves a re m u c h stlffer for

conditions of refusal. In fact. for the case of refusal, the posltlve peaks c o r ~ e s p o n d

ncre closely to points on !he static mi! load transfer curves than for the case of pile-in-

notion. a s 1s discussed below.

16) T ~ P 6 j ~ a m i c f - i ~ curves typically steepeced along the l o a d h g branch a s the

pile approached the bo:tom of t he downstroke (mz&murn w). Thls behavior is contrary

t o common soil modt!s c s - d for evaluating impact driving, In which a reduced slope, or

even a nrgstlve s lspe. eris:s a t ?h is point a s the pile velocity approaches zero. It is

believed that the reduced unit shaft resistafice near t he middle of the stroke was dlue

maln ly to t he d>?iamic mobility of t he s a n d >lr',!c!es nea r the pile-soil interface

produced by :he vibrat!on of t he pile. As !he pde decelerated near the bottom of the

downstroke, t he partlc!e inobility decreased a n d the ua l t shaft resistance Increased.

producirii the Increased slope.

(e) It is observed that t h e d j n a m i c q - w curves appear t o become convex with

lncrease in w. This bchair!or is be!ie\,ed to be the result of either continued lifting of t'le

toe off t he underlying soil on t he upstroke of t he pile. followed by impact o n t he

downstroke a n d / o r loosening of the u11derl)~ng soil. Thls suggests that during each

cycle the toe s ea t s itself before developing sfgnilicant toe resistance.

(0 From the dqnarnic f-w a n d q-w curves the, energy loss per cycle for pLle s h d t

and toe can be found separately a s the product of the area enciosed by the curve and the

corresponding contributing area of the ~ l l e . The total energy loss per cycle is obtained

as t5e sum of the energy loss per cycle for shaft and toe and Is summarled in Table 5.13.

Several obsena t lons can be n a d e :

(a) the t ~ t a l energy loss per cycle Is higher u n d e r higher chamber

pressure for both m d s r e s t s 9 and 17);

(b) the totai energy loss per cycle !s higher Ln sand of larger grain size

under higher relative density r r e s l 14 and 17 vs. Tests 5 and 9):

(c) t h e tstal energy loss per cycle is less in sand undeclower chamber

p r e s s u n and lower relative density Kests 7 and l l a / 13a).

(6) the total energy loss per cycle varies from 25% to 50036 of the total

pnrrgy delivered to the pile head per c).c!e.

Dynamlc ~1st load t ransfer (f-w a n d q-w) relationships arc coil:pa;ed :c the

static urJt load transfer curves (obtained during the static loadirlg tests) in F!gs. 5 35 to

5 .41 . Since the dbnamic f-w relations hi?^ a r e for t he pile a s a whole, the static

relationships that arc shown are the average of t he relationships denved for the o p p e r

and lower hal:.es CC the ptle for the part icular test unde r considera:ion. \Wli:r z u c h

ana lys i s c a n bc made of t h e differences a n d s imilar i t ies in thcse curves. i t is

appropriate lo point out the foL!cw!~f two I!en?s:

(a) the in it!^] slopes of the losdlng b ~ a n c h e s of the dynamic and static f-w c u n r e s

a r e generally similar S J R ( [he) S a n d a n d for 65% relative density in BLS (coarse)

Sand (Flgs. 5.35 - 5.33). but the dynamic curves are steeper than the correspondl?g sta!ic

curves for very dense BLS Sand (Figs. 5.49 - 5.41). However. the peak value o f f was

always less in #e d)marnlc f-w curves t h a n ln the static curves:

(b) the maximum slopes of the loadlng branches of the dynamic q-w c u n r e s

(correspcnd!ng 19 the cornpielion of seat ing in the s a n d s of high relative density) 2re

smal le r t h a n the corresponding s lopes of the s tat lc c u n 7 e s for effective chamber

pressures of 10 psi bu t are equal to or greater t h a n the corresponding statlc slopes for

effective chamber pressures of 2 0 psi. The peak value of q was always less in t he

d~marnlc q-w curves than ln t he static curves.

5.8 PHASE RELATIONSHIPS

I t is useful to describe phase relationships between motion fxnct!3ns at the ?ilc

head and pile toe. particularly for + b e reader who may want to use t he Lnfcrmat!on in

th i s s t u d y to develop o r to calibrate mathemat ica l models for uibro-driven p!!es.

Table 5.15 summarizes +he phase between plle-head and pile-toe accelerations. The

raw, measured phase angles were relatively large: however. much of L h t apparent 2hase

lead of t he toe accelerometer w a s d-e to electronic phase lag in the accelercmeter

TEST 5 D Y N A M I C V Z S T A T I C q - w C U R V E

9.8 -7 I

- - - STATIC

Fig. 5.35. Comp5ison of Dynan~lc and Static Unit h d ?hrsfer C I I N C S : Test 5

TEST 7 O Y N A H I C V 3 S T A T I C I - w CURVE

3 0 , i i I - DYNAMIC I

I - - - STATIC I

I

I 15 2 Q i i

I !

i _ _ _ - _ _ _ - - - - - - _ - - - - - _ - - - .

i

O - - !

I 1

TEST 7 DYNAMIC V% S T A T I C 9 - w c U R V E

7-

1 I I

- DY !;AM I C I

I - - - STATIC I

1 .2 I

4 I - ,a a K

I

wp'go 0.8

_ _ _ _ _ _ _ I _ _ C _ _ _ _ - - - - - - - - -

i I I

4 I

- 0 . 2 I I !

I 1 I I I 1

0 , i

0.1 0. a 0.4 0.e 1

w (In)

F!g. 5.36. Com~ut_wn of Eynamk a d Static Unit Load Transfer Curves; Test 7

- a V h { " U T 1 1 A I I I L

- - - STAT! C

--: z- S T rs - D Y N A M I C VS S T h l l C q - w C U R V E ---

I . a , I

TLg. 5.37. C a m p a w n of Dynamic and S t a W Uni t Load Trarsfer Cumes: Test 9

TEST 1 lo/i3c O Y H A M I C V Z S T A T I C f -w C U R V E

3 0 ,

F!g. 5.38. Comparison of Dynamjc and Static Urrit Load Transicr C ~ r v t s ; Test 1 l a / 13a

TEST 1 1 a/; 30 D Y N A M I C V S S T A T I C q - w C U R V E

1 . a -

1 . 6 - -

1.4 - -

1.2 -

- DYNAlYIC - - - STAT I C I

I I

- - - - .

! i

... -4 - I

-0.2 ; I 1 I I I I i I r 1

0 . 0.2 0.4 0.6 0.8 1

D Y N A M I C V 5 S T A T I C f - w C U R V E 3 0 ,

TEST lk DYNAMIC V S S T A T I C 4 - w C U R V E

1 . B -v I 7 I

- - - S T A T I C

Fig. 5.39. Comparison of wramjc and Static Unlt Load Transfcr Cumcs: Tcst 13

D Y N A M I C V S S T A T I C 1-w C U R V E

D Y N A M I C V"5 S T A T I C q-x, C U R V E 1 . a

Fig. 5.40. Comparison of J3ynamlc and Statlc Unit Lead Transfer Cumes: Test 17

?-EST 7 7 D Y N A M I C \/J S T A T I C f-.I C L l H V f

'O 0- 1

i I

O Y H A U l C \'5 S T A T I C q - u C U R V E 1 .a ,

- D Y t i A M I C - - - S T A T I C

Fg. 5.4 i. Comparison cf D y m c (We iir Rrfusall and Stat!c U n l t Lcad Pansfer Curves; Test ! 7

Table 5.15. Measured Phase Relationships Between P2e-Head aiid Pile-Tce Accelerations

" S = B = BlasUng / relattve density (%I / elTectWe chamber pressure (psi) : 1% = 10 psi horlz. and 20 psi vert. / V = vibro: R = r e s + h e

circuits 2t the pCe head. Once this el-ctronic lag was corrected, a s described in Chapier

3, the measured phase between the head and toe accelerations was generally 3 0 " or

less , with an avenge absolute value of 7" at 70 inches of penetration. 7unhcrmore.

s ince the maximum driving s t ress ' ln the pi!e dur:ng vibro-driving ranged from 3 to 9

k t (80h to 25% of thc yield strength of steel) while that for Lmpact driving was about 18

h i (5O0/0 of the yield strength of steel), the small s t ress level induced negligible strain to

the vibro-driven pile. I t c an be i n l e ~ e d from the above observations that the test pile

behaved generally a s a rigid body.

C W E R 6

ESTIMATION OF B-G CAPACITY iWi) S E ~ I O N OF VIBRO-DXFER

The major objective of thls chapter is to model the load-movement relationship

and predict the static bearing capacity of a vibro-driven pile. Seiective modelings of

impact-driven piles are also included for comparison purposes. Several methods are

proposed lo predict the load-movement behavior and the bearing capacity of vibro-

driven piles. Important soil parameters and driver parameters are Incorporated into

the bearing capacity formulation. The unit load transfer relationships are moaeied

using Ramberg-Osgood, eupo;ler,tinl and power relationships. In the Unit Load

Transfer Method (ULT Method) the unjt load transfer models are used to predict load-

movement relationshlps for vibro-driven and impact-driven piles. In the Power

Transfer Method (PT Method) nondlrnensional analysis is used to relate the power

transfered to the ptle head from the driver, static compression capacity and pile

penetration velocity under varlous pile and soll parameters. These nondfrnension21

relationships are also used Ln selecting a n appropriate \lbro-dxlver to achieve desired

bearing capacity. In the Ncrmallzed Capacity Method (NC Methcxl) a direct relationship

between b e a r - capacity and ptle penetration velocity h a s been established, which is

analogous to relating bearing capacity d Impact-driven piles to blow count. In the

-Ultimate Resistance Method LT7 Method) maxliinum unlt shaft and toe rtslstances are A

used to estlmate the static bearing capacity. I t should be noted that . while the

experiments a t t exp ted to model eaective s t resses in the soll and appropriate

unbalanced rorce and bias (quasi-static] force of the vlbro-drlver to represent fleld

cor.d!tions, no assurance e*sts that the predicti~re rnethods given !n tnis chapter can be

scaled directly to full-size. Ia fact. upscaling of t h e soil-pile behavior is not

recommended unless other.s,!se veflLieci in the fie!d. I t is believed. however. that the

parameters controlling the !sad-movement of displacement pilcs installed in sand by

v~bra tory driving have been identified and that :he general re la t lonshi?~ proposed are

considered a s:ep closer to better understanding and amproved modeling.

Various bearing capacity formulae for vlbro-driven piles have been discussed in

Chapter 2. Fig. 6.1 compares the measured bearing capacity for the test program urith

the capacity predicted by Schrnid's and Davisson's fonnulae. These bearing capaciiy

formulae tend to 01:erpredicl the bearing capacity but show the proper trend in the

relationship beiween bearing capacity and rate ol penetration a s observed in the

experiments. The other f o ~ ~ . u i a e (Chapter 2) are not included Ln LL7f.s con~parlson s t udy

because n l p ' s f o m u l a does not relate the bearing capacity to penetratlon veloclty and

Benlhard 's l o m u l a predcicts increasing bear!.ng capacity with lnc reashg penetratlon

i*elocity.

The load-movement relatlonshlp for piles can be predicted using the unit load

transfer relationships (unit shaft vs. pLle movement. f-w, and unit toe resistance vs. toe

mov?ment, q- iv) . Table 6.1 s u m m r j e s the relationships used by other researchers to

determine the unit load t . n ~ s f e r curves for Lrnpact-driven ptles in sand . It includes

power, exponential and modified Hsmberg-Osgood relationships. I.lowever. none of

these methods exp!lcltly tekes into account t he Ln-situ stress, relative density and grain

slze of sand. Furthermore. there is no method available to predlct the unit load transfer

curves for vibro-driven plles.

Pge drtvl?g fonnulae have been used to predict :he bearing capac!ty of !maact-

drfvtn piles since a s eariy as 1520 (20). Q1 the several formulae. the Hiley formula (5) Is

of greatest Interest and is expressed a s f~llows.

9 E x p e r i m e n t a l Qav isson

60

Rate Of Penetration (in./sGc.)

~ i g . 6.1. Comparison of Experimental and Predicted Bear!!g Capacity Vs. Rate of Pcne~a: jon

Tzble 6.1. Surriar)l of Llethcds Lo 05!211 f-w and q -w Czrves for S3r.d

qu= ultimate unlt toe ress tance w = pl!e rnovenent cor;es;;ondLng :o

u ! m t e \ d u e s

Procedure (1991)

- tiPcOm~T.cc,~::S;I

for f-w :

Wc = 0.2" :O 0.5"

for q-w :

w c = 3 ? 3 t 0 5 3

> ~ , P : ~ o c I

Coylc and S u ! r n a n (9)

Zrnplrlcal Procedure

( 1 967)

\'ij al;vergiya

(48)

E z z l r i c a l Procedure

I i 9771

2 ro q (1- v 2 ) W = E I \v

ro = radlus of ptle rm= zcne of influence

Equation

D* Gun=

f = f u (2 E-3

C = shear modulus a=fFir/f-x R[ = constant E = Young's modulus iw = shape factor

E f ? E q . f o . q o . E p f . Zpq , n and m = u n k n o w ~ paaInl!ers

Empirical Prcc tdur t

( 1987)

m= 1 and := 1 7 Eqw

9 = E w P 1;n + h w ( 1 + I L 1 I

qo

in m t i l e h ' s study

(21

4

where R = bearing capacit.,. of impact-dnven pile e = rff!ciency of h x x . . e r .

E = energ. of hammer.

s = p e n a ~ e n t s e t per blow, c = elastic rebound of the system. Wr = weight of ram.

n = coenicient of resritulion of cushion. and \Vp = weight oC pile.

The parameters used in this scudy are a s follows: E = 767 ft-lb. e I- Q.5. Wr = 363

lbs, n= I .O and TVp = 79 lbs. Fig. 6.2 conlpares the predicted bearlng cagaclty using Hiley

formula with the experimental results for ail t ipac t -dr iv ing and restrike tes t s for

various ..,a!uz of elastic rebound of the system Ic). !t seems that the measured data

match *.veil wt!h the predicted cclpacily wher! c Is equal to zero, which Is a cfiarateris!:~

of a rigid pile.

I t is possible to synthesize the load-movement relationship of vibro-driven

pUes by us1r.g appropriate shaft If-sv relationshtpl and toe (q-w re!atlonshlp) unit load

transfer curves. This section presents the mathematical modelling of e.uy,erimentally

developed unit load transfer curves and predlctlon of load-movement relatlonshfps for

the model pile.

Three relationsh!ps are investfgated to predict the static un i t shaft a n d toe load

transfer curves for vibro-dIrtven piles. These are the avo-parameter power model. three- 4

parameter exponential model and four-parameter inodlfied Ramberg-Osgood model

(351. The staiic u w t load transler ieiationshlps that are modeled are the average

relationship of the upper and lower halves of the pile (deyths of 20 inches and 60

60 1 ---.- ----.-- --

- H i l s y F'orrnuia

I m p a c t

~ i o w Count (b lows/ in. )

.A

Fig. 6.2. Cornpaison cf E-rYnentd a n d Frcdctcd Bearing Capacity Vs. Blow C 0 u ~ t

inches: a s used ir, Chapter 5 for comparison uri!h the dynamic unit load t rar~sfcr cui-:e

of vibro-driven piles). I t should be noted that all the parameters !n the x o d e l s are

related to the test variables such a s horizontal in-situ s t ress (10 psi 2 0 'h 520 psi), grain

size (0 2 rnrn < d l 0 5 1.2 rrm) and relative density (0 .65 5 Dr 5 0.90).

The measured residual stresses, which are s r n a l d u e to low driving s t resses and

a relatively rigid pi!e, are nonetheless taken Lnto accouni In rhe modeling. I t !S found

that the res!dual stresses d~:c!=ged a! t h e tce ar,d the shafl (a! 2 0 kches a n 3 5 0 !r.c.?~si

for vibro-driven piles are relarive!y constant (Tests 5. 6 . 7 . 9, 1 l a / 1 3 a , 14. 15 w:d i 7 ) .

The average value of residual s t ress aiong the s h d r . f,. is - 1 .32 psi, where the negative

sign m e a n s friction directed downward along the shaft. T h e average residual s t ress for

t he pile toe, qr, Is 8 6 psi. It is shown later that these values prcvide reasonably good

predict ion.

T\D-Parametcr Model

As shown in Table 6.1. Vgapergtya (17) expressed the I'-w and q - w rt.lat~onsi-:ips

by a power function of 1 / 2 and 1/3 respectfvely. The power funceion here Is descnbed in

t e rms of the tests variables. The two-parameter power rxlationship for 1-w and q-w can

where f is the unit shaft resistance (psi ) , q is the uni t toe resistance (psi) and w Is :he

local pile movement (in.). kf, kq, bf a n d bq are pile-sou sys tem parameters . The

relat ionship between system parameters and test variables can be represented a s

follows.

a

Q(pl = f i (di0If2 IDr)f=,(a 'h)fi(dlODi-)f5(dioa'hlf~(Dro'h). (6.4)

where p Is kf, kq. bf or bq. t'sing the test da ta , functional relationships, fi/$ (I= 1 to 6)

were determined. T h e least squares method was used to determine the constants of the

Iinear or logarithm!^ relationship between the parameters and test varisbles or their

combinations. The relationships are 2 s follows:

1% kf = 0.46 + 0.025 a'h + 0.063 d l 0 + 0.51 @ .

bf = -0.056 + 0.0077 d h + 0.087 d l 0 + 0.32 a. log kq = 1.88+0.151cg dh +0 .073d10+ 1.17Dr. and

The predicted curves for f-w and q-w are cornpared with the experimental data in

Figs. 6.3 to 6.5. In these relationships, f and q lncrease a s w kcreases without reaching

a limitlng value. which Is not tn agreement with the experimental observations

Three-Parameter Model

Constitutlve relationships are frequently modeled by exponentlal functions. -

The three-parameter exponential relationship is expressed a s

where fo and qo are the reference stresses. wfo and wqo are the corresponding reference

movements: bf and bq are the unknown parameters and related to o'h, d l 0 and Dr.

They are defined a s

lag b = 0.8: + 0.028 b h + 0.09 lcg(dl0 d h ) + 0.0957 d h 1% Dr (psi).

& = 11.79- 1 . 0 2 1 @ d h - 0 . 3 8 d 1 0 - 10.29Dy.

wro = 0.1 (lrl.1,

log% = 1 . !%+0 .012dh+O. l2d l0+ 1.324- (psi),

bq = 1 1 . 1 0 - 0 . 2 0 ~ d h + 0 . 6 8 d ~ 0 - 9 . 7 8 D f . znd

wqo = 0.3 (Ln.). 4

The predicted f-w7 and q-w curves a re c o r n p a ~ ~ d with the experimental data in

FIgs. 6.3 - 6.5. They agree reasonably well.

Tes: 5 1800 <

w (In.) w (in.)

Test 6

1200

800

aoo

0

w (In.) w (In.)

4

w (In.)

Fg. 6.3. Eqm-irnen:al &?xi PrtdCcteb f-w arLd q-w Curves; Tests 5. 6 and 7

w (In.) w (In.)

0 0.2 0.4 0.8 0.8 1.0

w (In.)

Flg. 6.4. Ejc3e9ii~fl.ta-l ad . W c t e d i -w and q-Y Curws: Tests 9, 1 !a/ 13a and 14

w (In.)

Test 17

I I I I 1

Flg. 6.5. Ekpemnmtal and Predicted 1-w and q-w Curves; T e s l 15. 16 u l d 17

Foc:r-?rlrnmere: ?IIsde]

The Ramberg-Osgood model Is one of t he most widely used analytica!

relationship for dynamic loadbgs ( 2 . 18. 371. The four-parameter modtfied Ramberg-

Osgood relationship is e x ~ r e s s e d a s

where Epr and Epq are the slopes of the plastic portton of the f-w and q-up c u r e s

respectlvely, fo and q , are the reference values. Ef and Eq are the dne rences of the

initial slope and the slope of the p1as:lc portion of curve. and m a n d n are the shape

factors. All these parameters are defined a s

1% El = 3.43 - 1.84 E+ - 0.034 dl0 & + 0.49 Dr 1% dh (wi),

log b = 0.71 + 0.027 d h + 0.074 log (dl0 d l l ) + 0.059 dh log 4- (psi).

m = 1.59.

bg Epf = - 1.59 + 0.023 dh + 0.16 d 10 + ! .85 Q (PI).

kg E+ = 3 . a + 0.013 dh + 0.2 1 d l 0 + 0.027 log 4- (pd,

kg q, = 1 . S + 0.012 + 0.12 dl0 + 1.32 I& [psi).

n=3.16. and

Epq = 0 (m. Figs. 6 . 3 throzgh 6.5 depict the e.uperimenta1 and pFeedicted f-w and q-w

relatlonshlps for Tests 5, 6. 7, 9. i la/ 13a. 14. 15. 16 and 17 respectlvely. I t Is obsened

tha t t he exponentizl relationship and t h e modified Ramberg-Osgood relat!onshlp

gel~erally provide reasonably gcod predictions. The rnodiiied Ramberg-Osgocd method

i s preierred because the plastic slcpe. Epf, helps to better match the experimental f-w

relat ionships. which generally do not reach a lli-niting value within t h e range 3l

displacement invesagatea

The modified bmberg-Osgood method is also used to predict the euperimeniai

i-w and q-w curves for impact-dnven ptles. The paramters in Eqs. (6 .6) and (6.7) lor

impact-driven piles are deliiied a s

= 197.00 (pi).

fo = -1.16 + 0.74 ash + 3.40 d l 0 + 5.2 Q- (psi).

m = 4.68 + 0.10 d h + 0.50 d l 0 + 1.20 Dr.

Ep[ = -1.56+0. 'L%dh ( ~ 3 ,

Eq = 6724.00 (y~"!).

q, 1- 299.00 + i4.0 d h a 3S.W d l 0 + W.CO & (psi).

% = 140 (psi)

It is observed that the t i t la1 slopes of unit load transfer curves for Fmpact-

diiven ptles a r t relatively constant compared to those for 1qSx-o-driven piles, which

vary more .Kith the test parameters. This obsemation m a y lndlczte that the rar,ge of

variables investigated do not have a significant effect on Initial slope for impact-driven

pi!es. Figs. 6.6 - 6.7 depict the measured and predicted f-w and q-w curves for Tests 13.

19. 20. 21 and 22 and the agreement is reasonable.

!jtat!c bad-Movement R~SDQPS

The unit load transfer relationships, f-w and q-w curves, a re often used to

s?nthesize the static behavior of the pile. !t is meaningful. to use the developed urJt load

transfer model described In the previous section to reconsiruct :he l o a d - m o v m t e ~ t

w (In.)

FQ 6.6. Ex;xr'mcntaJ and Prcdlctcd f-w and q-l.v Ccnfes; i 'rsl 18, I 9 and 20

w (in.)

Test 22 Test 22

Fig. 6.7. Expcrlrnen:al and PrtOlcted f-w and q-w Curves: Trs~s 21 and 22

relationships ;ar the xloae; p!le. In :his regard. computer p r o g m APILE (46) w a s u sed

Using embedded pile length of 6.58 It (4.75 !t far Test 3 ) . pile perimeter of 1.047 f t , cross

sectional area of pile of 0 .016 ft2. toe a rea of 0.057 ft2. modulus of pile material 3 f

30.000 ksl and the un!t load transfer curves a s input. the load-movement re!ar!or?;?i?

is generated. I t should be noted that residua! stresses are already taken irito accouxi Lr

the unit load transfer modzl. All t ~ r e e urLt load transfer rrlociels are used in predic:!o~i

of Tes ts 9 and 1 l a / 1 3 a as shown L n Fig. 6.9. The predicrion usicg the rnodu'led

Ramberg-Osgood model is the best of these three models. Hence, the node1 chosen for

the prediction o; other tests is the modified Ramberg-Osgood model. Figs. 6.8 through

6.10 show the measured and predicted load-movement relationships for !?ibro-driven

piles (Tests 5. 7. 9. 11a/13a. 14 and 17). and Figs. 6.1 1 depicts the cornparsion of load-

movement re la t io~ships for impact-driver. piles (Tests 19 and 2 1). 1; is concluded thzt

the pre4iction by the xodifird Ramberg-Osgcod mode! is reasoxabiy good in all cf rne

cases.

6 . 2 BEARING CAPACITY PXLATONSHIP

Several methods to predict t he bearing capacity of vibro-driven piles are

investigated: (a1 Power Transfer Method. (bl Normalized Capacity Method and (4

Ul!lmate Resistance Method. The Ultlmate Resistance Method is also used to predict

the bearing capacity of lmpact-driven piles.

Power Transfer Method

h e bearing capacity. Q, Is observed to be a function o i several variables : rate of

penetrallon, vp. absolute peak acceleration of pile head, ah, eccenZric moment of driver.

me& (where m is eccentric mass, e is eccentricity and o Q LFle angular velocity), mass of

the vibrator, M , bias weight. W. isolation spring stiifness (between bias weight and

I . 4 I

Flg. 6.3. Measured m d Predicted bad-Mwemect Curves; Tests 5 and 7

0 Measured - Ramberg-Osgc~od - - Exponect ia l -.- Power

Test 11d13a

Fig. 6.9. Measured a ? d PreCtctcd bad-Mwement Curves; Tests 9 a d 1 l a / 13a

Load Cdps)

5 1 0 15 2 0 2 5 30 3 5 4 0 4 5

F f g . 6.10. Measured and Predicted Load-Movacnt Cumts; Tests 14 and 17

204

Fig. 5.1 1. Measured and I'redlcted Load-h-Iovement Curves: Tests 19 and 2 1

vibrator]. k, horizontal eKective s tress . o ' h , relative density. Dr. and grain s u e of soil.

d 10. relationship can bt. repr~sen:ed a s follows,

Q = f ( v p , a h S n e , o,h~i.!V,lc c ' h . D r . d l o ) . (6 91

It !s shown in XppendL~ A that dynamic force. FD. delivered by the drivzr is a

function of it'. Xf. m, e, o and k. Furthermore. power is the product of fcrce and veicc:ty.

In which velocity is a hnc:ior, cf o ' h . Dr. d l 0 a n d a h . Using dLrr,ensional analysis.

several nondknensional terms can be otztafned a s 9 vp

n l = Ph *

A relationship is derived for t he s tat ic compresslon capacity. Q. of a vibro-

d r i v ~ n pile In saturated sand in te rms of veloclty of penetratlon. v . the power P

delivered to the pile head. P h . and the soil conditions. Since there is no conclusi\.e

evidence exists that restriking a v!bro-dri\.en pile afrects the compression capacity

(Chap te r 4) . the effect of restr ike is not considered in the relatlonslhip. The

nondirnensional parameters are related to the test variables a s follows.

The velocity of penetrat!on, v i s derined a s the average irelocity cbserved P '

during the terminal portlon of the dep'lh of penrtratlor, equal to the diameter cf the pGe

(Incremental distance driven ! tfme required to penetrate that incremental distance).

The $ factors in Eq. (6.13) are defined as follows:

P,(dh) = - 0.486 + 0.0743 bh , 10 psi 5 bh 5 20 pst

( ) 1 . - 1 . 1 65% <DrS9@%;r;nd

A frequmcy histogram 4sidicaLing r h e accuracy of i h i ~ method for the nine s;;lt!c

laboratory tests is s h o u a in Fg. 6.12.

In order for Eq. (6.13) to be used elTectivcly, a relationsnlp between vp (ips) and

ah (g) mus t t e developed. The approach adopted in this regard is to relate Ph and v:, to

ah that was measured directly at the pile head. Such a relation. which is expressed b.

Eq. (6.14). was deveioped from a n analysls of laboratory data. both pararrieter and

capacity tests. at various depths oT ptle penetration ranging frorri 12 diameters to 19.5

diameters. Eq. (6.1-1) is \.tTitren In :he follo\i8ing f c m ,

ivh ere

a , (D,) = -2.156-1 3.54 D,. 6596 S D, $ W / o .

3 (d ) = 8.99 + 2.76 d 0.2 mm 5 d10 2 1.2 m,

(dd = 1.71 - 0.%1 bh . 10 psi 5 Oh 5 20 pst.

Equations (6.13) and (6.14) contain implicitly the eaects of the interaction of the

pile. driver and sod through the power. velocity and acceleration te rms and the soil

coefficients a n d exponents. As ;vfth all emprlcial relat lonships. they rnust be

considered to be v a l ~ d only for the ranges of sou conditions described in the definition

of the a and p parameters. Funhelmore . they are considered vzlid only within the

range of pile and vibrator conditicns that were investtgated Fn this s tudy as follows: ( I )

T h c pea! sfngle.ampiitude unbal=ced force developed by the vibrator Is 0.1 Q to 0.3 Q.

and the vibrator body weight Is of tk,e order of 20% of the peak single-amplitude

unbalmced driver force. ( 2 ) The blas weight of the vibro-driver is 0.05 to 0.10 Q. (3) The

devtng fnequency is the opcr .um :requency fsr drivlag, 1.e.. 20 Hz in this study. and the 4

pile is driven contlnuo~~s!y ul thout i t o p p k ' .

The laborator] s tudy uras cor,duc!ed in soils with depthwise unlfonn soi!

properties in order to o h t a b a clear understandtng of the effects of the parameters.

No. of Tests

Fig. 6.12. Frequenq H l s : o g m o i Surnber of Laboratory Tests Vs. RaUo of Measured ro Computed Sormallzed StaUc Cornpressbe Plle Capacity

d c h c u g h i t mav be reasonable t.s idealize sand LT a n erlrire profile a s having a

aepthwlse uniform relcltive density, soils with u n l i o m lateral effective s t ress and

chaiac:er',stic gm31 size are se!dgm fouild In the field. Thc r~ fo re , in order to apply Eq.

(6 .13) to common field c o n d i t i o ~ s , it ts su_ggested that weighted averages of soil

propeittes Gh ar,d d10 bt. used in evaluating the C or P factors i? cases where these

parameters vary with d e p t h . I t is fur ther speculated. pending fur ther field

hves!igat!on, that t h ~ weighted values be assigned on the bas:s 01 the ratio of rneasured

toe rcsLstance to shaft res!stallce m the stat?c compression loading tests. If h represents

elther o ' ~ or d l O , then shg le , ~veighted values can be computed from Eqs. (6.15) and

The subscript ' toe" represents the value of the parameter at the levei of the toe of the

pile, while ?he subscript "~xiddepth" indicates a value midway between the ground

surface and the level of the pile toe. The coerflcients represent t he approximate

proportions of s tat ic load distributed to toe and shaft that were measured in the

laboratory dur ing stat ic ccmpression loading a: failure for the relative density

condftioris lnd!cated. For reizt!ve denslues belween 65% and 9096, h could be evaluated

by linear InterpolaUon.

Note Is made of the fact that Eq. (6.13) requlres 'mowledge of the lateral effectbe

s t resses in the SOU. which exercise s trocg control of the pile behavior. Any site

investigation that is undertaken mus t therdore Fnclude methods for evaluation of the

lateral eirect!ve stress prcfile.

Uslng Eq. (6.13), the capacity of tlbro-driven piles can bede te rmined by the

fo l loWg step-by-step prwedure. The procedure is logical and component relations are

al,w used in addition to Eq. (6.13).

(a) bieasure the average v ln the last or,e d m e t e r of penetraticn. ?

Ibl DetermtTle the peak pGr-head acce!ernCon ah f r ~ m v usiqg Eq. (6.14). P

(c) Compute Pt. the theoreucal power cf the hammer. from the brief procedure

described in Appendlx A

(dl Determine Ph, the actual power delivered to the pile head, from a h and Pt.

using Fg. 5.6.

(0 Finally, computc the static compressive capacity. 9, from Eq. (6.13).

Normallzed Capacity hlethod

The static compression capacirq., Q, is ~orma l i zed by multiplying the diameter

of pile. B , a n d divid!ng by the magnitude of the unbalanced force in the driver

( ~ , = r n e o ~ ; where m=unbalanced mass of the driver, e =eccentr!city of the unbalanced

mass and o=angular velocity) and the pile penetration. L and plotting the result

against !he average velccity of the pile. vp (ips: at terminal portion cf penetration equal

to the diameter of the plle) in Fig. 6.13. Eq. (6.17) represents such a re!ationship.

where y and y2are defined a s i '

y l (d ld = O.i97+0.072d10. 0 . 2 7 5 d 105 1.-

y2 = 0.21 1 (seclLr3.

Several comments a r e made regardkg this method : (a) The effects of relatlve

densi ty and horizontal effective s t r e s s of soil 2re incorporated implicitly in pile

penetrat ion velocity a n d t h u s no factors In Eq. (6.17) regarding these two soil

parameters are needed. Ib) The relationship is valid only within the range of pile and

vibrator conditions investigated in this s tudy a s descirbed pre\-iously.

L'ltlmate Resistacce Llethod

It is possible to compute the ultimate unit shait resistance fm, and uitimare

unit toe resistances qn &K

u s n g Ihe following expressions:

where p' = Nh tan 6. in which Nh is a factor :hat converts in-situ lateral effective stress

into a n equivalent efrective horizontal s t ress a t the pile-sou interface after pile

installation and leading to a failure state, 6 is the angle of pile-soil Lrterface shear.

oIh is the in-situ lateral effective stress in the sou mass lnto which the pLle is driven.

No is the bearing capacity factor at the pile toe. and G'o is the mean effective stress in

the sofl at the elevation of the toe equal to ( 1 + 2Ko) C T ' ~ / 3 , in which c s I v is the vertical

efiectlve stress In the soil at the eleva~ior? of !he toe and KO is the Ln-situ coefficient of

earth pressure at rest.

Assun15g Lhat both fmz and qmax e.ust at a common value of pile deflection.

the capacity of a pile can be determined as

in which Q is the compression capacity of the pile, N is the number of vertical

increments lnto which the pile is divided for computatlonal purposes. 1 is the

increment number, Asi is the peripheral area of increment I, and At is the area of the

toe. If a procedure such a s this is applled in practice. i t is also cle= Qat the lateral in-

situ efiective ground stresses must be established on a site through appropriate

exploration.

The values of both 3' and No c a n be computed i n princlplr: directly from the

nonnai ized uni t load t r a ~ s f e r g r aphs (Chapter 5) a s t he ord ina te va iues t ha t

correspond to a value of w /B of 0.1 ( P' 's the average value obtained from the top and

bottom halves of pile). 3 ~ 1 relati-rlg the values of P' and No to t he test variables such a s

relative density (0.65 5 Dr S 0.90) and grain size of s a n d (0.2 rnrn i d l 0 i 1.2 m i , the

fzctors a re fcund for x?bro-dri~~en piles usiqg least squares merhod a s follows:

p' = -0.85 -0.076 d l 0 i 2.53 2, , and (5.21)

No= -76.1 i 11.36d10 + !Si.G6 Dr. i6.22)

By the same approach. :he bearing capacity factors for impact-driven piles are

obtained a s

p = 0.67 -0.19 d 10 0.45 a r . a?d

N,=Fi,!.i:Z-ZI L U d l 0 - 4 . 1 3 Dr.

The lactors ?resented In Eqs. (6.21) lo (6.24) c a n be used with Eq. (6.201 to

compute t he s tat ic compression capacity of !he s imulated full-scale piles tha t were

tested Ln this laboratory s tudy, and I t may be possible 10 u se these equat ions h practice

for ?iles in sand with appropriate veriflcat!on a n d / o r modification, provided the

proille of i n - s l t u lateral effective stresses can be d e t e r m l ~ e d through appropriate In-

situ testing o r other r;:ear,s.

Table 6 2 presen ts a comparison of var ious m e t h o d s t o e s thna t e beartng

capacity oT driven ptjes in : e m s of prediction ratio (predicted capaci ty to measured

capacity) Methcd I denctes b a d Transfer >!ethod. which generTttes load-movement

relationship of wbro and impact-dnven pl1t.s by using the proposed uni t load t n n s l e r

model recommended ir, Eqs (5 71 and (6 8) Method I1 a n d Method 111 are Power

Transier >lethod and Soma l l zed Capacity !dcthod, respect~vely. which predict the

Table 6.2. Beark- Capaci? Ratio for Various Prediction ,Methods

1 Test No. Method 111

S t a n d a r d Deviat ion

Method I Met?od IV

Ratio Range

Method I = Load Transfer Method Method I1 = Power Transfer Method Method 111 = Normallzed Capacity Llethod &lethod TV = Ultimate Resistance Method

& , l e t h ~ d I1

0.~16- 1.29 I

0.76-1.17 1 0.86-1.25 I

0.70-1.19 :

'oeazng c a p a c i b of vibro-dr',ven piles only. Method W is :I:e U!timate Resis tance

&lethod which compu te s ul t imate bear -hg capacity of piles us ing Eq. (6.20) is.ith

r e c a n m e n d e d fac tors NG a n d P ' . The range of prediction rat ios a n d s t anda rd

dmiation. a. for biethods I . 11. I11 m d W 2re, respectively. 0 .76 to 1.17 (a = 0 . 1 1). 0 . 8 6 to

1.25 (cr= 0.12). 0 . 70 to 1.19 ( a= 0. i5) and 0.86 to 1.29 (a = 0.14) . I t is concluded that the

propcsed methods prct"le reasonably gocd estimation of b e e n g capacity of the model

pile.

In order to select the vibro-driver to a t ta in the necessary pile penetrat lon a n d

capacity, a s tep-by-step procedure based on the Power T ~ a n s f e r Method for estimation

of capaclly is r e c o n ~ x ~ n d e d as follows:

(a) Check the required c3pacity of the pile. 9, with attainable Limits usir:g either

the Ultimate Resistance Xfsthod (Eq. (6.20)) or Unit Tbad T r a ~ s f e r Method ( s ~ n t h e s i s of

:cad-movement re!ationshlp using Eqs. (6.7) a n d (6.8)). Eq. (6 .20) is shown aga in a s

rollows,

(b) Selec: a target value of v at fu!l penetration. v = 0.1 In / sec represents P P

refusal.

(c) Compute the required power at the plle head . Ph, a: full penet,-aUon from Eq. a

(dl Determine ah from the selected value of v from Eq. (6.141 a s P

(el FL~ally. esllrnate Pi , the vibrator power, from ah and Ph, using E q (5.6). ;El:

select the driver based on the conditions that the bias we!ght is 0 . 0 5 to 0 .10 Q and the

amplitude of unbalanced force is 0 .1 to 0.3 Q.

There is a f ~ n d a ~ e n t a . 1 ddrercnce be:ween the drivwg m e c h a n i s m ccl impact-

d r l ~ ~ e n piles and vibro-dri\,en plles Pile drib-ing by a n lmpact hammer Is usua:ly

regarded a s a p r ~ b l e m of st;ess wave propa2a:ion along a n e!astic rod. One dimensional

wave equation arialjrsis h a s been widely used to model impact-driven piles. On the

other hand, pile drivinz \!sing a \qbratory d n r e r is observed to more closely resemble

s teady state vibration of a rigid red. Atternpcs have also been made to apply wave

equation analysis to \ibro-driven piles (8. 27) . Table 7.1 summaries the proposed wave

equztion and ~ [ h e i soluti=iris found :n the literature. However, none of these solutions

incorpora tes directly the relevant soil fac tors , s o t h a t a more ratlonal and

fundamentally correct model for vtbl-o-driven piles is warranted to predlct !he observed

behavior .

mode!ing of \-~bro-driven piles described In this chapter is developed with

the assumption that the relevant mechanlcs hvoives a one dimensional steady state

vibration of a rigid rod. The success of the proposed model relies heavily on the

modeling of the vibro-driver and t h e pile-sofl interacilon. A vibro-drlving model

which incorporates the vlbro-driver, sol1 behavior and radiation damping through the

soil around the pile is developed. Fksponses predicted by the proposed vibro-driving

model are then compared with the measured responses in this study. A Wave equation

analysis is also performed to compa-e the predicted with the measured responses.

Table 7.1. Surrm,zry of Prcpcsed Theoretical Solutions Miter R=cger and Littlejohn !36)1

' ~ d d l t l o n to Rodger and Littlejohn's table : Satter (381, Fbdger and Littlejohn (361, Chua et al. (8) and Middendrop et al. (27)

-. Penetration by modllicat!on

of soil properties Penetrat ion k s u i n i n g a non-rigid

pile

Wave equation

Bar!- ( 1 1 c3Z i Parkin (1961) Chahraman i

( 19661 Griggs (i966)

Hill (1'367) Se rnha rd

(1967) Rockefeiler

(1968) Schxnid (1970)

Chua et.al. 11'357)' M!ddendrop e t . d .

(1 988) A

Penetration with no mcdLflcation of sofl properties

Empirical so!utian

Sc.i;nid and Hill

(1966, 1967) Bernhard

( 1963) Kondner and

Edwards ( 196G)

N - S h a w a f 1 1970)

Pheno- meno- logical

so lu t ion

Barkan (1957)

TNU (1965) Sa t t e r 11987)'

Semi empirical solut ion

Podol'nyy ( 19%)

Senator ( 1 967) Yang (1967)

S e n i - empirical solut ion

Snekhter (1955)

Barkan (1 962)

Schmid 11970)

Rodger and Littlejohn

(1980)'

Pheno- meno- logical

so lu t ion

Xeimark (1953)

B lekhman ( 1953)

Koushov and Shllalc\tin

[ 1954) B a r k a n (1962)

Savirlov and i u s k t n (1960)

Modeling the behavior of a vibro-driven pile h a s been basically based on two

approaches; (a) \ribration of a defoxmable rod and Ib) vibratlon of a rigid rod. The

solution to the vibrating deformable rod h a s been proposed (45, 31). and the governing

equaticn of motion. L~lovm as the wave equation. 1s

where w = long!tudina: displacement.

E = modulus of elasCci9 of the rod.

p = density of the rod.

z = dlrectlon of longitudinal axis, and

R = dymarnlc sou resistance.

A finite-denerenee method h a s been deireloped by Smith (41) to soive Eq. (7.1) by

discret9ing the pile into segments cmnected by internal springs and representing the

soil by external springs and dashpots . The soil resistance during pile driving is

described by the pile veloci& V and statid sou resistance RST a s

R=RsT( 1 +JV. (7 .2 )

where J = the darnping panmeter . and for practical purposes, it is assumed +hat 1

J (a t the shaft) = 3 J ((at the tce). (7.24

An elasto-plastic model is used to relate the stat!c soil resls tance with the

ultimate static soil resistance, Ru. d e h e d a s

FQ=kQ. .A (7.3)

where Q = delormation. called quake. corresponding to ultimate resistance, and

k = spring constant.

Values of Q and J ( a t the toe) for sand have been recommended a s 0.1 inch ai:S

0.15 sec/ft respectively. '1Vith RTJ. Q. J c e ~ e m e d , a simple computer p r o g r m (5) :s

available to solve for displacement that uses a numerical solution of Eq. (7.1).

In the case o: rigid-rod vibration. i?oger and Littlejohn (36) have proposed t ~ v c

types of vibratory drivL7g motion depending on the density of soil and amplitude of

acceleration. For soils with density less than critical density. fast vibratory d f i i ? ~ g

motion occurs when the peak acceleration of vibration exceeds a threshold value.

Penetrative motion in fast d r i v i ~ g is large enough s u c h that reversal of pile motion

does not occur and such that the relatively small vibratory motion can be seperated out

a s

and the penetntfve rnouon can he represen:?\! a s

where M = m a s s of vibrator and plle,

W = bias weight,

x = vibrational dlsplacement.

y = penetratjve displacement.

R p= soil resfstance to penetration, and

F = dynamic force amplitude.

For soil with density greater t han cri t icd density. slow driving motion occurs

as acceleration of 'v ibra t i~n is greater than a threshold ~ a l u e . Slnce the drlvtng motion 4

is relatively slow, reversal of motion will x c u r and thus the equation of motion is

written a s

where @= phase due rencc b e m e e n force and dtsplacement.

hlodeltng of dynanllc soil resistance plays a n importanr ro!r in the prediction of

the behavior of vibro-driven piles. T h e phenomenon of ~i l t r -soi l interactiori is co~np1e.u

dur ing ei ther impact o r Mbratory driving. .Azz e!z?sto-;>!astic r n ~ d e i with a d a r r i p i ~ g

factor (J) to account for dynarnic effect. a s shomq in Eq. (7.2) . is comn~only used for so2

behab9or in impact loading. The soil resistance during \?bratory ioading, hoxvever. is

believed to be reduced a s shea r s t rength reduction or d>m3~11c moblliiy occurs. Rcdger

and Littlejohn (36) have identified three distinct physical s ta tes of shea r s t rength Sor

soil a lcng the pile shaft in t e rms of l ibrat ional acceleration: ( a ) when accelerat io~i is

less t h a n 0 .6 g , shear s t renght h a s not Seen found lo decrease by inore than 501s. (b) as

acceleration ! s hetween 0.7 to 1.5 g. decrease of shea r s t rength Is governed by the

exponential func!)on of acceleration of vibration. a n d (c) shea r st^-ength i.eduction

rcaches a maximum a s acceleration arnplltcde reaches 1.5 g. The acceleration range of

2 to 13 g measured In this s tudy is well above the required accelerallon of 1.5 g to reach

the max imum s h e a r s t r eng th reduc t ion . Preobrajhenskaja (33) confi lmed t he

e .qonent ial function relatlng to the degree of reduction in side resistance: by proposing

where q= mtlo of amplitude of vibrational acceleration to that of gravity,

%= constan!.

% = dynamic side reslstance.

R&i = r m u m d y n a i c side rrsistancc (constazt men a s q increases). and

.-. RST = static side reslstance.

Schmid (39) Ln his laboratory model s tudy d!vlded the dyriamtc forre measured

a t the pUe toe into three possiSle dcmains: (a) the Sinusoldal Resistance Domain -

where the c l jm rn l c di-ivtr~g f c r c ~ is less than the maximum elastic resistance of the soil.

allowing no plast!c rnot!on and varying a s a sinusoidal function in phase with the soil

re ,s;s!acce, - . (b) the Impact Domain - the dynam:c force is no longer sinusoidal but

approaches short periods of .fi,pact followed by perfods of separatlor, of the pl!e from

tke sou. and (c) the Instablli~y Clomain - a phase dflerence occurs between the polnt

resistance and the dqnanllc force.

So far, hou-ever. there h a s been no any effort to relate the soil resistance In

terms of basic soil properties, such a s Fn-situ s tress , relative density and gram size of

soil. This h a s greatly curtailed the application ~i some of the models developed from

earlier studies. Interaction between the vibro-drlver and the pile-soil system are also

not we!l understood or directly modeled.

7 2 PROPOSED \,T3KO-DDLX'.TiSG MODEL -

A one-dimensional vibro-driving model is proposed a s shown Li Fig. 7.1, which

includes the driving force imparted a t the pLle head, Fh . the soil resistance at the pze

shaft. Fs, and at the toe. Ft. The radiation damping through the surroundLng soil are

represented with vlscous damping factors Cs and Ct at the pile shaft and toe.

respectively. As a result, the equation of motion ca be written a s

where rn? = mass cf pue,

.A

w = penetration dlspiacement of pile.

The second order ordinary dLfferential equation (Eq. (7.8)) will be solved

numericaily. 2s all the [actors (my, Cs, Ct, Fs, Ft and Fh) an quantified and discussed.

r B ~ a s Mass 1 Isolation Spring

C o nt r: t in

Pile-Vibrator Connection

Bias Mass m Vibro- Driver

es=3 Pile-Vibrator - Connect ion ~ / 7 % . , m 5 q

Rigid 1 I Pile I I n. Shaft Radiation

u - Toe Radiation r - ' &"

Toe Soil +! ,- x Damping, C,

Actual Model

hlode!ing of ?'ibro-=fiver aiicl D?v:nc Force

The driving force trmsmit:ed to the pile head, Fh . will he discussed in detail.

Vlbro-drivers operzite w ~ t h two counterrotating masses such that the horizolltal forces

cancel each other wh:le the vertical forces add. Static b ias -&eight is usually added to

the driver with a sprtrd system L?-between to produce additional downward force. The

time-dependent theoretical ~ lb ra t iona l force imparted by the driver (see AppendLx X for

derivauon) is t hus expressed a s

lvhere Z is the free amplitude of dhnamlc motion of the driver that can be urritten a s

r'h (t) = time-dependent force transrrdtted to the pile head.

W = Elas weight,

m = unbalanced rotating masses.

e = eccentricity of rotating masses.

o = angular velocity (rad/secl,

M = weight of the vibrator.

= natural frequency of bias mass and spring system = ( k / M ) 0.5, and

k = isolation spring constant.

Assuming 20 Hz frequency of vibration, k = 366 1bs/in and driver weight of 0.83

h p , the natural frequency of the \lbro-driver system is found to be 2337 rad/sec and Eq.

(7.10) yields 2 = 0.12 Inch. Wlth JV = 2.0 kips, driver weight of 0.83 kips and eccentric

moment (me&) of 0 .1 Kp-Lnch. the theoretical Fh !max) = 8.4 kips (Eq. (7.9)). These

parameters were common to most of the laboratory tests. Hov..ever, it Ls observed [ h a t

the measured maximum force at tke pi:e head (App~ndiu E) varied frorn test to test. I t is

bel!eved tha t there a re several reasons ior this variation : (a ) The ampli tudes of

dparn!c motion (2) cf the driver were dilferent frorn the theoretical value due to the

pflc-soil interaction (resistance to driving) under various soil conditions. a n d the

flexibtiity of the ~ F l e connector. (b) The bias welght may be vibrating during dri~ving

due to the imperfection of the bias mass-spring-vibrator system. It appears , therefore.

the contribution of bias weight and dynarntc force transmitted to thc pile head h a s to be

modaied. Hence. transmission ratios Tg and Tb are lntroduced tnto Eq. (7.9) to )ir!d

where Tg and Tg are found to be functions of effective horizontai insitu s tress (10 psi 5

0.5 < 20 psi), grain s k e of wFl (0.2 mm < d l 0 5 1.2 mmj and reIaUve density of soil (0.65 2

Dr i 0.90). and are defined a s

Tg = ( - 1 . 6 2 . r 0 . 4 d h + 9 . 6 d 1 0 ] (4- -0.651 - 7.0Dr -0.m). and (7.12)

TD = ( - 0 . 0 3 1 + 0 . 1 7 d h + 2 . 6 2 d l 0 ) ( D ~ -0.65)-2.7214- -0.90). (7.13)

I t is r,oted in Eqs. (7.12) and (7.13) that Tg and TD are lndependent of in-situ

s t ress and effective grain size at 65% relative density. Figs. 7.2 to 7.4 depict the

measured forces and the predcted forces by Eq. (7.11) for Tests 5, 7, 9. 1 l a j l 3 a . 14 and

1 7 , respectively and the agreement Is reasorable.

Radiat Ion Damolng

There are two posstble energy dissipating mechanisms during pFle driving; SOU

damping (hysteresis) and radlatlon darnpmg. In order to describeJhc sol1 reaction

which resul t s from soil inertia and the out-of-phase, damping part of the reactlon

gexerated by e n e r a dissipation through elastic waves, t he soil resistance at the pile

shaft u n d e r steady state vertical vibration was derived ustng elasto-dynamic t h e o q

TEST 5 PEN. 75" PlLf +!IUD F O R C E ' d 3 . T I M E

l o 7 i - Measured - - - Predicted

TEST 7 PEN. 71" P I S HEAD FORCE VS. TIME

10 r 1

- Measured - - - Predicted

~ l g . 7.2. :,feas& and Fllc Head Forccs: Tests 5 and 7

TEST 9 PEN. 53"

- M e z s u r e d - - - Predicted

TEST 1 1 o/13a PEN. 72" PILE HEAD F'BRCC VS. TIME

l a --r------- P - - - P r e d i c t e d

- 1 t 1 I I

0 200 40 0

TIME (mraa)

3 2 . 7.3. Mc.as*~md arid PrcdlcttO Pile Head Fcrccs: Tcsts 9 a d 1 la! 13a

TEST 14- PEN. 72" PIE HCACl YORCJ: VS. T I W E

2 0 1

--

l a i - Measured - -- Predic-d i

- 4 t I I I I 1 o aoo 4-00

TIME ( m e e e )

TEST 77 PEN. 72" F l u WEAD FQWCK '43. TIME

SO -- --i I 1 - ~Yeasu red - - -n P r e d i c t e d

F!g. 7.4. hteasurtd ar.d F?~dicrcb Pile Scad Forces; Tests 14 m.d 17

developed by Novak c.t 21. (29). 'me sol1 resistance a t the pile s h d ? may be represer,:r_d

where Qs = shaft resistance per lurdt length of pfle,

K, = soil spr'ng stltlness per unit length of pile.

Cs = radiation damplng coelficient per unit length of pile.

w = pile disp!acement.

t = time. and

Ks and Cs are defined a s

&'Swl Cs, and

%v2 Cs To Cs = a. Vs '

where Cs = soil shear modulus.

a. = the dlrnensiorJess frequency ratio = wro/Vs.

o = excitation frequency.

V, = shear wave velocity In the soil,

ro = radius of pile, and

SW1 and h2 = functions of a. (derived by Novak et al. (29)).

The contribution of resistance from sou inertfa during vlbro-drlmg. similar to

the term Ksw In Eq. (7.14). will be represented by a proposed soi: model discussed later

In this chapter. The radlatlon damplng, Cs , is used to desczbed t h e energy loss through

radiation of elastlc waves into the surrounding soil during vibratory pffe driving.

A smpiicatfon can be made to replace the frequency dependent ratio SLr2 / a.

(25. 33). and Eq. (7.16) can be rewritten as

where ps = PASS density of the sou = C ~ / V , ~ .

The radiation da rnphg at the tor is appro.dmated from acalysis of vertical

kdbration of a ggld disc on the surface of an elastic half-space (24). The value of t h e

darnplng coefficient. Ct . is given a s

uphere vs= Poisson's mtio of the sou.

Eqs. (7.17) and (7 .18) have b e ~ n used hy Randolph et al. (34) and Lee et al. (23) in

analysis of impact-driven piles a n d have compared results favorably with fie!d

measurements .

In order to f h r ! the radiation damplng coefficient. Cs and Ct , the PoFsson's ra:io

and shear rnodulus of soil must be dr te rnf r~ed. Polsson's ratio can be obtalned from !k:e

drained triaxial compression test u s b g the following relationship.

where d I AV/V /dc l is t h t initial slope of the relat!onshlp of volumetric straixi vs. a..al

strain in a triaxial test.

Shear modulus of soil. C s . can also be estimated from the triaxlal compression

u,here "3 b tkiz mitial tangent r n s d u i u s of the so:i.

Table 7 .2 presents the summary of !t.e dainpirlg coefficierlt found for this s t u d y

acd al-so the sou parameters used !P Eqs. (7 17) acd (7.18).

Sot1 > i c ) ~ i ~ 1

in order to better represent the pile-soil load transler characteristics during

vibratory pile driving, a panlinear s trzss-deformation relat ionship capable of

modeling maLena1 damping (hystersis) is uzr ranted . The soil model is dev~ loped by

rnodiiying the stat!c u n i t load transfer mode! by (a) multiplying the static unit load

transfer model (Chapter 6) by a degradation iaclor. 15) accounting fer thz negative s k n

f r ic~ion generated on the upstroke oi the pils, and ic) cocsidering t he reloading and

unloading behaviors separate!^. The degradation factor is derived a s a ratio of the

maximum value of the dynamic unit !oad transfer to the maximum value of the static

unit load transfer, T h e definition of degradation fzrtor 1s not well Jus t i f ed for the toe

load transfer relationship because no mau?mum value Is obseived. However, It is

shown later tha t t h t use of the degradatiorl {actor nonetheless provides a reasonably

good soil model for this s t u d y . It sh3uld be noted that the measured d j m i c unlt load

transfer relat io~lships Fn thfs s tudy (Cliapter 5) h c l u d e s the effects of hysteresis and

radiation danlpizg. However, the proposed soil model is developed by modFTyFng the

maximum value of static unit load transfer to the m-um value of dynamlc unit ioad

transfer at which out-of-phase resistance is zero ( Ins tantaneous pile penetration

velocity is zero). Thus . the proposed sou model is intended to represent the soil

stiffness and hysteresis only.

Based on the best performance trl predlctlng the static unit load transfer curves.

the modlfied Rarnberg-Osg~od model was selected to r e p r e s e ~ t ~ t h e dynamfc soil

behavior. The degradation factor and the m a d m u m negative sk ln friction were Sound

to be functions o!'effectivt horimntcl ln-situ stress (10 psi 5 a'h 6 20 psi), g r a b size (0.2

Table 7. 2. Summary of IiaCiation Damping Ccefficients

* Relative Density ( O h ) / EEecttve HorizontdCharnber Pressur ,~ (psi) / C r L ? Size (rrm)

Lnlt !Ve:ght of Sofl

( pcfl .b

Poisson s Rat io

Condit ions "

cs

(lb s/ln2)

Shea r ?Aodulus

(ps i )

Test So. ct

ilb s /~n i

nvrl 5 d 10 1 1 . 2 m) and re1a;ive d e ~ s ! t y of soil (0.65 5 Dr 5 0.90). The reloacil~g path oi

the proposed i-w relathns5ip. a s shown ln F!g. 7.5a. is e>rpressed a s

fa = ( Ef

E l w d m - + Ep- w ) Fi - fn . ( l + I - I 1

'0

where f, = maximurn negative skin friction

= -3.35 + 0.22 d h - 0.93 d l ~ + 4.0 I&-.

Ff = sMn degradation factor

= 4 . 5 1 - 0.015 d h - 0 .15d lo+ 1.72 4..

Ef , Epf . d, fo u e the Ramberg-Osgood panmete;s de f i ed Ln Eq. (6.71, a d

w = the local displacement = w? - wc + wt , where wp is the present displacement.

wc :S the net dlsg!acenent at !he last reversal. and wt is the local displacement

correspor,dLn.g to the s tress level at the previous reversal. The skin degradation factor.

Ff. ts the ratio oi the maximum ua!ues of the djna!nic and static unit skin fnctlon.

Using rhe least squares method and assuming a !!near reIationship between test

variables. Ff Is related to a'h. d l 0 and Dr.

There are two types 01 displacements In the vibratory driving motion. namely.

t he vibrationai d isp lacement a n d t h e penet ra t ion d isp lacement . The local

displacement (w) is essentially the vibrational displacement while the present

d1spiacemer.t (wp) is the penetration displacement. The local displacement c a n be

found at any part!cl-llar s t r e s s level by the reverse relatlonshlp of the mcdlfied

Ramberg-Osgood model. SLnct the modLTled Ramberg-Osgood model cannot be

expressed tn reverse form analytically, an iterative procedure, called Newton-Fkphson

m e t h d (7) is used :o rind the local displacement at any stress level. The procedure is a s .A

follows,

\rJt w c ";YP W

(a3 Reloading Path

(W r: W p - WC + S Y t )

(b) Unloading Path A

( W = W , - W,)

Flg. 7.5. Reloading and Urioadlng Paths of .%fl ?dodc!

where fRI, (w) is :he Si r s t dzriv;i:?:: oL fRLin Eq. (7 .2 1 ) .

2 s the dnerence between the c.uccessi\.r dispiacernent (wi+l and wij converges :o

withir, a specified tolerance (0 9~3301 inch :ri :!;is study]. wi-1 Is round tn be t h e local

dlsplacrment correspondiiig to a specLlle.3 s tress . The procedure requires cniy a re:v

iterations for corn.ergenc?

The udoading path of t h e proposed f-rv rela:lonzhip, a s sho rm in Fig. 7.5b, is

written a s

where fc is the unit sk in res!stance at t h e previous reversal (end of reloading pa!:^) of

the proposed S-w relationship.

The modelhg of the proposed unlt toe resistance, q-w, relationship required a

more involved modllicatian. I t was observed t h a t the reloading and anloadtng paths or

t h e expertnlen!al unit toe resis tance curves a re convex for most tes t s . This

p h e n o m e ~ o n was modeled by rr,u!tlplying the modified Ramberg-Osgood model by an

exponential function. It is shown later that this function prov1d:s reasonably goo(.!

prediction for all cases. I t is :unh~rmore obscrved that in some cases in blasting sand

there Is no resistance at the initial 0.04 inch displacement o n the reloading path, which

I s d u e to the fact that the llfting of the pile toe rrom the underlying sofl and /o r seatlqg

problem d u e to locsenIn4, of soil on the highest point of the upstroke. This "slack" h a s

to be incorporated fnlo the model. However. there Is no measGrable negative toe

resfstancc (tension or suc!lonJ observed tn any of the proposed q-w curves. With all the

above considerations, the reload!ng path of the proposed q -w re!a:ionship can be

expressed a s

where q = 9 , when w 5 0.04 Lnch and d l 0 = 1.2 mm, Eq , qo and nq are Ramberg- RL

Osgood parameters, uVhich are defhed in Eq. (6.8). K is a constant and by trial and error

11 is chosen to be 10.0 for this study and Fq is toe degradation {actor defined a s

Fq = 0.19 + 0.064 ~ ' h + 0.30 d l 9 - 0.36 Dr

The unloading path 0: the proposed q-u7 relationship Is shown a s

where qc is the unit toe resistance at the previous reversal (end of reloading path1 of the

proposed q-w relationshfp.

Flgs. 7.6 to 7.1 1 show the experimental and proposed f-w and q-w curves for

Tests 5. 7, 9, 1 l a / 13a. 14 and 17 respect*ely. Trends are clearly established in t e r n s of

the test variables such a s in-situ stress. grain size and relative density of SOU. :t Is

agafn emphasized that the proposed soil model is intended to represent the nonlhear

behavior and hysteresis of soil during vibratory pile driving. Thus. Flgs. 7.6 to 7.1 1

compare only the max!mum value of dynamic unit load transfer at which out-of-phase

resistance is zem.

TEST 5 ,?EN. 75" D Y N A U l C f - w C U R V E

1 0 .

Q 4 i - Measured I

I - - - P r o p o s e d S o i 1 !Yodel

- - - P r o p o s e d S o i 1 y o d e l

0.9

- 7 7 ; = S T ! 75" L , .

D Y N A M I C q - w C U R V E 1 . 4

Fig. 7.6. Proposed SQU Model and Expcrmcntal W a m l c UNt Load Transfcr Curves: Test 5

1.3 - 1.2 - - Measured

i s reachu-$ the nead of the nGe before the rr?&xIrmrn cofnpress:on I b r c t due to Lipact

would have been achieved had the pfle been ccnslderably longer. This behavior

observed in the mode! pile is ngt consistent with the behavior of relatively longer plies

in the fle!d bclt is generally carisistent m o n g all of the tests conducted in this study.

wh:ch suggests that conclusions drawn regarding the relattve effects of Lrnpact drivlng

versus restiiklr-g are vdld . The conslstent time cf initial departure of the two traces

from one anoikzr also sugzests that neither impact drivLng nor vibi-atory driking had

prod::ced drzstlczily dsereri t values of statlc shaft resistance.

2 . h relaUvely strong s t rond pos!tive peak occurs Ln the force trace and Ln the

velocity-impedance trace: at the pile head 3.0 to 4.9 milliseconds after the tnitial peaks

produced by the impact of the r m . These times correlate closely to the times that are

required for a compression (p) wave to travel down the pfle, through the sofl below the

pile toe and be reflected back to thc toe and u p thc pfle, Sased o n the sol1 modull

measured in the resopant column test (Chapter 41. For the pfles installed by vibration.

the srcond peak occurs at a m e lapse that Is about double that which is computed using

rhe s5ear rnodull from the resonant column test at a shear s t r a h magnitude of 1ge2%

lor the sl tuatlons &I whlch the relative density was 65% and the efiective lateral

conflrLig pressure was 10 psi (Figs. (2.2 and C.6). Otherwise the !apses for the vlbro-

2 driven plles conputed using shear modull at a shear str- magnitude of 10' ?6 are

within 5 to 10 percent of those that are obtained from the t h e histories. Ti-~s behavior

sugges ts either a possible !oosenLng effect, generation of very high mean sofl s t r a h s , or

installation-induced reduction in effectlvc soil s t r e s s below the pile toe for the

conditions of 65% rela?lve aens!ty and 10 psi effectiv:: lateral pressure. but not for other

test conditions. For t t i e impacidriven pflc tests. the observed t h e k p s e was always

20% to 4046 greater thal the computed value, which suggests that one of the p h e n o m e r ~

speculated above cccurred for all Lmpact-dr-iven piles, regardless of soil density or

corS~ntng pressure.

suite of blows that was applled to the pFle can be obtaixed by comparing the blow

numbers on the respective flgures with the drivina records (lmpact-driven rides) or

number of blows for each inch of restrike driving (vibro-dris7en-and-restruck plles)

shown in Chapter 4.

Wave propagation theory indicates that ln a n infinitely 1or.g plle that !s not

supported by sac. +he force time history shculd correspond to the vclcxity t!me history

provided that the velocity is multiplied by the mechanical impedance of the pUe. which

is characterized t;j- the term AE/c, where A = the cross-sectional area of the pile

material (2.251 square inches for the test pile used in this study). E = the Young's

6 modulus of elast!c!ty of the pile (29 X 10 psl (steel) for the test pfle used in this study).

and c = the compression wave velocity of the material out of whlch the pfle Is made

( 2 0 1 . 0 lnches per second for the test pUe). Ln a pile of flrilte length interacting with

the scpporting soil. the wave f o ~ s & I l l deviate from one another a: some point in the

Urne history when D-waves reflected from the toe cf the pUe or p-waves produced by

transfer of energy lnto the soil along the shaft through shearlng at the s h d i - s o u

interface return to the head of the pile.

In Flgs. C . l - C. 11 the time scale is dLre:t, in mflllseconds; however. the

magnitude cf a quzntdty shown a s 2L/c is also shown o n Lhe graphs for the pi!e-head

time nistorfes. In this expression L Is the length of the pile (&stance from the pile-head

force and accelcratlon transducers to the toe of the pile; Chapter 3). Therefore. 2L/c

rcpresents the required for a wave to trzvel down to the toe of the plle and kc

reflected back to the transducers at the head. The value of 2L/c for the model test pile

was approximately 0.80 millisecond.

4

Several observations can be made from Fgs. C. 1 - C. 1 1:

1. The force and velocity-lmpedmce traces at the pUe head depart from each

other at a time of 2L/c from the time of initial rise. with the fcrce generally dropplng ol'f

more rapidly than the velocity-impedance, Lndlcatlng that the returning tension wave

TEST 22 PEr\l. 79" IUFACT artlviwa I SLDUS 1 a ? - i 7 a

p i l e Hea? Velocity T i r e s P l l e i-ce

- - - - .?!esurec! F i l e Head Force

r : ~ ~ ~ ~ ~ ~ l ~ ~ ~ ~ ' ~ ~ ~ ' ~ i

0 1 4 3 63 10 92 I 4 1 1 1 10

YlkdC ( m e s a )

--- P i l e T x Veloc i ty ?Lx?s P i l e Lq3k..?~?ce

F!g. C. 1 1. Measured Head and Tcx Force and Velocity-Impedance Tlmc Histories: Impact-Drlvlng a t Full ?tnemtlon: Test 22

TEST 21 PEN. 79" I Y P A C T O W l W N O I OLOW3 5 1 8 - 3 2 1

-1 Plle H P A V e i x l t j ' YLXS Pl le LqAir ,ce

- - - - Y e a s u r d Piis He& Force

n M f (mra-aa)

TEST 24 PEN. -79" IMPACT ORlVlNQl 1 BLOWS $19-32hB

38 ?---- ________7

"1e Re Velcclty T ~ Y S P i l e I,rpda-".ze

- - - - ;-wed P i l e Tze Force

n M K (ma-)

f ip. C, 10. Measured Head and Tee Force and Vela-ity-Impedance TLne Histories: Impact-Drivtng at Full Pcnetnt ion; Test 2 1

T E S T 20 PEN. 79" IB lF 'ACl D K M H C I DLCWS 1 9 8 - 1 U

3s ?- - I

-- P i l e Head Velocity T i r e s P i l e L w a n c e

- - - - lYElasqxed P i l e Aead Fcrce

0 4 6) 10 12 14 1a (€3 t o

TlMt ( m m a o )

TEST 20 FEN. 79"

- P i l e Toe Velocity T i r e s

---- ? i s * x d P i l e 'ke F3rce

- 4 - 0

T l l 1 1 1 ' 2 4 s D 10 12 la 1 6 10 10

R Y t (msaa)

Fig. C.9. hzeasured Head and Toe Force and Velocity-Impedance Tlme Histories; Impact-Drivilng at Ful! Penetration; Test 20

TEST 19 FEN. 7'9"

-- F i l e 2x Velacity TLXS

? ~ l e E W , - . c e

~ l g . C.8. !deasured Head and Toe Force and Velocity-Impedance TLme HLsforles: Impact-Driving at Full Penetration: Test 19

TEST 17 P E N . 76"

TEST 17 PEN. 76"

Flg. C.7 . !v{e=tsured Head and Toe Forcc m d Vtlwitv-im-,ec'ance Time HLsrories: Res?fike at Fid11 Prne:.zitl;n: Tzs! 17

TEST 1 6 PEN. 79" R K S T R I K K I BUS&% 1 - 3

40 7 1

- - - - Y ~ z - L - ~ F i l s :-:3& 'crce

I

- 3 , , , , . , , , , a

o 2 A rb da t o 1 2 1 4 1 6 ca 20

Y l M K ( m o e o )

TEST 1 6 PEN. 79" R t S m r K L I SLOWS 3-l

3 , I

F i l e ?EX? Velocity T i ~ s Pile i-e

~ g . c.6. Measured Hmd and Toe Form and Velocity-Impedance Tlme Histories; Restrike a: Full Pmctration: Test 16

TEST 15 PEN. 77" RL3TRIKL: 1 U f - D W 4-0

stl ,

I

25{ 1 ; \ - - - - ~ e s z e d P i l e Lea2 Farce

TEST 1 5 FEN. 77" RESTRIKE I B L O W 3 4-a

a , 1

- - - - ?&as=& Pile %e F3rce

Fig. C.5. Measured Xead and Toe Force znd Vekity-Impedance Time Elstode-; Restrike at Full Penetraticn: Test 15

TEST 9 PEN. 57"

P i l e I r pedmce i h ?lie Head Veloc~zy T z e s I

- - - - k 'et~~urr j . Pile Eel2 Fcrce I

TEST 9 PEN. 57" R C S Y H I K E I BLOWS e-t a

- - - - .%-~rec! Pile 2~ Force

FQ. C.4. Measured Head and TGC Force a ~ ~ d Velocity-Impedance Time Histories: Rest* at Full Per,etraUon: Test 9

TEST F1 PEN. 77" R T S I T X I K E t B L O W S 8-1 0

1

TEST 8 PEN. 77" Ba%STRIKt t B L B W 6 - 1 0

31 -7

P i l e Tee Veloc i ty T i r e s Tile LT&E-L,P

- - - - Yeasure? Pile ;5e F3r:e

FQ. c.3. &feasurcd Head and Toe Force and Velocity-Impedance Tme Histories: Rest-ikc at Full Ptnetration: Test 8

TEST 7 PEK. 77" R E S T R I K E : BLOW^ 2-4

3 5

Pile Ee& L-elx lzy TL-s I

J C I

Pile L-&?ce , 2 5 - - - - I

-3:ie K 3 2 d C3rce I

2 0 I I \ I - n i

I

! -- i \ ! , ! ;

\

0 \

, I ?- tj' ' - 1 0 ,

0 1 a 1 2 1 6 2 0

TIME ( m s r c )

TEST 7 PEP<. 77" R E S T R I K E : B L O W S 2-4

3s ,

Flg. C.2. Measured Head a i d Toe Force and Veioclty-Impedance Tlme tiistories: Restrike at FuU Penetration: Test 7

R E S T R I K E : B L O W S 5-7

A 1

Fig. C. 1. Measurtld Hcad and Toe Force a d Velwiy-Impedance Tm.? Hktor ies : 2estrlke a t Full P e n e t ~ G o n : T e a 6

TL9AE HISTORES AT F L U E h m m T X O N F 3 R LWACT AW RESTRIKE TESTS

Time histories of pi!e-head and p!le toe-force superimposed on tinie his:orfes of

piie-head a n d pile-toe velocities for the average of several blows of the impact hammer

are shawl in Figs. C . 1 .- C. 1 1 . These figures represent all capacity tests that involved

only impact driving of the pile or that !nvol\.ed restriking the pile after the pile had

been driven to within one-half diameter of full penetration by vibration. The forces

t h a t a re s h o u n in these rigcres are those that were measured directly from the strain

gages at the head of the pile or the load cell a t the tm of the pup. The velocities were

obtained from integration of the average accelerometer signal from t h e pile-head

accelerometers a n d from the slngle high-g accelerometer al the toe of t he pile, as

described for the cornpuration of energy in Ckapter 5. (description of these instruments

and instrument calibration procedures are presented in Chapter 3) The ve1ocit.j traces

have been shifted to account (or the phase lag L? rhe averag!rrg circuit for the pile-head

accelerometers described in Chapter 3.

The purpose of dweioptng these records was to provide z b a s h for determining

whether vibrated-and-restruck piles (Figs. C. 1 - (2.7) exhibited dynarnlc charac!eris:!cs

sjgntncantly dilferent irom Impact-driven plles (Figs. C.8 - C.11) when being s t ruck

.with an impact harnriier. Because the application of the first blow, o r first several 4

blows in the derlser sand at high chamber pressure, produced very little permanent set.

only the final three !o ten blows were included in the averaged records. iW. exception to

this rule is Test 16, for which all res:rike blows Ithre:: in all) were averaged. The blows

for which !he average traces presented in this zppendtu are given relative to the en!ire

higher mtes of penetraaon of the pile in the medium-dense s a n d compared to those in

dense s a n d , where no ambient p o ~ pressure change was indicated during v ib ro -ch -~ng .

positive forct: corresponds to conprcss lon ln the plle: positive pressure correspcnds ro

pressure p a t e r than ariilospheric (i. e.. b "gage pressure").

It is observed that acc~lerat iori signals for BLS Sand are generall:.~ more r,clsy

than chose for the Sjii S d . ~ . ~ h ! c h n u y be due to more severe grair-to-graLq sslips by

the larger , X E ~ more u lgular sand gralns of the BLS S a n d . Total pressure signals are

noisy, and unreasonable in some cas r s . especially for BLS Sand. presumably because of

the fact that s a n d grains were large relative to t h e size of the sens ing face of the

t ransducer and perhaps falied to exen pressure everrly on the relatively sna l l sensor

faces. Xo electrical problems could be detected tha t would otherwise rxplain the notsy

traces.

In Tests 9. 14, and 17 (densest sand 1, a slightly negative toe force was observed

b a t remained essential& co~lstar i t over about one-forth to one-third of a cycle. which

was followed by a high peak ccrnpressive force in the rematnder of the cycle. This

behavior indicated that the toe w a s being llfted off t he sofl ( and /o r !oosen~ng of s and

d u e to local stress condltfon), and later t h r u s t back against the sofl to give very h!gh

peak toe forces. In the other tests. especially for sand a t the medlum-dense state , near-

sinusoidal toe force signals hlth lower ampli tudes t h a n those In the above tes t s were

recorded. wh!ch suggests a dae ren : mechanism of toe penetratlon. All velocity s i g ~ a l s

were generally stnuso1dal with excursions of apptaxtmately one foot per second about

the zero veioclty h e .

In den-- sand (relative density = 90%). the po r t water pressure on the pile shaft

nea r the pile toe &~Slted steady state sinusoidal behavior with mean values wry close

to.the gmstatLc pore water pressure Fn t?e chmber a t half and full penetration and with 4

m u m i o n s of from 0.5 to 2.0 psi about the mean. In the medium-dense sand . the pore

water prtssurr : was usually ?I1 the tnnslent s t a t e of increasing as the pile was

p c n e m t q (or dissipating d the vibrator was in Lie process of being s h u t down). This

phcnomcnon of port p r e s s u ~ @hudup agaFnst the pl!e wall may ocplaln thc rclatlvciy

TEST 17 ?Er\l. 74" T O T A L P R E S L I U H E VS. T I M E

37 . n I

I

- - - ; --ST ; 7 3EF1. / L i t

FORE W A T E R ~ r g E 3 3 f J R E V S . T I M E 3.2 7 I

i

Pig. B.Sd Totai and Pore U7ater FYcssurr Vs. T l m e at Bottom d Pllc Shaft: PcnetraUon=74 I n c n ~ : Test 17 (;iei~d)

TEST i 7 ?EN. 74" PILE T O E VEL V¶. T l W C

1

TEST 17 ?EN. 74'' Pllf TOE F O R C E VS. T I M E

1

.%. B.8c. P L ~ c - T ~ ~ Velcclty and Force Vs. Time: Penetratlor,=74 Inches; Test 17 \m~sall

TEST 17 [PEN. 74" P l U H-0 V C L '43. TIME

-- a - 7 - ; t S T i , r t b l . 74" BILE u U O F O R C E V3. T l u E

Fg. B.8b. Pile-Head Velwity ar?d Force Vs. Tlrne; Penttntlon=74 Inches; T=t 17 ( i idusal)

TEST 17 ?EN. 74" PlLf H E A D ACC. VS. T I M E

TEST 1 7 FErq. 7 4 1 1 PILE T O C A C C . VS. T I M E

I

nuf ( m a r a )

FQ. B.8a. Pflc-Head and Toe Acceleration Vs. Tlmc: Penetration=74 Inches: Test 17 (Refusal)

TEST 17 PEN. 72" T O T A L PIYEJXUf4I: V I . TIkdL

2 1 f 0 2 0 0 r o o

TIME j r n o o c )

TEST 17 FEN. 7'2" $OWE W A T E R PRES3UKX VS. TIME

3.2 I 1

1 . s -+- 1 1

280 1

3 . roo n 9 d C (merr)

Flg. 3.7d. Tctai and Port %'a:cr Prcssux Vs. TIme at Bottom o; Pile Shaft: Penetrat!cn=72 Inches: Test 17

TEST 77 P E N . 72'' p11-5 T O E VEL. V > TIME

I ' I

I : ,

1

2 0 0 4 3 0 0

TIME ( r n v e c )

- - - ; :ST 7 7 .FEN. 1'2''

PILE T O T F O R C E V S TIME 17 , -

I

¶ME (mar-)

~ l g . 3.7~. He-Tw Ve]&ty and Force Vs. Tlme: Penetratlon=72 hches: Test 17

TEST 17 ,FEN. 72" VILX HUO v r L v x T I M E

1.a -.

-- I t S T i 7 FEN. 72"

PILE H F A D F O R C E V S T I M E

Fg. B . 2 . Pllc-Ficad Velcxipy X-,d Form Vs. Tlmc; PenetraUon=72 Inches; Test 17

TEST 17 FEN. 72" PlUT H E A D ACC. V4. T l Y C

10 . - I

TEST 17 FEN, 72" r r u TDI: ACC. VJ. ~ Y C

a .

Fig. B,7a. Pfle-Hcad and Tce Acce!czUon Vs. Tme: Peneuation=72 Inches; Test 17

-- --7

; t S T : 6 F E N . , 2" T O T A L P R E J 5 U R E '43. T I M E

i I

1 I

!

2 0 i I I !

- 17

4 1 j W ' 5 1 LL 3

I * 1 ~n 13 4 ,A

! W - 1 2 4 ... n

I 1 1 -

7 - 6 - 3 -. 4 + 3

---- , r > , j 4- F E N . 72"

P O R E W'ATCF? P R E Z S U R C V S . T l u E

Fig. B.Sd. Total and Pore Water Wssure Vs. Tlme at Bottom cf We Shaf:; Penc+ration=72 Inches; TESL 1.1

TC I t S T 1 4 PEN. 72"

PILE YOlC VEL. '43 T I U I : 1

TEST 14 PEN. 72" r lu T O E F O R C E v s T I M E

13 ,

Fig. B.6c. Pile-Toe Velocity and Force Vs. Time; Pcnetration=72 Inches: Test 13

TEST 1 4 PEN. 72" PILX H-0 V C L V 3 TIME

TEST 1 4 PEN. 72" PILE HEAD FO R C E VS TIME

TEST 1 4 PEN. 72''

PILE TOE A C C . VS. T l k E 7 ,

Ng. B.6a. We-Head and Toe Acceleration Vs. Time: Pcnctration=72 Inches: Test : 4

TEST I la &: 1 3 3 PEN. 75" T O T A L P R L S J l J R L V3 . T I M E

10.3

I 5 . 5 :

0 200 A 0 0

T I M E ( m a r c )

TEST 1 1 o & 13a FEN. 75" PORE W A T E R PWCSSURL: VS. T I N E

'-= 7-

4 J I

0 100 a0

TlMC (moue)

Flg. B.5d. Total and ?on Water iJrcssure Vs. Tlme at Bottom of Pile Shaft; PtnctraUon=75 inches; Test 1 l a / 13a

TEST 1 la Sc 13c PEN. 75" PlLE TOE V E L V S T I M E

- 1 . 2 i I , o ZOO a00

T I M E ( r n n r a c )

TEST 1 1 a & 13a F E N . 75" PILE T O E F O R C E V S T IME

~ i g . 8 . 5 ~ . Pfle-Toe Velocity and Force Vs. T h e : PenetraUon=75 Incnes: Test 1 la/ 13a

T E S T ; ; a & 130 PEN. 75'' PILE H E A D V E L V J T I Y E

i

!

i 1 I

0 2 0 0 r o o

T I M E ( m a r c )

r-. 7 7 - 1 1

TEST i 1 o & 13c , ~ t N i , 3 P I L E H E A D F O R C E V S T I W E

I

F&. B.5b. We-Head Ve!oclty w,d Force \ is . TLne; ?cne:ntion=75 Inches: TG: : la/13a

...-.--- - - ! tZ. I 1 ; a & ?E.:\:, /zl'

PILr TOE A C C . Y S . T l U C A

Fg . B.5a. Pile-Head and Toe Acceleration VS. Time: PcnetraUon=75 Inches; Ttst ! la/13a

- TEST 9 PEN. 25''

TOTAL PRESSURE VK. T I M E 17 1-

" 1 V

I 7 '

I

o Z O O roo TlMK ( r n a a o )

TEST 9 PEN. 55" P O R E W A T E R PRESSURE '4%. T I M E

r- -- I I 1

Fig. B.4d. Total and Pan Water p m s u ; t Vs. Tlme at Bottom of Pile Shaft: Pcnetrat:or,=55 Inches: Tcst 9 Ifitfusal)

TEST 9 PEN. 55" PILE TOL VCL. V 3 . T I W E

0.5 7

TEST 9 PEN. 55" PILE TOE FORCE V9. TIME

1 1 [ I

Flg. B.4c. Pile-Toe Velocity and Force Vs. TL?c; Penetration=55 Inches: Test 9 (Refusal)

TEST 9 ?Ei\J. 55" PILE H L ~ D VZL v3. r ~ u e

0.9 7 I

-- - - t S i 9 r t N . 55'' PILE H U D F O R C E VS. TIME

~ g . p,.4b. Pfle-Head Veiccify m d Force VS. firr.e; Pcnetration=55 Inches: Tcst 9 ( R e i u d )

T E S T 9 F E N . 55'' rlu HEAD A C C . vs. T I M E -- _ _ _ _ - i

-7 ;tST 9 PEN. 55" PILE: T O E ACC. V"f. T I M E - ---

a I-----

- 4 -, I

0 2 0 0 400

TlLIt (msea)

Ftg. B.4a. Pile-Xead arld Toe Accclerauon Vs. ?me: Penerration=SS I ~ c n e s : Test 9 ( R e f u d )

-- i t S T 9 ?EN. 53" T O T A L P R E Z J U R E V S . T I M E

1 6 - I

TEST 9 PEN. 53" P O R E W A T E R P R E S S U R E V S . T I H E

2.7 I !

1.8 f I I I

6 2 00 -0

T l Y K ( m a a r )

Fig. B.3d. To td and p o x Water ~rtssure Vs. Tlmc at Bottom oi Pile Shaft; Penetration=% ?nchts: Test 9

TEST 9 ,?EN. 53" P I L L T O E V C L V 3 T I M E

---- - - 5 ,ZEr\!. 22" I E l l d

PILE T O E f O R C E V 3 T I M E

FQ. B.3c. Pile-Toc Veiocity and Force Vs. Tlmc: Penetratlon=53 Inches; Test 9

---- , E L , 9 ;>C,.<. 53" P I L E H E A D F O R C E V S T l U E

Ftg. B.3b. Flle-Hcad Velocity and Y o r e Vs. Time; Penetratlon=53 Inches; Test 9

-7 l t S T 9 PEN. 53" PILE H E A O A C C . V S . T I M E

8 7-

7 - - -

, t>, g ;=EX. 53" P I L E T O E A C C . VS. TIME

-(I I I I I 1

0 zoo r o o T l w r ( r n w r * )

Fig. B.3a. Pile-Head and Toe Acctlzration Vs. Tlm~: Pmetratlon=53 Inches; Test 9

TEST 7 PEN. 71" TOTAL P R L S J L I N S vn. nuc

0 2 00

TEST 7 F E N . 7 1 "

Fig. B.2d. Total and FOR Water F~essure Vs. Tliinc at Bottom of Plle Shalt: Penetiatlon=7 i Inches; Tes: 7

*-- s l y

TEST 7 FEN. 77" PILE T O E V r L V J . T I M E

' I 1

PILE T O E F O R C E V S . T I M E 4

a

-0.5 I i I o 2 00 r o o

T I M E (mnrs)

Fig. 8.2~. Pile-Toe Veiocity mad Force Vs. Time: Penetration-71 !riches; Test 7

- 4 , , TEST 7 PEN.

PILE H C A O V E L V S T I u C o.a ,

-- I t S T 7 P E N . 71"

F!g. B.25. Xe-Xead Velccliy and Fcrce VS. TJAne; Pene t ra~on=7 1 Inches; Test 7

--- I LLT 7 FEN. 71"

PILE T O E A C C . V 5 . T I M E 1

F!g B . 2 a Pile-Hrad and Toe Acceleration Vs. Tlmc: Pcnetratlon=71 Inches: Tesr 7

TEST 5 PEN. 75" T O T A L P R E 3 3 U R E V S . T I N E

n

8 v 7.8 1 I I

0 100 400

TIME ( m s e o )

TEST 5 FEN. 75" PORE WATER P W E S S U W Z V9. T IME

3.8

Fig. El. Id. Total and Pore Water p ~ s s u r c Vs. Tm.: at Bottom of Pllc Shaft: Penetration=75 Inchs ; Test 5

TEST 5 PEN. 75" P I L E H E A D FORCE VJ TIME -

I

F Q . 9. Ib. %e-licad '/eio :it). x ~ d Fo;cc V j . Tmx: ? e n ~ t ~ t i o n = 7 5 Inches: Test 5

TEST 5 PEN. 75" PILE HEAD ACC. VS. T I Y E

4 , 1

TEST 5 PEN. 75" PILE T O E ACC. V f . TIME

4 .

Fig. B. l a . Pile-Head and TM Acceleration Vs. Tlmc: Ptsnetratlcr,=75 !n&?es: Test 5

Tl3E TO^ AT FULL PILE PENETRA'EO?! FOR V I B R O - D W G TESTS

Xepsesen:ative graphs of half-second tLme h i s t c ~ e s of accelerzt!on, velocity,

force. gore and total pressure signals measured on the pile during vibro-dri\?nq a t

pene:rations into the chamber near full penetration (about eightern pile diameters) for

each "capacity" test. All signals presented are direct, uncorrected output from the

indicated ins t ruments , exce7t for the velocity s i g n a ! ~ . which were obtained by

numerically integrating the measured average acceleration signal at the pile head and

the single acceleration signal at the plle toe. The signals presented have been filtered

and/or nmplliied as described ir Chapter 3. For eac:h reccrd, except a s described below,

the pile was in mctlon (had not met reiusal!.

Tlme htstorles are arranged in Flgs. B. la - B.8d for Tests 5, 7 , 9, 1 l a /13a . 14 and

17 tn the following order: pile-head and pile-toe acceleration. plle-head velocity and

iorce, pile-toe v e i o c i ~ . and force, and total and pore -.vater pressure signals obtained

from the pressure t ra r~sducers al the bottom of the pile. For Tes:s 9 ar,d 17 data were

recorded when the pile was a t a s ta te of refusal (was not penetrating while under

vibratory load). and additional time histories are tncluded for those tes t s for that

condition. Time histories for the other tests can be found in the project report of th!s

study (301.

The sign conl~rtntior, for the signals is as f o l l ~ w s . Positive acceleration *

corresponds to the accelzratlon during the bottom half of the downstroke and so !s

actually dece!eration; positive velocity c o ~ e s p o n d s !o dawnward movement of the plle:

e, the eccentriciiy of +he ro ta tkg weights;

W, the weight of the blas mass;

k. the combined spring constant of 'he springs separating the bias

nlass from the vibrator m a s s ; and

f , the frequency of vibration

Units should be consistent among ail panmetc r s .

2. Compute O from Eq. M 11).

3. Compu:e an = !k/~i1!0.5.

4. Compute Zfrom Eq. h . 5 a ) .

5. Finally, compute the theoretical power. PI, from Eq. (A.10).

v(t) = Z o cos ol (A. 61

a(t) = - Z oL sin wt , (-4.7)

and. frorn Eq. (A-1). t h e time-dependent ~ lbra t lonal force exerted on the spring kz(t) is

2 2 . k z(t) = rneo2 sin tot - Xi a(() = (mew + MZw ) s ~ n wt (A.8)

If blas m a s s c d s t s above the spring, such that the natural frequency of the bias mass-

spring system is much !ower than the natural frequency of the primary mass-spring

system, an additior.al t t ne -hd rpenden t downward blas force W (equal to the we!ght of

rhe bias mass) !s alwa1.s exerted on the spnng, such !h3t the net force F(t) on the spring

is the s u m of h e statlc bias weght (assume weight does not accelerate) and the dynamic

force is

2 F(i) = \V i (rnco + hlZu2) sin or .

Substi:uUng Eqs. C4.6) and (A.9) trto Eq. (A. ;) yields

T 1

P = - [ ?il + (rneo2 I hlzco2) sin il,i ] Z o cos at dt [ T

2 2 = [ 4')V + 2 (meo + kIZw ) ] Z f, where (A. 10)

In practice. the followhg steps would be followed to compute the theoretical

power of a ebr2 tor .

1. Iletermine 4

& I , the mass of the vibrator (w-cludfrg b!as mass), which is equal to the

vibrator weight divided by t h e acceleration 0,' gravity:

m. the mmbined mass of the roca!in,d eccentr ' ,~ (cnbalanced) weights;

each have mass m / 2 and rotate with a n eccentricity e in opposite directicns wi th

angular veloclty w. The Sre?-body diagrams of the system are shown in Fig. A.2. 7%::

hor&ontal components of Corce always balance each other , s o that only the vertical

components need be considered. From Fig. A.2a the equation of motion for a n eccentric

m a s s undergoing I..amon!c excitation can be written as

In Eq. A.2 z is x'e13icaI displacement and a is vertical acceleration. From Fig. A.2b the

equation of motion lor (fie entire vibrator can be wdt ten a s

- 2 F - k z(:) = (3.1 - m) a([) . (A.3)

Conbinir,g Eqs. (A.2) 2nd W.3) ytelds

2 IM a(t) i- k z(t) = rn e w sin wt ,

The steady state response solution of Eq. (A.4) Is

z(t) = Z sin mt ,

where Z is the amplitude of dynamic motion of the drlver. which can be e-qressed a s

2 m e o z =

m which wn is the natural frequency of the primary mass and spring system. C K / ! V I ) ~ . ~

Thc velocity and accelerat!ori can then be expressed a s A

Fig. A. 1 . Single-Degree-of-Freedom System Model of Vibro-Dnver

2 ( 1 ) + o sin (wl)

i

Flg. A.2. Re-Body Dhgmn cf the System

APPENDIX A

COMPUTATION OF THEORETICAL POWER

It is desirable to develop a definition of blbrator power t5at is independent of the

impedance that is offered by the pile to which it is attached. In the following

development oi theoretical vibrator power only the dynamic and static forces acting

upon a freestanding vibrator and vertlcal displacements and velocities of the vibrator

are considered. Under such physical conditions the theoretical pourer is a s follows,

in which Pt = theoretical power.

T = period of vibration. equal to IjFrequency,

t = tlme,

FW = net force acting on the vibrator (functfon of time), and

\(U = vertical velocity of the vibrator (function of tlrne).

The net force produced by the vibro-driver. F(t1, and the Llbrational vclocfty,

v(t), may be derived from a simplified single -degree-of-freedom system model shown in

'Fig. h l . The spring constant k may be assumed to represent the stiffness of the 4

isolation spring or springs located between the primary mass of the vibrator and bias

mass that may be present. The vibrator itself consists of a primary mass (>I ) and the

combined masses of the unbalanced rotators (m). The unbalanced. or eccentric. n- A asses

( - ! G ) Tucker.L., Program MILE. Notes from a Short C o u ~ s e on " Computer Programs for

Ceotechnical Engbleers," Texas A and 51 'iiniversity (1987).

(47) 'Vibratory Hammer Study: Field Measurements." Prellrninary Report Prepared fcr

Deep Fol.lndations Institute by Coldberg-Zolno & Associates. Inc.. Newton Upper

Falls, Massachusets , FCe Xo. B-7946 (1 987). 42 pp.

(48) Vfjavergiya. V . N.. " Lead-blovement Cha-acteristic of Piles," Roc.. 4th Symposium

on Wzterways, Ports, Costal & Ocean Di-.%ions, Val. 2 , S C E (1977). pp. 269-284.

(49) Wor,g. D.,"Design and m a l y s i s of'An -4pparatus to SLmulate rjensity and Stresses

in Deep Deposits of Granular Sofls." M.S. Thesis, Departmen: cf Clvfl Engineering,

UrLverslty of Houston (1985). pp. 53-55.

131) Po~-llos, H. C.. and DaL-is. E. H.. Pile Foundation Ana!ysis and Design. J o h n Wi!ey d:

Sons. New York (1980). pp. 59-66.

( 3 2 ) Preliminary Report on Hur:ter's Point Vibro-Driving Test . Texas A and .\!

University ( 1988).

(33) Pr~.obrafhenskaja. N. A,. " The Innuence of Vibration Factors on the Penetration ol

Piles and Sheet Pfles." Pap. of LleetFng of Inst. of Fdns. (1956).

(33) Randolph. 5.i. F.. a ~ d S t n o n . I i . A , " An Improved Soil Model for One-Dimensicnai

Pge Dr ivkg Analysis." Numerical Methods in Onshore Piling. 3 rd Internationai

Conference, Nantss, France. STay 2 1-22 (1986). pp. 3- 17.

(35) Richard. R 51.. and Abbott. B. J . , 'Vcrsatde Elastlc-Plastic Stress-Strain Formula."

Jou rna l of the EngLneering Mechanics Dlv',sion. ASCE. Vol. 101. No. E,M4 (1975).

pp. 511-515.

(36) Rodger. A . A , and Lit:lejohn. C . S . . "A Study of V ib ra tov Drivlng on Granular

Soils." GeotecWJque, Vol. 30. So. 3 (1980). pp. 269-293.

(37) Rosenblueth. E.. 2nd Henera . I . , "On a Kind of Hysteretic Damping." Jo~!rnal of the

E n g b e e r h g Mechanics Division, ASCE, Vol. 30. NO. EM4 (1964). pp. 37-47.

(38) Satter , M. A.. "Low Freq1.1ency Vlbropi!e Driving and Prediction of w n a r n i c Ti?

Resistance of Open PLles." Personal Coim.unication.

(39) Schm1d.W. E. , "Drldng Resistance and Bearing Capacity of Vlbro-Driven Sfode1

Pfles." SIT 43. Anerican Society for Testing and Materials (1968), pp. 362-375.

(GO) Schmid. W . E . , "Low Frequency Plle Vibrators." Conference on Design and

Instal lat ion of Plle Foundat ion of Cellular S t ruc tu re s . Lehigh L'niversity.

Bethlehem. P A P m . (1970). pp. 257-265.

(41) Shekhter . O.J.. 'The Amplitude of Force Vibrations of Pfles a s a Function of

Vlbrator Charactzristics." Science Research Institute Foundations. R o c . No. 27

(1 955).

(42) SrnIth. E. A. L., " Pfle Dri\Wg Analysis by the U'ave Equation." JSMFD. ASCE, Vol.

86, S M 4 (1960). pp. 35-61.

(43) Steffanof, G.. and Boshinov, B.. 'Bearing Capacity of Hollow Piles Driven by

Vibration." 9th Int. Conf. on Soil Xech. and Found. Eng.. Tokyo. Japan, Proc. Vol. 2

(1977). pp. 753-755.

(44) Szechy. C.. 'me Effects of Vibration and 3rlvFng upon !he old; on Granular Soil

Surrounding a Pile." 5th Int. Conf. of Sou hlech. and Found. Eng.. R o c . Vo1.2

(1961). pp. 161-16.1.

(45) Timoshenko. S . , and Goodier. J. N., The Theory of Elas!icity. 3 rd Edition. McCraw-

HilJ Book Co. (19701, 567 pp.

(15) Hirsch, T.J.. Can.. L., and h:;erq.. L. L.. Jr, ,"Plle Driving A~a!ys i s - V!avs Equat ion

Users Manua1 .m F ~ o ~ p r n , " F%irA Report So . IP-76-13.2, (19761.

(16) Euck. R.W., and Hall. J .R . "Resonant Drivirg in Pemaf ros t . " Foundation Facts.

Val. 7, NO. 3 (1971). pp. 11-15,

(17) Huxter. AH., and Davisson. !.I.?'.. ">?easurements of Pile h a d P a n s i e r , " STF 444.

American Scciety for Test&& and Materials ( 1 968). pp. 1C6- 1 17.

(is) Idriss, I . M.. Dcbry, R. Doyle. E. H., aqd SLngh, R. D., 'Behavior of Soft Cla3-s Gfider

Earthquake Loading Cond!t!ons." Pzper No. 2671. m C . Houston. Tx. (1975). pp.

605-616.

(19) JeyapaIan, J . K . . "Ada1 Capaci ty of Vibro-drlven PLIes." Unpublished Internal

Report. U. S. A E. \Vatenr.ays Z.uperbnent Statlan (1986). 123 pp.

(20) JumIkLs. A. R.. Foundatlon Zngineerlng. !nternational Textbook Co.. Xew York.

(197 1). pp. 598-609.

(21) Kraft. L. M.. Ray. R P., and &gau,a. T.. "Theoretical t-z Curves,"JCED. ASCE (1981).

pp. 1543- 1561.

(22) Larnach. W. 3,. and A l - S h a ~ ~ d . N A . . ' The Vibratory Driving of Piles ln Sand,"

Ground Engineering. 'v'ol. 5. So. 5 (1972). pp. 22-24.

(23) Lee. S. L.. Chow. Y. K. Karynaratne. C . P.. and JVong. K Y . . " Ratlonal Wave EquaClon

Model for Pile-Driving Analysis.'' JCED. ASCE. Val. 1 1 4 . No. 3 . March (19881. pp.

306-325.

(24) Lysmer. J., and Rchar t . F. E.. " r)ynmic Response of Footing to Vertical Loading,"

JSMFD, S C E , Vol. 92, (1 966), pp. 65-9 1.

(25) Mao. T.E.. Discussion. Session 6. 4th Inl. Conl. on Soil Mech. and Found. Eng..

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(26) Mao, T.E.. 'The Yangtze a v e r Eridge at Hankow, China." Civil Engineering. Vol. 23.

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(27) Middendrop. P. and Jonker, C. . " Prcdktion of Vibratory Hammer Perfomlance by

Stress Wave Analysis," Personal cornmunlcatlon.

(28) Mosher. R L.. "Comparison of Axial Capacity of Vibratory Driven Piles to Impact

Driven Piles." USAE\\TS Technicxi a p o r t ITr,-87-7 (1987). 36 ~ p .

(29) Novak. M., Kogaml. T.. a n d Aboul-Ella. F.. " Dynamlc Sol1 Reactions for Plane

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953-959.

(30) O'Xefl1. M. W., and Vipulanandar,, C . , "Laboratory Evaluation of Piles Installed

with Vibrato?: Drivers," Dral: FLnal R e p ~ r t to National Cooperatlve Highway

&search Program, SCHEiP Project 24-3, J u l y ((19831. 534 p~

(1) Annual Book of ASTXI Staridards, Aner ican Society for Testing and Materials.

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(3) Barkan, D.D., "Fouildztion E n g i n e e r i ~ g and Drilling by Vibration Method." 41h

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(4) Bernhard . R.K.. "File-Sail-Interactions During Vibro-Pfle Brivlng." Jou rna l of

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New York ( 1 969).

(7) Chapra, S .C . . and Canale, R P.. Numerical Methods for Engineers with Personal

Computer Appl!cat:cns. YlcGraw-Hill Book Co., New York (1985). 570 pp.

(8) C h u a , K..?/I.. Cardner. S . , and Lowery. L.L., J r . . '?lTave Equation Analys!s of a

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(13) Gardner S., "Analysis of Vibratory Driven Pfle," NCLE Technical Note. Yo. TX-

1779. (19S71, 29 ?p.

( 1 4 ) Goble, C.G. and Rausche. F., 'TVave Equatlon Analysis of Pfle Founc!ations; \ 'vrCE

86 Program." FH\V.?I Report No. 3'-86/2 1. (1985).

Genetrative ~ 3 t i i ) i l of v:bro-driven d i s ~ l a c e m e n t pile in suSmergt.d s a ~ ~ d a t 3r.y

penetra:ion under any soil c o n d ~ l l o n s Lnvzstlfiated In t h i s s tudy .

!vfethods to est!mate the bear ing capacl ty of vibro-driven piles a n d model the

v i b r o - d r i v ~ ~ g of d:splacement pile were verliied u s i n g t h e laboratory d a t a . The

foiicu~~r!g r e c o m n e n d a t ~ o n s a re needed to verily or modily the proposed methods a n d

:nodeis.

( 1 ) Fie:d tes:s a re necessa ry t o cover all combina t ions of pa ramete rs u n d e r

Invesrlgaiion in this s:udy in order to verify the proposed bearing capacity methods and

vlbro-drli-ing model.

(2) Pi!e groups inst2l;ed by vibratory dri\?ng should be s tudied LO investigate the

efJec!s of the 1rl:ernc:ian between the pLles in t h e g roup !a t e r n s of dr?veabllity and load

t ransler charac:erisi:cs.

(3) LaSor2t3n ' and field s t u d i e s related to nondisplacement ptles using vibro-

dri1:er are recommended.

measured force amplitudes at the pfle head is due to the difference in the free

\lbration;,l displacement amplitude of the driver and the experiinental vibrational

displacement amplitude of the bias-vibrator-connector-pile system under various soil

conditions. Thus , transmission factors. which were derived a s function of effective

horimfital Fnsitu stress, euectfve graln size and relative density of soil, were used to

m o m the theoretical force to predict the measured pile head force.

Soil Model. Soil behavior under vibratory driving was stmulated by a modified

Ramberg-Osgood model that represents the nonlinear behavior and hystersls of pile-

soil intei'action. The model was developed by modifying the static unit load transfer

relationship with a degradation factor (a ratio of tt.e maximum values of dynamic to

static unit load transfer). The parameters of the modfled Rarnberg-Osgood model were

related to the effective horizontal insitu stress, effect:ve graln slze and relative density

cf the sofl. Reloading and udoading behaviors (hysteresis) were considered in the

model. Both shaft and toe soil models were developed separately.

Radiation Damping. The mechanism of energy dissipation through the

surrounding sou during pile driving is called radiation damping., The radiation

damping coefficient for the pile shaft was derived using elasto-dqzamic theory. The

radiation damping coefficient for the pile toe was appraxt ia ted by that of a vibrating

disc on the surface of an half space.

Vibro-Driving Model. A vibro-driving model was proposed by idealizing the pile

a s a rigid body in vibratory motion. The Lqput vibratory force, the soil resistance and

the radiation damping effect were provided by the vibro-drlver model, the soil model

. a n d the radiation damping coefficients discussed above. The equation of motion 2

derived from the vibro-driving model was sclved nurnerfcal!y with a computer program

called UH-VIBRO using the classical fourth order Runge-Kurta method for integraticn of

the governing dLfferentia1 equation. The model was capable of predicting the

Erects of X;iestrlk>ng the.Vibt-Q-Driven ?!lg

Sol1 w!th rz!at:ve ders l tv of 55%. Th? effect of restriking r e s u l t ~ d In the same

static compression capacity wfth respect to that of a corresponding pile that was vibro-

driven but not restruck. The restruck vibro-brr:en plle developed a capacity that was

about 85% of that of a corresponding continuously Impact-driven pLle.

S ~ i i with relartve densitv of 9O0h. The eifect of restriking w a s not clearly

defined by the tests. bu t no consistent Improvement ln capaclty was obsemed. Vibrated

and bebrated-restruck piles alike developed higher capacities than Fnlpact-driven ptles

at this relative density.

Jt'ave-eauatlon nararnekrs, Back calculation of wave-equation p a r m e t e r s was

difficult because of the short length of the test pfle. However. It appeared that the wave-

equation parameters for the restruck vibro-drlven pfle dld not U e r considerably from

those for the co~lt lnuously Impact-driven pile t-1 fine sand.

Estlmatfon of Bearing Cawacity

Four methods were proposed to estimate the be&lng capacity of vihro-driven

pfles: (a) Load Tmnsfer Method, (b) Power T r a r ~ f e r Method. (c) Nornlallzed Capaclty

;Aehtod and (d) Ultimate Resistance Method. The parameters in these methods were

related to the test variables such as dec l lve horizontal In-situ stress, gram size and

relative density of soil. It was shcwn that the 7roposed methcds provide seasonably

good estlmauon of the bearlng capacity of the test pLle. Furthermore, a procedure was

aiso developed to select a vibro-driven to attain desirable penetration under known sou

conditions (Chapter 61.

d

Mcdc!!nc of Vlbntont Dritlng

Vlbro-Drfv~r Model, !t was observed t!at the peak m e a s u ~ d pile head !bmes are

dfferent 'than the theoretically calculated forces using the bias mass and the rotating

masses i n the vibrator. It believed that the difference between the theoretical and

The predicted f-w ar.d q - . s relationships were used to sj-nthesize the lozd-moverrent

relationship of Impact- and -4bro-driver. piles. It was observed that the predicted load-

movement relationships using the rnodLfied Xamberg-Osgood model had the bes:

agreement with the experimental results.

M a d Transfer Dur ing V i $ r o - D r i ~ l n ~

Shaft resistance. The maximum s h d t resistance during vlbro-drixmg varied

between 30% and 65Oh of the corresponding static resistance in compression.

Toe resis tance. The maximum statlc toe resistance was not reached during

vibro-driving. but t h e peak sou resistances that developed were on the order of 50°/o to

900/0 of the static toe resistances at corresponding values of toe movement. it was found

tha t for Blastlng sand (coarse) at higher relatlve density a rapid impact type

phenomenon occurs, in which the pile toe lilts off the soil on the upstroke and impacts

the sofl c;n the downstroke.

E n e r n Lass. E n e r B loss per q c I e was determined as the product of the enclosed

area within the d ~ n a m i c f-w and q-w curves a n d the respective pile area. I t was

observed tha t total energy loss per cycle (shaft and toe) was smaller u n d e r the

conditions of lower relattve density (65%) lower chamber pressure (10 psi). \\'hen

effective chamber pressure was higher (20 psl). the total energy loss per cyc!e was

higher. The increase In grain slze (from 0 . 2 m m to 1.2 mm) also increased the total

energy loss per cycle. These effects of el'fectlve chamber pressure, relative density and

graln size on the total energy loss per cycle were observed to exhibit the same trend on

the power transrnIssfon from the t-ibro-driver to the pile head.

Residual S!resse$

Residual s t resses were developed at the toe a n d along tH% shaft. b u t their

magnitude was generally s n a i l Ln 30th Impact- and vibro-driven pfles, most likely due

to the fact that the t e s t pile was relathely figid.

Effect of S ~ i 1 Parameters gn \;ivrg-Driveabilitv -

J?~lat!ve densitv, The rate of penetration. v decreased with lncrezshg ielaiive P'

density. Thls parameter had the most important d e c t on rate of penetnuon.

m z c n t a ! e!rftlct:ve tress (simulated v decreased with lncreas~qg P

horii;ontal eiiectlve stress, but the effect of this pardmeter was less pronoucced than

that of relatlvc density.

Coeff!c!ent cf p 2 5 h preyjurc at rest , KO had l!ttle effect on driveabtllty. Tho,

control!i~g factor was horizontal effective skess .

Effect 01 Vlbro-Driving on Static Behador -

The most important parameter in relatlng comparative capacities of ptles

driven by vibration and by impact was found to be its relative density, and by

implication. its volume-charge characteristics. The following trends were observed :

Sol1 with relativ: der.sttv of 65516, The impact-driven pL!e developed 2596

hIgher m a m u m average unlt shaft resistance ln compression and 15 - 2004~ higher

maximum unit toe res!stance than the vibro-driven pile. This finding is in general

agreement with the recent stlldy of fleld tests by the Corps of Engineers (28).

Soil with relative denslty ~f 90'34~~ The lmpact-drlven pile developed 20 - 300h

lower rnaxlrnum average unit shdl resistmce ln compression and approxF.7nately 300h

lower m a d m u m unit toe r e s i s t a ~ , ~ e thzt the vibro-driven pile.

Mdcl lne of S!a:ic L'nlt b a d Transfer Chilracterist!~~.

m o - p a r a m e t e r power, three-parameter q o r , e n t i a l a n d four-parameter

modifred Rarnbcrg-Osgood models were used to predicted the static f-w and q-w cumes.

The parameters ln each model are related to effectlve horizontal In-sltu stress, effective

graln size and relative density of thc soil. In the power model;.predictlon of f and q

would Fxrease without reachlng a llmltlng valilue as w increased. which does not agree

with ~xper imenta l observation. The predictions by t5.z c.qonentia1 model and

rnodlfied &aherg-Osgocd rncdc: agree reasorably well with *.e ~xper imenta l results.

larger the vzlue of biased weight, the greater t he ra te of penetration. The v a i u e

associated wirh the eccentric moment and vibrator weight described abovc was 2,600

lb. or 5 to 10% of the static pile capacity. It is clear that the values of the bias mass

we!ght. unbalmced moment and vibratory body weight are coupled -xlth rcspect to Lhei;

ability to produce pile penetration.

Vibrator power and Dower transmission. The total theoretical pcwer developed

by the ~ i b r a t o r was not transmitted to the yile head . The ratio of pil2-head power ro

power produced by the vibraror appea r s to be related to t he maximurn value of

acceleration (more precisely, deceleration) t ha t w a s observed at the plle-head or, the

downstroke (Eq. (6.14)). which could. in turn . be related to soil parameters (Eq. 15 6)).

The minimum power transfer was approximately 40% of the theoretical vlbratcr power

during d r i ~ l n g in mediurn dense condition (relative density of 65Oh;. this power transley

occured at a peak pCe-head acceleration of 3 g, which appears to be a piactical threshold

from the perspective of power. Practical refusal d u e % vibro-d;ivtng could be consider

to correspond to a rate of penetration of 0.1 lnch per second.

C o m ~ a r a t l v ~ total energy for vibro-driving and i m ~ a c t - d r i v i n g The vibro-

driver-installed pile required about 65% of the total energy required for the impact-

driven pile at the lower relative density (65%). in te rms of mechanical energy produced

by the driver, for the easiest driving conditions (10 psi effective chamber pressure; 1. e.,

sknulated toe depth of 50 feet in terms of effective soil stresses) but required 200 - SCXIok,

more energy than the impact driver at t he higher relative density (90%) and 20 psl

effective chamber pressure (100 feet s imulated toe depth) . Somewhat less vibrator

power was required to install the pile in coarse s a n d t h a n in fine s a n d . For all

cocciitions. however. vibro-driving produced cons:derably lower str'esses in the pile

than did impact drivhg.

Constitutive rnodrlling of the static unit load t ransfer re!nti3nships was d o ~ e

using power, ex?cnriltial a n d moddied Ramberg-Osgood models. With appropca te

degradation factors a n 3 reloadLng and unloadLng g a t h s and using mcdU*!ed i a m b e r g -

Osgood model, a nonlfnear soil model w a s also developed. I t Is en~phas lzed that the

parameters In the constitutive model =e related to the sou parameters in:,es:igated i i?

th i s s tudy: el-fectivc horizontal in-sttil s t ress . $rain size a n d relative density of soil.

h,lethods to estimate the bearing czpacity of vibro-driven piles werz proposed and a

procedure to select a?propriate drivers under given soil conditions .x7as xcornmended.

Flnally, a one-dlrner,slonal vibro-driving model with c c n s i d e r a ~ l o n of radiat ion

damping was developed to s imulate !he driveabllity of pile under the test conditions

i n~~es t fga t ed .

Lribro-Driver and Pi!e Para ine t r r s

The cp t lmum frequency of the driver was found to

be 30 1-12 over virtually all soil conditions and for all values of unbalanced and bias

mass forces. Tests l o evaluate pile c a p a c i v were all cofiducted by installing the pLle at

th i s frequency.

Eccentric mornen; 2nd vibrator u ~ e t p h t ~ I t was found to be necessary for the

eccent r !~ moments to produce a dynamic force of a t least 4.100 Ib (10% to 30% of the

static pfle capacity) In order to drive the p9e ellec:rvel:r a t the opt imum frequency of 20

Hz. This observation !s relevant for a vibrator body weight (e?tcluding the blas masses)

of appro>ctqately 2C46 of the unbalanced force and for the bias d s s we!ght documenred

below.

Ogt!mum bras mass . The optknurn value o i the weight of the bias mass was not

established. It was observed that h the rar-ige In.~estlgated (350 ibs to 2000 lbs) the

&late d u w g shear and of the upper ;knit of relatlve density of s ands Into :vhich p!les

would normally be driven.

The pile was a closed-ended steel p:r,e. 4.GO izches in outside diameter, was

installed to penetrat ions in the test chamber of u p to 19 5 diameters . a n d was

demonstrated during the tests to have behaved esser;tlally a s a rigid body during vibro-

installation. The pile was l n s t r ~ m e n t e d to permit measurenent of head and toe force

and accelerat!on, force along the pile under static loading, and lateral total and pore

water pressure at the pile-sol1 interface. All Lystrilmentation systems were successful

except for the total pressure measurement system.

Several physical pr inc~ples were followed in the design of the vibro-driver, so

that the behavior of the vibro-driver would be representative, at the large-model scale.

of vibro-drivers in !he field. Several parameters influence the driving rate. These

paramzters . which may Interact n l th one anoiher. are bias mass weight. unbala:lced

force magnitude and frequency. vibrator body weight. and fle.xlbillty of the connections

between the driver and ihe pfle head. Only the first two parameters were k~vestigated

q l i c i t l y d u r h g the testing program, but the ratio of the vlbraror body weight to static

pile capacity was establkhed at a value that is typical of fleld conditions. The vibrator

body weght was 832 Ibs in this study. The operating frequescy (5 Hz to 60 Hz) was in the

low frequency range, well below the fundamental frequency of the pile itself. Bias

weight was v d - e d u p to 2000 15s and the range of eccentric moment varied from 50 in-

Ibs to in-lbs.

The impact driver w a s a single-acting impact h a m m e r t h a t delivered

.appraxknately 20 - 25 blows per minute. The hainmer was designed so that the pLle J

wouId be driven Ln sxch a manner as to produce a set of at Ieast 0.1 inch per blow, which

!s typical of p r o t o m e hammers. T i e characteristic> of the impact hammer were not

vx-ied d u m g the e-er i rnexts .

CONCLUSIONS ATTD R Z C O ~ r X 3 E ~ A T I O : i S

The cornplimen!aq pile-driving tests and analytical s tudy were conducted to

identify the effects of soil and driver parameters on the behavior o i vibro-driven

displacement piles Ln submerged sand io compare the behavior of vibro-driven piles

with Impact-driven piles and to assess the effects of restriking Nbro-driven piles. The

data were analyzed, and , based on the patterns of observed phenomena, design methods

to estlmate bearing capacity of vlbro-dfiven piles ar,d a tibratory driving model have

been dmeloped.

The parameters that were hvestigated in this s tudy are particle size. in-situ

s t ress , relative density, dri~Ti~,g frequency, blas weight and ezcentric moment. n o

u n i f o m ~ sands . S a n Jacinto River sand and B1ast:r.g sand, with effective grain slze of

0 . 2 mm zr.d 1.2 m m , respect!vely, were used in this study. Driveabili~y in s a n d was

investigated at two relative densities. two Ln-situ s t ress and two & conditions. An

effective pressure of 10 psi was used to simulate a pile penet ra tbg 50 feet. Such a value

of prczsare wouid be that which would occur tn situ a t a depth of appro.uimate!y 25 feet

( the middepth of a 50-foot-long pile) L~I a submerged sand of normal density. An

effectixre pressure of 20 psi UQS used to slmulatz a pLle penetrzting 100 feet. ln which the

value of pressure wocld be that at the mddepth of t?e pile.

The effect of KO was Investigated by conducting some a t Xo of 0.5. The

relative densi ty of the soil was varied from 65% to 909.0. The former value is

representative of soi:s that contract during shear a r ~ d of the general range of 50Ch to

70°h found Fn inany natural deposits. The latter value Is representative of soils that

2 0 0

T I H E ( m a r c )

Fig. 7. 18. hfeasurcd and Predicted Displacement Tline Histories of Vlbro-Driven Pile by LX-VIB3O and T O P D W T

The purpose of this sec::on is to investigate the validity of wave equation

algorithm for \-ibratory 6ri:tng ::,st 7 uras s:adied using computer program TOPDFUL",

(Appendix D!. Because c;i the Lnstabtlity cf [he soluiion with too many ptle elements !i.e.

time s t ep is u r ~ r e a l i s t i c a i l ~ ~ srna!] ) , t he pile was f!nally d i sc re tked into 2 elements

interconnected by plle "s?iings" s t e p oi 0.00005 sec) . The input forcing function

was the measured pfle head force rLrne history in place of the u sua l drisring mechan i sn .

The valus of Smi th ' s s h d t quake . Qs , and toe quake , Qp . were estimated from the

dy~ iamic load transfer r? l~ t ionsh i? (Fig 5.301 to be 0.03 In. a n d 0 .12 in. respect!vely.

Parametric studies using the TOPDRqX program were conducted on Test 7, and

Js and Jp were found to ke 0.038 =/in. and 0.024 sec / i n respectively.

Fig. 7.18 depicts :he c o r r p x i s c n of measured displacement- t ime h1s:ory wiLh

predicted ttme histories \>sing UH-\?Bi?O ar.d TOPDFJVE for Test 7. I t Is observed that

TOPDRIVE predicts much lower overall pile penetration over' a halt 'second p ~ r o i d and a

more erratic trace of dlsp!acement-t.me his:ory. Furthermore. the UH-'JIBRO program

is more efficient, a s !t requires only abcu t one - t en th t h e compu te r t ime of the

T O P D I V E p r o g m to predict the hail-second displacement time history.

Flg. 7 .17. .?,feasuxd m d Prtdkted Rate of Penetration Vs. Depth-to-Dtametcr FiaCc (D/E): Tests 14 and 17

FQ. 7.16. 51easured znd kcd!ctcd mtc of Pcr,e:rat.!cn Vs. Grpth-to-Diamcier &!LC (D;S); T e s s 9 a d 1 !a!!3a

P T e s t 7 ; Measured --- Tes t 7; Predicted

Fig. 7.15. ;Lie=u& a ~ d Prcdk?cd Rate of Pcnetratlon Vs. Depth-to-Diameter %tlo [T3/B!: Trs's 5 and 7

TEST 1.1 PEN. 72" O I ~ P L A C E M E N T VS. T!ME

- ,?easured i

0.8 --- ?redicted I

TEST 17 FEN. 72" 31s P U C E M E H T V S . T I M E

1 j I

Flg. 7.14. Measuxd aqd Predlctcd Dlsplacemcnt TLrne H!storlcs cf Vlbro-Driver. PGt; Tests 14 and 17

TEST 9 PEN. 50" DISPLACEMENT va. T I M E

1 ,

- Measured

--- P r e d i c t e d

- - i t S T 1 1 a/13a F E N . 72"

D I S P C A C E M E N T VS. TIME 1.8 , 1

Flg. 7.13. ~ c z s u n d and Predicted Dlsplaceri?ent TY~c H l s t o r ! ~ ~ of Vlbro-Driven Tests 9 and 1 l a / 13a

- Measured --- P r e d i c t e d

- - . - w e -

I t > ~ 7 FEN. 71" O I S P U C E M E N T VS. T I M E

F"15. 7.12. Mcasurrd and Predicted DLsplacment Tlme Hlstorfes of Vibro-Drtven We: Tests 5 and 7

1 1 1 kt3 = g ( t + ~ h . w + 3 h L 2 , z + ~ h k . , ~ I ,

"'t.4 = f ( t + h , w + h Lkn3 . z + h kZg ).

Q4 = g ( t + h . w + h b 3 , z + h s 3 ) .

h = txre step, and

i = increment number.

The order of the Runge-Kutta method Is determined by setting ten-rls equal to a

.- I aylor series expansion of the same order. Carnahan et al. (6) demonstrated that global

t runcat ion errors. Eg . are proportional to the s tep s k e . Thus lor the Courth-ordfr

Runge-Kutta method. Eg Is expressed a s

Eg = O ( h 4 ) . (7.29)

Sma!ler step sQes reduce global trunc3tion errors and error-free prediction is

possible if the order of the under1)ing function is equal to or less than the order of the

method.

A computer program called UH-VIBRO was written to solve Eq. (7.26). The user 's

manual and a Listlng of the program are presented in Appendk F.

Half-second time h!storfes of plle dfsp!acement at final penet-ation t.1 Tests 5,

7. 9, 1 la/13a. 14 and 17 were predicted using UH-VISRO (m.e step ts 0.000976562 sec)

and are superimposed on the mezsured time histories and presented In Figs. 7.12 to

7.14.

Furthermore. the vibro-driving model was used to predict t he rate of pile

penetration durlng pile d m - g . F!gs. 7.15 and 7.17 show the predicted and measured

rate of penetration , v versus nondirnensfonal depth. D /B (where D is thc depth of pile P'

toe below the top of c h m b e r and B is Ule diameter of pile) for Tests 5, 7, 9. 1 l a / 13a, 14

and 17, respectively. The predictlons prwi6.e satisfactory results.

Eq. (7.8) can be furthe; s e p a a t e d Into a system or sumul t aneous first order

dUTerentla1 equat ions a s

The classical fourth-.order Runge-Kutta method (7 ) is used to solve the abo1.e

system of equations. The following gives a brief introduction of the classical fourth

order Runge-Kutta method. Suppose there are tu70 simultaneous dneren t la l equations

gl\'en by

where

The solution for Eq. (7.27) is

TEST 77 PEN. 72" D Y W A U I C I - w C U R V E

1

- Measured

., (In)

TEST 17 P Z N . 72" C Y N A S I C 0 - W CURVE

1 .Q

F:g. 7.11. &posed SOU Model and Ex-permentaI Q~iaxnic Uni t Load Transfer Cumcs; Tcst 17

-1 TEST 7 4 PEN. /2" D Y N A M I C f - v C U 1 ( V E

1 0 7 !

- Measured P r g p o j e d S o i l ?!ode\

TEST 1 4 I . 72" DYHAUIC 0 - W C U R V E

I 1.2 Reasured 1 I.l r ? t o p o s e d S a i l Model

Flg. 7.10. Proposed Soll Model and Expermental Dynm-!!c Unlt Load Transfer Curves: Test 14

7---.--

, L I 1 1 o/13a P E N . 75" D Y N A U I C f - w C U R V E

'0 ,

- :-ieasured ...-- Prcposed So i 1 #ode1

TEST 1 1 a/? 3a PEN. 75" D Y N A M I C Q-W CURVE

1.4 j I

1 . 1 I - - - Proposed S o i l Model ! 1

0.0 i I - 0.8 I

a cz 0.7 I I

2: o.r :; 0.6 w

I 0.4

0.3

0.2

0. f

0

F!g. 7.9. Proposed Soil Mcde l and "rjrpcrmental ~ n a m f c U r ~ t Load Transfer Curves: T& 1 l a / 13a

TEST 9 P E I N . 52" D Y N A M I C f - w CURVE

10 I

I ~Veas i l r ed I a I

i I - - A P r c o o s e a S o i 1 Model !

TEST 9 PEN. 52" DYNAMIC Q-W CUXVE

1 .* t . 3 1 I I

I . " 'I :lez s u r e d I I

- - - i Propozed S o i 1 :.lode1 I

1 I . ' 1 i

Fig. 7.8. Proposed 5011 M d t l ar.d rqennrntd r ) y n m ? c Unlt L a d T r a n s f e r CunPcs: Test 9

TEST 7 PEN. 73" DYNZIUIC 1-w C U R V E

1 0 :

- Measured - - - Proposed Soi 1 1Yode1

'5- - : = S T 7' ; 7 P E " J . 75" D Y N A M I C q - w C U R V E

- 1 . 2 Measured

- - - Proposed S o i l nzde l

0.9

Fg. 7.7. Proposed Soil Modd and Expenncntal Dynamlc Unit Load ~ransfcr Curves: T c i 7

3. Under similar soil cond1t:ors the measured peak toe forces were geneni iy

slrnilar, regardless of whether t he plies were fmpact-driven or vibro-driven, although

some differences Ln the wave forms are observed. For euam~;le. Flgs. C. 1 and C. I I . C.2

and C.9, and C . 3 and C.10, and C.5 and C.8 can be compared. Thts observatton may

suggest that there were no large effects due to method of Lnstallat!on on toe capac!ty.

APPENDLY D

OiNE-DIMENSION,45 WAVE EQUATIOX Aep\iALYSIS

One-dimensionai wave eqluatlon anaiyses were used to ascer ta in whether

differences could be o b s e r i ~ d In Smith ' s parameters for plles t ha t were driven by

impact a n d thcse that were dr;.ven by >?bration . v i t h rcstrilkhg. This was accomplished

with a digital coniputer progrui1 er,:it!ed TOPDXJJ'E, u7h!ch back-computed the various

soil parameters .

TOPDFIJIE Alporit h m

The T O P D W L algorithin used for back-computing the soil characterist1,cs for

lmpacl and restrike tests is based on a finite aiflerence solut ior~ t 3 the one-dimensional

wave equation. specifica!ly or] t h e version developed by the Texas Transportat ion

Inst i tute (TI31 (151. The program Incorporates all of the assurnpt ions in the TTl

algori thm and models the so!l according to the E. A. L. Smi th elast ic-plast ic

representation with veloc!ty-tndepefident vlscous damping constants . The soil is t h u s

charactertzed by a maximum statlc sh* resistance, a maximum stallc toe resistance, a

shaft quakc iQs) (yield pot?!), a toe quake rQp) , a value of shaft damping (J,), a value of

toe darnplng (Jp) a d a ratio of toe resistance to total resistance (Rp/RT). The pile is

characterized by e!astic s tf lness (EX). length, number c f increments (for numerical

colnputatlon purposes), weight of each increment, c!rcumference of the pile. and cross-

sectional area. The cf the Lncrernent r-presenting the part of thFpile nearest the

toe was increased In this s tudy to account for the added weight of t he toe load cell

(approximately 8 :b). The sha l t resistance may vary in any prescribed manner from

head to toe.

The input forcing function is a force-time his!ory. applied a t the ?op of the pfle.

ln place of the usual drivFng mechanisin (e. 9.. ram impact velccity, weight and cushion

and helmet properties). The input function for this s tudy is a force-time history

measured by straln gage level 1 (averaged over several blows). The static and dynamic

soil reactions. pile forces, dlsp~acernents and ve1oc:ties are computed a t ?rcscnbed t-me

steps. When the program-computed lntegratlon t m e s tep (0.0000156 sec.) is smaller

than the t w e step of the input force-t?me history at the pile head (O.COU078125 see.), the

input forces are kterpolated llnearly with respect to t h e .

For a n y glven se t of sofl inputs (such a s Qs, Q P J,, Jp, a n d R p / R v a n d

distributions of plle stiffness m d mass, the following information I s output:

a. Permanent s e t of the plle head.

b. Velocity and force tLme histories at any pile segment (viz.. velocity at the

pile head, velocity a t the pile toe, and force at the pile toe, which were compared with

ineasurements),

c. Maximum forcrs and dlsplacernents at all pfle segments.

Fifteen pfle segments were used in the calculations descrfbed In thls study. ana the wave

equation computations were stoppecl (plle permanent set achieved) when t h e pile head

motlon stopped (20 to 25 rnsec after inltlal impact). This lnvolved the u s e of more

number of tlme steps than ~orrnally used in the wave equaUon analysts. No residual

forces were considered in the analyses described, so the back-corriputed values of quake.

damplng and resistance ratio must be considered approprtate for the condition of a n

assumed Initially stress-free plle.

Values of the sou parameters were varied systematically, and the results

(pile-head and toe vejocity. pfle-toe force, and permanent set) were'compared with

measurcd values in order to arrive at the set cf sou parsmeters tha t most closely

satisfied the three tlme histories described above and the permanent set. This

variation was accomplbhed by making separate r u n s with numerous combFiatlons of

?he pararr,e::rs and manually corAlparhg L5e outps! with the physica! measurzments .

O~t!;~.L7atlon S tudy

Tests 9 ( vibration with restrtke). 17 (vlbratlon uith restr-Lkel. 2 1 ( L ~ p a c t ) and 22

( impact) wlere s tudied using TOT-7DFWE. It was a s sumed lnltlally t h a t t h e shaf t

res!star,ce w a s uniform with depth . a reasonable a s sunp t lon based on analysls of the

s i a t ! ~ test data Ln Chapter 5. Shaft and toe qu*. shal l and toe damping and shaft a d

toe sta:lc resistpnce were varied, a n d pile-head set. and time histofies of pile-head

velocity, pile-toe velcc!ty a n d pile-toe force were computed a n d compared with

measured values un&! an optLmum set of Lnputs was found. The results are summartzed

Ln Tzbles D. 1 - D.4 . ln whlch only the maximum vel~cl t lcs and force outputs are given.

Graphs of the veiocity and force traces. both compbted and measured , are compared in

Figs. D. 1. - D . 8 for the set of parameters that were selected a s optimum. Because the test

pile w a s ve ry short and wave return times could not be scaled. very compiex force a n d

veiocicy traces developed once the reflected tension wave began LnterferLng with the

tncicient compression wave. In fact. I t appears that LIe incident compress:on wave was

not fully deve!oped at the pile head before effects of the return wave were felt. For tha t

r e a w n , emphas ls was placed on matching measured and computed wave forms for the

flrst 3 t o 4 mtlllseconds after impact. where ptle velocities were highest. me time

requlred for a s t ress wave to travel down the pile and re tu rn (2 X pfle length /

rompresslon wave velocity in steel) was abaut 0.8 milliseconds.] The comparisons of

meesured and computed wave forms should be considered satisfactory for the case of

the: vpry short pLle utflized tn this s tudy.

POP Tes ts 2 1 and 22. soiutlons from program WGZP 86 (14). a n Industrial-type

program for a r a l y s b of ptlc drhlng. were also obtalqed with the opt?;;lum set of input

pnrzimeten derived from ?Y)PT)FtrL'E and are compared with the measured traces a n d

~9th TOPDRY2 solutions in Figs. D.5 - D.8. I t was necessary to input L3e ram weight

and drop he!ght tha t produced the s a x e energy tha t wzs rncasured at the pflc head Into

E . . 8 f 0 - ~ - ~ ~ ~ ~ r D ~ ~ ~ ~ i O ~ ~ i c ~ ~ ~ , ~ ~ a ~ ) m ~ ) ~ ' $ ~ r n r n a ) ~ ~

O n & & N - - c - r - " " " " - - - - - * - - . - - P F - 3 I

> 4 t- 0 c

3 3 S :

- r - o o o 3 3 e d 0;- ~ ~ , - - m Q ) m g a ~ ~ ~ u ~ w ~ Q t c D Q ~ Q ~ ? 9 P m Q Q 3. - i; - 'E' ts

S g

I I a$ -. - L : ~ ~ : ~ ~ ~ z n ~ ~ ~ g ~ ; ~ ~ : 8 ? g g ~ g x d d d d d d d d d o o d d o o d o o o o d o o o o o

0) 0 0 N - N h m ~ W 0 D Q 0 h O ~ W ~ N N - ~ N

=?

Yl ,., 3 I r- . . 'A > 2 .... fl - ? - '=c - - V?

3 a c

$ > = --. a

- A

aJ c

i l m - 0 3 0 - h O N m 1 4 f i h t ~ h O Q O O r O 63 h ~ ~ w o ~ ? o t n o o + w o ~ m p q q q q ~ . q c , m m c m m m a Q a a b + b b ~ b a b a b b @

m - m m , ~ ~ ~ - h m ~ ~ ~ ~ ~ t r n ~ m ~ c ~ m PJ 0 0 ~ ? 0 0 U h h 0 Q ~ Q O O O h h - ~ ~ V V V 0 0 0 0 0 ~ 0 0 0 0 0 0 - - - - - W - O - - - - - v-

0 3 ; i ~ 0 o o s o o o - ' o o - d o o o 6 o i o d o o

0 m 0

a a: f. '5

H Q - A

r

?3

c - 10

2 Y

C ) - 8 -4 C - . d

- n . - .-?. -

C -

cr) 0 i- a

+ 0: 5 - i- r L.

2 8 2 3 + % - 2

'3 d

&:

2 t:

.- N ~ O O O O O ~ N N N W - - - - - N N 0 3 , N N N N N C d N N N N N W ? m W N N N N m N 2

P

~ m o o u ~ ~ a m ~ ~ m m m ~ s a v w m m ~ ~ 2

-3 g

C

L .

? a . w -

s- 3%

d d d d d d d o o o d ~ w ~ o o o o o o o o

~ ~ o o a a m ~ w t v * * B - r ~ . - , r r - g q q q q q q q d q q 4 ? g a 2 5 o o p o o o o o o o o o o . 000000~0

2 -'- m > - CO .= P

~ , d d d d d d o a d d d P o o o o o o o o

f

O R m w ~ a t l P N w e 4 - N ~ , '=?4999*9*99=?9=? O O Q O O O O O O O O O O O

PILE H m D VELOCITIES

- - - - cor.pu:ed, TST22.155

( F i l t e r e d , A=0.93)

PILE HEAD FORCES

Flg. D. 1. Measured and Computed We-Head Velocities and Fcrces: Test 9

PlbE TCE VELOCITIES

PILE TOE FORCES "PfltT @I 3 J R WD; Dm RC% X o ~ 1 . 0

1

~ ! g . D.2. Measured ar.d Compu:ed Pile-Toe VelociUcs and Forces; Test 9

PILE HFAD VELOCITIES

- - - - C x y o t e r ? , T C F X F T Z

(Filtered, A = 0 . 9 0 )

PILE HE3.D FOECES

nwr ( M U J S Z ~

FQ. D.3 . 3ltasured aqd Computed Pdt-Head Ve!cci:les and Forces; Test 17

PILE 'TGE VFLOClTlES T257 171 W T P 4 Q W, PC24 RD

- - - - Computed, T O P C R Z m

(Plltered, A10.90)

PILE TOE FORCES .

n3-T 171 I 1 u m N a WD; P r n WD 1 4

1 a 12

1 1 - - - - Con?ute<, TC??aRTVE 10 (filtered, As3.90)

0

0

7

6

L

4

24

a 0

8

F g . D.4. !,!eaured and Ccm;;uted Pile-Tce Velocities znd Forces; Test 17

PILE HEAD VELOClTlES

I

B h

8 B 2 k u 6

-2

-4 - Measured - @ - - - - C m p u t ed, TO?I)RIV': -B (FiltzieC, A-0.9)

-91 0 - - C u z p u t e d , LEA? 36

-14 ! I I I I I I r I I I

8 4 8 12 1 I 2 0

nve (MIU~~COMDI)

PILE h'EAD F O R C E S

-- yeasured

_ - - - C m p u t e d , TOPDRIVE ( F i l t e r e d , A m 0 . 9 )

-- C m p u t e d , LEAP 86

Fig. D.5. Measured arid Corriputed Pile-Head Velxl t ies and Forces; Test 2 1

PILE T 3 E VELOCITIES T T X 111 3 J R W 3 ; 90'3 R P , #e.al ,O

- - - - Cocpu: e d , TC?3a :VE (F:L:e:?d* A - 9 . 9 )

-- C 3 r - , - : e c , K E . 2 9 5

PILE TOE FORCES m. : 21; SJR WD; O C Z i RD; Ko=31.L% - 1

Fg . D.6. Measured and To--.pu!ed Pile-Toc Ve!ocitles and Farccs: Test 21

PILE HC&D VELOCITIES T911T 22; U R %bV1fa 0- OL31 #*-0.a

14

12

10

8

I

4

2

0

-9

-4 --.-------- Z e a s u r e d

--a - - - - Cmpuced, T C P 3 X I V E

-I ( F i l t e r e d , ~ ~ 0 . 9 5 )

-1 8 - -...-. C m p u t e d , KEk' 8 6

-q2

-1 4 9 1 3 0 P 0

PILE PiWD F O R C E S 4.0

ew

2L-O --.-.-- Hcasured

.--= -.- Cm,puted, E;W 8 6 $1 0

9 8

B

4

-a

Fig. D.7. Measured and Computed We-Head Velwit!ts and Forces: Test 22

PILE TOE VELOCITIES

--% ---- CC,?U: ed , TOP~RI 'V '? .

-I ( F i l t e r e d , A m 0 . 9 5 j -- -1 0 Cocpucec!, W E . U 86

-12

- 1 4 ---r--Y

Q a t 2 0

PILE TOE FORCES

Flg. D.8. :~icasurcd and Computed Pile-Toe V e l d t i e s and Forces: Test 22

! V W 86, resulllng Ln a hammer efficiency o i a p p r o x a a t e l y 85%. rzther than

measured plle-head force-time hlstory. the stiffness of the plywood cushion ( 1 100

k/ lnch. a s measured Ln static tests on the plywood cushlcn] and the coefficient of

restl!utton for the cushion recommended by Gobi- and Rausche (14) (0.50). Therefcrr.

the boundzry conditions for &e +avo solutions were not identical. and Identical results

were not obt-ed. However. the results compared well enough to prcvide conf ide~ce

that results obtained u s h g TOPDIirVE could be a2plied to \EAP 36.

' f i e computed results that are presented Ln t5ls apprndlx are filtered wiLh a

Qigital fi!ter to remove the eflect of mathematical nolse that cnay have resuited from

modelling of a pUe of very short length. The dlgltal filter is of the Sype described by Eq.

D.1.

in which g 1s the flltered value of the function belng plotted. f is the xnfUtered value of

the function, n Is the Ume step number, and A is the filter c m ~ c i e n l . Values of X are

designated Lr Figs. D. 1 to D. 16.

The optimum Srnlth-type sol1 parameters obtained from the TOPDRIYE study

are tabulated in Table D.5 .

3ensttivity Analvsed

The sensitivity of the TOPDFWE solution to the variation of certat? Input

parameters was studied through a further analysb of Test 9. This study was conducted

to determine the effects of parameters tha t were not generally varied in the

optirnkzation study described In the precediiig section, specifically, distr;lbutlon of shaft

resistance along the pile, dlstribution of weight along the pile (particularly. !he

addition of extra weight to the toe to s l au la te soil that mlght be rn0tir.g in phase with

U-,e pUe) and the length of the triteeration Ume step. 7% conditrons for the SensltMty

Table D.S. Summary of Optlmum T O P D R N E Pam-eters

Z ' e s t / ~ o n d i t i o n Q(snait) Q(toe1 ~ j s h a l t ) J(toe) RLtoe)/ ( h c h e s ) (Lqches) :sec/foot) (sec/:oot) R(tota1)

3 / SJR sand 0.03 0.03 0.06 0.06 0.44 D,= W ?

K = 1 0

Ch. h s s . = 20 psl

(RestrLke)

17 / BLS sand 0.08 0.48 D, = 3CP/o

ii = 1 0

Ch. Press. = 20 p i

(Restrike)

21 / S r i i d 0.04 0.24 Dr = 'D? KO" l Ch. Rcss.

= 20 psi (ContLnu ous

impact )

p2 / S R s m d 0.02 C.3 1 D, = W h

KO = 0.5

C h. Press. = 20 psi (fioriz.)

(Cc.nllnuou% impact) A

1

analys is a r e shown ln Table D.G. The q~~a ic , - and demplqg values and ra:!o of :oe

resis tance to shaf t resistance were the optilxurn V ~ ' J ~ S from Table D.5 for Test 9. For

pu rposes of comparison with Table 9.6. t h e values of toe element weight , shaft

resistance pat tern and tFm- s tep from the s t m d z r d solutlorls reported Ln Table D.5 were

9.9 Ibs, u d o r m . and 15.6 met, respectively.

The time hLstorIes that were cornputed with each sf the se ts o l lnputs described

in Table D . 6 are shown t? Figs. D.9 - D . 16. By comparing these figures with the results

gtven in Flgs. D . l and D.2, it i s obsenfed that r:?e restllts are relatively Lnsens1l:ve to the

parameters that were varied In the sens l t l~ l ty s t udy , so t h a t the conditions a s u r n e d for

the standard solutions (for which the optimum parameters a re tabulated in 'Table D.5)

appear to be approprkte.

Fw,ally, another sensi t l~l ty s tudy was conducted using JVEAP 86 to hvest lgate

the effect of the value of cushlon stLClness on the pile-head force time hbtory . Kesu!ts of

W W 86 solut lons for two values of c . ~ s h i o n stlfiness ( t he va l~ ie rneasurec\ in static

loading t e s t s and the value obtained by using the recommendation of C;c;ble a ~ d

Rausche (14) of cushicn modulus of 30 ksl) are shown In Flgs. D.17. ?'he measured

cushlon stLffness of 1100 k/lnch. which was used in producing t h e relations s h o ~ n in

Flgs. D.5 - D.8 provided the best match , whlch suggests that the L V E , V 86 solutlons

shown Ln those figures are apparently appropriate.

Table D.6. Varibles in T O P D W E Sensitivity Study (Test 91

step

step

Toe Segment Shaft Resistance Time Step Figures

Ve!qht (Ibs.) Distribut!on (mfcrosecs)

1 16.0 step 10.0 D. 15.D. 16 I

I

Note: in the "step" dlstrlbutlon. the bottom half of the piIe was asslgned W c e a s much

resistance a s the top half of the ptle.

PILE HEAD VELOClTiES f I S T a

I

- Heasured

- - - Computed, TOPSRIVE ( ? ~ l : e r e i . A = 0 . 3 0 1

nlec (MILUSECOHOS)

PILE TOE VELOCITIES YfST s

10

0

I - geasured

- - - C3r .=? l ted , T3F;X;VE 7 (Frltered, A'3.92)

I W

S 2 W

4

BI ! 2

!i 1

Q

-1

-2

-3

Fig. D.9. TOPDRIVE Analysis of Test 9; Increased Toe Weight; V = l ~ l t i e s

PILE TOE FORCES T X f T 8

I

nM (IdtU,1O]ICMdDB)

Fig. D. 10. T C P D R W Analjsls of Test 9; Increased Toe We!ght: Forces

F I L E HE3D VELOCII-IES R S T 3

8 , 7- I

FILE TOE VELOCITIES Trn s

10

€3

1 - Measured

I - - - C c ~ ~ ? U t e e , TZT32IVF. (Filtered, kx2.90)

(I

B

4

I

2

I

a - 1

-2

- 0 i3 4 B 1%

mfa g.a?L1azcmfl

~ g . D. 11. TOPDW'C, Xnalys1.s of Test 9; \'artable Shaft ,~ s l s t z?ce : Velocitks

PILE TOE FORCES TEST I

1

FILE HEAL) FCIRCE TBST 8

40

Flg. D. 12. TOPDRIVE Ana1)sL.s 31Test 9; Vazable Shal? Rcslstance; Forces

sr) - Heasured

- - - Computed, T S P 2 A i V E

( F r l e e r e d , A-0 .90 )

2. a

10

a

- J , ~ i r i i i i i ~ r ~ ; i l t r r r l r

0 2 4 1 10 12 14 18 I1 40

PILE hEAD VELOCiTlES

PILE TCE VELOCITIES

- -. - Conput e l , ';,^P3RIVE: (FiLtereZ, A = C . S C )

Fg. D. 13. TOPL)FUVE AIX@,~'s of Test 9: Increased Toe Weight and Variable Shzft Resistance; Velcc!tles

PILE H F O R C E TXST e,

"7- I

FM. 0.14. TJPDFXVE Ar?.a!ysis of Test 9: Increased Toe Weight 2nd Variable S h d t Resistance: Forces

PlLE YEAD VELOCITIES

-- M e a s x e d

--- Computed , T 2 P 3 R i ' J E

( F i l t e r e d , A - 3 . 9 0 )

4 -

- 1 -

PlLE TOE VELOCIT1ES

- - - Coqnputed, :O?>RI'JE (Filtered, A = 0 . 9 0 )

F@. D.15. TOPDRNE Analysis ofTest 9; Increased Toe Welght. Varfable Shaft %Sfstance and Decreased TL-e Step; Veiccities

FILE HrAD FORCE

Measured

Fig, D. 16. TOPDRPJE Analysis of Test 9: Increased Toe Weight. Variable S . h d 2s:srance and Dccrcaxd Tlme Step: Forces

PlLE TOP FOZCES

PlLE TOP FORCES 22

1

i I 1 I 1 1 I I 1 1 0 4 I 12 18 2 0

J

nur (ufu~3ccocolr)

Flg. D. 17. i C W 86 Aaalysls of Test 9 U s a g Optlmum Parameters from TOPDF3VE Analysis wth Dffferznt Cush!on Stllfness

STATIC LOAD TESTING AW FXZL'URE LOADS

This appendix describes briefly the procedures used to conduct the staUc l o a d i ~ g

tes t s , which were performed In conrlection with the "capacity" tes t s on vibro-driven

piles, vihro-driven ptles ~srith restriking and impact-dr:ven piles described in tables 1 . 1

through 1 3 (static load-movement relations are presented in Chapter 4) and discusses

the interpretation of failure loads.

T ? s ~ lnP Procedures

The following testing protocol was folloureY:

a . JV+.ile the pile was sitting vertically on top of the sand column, unstressed

e.uce?t for Its own dead weight. all s train gages, pressure cells and load cells were read.

These readings constituted the zeroes for all static rest data. so ;hat all data taken alter

installation and during static testing contain the eflects of residual s tresses that emsted

In the pile al ter installation. The instrument leads remained connected to the s tat ic

da ta scanner. a s well a s the dynamic da ta acquisition sys tem, from the time the

predrlve zeroes were taken throughout lnstallation and testing, slnce the s tat ic da ta

acquislCon system scanner a n d microcomputer had a very 'nigh electrical impedance

and did not therefore sect the performance of the dynamic d a t a acquisition system.

b. Once the pile had been drh..en to its full penetrat!on, the lrnpact hammer or 4

~:bro-d;ivcr was removed. and the pfle head was recoxrlgared for static testing. Th!s

s tep included. fist. the r e a d k g of all instruments to check operability wi:h the s tat ic

da t a acquhit ion system a d then the remcval of the articulated connection (vibratory

tests) or e.xtractiGn of the anvil of the Lmpact hammer (lmpac! or restrike tests) . A

reaction beam was hoisted k.to pl3ce, a n 3 a flat. machined steel loading plate was

positfoned on the head of the pile.

c. One horfzontal instrument arm w a s attached to each rr,ain uprlght of the

service gantry. which served a s a deiomation-measurement reference for the loading

tests. (Ver?ica! deformations in the service gantry were less than 0.02 inch at a load of

4 5 klps on the pile. Such movements of the reference system were not accounted for !n

the reduction of the data. but they represerit a very small percentage of tne movement of

the pile and. in any went . were generally corlsistent from test to test. 1 At the ends of

these a r m s were at tached two linear variable dirreren::al transfoimers fLVDT4s).

r n o u ~ t e d at the northwest and southeast of the pile head, and two mechanical dial

gages, mounted at the northeast and southwest of the pile head. The s tems of these

tnstruments. which were used to rneasure se t t len~rnt (and later uplift), were rested q n

machined extensions that emanated from the loading plate that had been placed on the

head ol the pile. The output from the LVDT's fed directly into the stat ic data

acquisition system (Chapter 3 ) . and the mechanical dial gages were read by eye and

recorded manually. The dial gages served to prohqde a check on the L'DTs, whlch were

the ins t ru~nents that were ultimately used in the reduction of the data. The dial gages

also provided par: of a four-point measurement system, which allowed for careful

tracking of the rotation of the pile head. No specific data on p!le-head rota:ion are

reported for this study. but in no case did the rotation exceed 0.003 radian about either

axis of measurement during a n a..al loading test.

d. A hydraulic jack was placed, centered. on the loadlng head. A 50-k electronic

d

load ceii was placed above the jack to measure load, and a simple swivel head was

placed between the load cell and the reacuon beam. A schematic of the resulttqg test

system ls shown Ln Fig. E. 1 . With !he load celi in the 3osttion shoun. it is obvicus tha t

tFle loads recorded were those In excess of t h e jack weight (about 40 Ib.).

e. Another set of readhgs was taken, referenced to the predrtve zeroes. bt this

point, apprcximately hvo hours alter completion of driving, tilere were no iridicated

excess pore water pressures ~n the sand. In fact, all excess pore water pressures appeared

to dissipate withtn about 90 seconds of the completion of d r fv i~g . a s evidenced by the

flow from the lateral drains within the chamber (Chapter 31.1 The compressicn loading

test then began by rnznua;ly stroking a small-displacement pump that powered the

jack. A constarlt rate of penetration of 0.033 lnch per minute was maintained at the

pile head. Initially, readings of all instruments were made at every 0.01 inch of

penetra tlon. As the soil began to undergo significant ylastic deformation. the internal

of data collection was increased to ex-ery 0.02 inch of penetration. The loadlng portion

of the lest was halted after the pfle head had settled l . C lnch, so that the loadlng portlon

oi the test required about 3 0 minutes to complete. The pile was then unloaded in three

to four decrements, pausing just long enough at each decrement to make a set of

readings.

The electronic lnstruments that were read d u q a static test are shown ln Fig.

3 .14 . In addillon to these instruments. the two dial gages a t the top of the plle were read

and the readings recorded simultaneously with the acquisition of electronic data. The

scanner-computer system that was used could read ail tnstruments in approxtmately

0.5 second, so that a set of readings represents essentially a n instantaneous plle state .

Tabular values -sf the loads measured along the ptle during each of the statlc tests are

g!ven in Chzpter 5. In some cases strain gage clrcuits did not yield variations ln 4

readings from load to load that could be ratlonaify explained. and their resistance to

ground became low. lndicatlng water intrusion somewliere in the clrcult. Readlngs

Main Test Frame (Stoel, w i 4 Uprights)

e Fixture (4 Arms: NE, SW: (Cial Gages); SE, NW: (LVDT's)]

Note: 2 Dial Gages and 2 LVDTs Supponed on Aluminum Arms Clamped to Main Frame Uprights

Flg. E. 1. E!oTaUon Schem3Uc af Static Comprcssion Testing Aqpgemen t

under s31ch ckcumstances were excluded when reducing the data. and those readings are

absent from the tabulations in Chapter 5.

f. Once ;he compression test was con:?leted, the head of the pfle. the react1011

beam and the jack were recorfgured for the uglifr tesr, a s shown schematically in Fig.

E.2. This procedure required about oze hour. The uplLft test was then conducted !n a

mariner identical to the com?ression test, with one exception. inn initial frictional

failure apparently occurred betweel; the sand and the wall of the plle once the pile had

moved upward 0.1 to 0 .2 lnch. At this polnt, considerable strain energy was stored in

the up;ift yoke. That energy was partially dissipated while the pile slid u p y a r d

momentarily with respect to !he soll, apparently a s static friction was converted to

sliding friction at the wall of the pile. Once a sufficient amount of energy had been

released. the pile stopped moving and the pile-soil system was zgain in equilibrium

with the applied load with static friction in force. This process, howevLr. which

repeated numerous times a s further uplut load was applied, resulted in a series ofjerks.

in which the pile moved suddenly 0.02 to 0.04 inch en each jerk. making it impossible

to mai r~ ta ln a constant rate of uplllt of 0.G33 inch per minute. That rate was

maintained between the jerks, however. Because of this phenomenon, the completion

of a typical upllft test to a total ?fie-head movement of 1.0 Lnch required o1G-y about 20

minutes.

I t is of significance to note that the entire process of driving and static load

testing required approximately six to seven clock hours from the time the Lnltial zeroes

were taken and the installation began. Thc tests were all conducted in a n a i r

ccndltioned room, with no direct sunlight on any of the components of the test - r 4

Lnstrumcntation system. so that electronic drift due to temperature chcmges over the six

to w e n hours of the maintenance of the zeroes was small enough so that It had

essentially no effect on the results.

0.75 In. Allthread Rods (4) Steel Yake ip Load Cell wl Swivel

?.,lain Test Frame (S~eel , w/ 4 Uprishts)

Note: 2 Dial Gages a d 2 LYDTs Suppcrted on Aluminum Arms Clamped to Main Frame Uprights

4

F!g. E.2. Elevation Schematic of Statlc UpiLft Testing Arrangement

] n { y x r r t a : ! ~ n 3: F;?i!::r=J6:32,

Although the term "capacity" h a s been used loosely in the p r ~ c e d i n g section to

descrlbe the general t rends in :he test ing pr-ogram. precise deSinftlons of failure or

lbn-i!tLng :oads are cot readi!y obvious in the load-movement relat!onshlps presented In

Figs. 4 . 2 8 - 4.43 Thttrt,'ore, s-eral d r f i d t l o n s of lailure have S t e n employed and

compared In tabular iomi kn Chapter 5 for each of [he s tat ic load tests. Five methods

are pi-opcsed to SeIir~e slatic f a l l ~ r e load from the !oad-settlement data . In order to

eniploy t h c ~ e deTini:!ons, load-movement relations with co r i t l nuou~ ly ."?arying slopes

a;: required. \\"nere s ~ . ~ v t o o t h pa t te rns de~ieloped durIng a tes:. contLrluously sloping

cu rves were interpreted by ta-klns the upper emrelope to t he sawtooth curve. The

methods are s u r ~ n z r ~ , e 3 below.

(a ) The ofisel (or Davisson) method (1 1). tn which the iallure load is defined a s

t h e intersection o l t h e :!le-head load-movement curve a n d a line intersect ing the

nlovement axls ai a valu:: of 0.15 + 0.008338 Lnches (where B Is the plle dlameler) and

h a v b g a slope (movement/load) of L/AE where L, A and E are length. a-oss-sectional

area ancl Young's n:xlul~is of the plle material, respectively. LVhlle thfs method was

developed fcr ti.,? Interpre(al1on of compression loading tes t s , it h a s a!so been applied

In this s tudy to :he interpretztion of uplilt loading behavior.

(b) ?he slope (or Nordlund) method 112). where f d u r e Ls de fhed as the polnt on

load-movement cum? 2: \xh!ch i ts slope is 0.05 inch/ ton.

(c) The !vi.iazur'dtr$iia n-e'hod (1 1). which assumes tha! the load-movement curve

1s parabolic a t id lure . h set of load va lues are found from a correspondtng set of

equaliy spaced pile-head movement values that a re arbitrarily chosen. A 45' line is

d1-a- fro.- each Icad value on the load axis to intersect with a lin? drawn parallel to

[he movernext =is at the xext larger value of load . These fntersections a r e joined by a

straight line which Lqtersects the load That intersection is defined the izi!ure

load.

(dl Failure ioad defined a s the load corrusponding to a pile-head movement of

O10B.

(el Failure load deflned a s the !oad c o r r e s p o n d ~ g to a pile-head movement or

1 .O inch (0.25 B).

MPESDIX F

'USER'S ,%.4,XdAL iL'L1) LXSTPiG O F PROGRAM UH-WBRO

Th i s appendix d i scusses the r e q u ~ r e d information a n d i n p u t paran ie te rs ro

:lna!yse vibro-driven disp1ncemer;t pGes in sa tura ted s a n d using UW-WBRO interact::.:

progrzm. A 1istir.g oi the prognrn is &so provided.

T?le program Li-I-WBRO is written in FOR?%Y language a n d is ready to be used

i n IHhI PCs o r IBA1 compa[ibies. Input da ta can be entered with ei ther integer. or reai

m o d e s if no speciiication 1s made and they a r e not Ilrniied by a n y Mnd of iornlat.

I lowever, integer number is required If Integer mode is specified. Ou tpu t is optiorlal and

corisisis of t h e histories of pi!e acceleration, velocity and d isp lacement which a re

required to he specified in dmerent files unde r dirferent file n a m e s . Dimension of t h e

variables h the prograrn is se t u p fc;r output slgnal u p t o 520 d a t a pofnts. If more data

poh-~ts a re required. the dimenslorn of the variables in the program have to be changed.

The m p u t is compieted by answertrlg t he following ques t ions in sequence (9

m e a n s quest lon appearing o n the screen and the values used in this s t ~ ~ a y a r e gieren in

parenthesis) :

CJI : m R m UPVER LrMrr OF ??P6E IF(TEX;RATION (sec) :

Ente r ;he required time lirrcit (Fn seconds) for analysis.

(0.5 second In this study).

92 : E;'NF,R rTvTlxM??ON STEP (sec) :

Ente r the rime kcrernent (;n seconds).

(0.000976562 second in this s tudy) .

93 : GVTER THE m I G Z 0% P!LE (Ib) :

Enter the weight of piie (in pounds).

(78.8 lbs in this study).

94: ENTERTKETiADrUSOFPLllEw:

Enter the n d l u s of pile (in inches).

(2.0 inches in this s:udy).

Q5 : ENTER TEE DXMi1L PEXETRAXOIV OF ?EE (4 :

Enter th:: penetration ol pflc (a inches) whicn is established a s the Wta l point

for analysis.

(0.0 to 80.0 lnches in this study).

CJf3 : ENTER EFFECTTVE COhCTNIPiG PRESSURE OF SOIL @sl) :

Enter the effective horizontal confining pressure of soil, o'h (Fn psi).

(10.0 to 20.0 psi in this study).

97 : E ~ T E R R E t A m DLriSXTI OF ,SOL (in decim.11) :

Enter relative density of soil, Dr (eg. 0.9 for 90% relatjve density).

(0.65 to 0.9 Ln this study).

g8 : E . ? ? GRAlS SIZE OF fjOL (mm! :

Enter the effective graln size of soil, d l 0 (ln mllllmeter).

(0.2 to 1.2 mrn in this study).

gs : 33TER S m RADXATZON DAMPING COE1FFICILNT IIbsec/in"2) :

Enter t.he shaft radiation damping coefilcient, Cs (Eq. 7.17 : in lb-sec/ln2), as

where ps = unit we+t of mil,

Gs = sou shear modulus. and

ro = radius of pile.

(4.0 to 9.0 lb-sec/~q~ In this study).

910 : E A T E X TOE .FL.IDL4TXON DA?d??MG COEFFICiEXT W/h) :

Enter the toe radiation damping c~eTicient, Ct (Eq. 7.18 : trl lb-sec/in). a s

wherc vs= Potsson's ratio of sou.

(5.0 to 13.Q Ib-secjln in thls ctudy)

Enter 0 or 1 (ln integer mode) to specify the separation beraeen the pfle toe and

the underlying soil on the highest p o k ~ t on upstroke during driving.

0 = to enter slack by the user.

1 = to generate the slack by computer as follows.

for d l 3 -< 0.2 m . slack is 0 inch,

for d l 0 2 1.2 mm, slack is 0.04 lnch,

for 0 .2 m 5 d 10 5 1.2 rnm . slack is found by interpolauon.

X 0 ts entered. Q 12 appears.

If 1 is e ~ t e r e d . Q 13 appears.

912 : E3TER SLACK (fr-1:

Enter your own slack (Fn inches).

913 : E-XEX WEJCST OF VE3R0-DRIVER (Ib) :

Enter t\e weight of the vlbro-driver only (hi pounds).

(832.0 Ibs in thLs study).

914: E ; ~ ~ R ~ G H T o F B I A ~ M A S S C ~ ~ ) :

Enter the welg5t of the bias mass (h p c u ~ d s ) .

(2000.0 Ibs In tNs study).

915 : ENTER ~ * ~ C M0.MEZ-r OF DF2rvER Win) :

Enter the eccentric moment of the driver (ln pound-inch].

(100.0 lb-Ln in this study).

916 : EYTER DRIVING mWCP W ] :

Enter the drlvlng frequency [in Hz).

(20.0 Hz in this stuciy-I.

9 17 : ENTER DfiIVER DIS-T .UEPLIm70E (in) :

5nter t l e theoretical driver displacement mpl i tude. Z (Eq. 7.10 : in bches) . as

where m = unbalanced masses.

e = eccentricity of r0taUr.g masses.

o = angular velocity,

M = weight of the vibrator,

yl = natural frequency of bias mass and spring system = I k/M ) O s 5 , and

k = spring constant.

(0.12 inch in this study).

g 18 : DO YOU WANT TO OUTPUT DIS- T I X E ElIS?'ORY ?

ePES , k V 0

Enter 0 (in integer) to indicate output of displacement tlme hbtoly !s wanted,

Enter 1 (in integer) to skip output of dbplacement me history

If 0 s entered, Q 19 appears.

If 1 is entered, G20 appears. 4

919 : GNTER FTX;ENk?UE m R O L m DKSAPL%EZZ.EXT :

Enter the file name in which the output of displzcement W,,e history is stored

(Nename.fflemode : eq. DISP.OUT where DISP is the W e n m e and O L ! is the

filenode!.

C ~ * + r + + + + r + + + + + + + * + + ~ * ~ ~ + + + t + + * r ) o + I I * + + * + * * o + + + * + + * + * + + * + + * + + * + + + + ~ * * * * +

C GENE8AT I N G THEOFET ICAL DYFI4MIC FORCE S I G N A L C l + t + * + * + + 4 1 ~ + ~ . ~ + + + * + * * d * * t + + + + Q 4 * + + t t I ) t + + + * * * + + + * * + + * * * Q * * * + V + * * + * * + * *

ONEGU2= ( 2 . 0 c 3 . 1 4 1 5 9 2 6 5 4 * F R E Q ) *+2. C? ~ f l = ( E f l + V f l * D D ) * U M E G A 2 DO 30 I = 1 ,.JSTEP P1IFF(I)~~0B+DFfl~SIN(2.0*3.141S92654*F?E0*T*1~

30 C O N 1 IFIUE i I= l4QFF DO 20 111 .NSlEP F G R C E ( I ) = B C I F F ( I I ) I I = I i + l

?cl CON r I NlIE Cl++++r+rs4a,++++**+1***+t++***a++*+++*++,**++b++*+E***+*+***+*+@+++*++

C flO!lEL-L I F I G THE A R T I C U L A T E D P I N N E D P I LE-Dt? I ' JER CONNECT IOFd C * ~ t + * + * t * * r * * * * * t * ~ + * * + * * * + * * + * * * * + * * * * + * ~ * ~ + ~ * + + * * * * * * ~ + * * + * * * * * * ~ * * *

F&CTOR= ( -<:I .<1755+0 . C I ~ Z ~ + S I G : I A + O . 5 , 5 5 + G F S i , + i FED€-<). 6 5 ) *L t - 1 1

1 -?. 72% i F'EDE-i:l. 9 )

WFACTOx (-43, j1 :15+i t . 1 *S IGf lA+2 .4*GF.S I ) *(RED€-c3, 6 5 ) * 4 . % 1 - 7 , 0 * ( F E U f - ' 1 . 9 )

DO 4 0 1 x 1 .lrlSrEF. F U P C E t I )=FORCE ( I ) - L I O P FORCEi I )=UOP*wFACTO+FORCE<I)*FACT~lP

4,:) COP17 I PJIIE ~ ~ t ~ + + ~ o + ~ + + + ~ ~ I b o ~ + ~ ~ ~ * ~ ~ C t ~ * ~ I ( ~ 6 ~ * + ~ + ~ o o * + b ~ ~ ~ * * * t * ~ ~ ~ * ~ + + + ~ ~ ~ * * b ~ ~ * +

C SET U P THE Sl. IF1 F F I C T I O N PARAMETERS ~ 4 1 ~ ~ ~ 0 + ~ ~ ~ 6 ~ ~ + ~ ~ t ~ r + ~ Q t ~ ~ ~ O ~ t ~ * ~ t ~ ~ t + ) L ~ D + + ~ ~ ~ ~ + ~ ~ + ~ + ~ ~ ~ + ~ ~ ~ * ~ ~ Q r ) + ~ ~ ~ ~ t

5E I = l Ct. <.I** ! 3 . 4 2 6 8 - 1 . 8 i 2 b r R E D E - 3 : 1 . : ,3443+GF:SI +FtEi)E+O. 4 9 1 7 s l A L O G l O ( S I G N 6 i I * R E D € ) SFd= 1 0 . 0 1 * ( 0 . 7 1 44+il. 0 2 6 7 2 ' S 1 5 M A + 0 . 0 7 3 5 9 + A L O G l O ( G R S I *S I GMA)

1 4 i l . O S 9 2 5 + A i O G 1 0 ( KELE 1 *S I G m A ) SF.I=1O.O+*!-l.5934+O.022CJS*SiGM~+O.15BS+GRSl+1.P46*REDE) S f A C = - u . 5 ~ ? 3 i~.Q15*5IGflA-O.l5*GHSI+l .72*REDE SfIIt4=-3.347+i1.2?*SIGMA-i7.9333*GRSI + 4 .Cl+FEDE Sti=l ..;9

~ * t + * * * t + * + + t * * * C * + O ~ + * r * * * ~ + ~ * ~ * ~ * + + ~ * I o * * o * * o * o + * + * * * + * + * * + * * + ~ + + * * ~ +

L 3 E 7 UP THE TOE F.ES1STAFcCE F'ARAP1ETEL'S C + ~ a * + ~ + s * ~ * ~ + + * + 6 ~ e Q b c I ( 4 t C * * ~ + ~ + + + + * + + + + + * t * + * + + + + * + * + 4 ~ i * + U E * * * * * t o * ~

T E I m 1 0 . i t + * ( ,7.599&+0.013C~6*SICM4+~:~.2<~7*GRSI+O. 0 2 7 0 & + A L @GlO(RECE ) * I k S I G M A )

If?@= 1 0 . 0 * + ( 1 . 74 1 + I > . 0 1 2 2 2 ~ 5 IG f lA+$? . 1 1 bB-cCPS I + 1 . 3 2 3 + F E D E )

TNr3. I 6 T P I = O . O , T M I N - 0 . 0 IFAC=0.1913~O.063S*SiGMA+O.2967+GRSI-O.36*REDE

C**.******.***i**.*+*++******t*t*~t**t+*ts+***+*********+********u**~++

C SOLVE At4U 0tITF.I IT THE D I S P L A C E M E N T AND 'JELOCI TY ~ ~ 1 0 + ~ ~ * ~ ~ ~ ~ 1 ~ l t B ~ + ~ * + ~ ~ ~ * * * * ~ * * + * * + ~ ~ ~ C b + * * + ~ ~ * 4 4 ~ * ~ ~ * * * * * * * * * ~ ~ * * ~ ~ V U

S S r A l = i ) . O SSTR I =<I. O 3STP2-15 . 8:) S S T K F I =O .0 S S T R O I = ~ 3 . 0 SSTA 1-0.0 SCHEC).:=O. 0 J 7SlGN= 1 351-v . 0 SOT =<I . 0 SSTRF 1 =0.0 SSTHQ 1 -G .O SS r A 3 4 . CI SSTUQ-O. O XR=O. O SSTF.?=GaP v=<:I . ( j

W R I T E ( s, 0 ) ' DO YOU WANT TO OUPUT D I 3 F L A C E M t N T T i V E H I S T O K Y : ' U R I l E ( * . a j ' O=YES , l = N O ' P E A D ( * , * ) H b IF(HD.EO.I) GO TO 1 1 1

lb.2 U R I T E ! * , ' ! A \ ) ' ) ' ENS€% F I L E NAnE FOR DISPLACEEENT OUTPUT : ' R E A D ( * , ' ( A ) ' ) FFIAME OPEN( 5 ,F ? L E = F t J A f l E , ACCESS- ' SEOUENT I Ai' , STATUSn 'NEW ' )

1 1 1 L I R I T E ( u , + ) ' DO YOU LIPNT TO OUTPUT V E L O C I T Y T I M E H I S T G K Y : ' U R I T E ( * , + I ' O=YES l = N O ' R E A D ( * , * ) HV I F ( H V . E Q . 1 ) GO TO 1 1 2 W P I T E ( e . ' ( A \ ) ' 1 ' ENTER F I L E NfiME FOR V E L O C I T Y OUTFUT : ' K E h D ( + , ' ( A ) ' ) FrIAME OPEN(b,FILE=FNAME,ACCESS='SEOUEf4TIACC,STfiTUS='N€W')

11 ; W f i I T E ( * , * ) ' GO Y O U WANT TO OUTPUT ACCELERATiON T I M E H I S T O R Y : ' WF::TE!v.*) ' O = Y E 3 , l = N O ' FEAD(*,al HA

I F ( H A . E O . 1 ) GO TCI 1 1 3 W R I T E ( + . ' ( A \ 8 ' t ' El4TEi i F I L E f . l&YE F i t ? GCCELERATION OIJTF1.IT : ' F f A D ' * , ' ! A j - I F N A F E QF.ElJ( 7 . F I L E = F t l A l l E ,ACCESS= 'SEi,LJEf.lT IuL ' . 3TATIJS.; 'NEW ' )

1 1 3 C GPll 1 :it I€

GCI 1 #.I I = 1 . I !STEP- 1 1 F ( t tV . PIE . I ) LJt3 11 E i 5 1 t:!l:ll:~ ) X C * 1 ':I<~#:I. <I , Y O ( 2 ) I F ( t l D .NE. 1 1 WP I T E ! 5 , 1ljt:lO) XG P 1 s.I~:~(:I. [:I, YE! 1

l ~ . ~ ~ ~ t . l P O 8 R A 7 ( F J 3 . 5 , ' , ' aF13.5) d C l . = i Y O < 2 ) - ' V l / T I F ( HA. Id€ . 1 1 biF: I TE ( ? , 1 i l r ? ~ 1 ) XO* 1 LI,:I<:I. ~ 3 , ACC

C:r( ( E&HF ( f C i . SS i A 1 . S S T F 1 . SSTFt2. SSTPF I .C,STF.O; SSTGI *SCHECE: J J S I G P i . : I J ~ P , S S T R F , S S T R O , S ~ T , S L ' T , S S T R F ~ , S S ~ F ~ O ~ , S S T d 3 . S S T A Q , X R ) F O R 1 =FORCE t I I FOR2=FGhCE( I + l ) C'= YO ! 2 ) C A L L H~:M!in,Y~,T,FGhl,FOF:;!,GCF,SSTAl.SSThl,SSTR%,SSTRFI.SST~OI~ ~ ~ S T ~ I , S C I ~ E C ~ . , J J S I G N , ~ ~ , ~ P S , C R T , ~ A D , P E N , S S T , ~ ~ T , S S T R F I , S S T R O : , ? 3 S f A 3 . S 3 1 A Q V X F ? )

Iv CON7 INlJE s r CIP END

C W * Q ~ Q C ~ ~ B + ~ ~ B ~ I B Q ~ B ~ E ) B ~ + ~ ) ~ + B + ~ ~ + + + + + ~ ~ Q - B * ~ ~ ~ ~ ~ + + + ~ * + ~ ~ * * + * ~ * ~ * ~ * * ~ ~ + ~ * C END O F M A I N PROGRAH C ~ o r r e s n a e a s ~ a + r ~ + a v ~ ~ e a 0 ~ 0 + e ~ d ~ ~ ( t e u v ~ + ~ ~ ~ a ~ e 0 u ~ + * ~ ~ ~ U e + * ~ ~ ~ ~ ~ u ~ ~ ~ ~ ~ % ~ ~

~ ~ s a ~ r ~ a e d r ~ ~ a e r r + s d u ~ a ~ ~ s ~ + t ~ ~ u b e ~ + c . ~ + 1 ) ~ # e o d e + e + e ~ u ~ ~ ~ ~ ~ ~ ) + u ~ ~ ~ 4 ~ ~ 0 ~ 4 ~ u

C T H I S 5 l l R P O l l T I N E IS T O SOLVE A SECGI4D ORDER ORDINAi iY D I F F E N E R T I A L C L ' ~ ~ k O - D R l ' , ' I t l G ECIJATIOPI 6'f FOURTH ORDER FiUkCE-k.UTTA PfETHaD C + I B B ~ B ~ ~ A ~ ~ B Q Q ~ ~ ~ ~ ~ + ( ~ ~ ~ O ~ ~ + + O + O + ~ ~ U ~ ~ O ~ + + ~ + + # ~ ~ ~ ~ ~ + V ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Q ~ ~ ~ ~ ~ + ~

SUbFtOUTINE Rt:MiXO,t 'G,T,FOF( l ,FOFt2,GAP,SSfAl,SSTRltSSTR2,SSTRFI, 1SSiRQI,SSTAI,SCHECYrJJS1GtJ,PM,CRS,CHT~RAT)tPEN~SST,SOT,SSTHFl, 2 S S I R O I , S S T A 3 , S S T A O s X R )

U I I t E I S S I O N Y O ( 2 ) p S ( 2 ) V Y ( 2 ) s W ( 2 ) COFIRON S E I s S R ~ , S ~ K ~ S F ~ C , S ~ I N , S M M M i E I ~ i F O ~ T N ~ Y P I ~ T H I N q T F A C SSI = S S T A l S S 2 = S S l R l S:G'A=SS TH2 S S 3 z S S T R F I S I 4 = S S T R O I

- EiSS~SS7 (11 S S = S C > I E C f . : JJS1JJSIGt l SS7=SST SS7AuSOT 593aSSTRFl SS4-SSTRQ1 S'j 1 ~ I = S S T A ~ 5s l 1-557 A 0 5; 121 iF (

DO ! I + : = I t 2 S(L:)=YO(K) YfK)=S(h) U(K)=S(I.:)

I 1 CONTINUE C;=o

F OR=FOR 1 C X L RAMF(Y.SS~,SS~,SS~A,SS~,SS~~SSS~SS~~JJS~GAP~STRFFVSTROQ~ 1SS7,SS7A,SS8,SS9,SS101SS11sSS12)

1 1 9 0 K=K+ 1 COCL EOUA(K,Y,F.STRFF,STF:OQ,PM,F@R,CRS,CRT,RAD~PEN) D = T * f u!t:)=u(k.)+Ll/e. Y(b:)=S(k:)+D/2. IF(E.LT.2) GO TO 1190 FOR=(FOR2+FORl)/?.9 I ..'.I SSl=SSIAl SS2=SS TR 1 - - > 2'h=SSl&,? 553=3S i i F 1 5S*=S'l F . 0 1 - .. L. ,-.2=S5 - rci I

> S o = S C H E C t . I.T;=J_?S I GI4 527=-;-;1 - -- :s :A=SGT SS6-SSTRFI 553=S;TF<Ol SS I O=SS1 A 3 33 1 1 =SS TAO SSlZ=XR CA4.L F.&MF!r'.SS1.SS;.,SS2A.SS3,SS4.SSS,SSarJJS,GAP,STRFF,STROO, ~ ~ ~ ~ , S S ~ A , ~ S ~ . S S ~ , S S ~ ~ I , ~ S ~ ~ , S S ~ ~ ~

127'1 t x t . + 1 CALL E O t i A ( r .Y.F,STRFi.STROQ,PM.FOF(.CRS.CRT.RAD.F'Ef.I) D=Tf fF

U O . ) = L J ( F ) + U J ~ . k4kJ.=S(k,)iDJ 2 . I F ; k . L 1 . 2 ) GO TO 12°C) FClR=(CCF.?*FORl ) / 2 . 0 t SSlmSSTAl S5FuSSTR I SS2A=SSTR2

, SS3-SSTRFI S5-r-SSTHO I 5 5 5 - S S T A I SS5-SCHECK JJS-JJSIGN SS7=SST SS7A-SGT SSR=SS T R F 1 SSS=SSTRQl SSlO=SSTA3 SSII-SSTAO 551?=XR CALL i?Ar!F(';.SSI rSS2.SS2A,CS3rSS4,SS5.SSb.JIS,GAP*STF.FF,STF(C3@r ISS7.SSiA,L~SS~SS9,SS10~SS11,SS12) 4

1 I+(-1 ! . = + . I 1 CALL EDUA(t',Y,F,STRFF,STROO,PMrFOR.CF:SrCliT,FtADrPEN) U p 1 *F U.t:I=W(k.)+~J/3. t ! i ) = 5 ! b ) t V

IFO:.LT.E) GLI TO 1340 FljF:=FQF;?

K-O SSl=SSTQl SS2=SSTH I SS2A-SS1 R 2 SS3sSSTRFI SS4=SSTRQl SSS-SSTA I SS5-SCHEW; J;TS-.~JSIG14 5S7=SST SS7Li-SOT SSE=SSI.S.C.I SS9=SSTf?O 1 SS13=SS1d3 SS11 =C,STUO SSI 2=ZR C U I PAi~F;Y.S51.SS'S~SS2AtSS3rSS.i,SS5rS56.ZJS,GAP,STFFFrSTFO@,

1 5 5 7 . S 5 7 A , S S 8 , S S ~ , 5 S l O , S S : 2 ) 142(.1 k =!:+I

A 1 ECil IC f t- . Y . F , S TRFF . SiF 'CO , Pf l ,FOP. CRS CRT. F:dD. PEI.1) c=t < F N i l ) = U O )+(1!6.

1F ( 1 - 1 1.2) GO TO 14F:i:)

@ ( I 12 i ~ 1 . 2 ' (0 i 1 ~ ) = W ! 1. )

12 CON; i 141 lE xn=xo+T F;ETCIRt,i EPlD

C + * * * * t + * + ~ * + w ~ * * * * + * * * + * * * + * + + I ) + * * * + * * + ~ * * * * * * * * * + ~ * * ~ + + + ~ * + * * ~ C THIS fUEcF.OCIT I N € IS TO CALCULATE THE St. IN AND TOE RESISTGFICE , Ct~+t.t**.*****~.I*+****~+i**wt***+**+***.*********R***********~*+*~+*~

SIJBROlllINE f?A~F!Y~STAl,STR!~STFi2~51RF~rSTFr@I~STAI~CHECl::,JSIGhi.GGF~~ 1SIRF.SrRO.SI . O T , S T R F l >ST3121 sSTG3-SrAOIXR) DlflEPISIClN Y(2) CiIEflOr4 SEI,5PO,S~I,SFAC,StlIN.St~l,fEI , T F C ! r T t . I , T P I , T M I N . T F A C STA2sY ( 1 ) C):I=STA2-STAI Ck.2=5TAl -CHECK CF.3-a : 1 *Cb.2 1F(Cb 3.GE.T) .0) G O TO 1 1 3 1 SlAI=STAl STROI=STRQl S rRFl-STRFl ?SIGN=-lrJ3IGN sr-0.0 QT-0.0 ! F ( J S I G ? J . E R , - 1 ) (30 TO 1191 XRmO. 0 CALL Nkfl(XR~ST,STRFI,SEI*SRO*SN,SPI) CALL ~H(XR,QT,STROI*TEI*TRO,TN,TP:) STR 1 =STA i -S7 STR2rSTGI - (?I I F ( S T R Q 1 .I E . o . 0 ) STR2=STR2+0AP STRO I=O. 0 STRF 1-0 .O

I 1 9 1 CHECK-STA~ S TA314BS ( S TA2-STA 1 +5T, IF(jSIGFI.EQ.-1) SfA3*48S(STfi2-3TAI) C N L RMS(STRF,STA3,SEI,SRQ,SN*SFvI) IF(JSIW4.E0.-1) GO TO 1104 I F ( S T A I . G T . S T R ? ) GO TO 1200 SlAO=AES(STA%-STAI+OT)-GAP IF!STA@3.LE.O.O) 00 TO 1192 GO TO 1201

1200 Sl=-ABS(S?A2-STAI+OT)