Assessment of Multi-Wythe Stone Masonry Subjected to Seismic Hazards

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Assessment of Multi-Wythe StoneMasonry Subjected to Seismic HazardsAbdelsamie Elmenshawiab & Nigel Shriveb

a Department of Structural Engineering, Mansoura University,Mansoura, Egyptb Department of Civil Engineering, Schulich School of Engineering,University of Calgary, Calgary, AB, CanadaAccepted author version posted online: 10 Jul 2014.Publishedonline: 17 Nov 2015.

To cite this article: Abdelsamie Elmenshawi & Nigel Shrive (2015) Assessment of Multi-Wythe StoneMasonry Subjected to Seismic Hazards, Journal of Earthquake Engineering, 19:1, 85-106, DOI:10.1080/13632469.2014.940631

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Assessment of Multi-Wythe Stone MasonrySubjected to Seismic Hazards

ABDELSAMIE ELMENSHAWI1,2 and NIGEL SHRIVE2

1Department of Structural Engineering, Mansoura University, Mansoura, Egypt2Department of Civil Engineering, Schulich School of Engineering, University ofCalgary, Calgary, AB, Canada

Heritage stone buildings are typically vulnerable to seismic events. Results of an experimentalprogram were analyzed to evaluate the shear strength and intrinsic damping of stone masonryrepresentative of the West Block of the Canadian Parliamentary Precinct in Ottawa. Eight repre-sentative wall specimens with different rehabilitation schemes had been tested under different staticand dynamic loadings. Each wall had wythes of sandstone and limestone connected by a rubble core.The results show the shear strength of the walls could be predicted accurately and that no strength-ening scheme was particularly beneficial. The effective viscous damping ratios varied between7 and 9%.

Keywords Stone Masonry; Rehabilitation; Shear Strength; Damping; Elastic Moduli

1. Introduction

Masonry is one of the oldest known building materials. Past civilizations have left inven-tories of unreinforced masonry (URM) structures that convey the architectural heritage oftheir eras. Many historic structures that remain were constructed from URM, because it isdurable and could be manufactured using local materials. Unfortunately URM is vulner-able to certain structural actions because it lacks resistance to tensile and shear stresses.In old buildings, URM walls tend to be very thick, often comprised of several wythes ofstone and/or brickwork connected together by weak mortar: in stonework, connectivity isoften through shear keys created by stones of different depths into the wall. These his-toric structures were constructed in times when mild steel and the techniques to designductile structures that can withstand the earthquakes expected in a given region withoutcomplete collapse were not available. Thus, although these structures may have survivedearthquakes already during their life, they are potentially at risk if a seismic event of largermagnitude occurs. Vulnerability to earthquakes is not like other environmental hazards(e.g., wind), as the probability of their occurrence is very small, and the magnitude of thenext earthquake is unpredictable. Nevertheless, we now have a much better understandingof the probability distributions of the magnitudes of earthquakes around the world, and thusthe likelihood of occurrence of earthquakes of high magnitudes. Recent earthquakes haveshown that URM structures are vulnerable in such events [EERI, 2005]. In Canada [NBCC,

Received 19 January 2013; accepted 17 June 2014.Address correspondence to Abdelsamie Elmenshawi, Department of Civil Engineering, Schulich School

of Engineering, University of Calgary, 2500 University Drive NW, Calgary, AB, Canada, T2N 1N4. E-mail:asmensh@ucalgary.ca

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ueqe.

86 A. Elmenshawi and N. Shrive

FIGURE 1 The West Block building on the Parliament Hill in Ottawa, Canada.

2005], structures built before 1970 are thought to be vulnerable to severe damage or com-plete failure in moderate or strong earthquakes, with URM being classified as the mostvulnerable construction material. Therefore, old buildings assessed as having deficienciesare required to be upgraded to reach a performance level similar to newer construction [Fooand Davenport, 2003]. An example of an unreinforced stone masonry heritage structure inCanada is the West Block building of the Canadian Parliamentary Precinct in Ottawa shownin Fig. 1. The seismic resistance of stone walls similar to those in this building is evaluatedhere.

There are several possible causes for the lack of resistance of unreinforced multi-wythestone masonry buildings to seismic events, including the absence of proper bond betweenthe wythes and between the walls and the roof, the use of weak and/or loose filling materialbetween the outer wythes, flexible diaphragms, and degradation of the constituent mate-rials through weathering and aging. Although stone masonry walls attract high seismicforces owing to their heavy weight and high lateral stiffness, they lack sources of duc-tility to dissipate the earthquake-induced energy. Other factors that can equally affect theseismic performance of stone masonry buildings are layout in plan and elevation, structuralintegrity, and the quality of the workmanship. Stone masonry walls do not have a uniquebond pattern, unit shape, topology, or dimensions. In addition, a single structure is typi-cally built by many masons. Geography also plays an important role because in historicstructures, local non engineered materials were usually used to construct the building, andthe masons in different regions built the masonry differently. It thus becomes difficult tospecify engineering properties for masonry in one area based on those from another. Allthese factors make the assessment of the seismic resistance of a historic building a complexand challenging task.

The vulnerability of multi-wythe stone masonry walls to axial compressive loads hasbeen observed experimentally [Vintzileou and Tassios, 1995; Valluzzi et al., 2004] with theearly separation of the wythes from each other due to the second-order effect becoming arecognized symptom of impending distress. The presence of transverse wythes (shear keyswhich connect the outer wythes) within a wall also improved wall behavior. Earthquakecharacteristics such as frequency content, acceleration amplitude, and the ratio of verticalto horizontal acceleration play a significant role in the possible failure of multi-wythe stonewalls. High-frequency components of waves traveling through multi-wythe stone masonrycan trigger wall delamination and crumbling [Meyer et al., 2007]. Also, the amplitude of

Assessment of Multi-Wythe Stone Masonry 87

the vertical acceleration can trigger the failure of the inner core with loose filling material,as the friction between the core and the outer wythes becomes less effective if the verticalacceleration increases. In this case, the inner core would exert lateral pressure on the outerwythes which could cause out-of-plane failure [Costa, 2002; Meyer et al., 2007].

Techniques are required to reduce or eliminate such vulnerabilities in historic stonemasonry structures. These techniques should involve minimal intervention to preserve her-itage values, be cost effective and achieve life safety of the occupants. Therefore, theoptions available for the rehabilitation of other structural systems, such as bonding FRPsheets externally on the structure, will be of limited use in heritage structures. Interventionsinternal to a wall such as re-bonding, grouting, or creating a cemented network can be usedfor multi-wythe stone walls [Lizzi, 1981]. In these interventions, the injection materialneeds to be selected to be compatible with the original constituents in respect of mechan-ical, chemical, and physical criteria. The effectiveness of using cement-based materials instrengthening multi-wythe stone walls has been examined (e.g., Vintzileou and Tassios,1995; Tomaževic, 2000). Such materials can improve the structural behavior of the wallsby postponing or preventing wall delamination until ultimate capacity is reached. Thelevel of improvement depends on the quality of the stone masonry with larger effects inpoor quality, and lower effects in good quality, stone walls. On the other hand, cement-based materials have some disadvantages such as low penetrability into narrow voids[Vintzileou and Tassios, 1995], and the formation of a capillary system that can absorbsalts with water from the surrounding environment [Tomaževic, 2000]. Although the lat-ter disadvantage can be minimized without impairing the lateral resistance significantly byreplacing part of the cement with inert aggregates [Tomaževic, 2000], other strengthen-ing schemes can be used in conjunction with the cement material or alone, to retain wallintegrity.

Costa [2002] examined the use of cement-grouting to fill the voids in stone masonryand the use of welded steel mesh with mortar on both sides of the stone walls. He observedthat the use of the steel mesh covered by mortar on both sides of a stone wall showed anincrease in the load bearing capacity of the wall compared to the un-strengthened case.Valluzzi et al. [2004] compared three strengthening schemes to rehabilitate three-wythestone masonry walls; injection (filling the voids in the inner core), repointing (for the bedjoints), and using transverse steel ties across the three wythes. The results showed that theinjected walls were significantly stronger in compression and had a higher elastic modulusthan the un-strengthened walls. The other two strengthening schemes did not provide anysignificant improvement in either the compressive strength or the elastic modulus comparedto the un-strengthened walls, unless they were combined with the injection (the combi-nation of the three schemes led to the strongest and most stiff behavior). The possibleeffect of using metal anchors alone to improve masonry behavior was investigated numer-ically [Brookes and Tilly, 1999; Brookes and Swift, 2000; Jordan and Brookes, 2004].The models used were for anchors in the plane of the stone walls as opposed to acrossthe wall width. Although several attempts were made to evaluate possible strengtheningschemes, trials to predict the lateral shear strength or evaluate the hysteretic behavior of themulti-wythe stone walls are very scarce [Tomaževic, 1999]. Therefore, the current anal-ysis aims at assessing seismic behavior of multi-wythe stone walls and investigating theeffectiveness of tying the external wythes in the transverse direction by means of metalanchors and the use of traditional stone-interlocking in reducing the seismic vulnerabil-ity of walls. Particular interest will be given herein to the evaluation of the shear strengthof the walls, intrinsic damping, and elastic moduli through analytical and experimentalprocedures.

2. Testing Program

The experimental programme was designed and executed to investigate the behavior ofthe stone walls under monotonic and cyclic loading as well as static and dynamic effects.The mechanical static characteristics of the walls including Young’s and shear moduli wereinvestigated by Sorour et al. [2011]. The behavior of the walls under in-plane cyclic anddynamic loading has been investigated and reported by Elmenshawi et al. [2010a; 2010b;2010c]. The work presented here is concerned with the evaluation of the lateral shearstrength and the elastic moduli of the walls.

2.1. Test Specimens

The testing program was planned to evaluate the seismic resistance of walls repre-sentative of those in the West Block (Fig. 1) building of the Parliamentary Precinctin Ottawa. Briefly, eight walls were constructed with six containing different possiblestrengthening/rehabilitation schemes [Sorour et al., 2011]. The walls were subjected todifferent static and dynamic loading scenarios. Each wall was 2.0×2.75×0.54 m (width,� × height, h × thickness, t), thus having an aspect ratio λ (= h/�) of 1.38. The walls inthe actual building are of varying thickness, being thicker at the bottom than the top. Thewalls tested were of similar thickness to those at the top of the building, built to a sizethat would be representative of the topology of the actual walls and an aspect ratio simi-lar to those found in the actual building, between windows. Each wall was comprised oftwo stone wythes with an inner core of rubble masonry. One outer wythe was of sandstonein a sneck pattern and the other was of limestone arranged in running bond, as shown inFig. 2. The sandstone and limestone used to construct the test specimens were obtainedfrom quarries that gave a close match to the original stones in the West Block building.The variability of the textures and construction of the walls was aimed at imitating thelower bound of the quality range in the actual structure that would result from the differentmasons involved during the construction of the building and maintenance over its lifespan.The wall specimens were constructed in two batches (I and II) by different masons with dif-ferent mortar quality as indicated in Table 1. For walls in batch (I), the mortar joints werethicker than those of the batch (II), and the bond strength between the core and externalwythes was reduced by dressing the interior faces of stone units (the stones were dressedsquare and smooth on their back faces instead of being left rough in order to minimize thebond strength). The strengthening techniques were aimed at tying the stone wythes together

Running bond in the limestone wythe with the rubble core behind

Sneck pattern in the sandstone wythe

FIGURE 2 Bond patterns used in the stone walls.

TABLE 1 Batches and strengthening schemes of the wall specimens

Wall No. Batch No.Anchoragedescription Remark

W3W4W5

Cintec anchors placed duringconstruction

Fully-socked Cintec anchors placedafter construction

W6 I Helifix Anchors

W7 II Stainless steel cramps every 1.0 m2

W8 II Overlapping stones every 1.0 m2

in the transverse direction. Three types of metal anchor and traditional stone interlockingwere employed in the walls as illustrated in Table 1. Generally, the anchors or overlappingstones were placed in a diamond pattern at 1.0 m spacing.

To produce a weak mortar reflecting the lower bound of expected strength in theexisting building, a mortar with a ratio of 1–3 (lime to sand) by volume was used. Thecompressive strengths of cube samples from one of the many batches of mortar used in theconstruction of the group (I) walls were 1.67 and 2.58 MPa at 6 and 9 months, respectively,and the strengths of a batch of mortar from group (II) construction were 0.34 and 0.7 MPaat 28 days and 6 months, respectively. The objective of utilizing weak mortar was met.Stone samples were cored from random stones in the batches sent, and some samples werestrain-gauged prior to compression testing to obtain their elastic modulus. The stress-strainrelationship observed for the stone samples was linear. The compressive strengths of twostone cylinders (75×150 mm) cored from the limestone were 99.3 and 105.6 MPa, withYoung’s Moduli of 21.6 and 62.1 GPa, respectively. Three similar cylinders were coredfrom the sandstone giving compressive strengths of 232, 247, and 202 MPa and Young’sModuli of 59 and 67.2, and 58.7 GPa. As the stones are so stiff relative to the mortar, theresponses of the walls will be dominated by the deformation of the mortar and the effectsof the mortar/stone interfaces.

Each wall was constructed on a steel base beam. The base beams had shear pins anda channel around the base of the wall to restrain lateral movement of the wall. A similarbeam was designed for use at the tops of the walls during transportation and testing. Eachwall was capped with a concrete beam. Shear pins were inserted in the top of the wall toconnect the wall and the concrete beam. The walls were tested six months or more aftercompletion of construction.

2.2. Loading Scenarios

An in-plane lateral cyclic static test was conducted while the wall was under an averageaxial stress of 0.3 MPa – representing the axial stress near mid-height of the building —except for wall no. 2 where double this axial stress was applied. Once the specified averageaxial stress had been achieved, the top and bottom of the wall were restrained against in-plane rotation, as the actuators applying the axial load were placed in displacement controland commanded to hold their current position [Sorour et al., 2011]. The lateral actuator wasactivated in displacement control to apply increasing drift (= δ/h; δ = lateral displacement)amplitude following the excursion scheme shown in Fig. 3b. The targeted drift ratio for the

(a) Configuration of the in-plane cyclic static tests

1.5MN MTS 1.5MN MTS

150 kN MTS

Base beam300

Transverse Ø25mm

Ø19mm pins

Flat rod

(b) Drift amplitudes of the in-plane cyclic tests

No. of Cycles

–0.20

–0.10

0 1 2 3 4 5 6 7 8

FIGURE 3 Layout of the in-plane cyclic static tests and their drift amplitudes.

wall specimens to achieve was at a lateral displacement of 5.0 mm corresponding to theexpected spectral displacement scaled from past shakings to match the current requirementsof the uniform hazard spectrum (UHS), employed in the National Building Code of Canada[NBCC, 2005]. Two displacement transducers were mounted at the level of the actuatorto capture the wall response (one on each outer wythe of the wall). Neither slippage nortorsion was observed between the wythes, so the average of the two transducers was takento be the displacement at the level of the lateral actuator.

After the cyclic static in-plane racking, two dynamic loadings were applied to thewalls. The first was in-plane cyclic loading with sinusoidal waveform at a frequency of5.0 Hz. The amplitude of the load was increased monotonically to ±10 kN. The seconddynamic loading was out-of-plane shaking on a uniaxial shake table. The shaking scenarioscomprised real and synthetic records. The real records were those from the EW componentof the 2002 Ottawa earthquake scaled by a factor of 183 to match the seismic risk levelin the current UHS for the city of Ottawa. Using this record would clarify whether thebuilding requires strengthening to comply with the current code. The synthetic record wasgenerated to comply with the short period end of the UHS with a probability of 2% beingexceeded in 50 years as described by Atkinson [2009]. This artificial record was able togive a realistic time history matching the UHS for the City of Ottawa and to simulate amoderate earthquake with a moment magnitude of M6 at a distance of 30 km. The testsstarted with the application of 60% of the displacements of the scaled real earthquake,followed by the synthetic record at 60% amplitude. The shakings were repeated at 100%and again at 110% amplitudes. Accordingly, each wall experienced six shakings. The out-of-plane testing configuration and scenario are shown in Fig. 4; additional information isavailable in [Elmenshawi et al., 2010c].

Period, T– sec

1.42002–04–20 EW

Ottawa short period

Time, t – sec.

t – m

ζ = 5%

0.0 0.4 0.8 1.2 1.6 2.0

0 5 10 15 20 25 30 35 40

Ottawa short period

2002–04–20 EW

FIGURE 4 Configuration of the out-of-plane tests: left is the general layout of the wall;right top is the imposed displacement amplitudes; and right bottom is the associated spectralacceleration.

Free vibration tests were carried out on the walls in the in-plane direction at threespecific times during the test sequence. The three times were (I) on the undamaged wallbefore the in-plane static and dynamic loadings were applied, (II) immediately after thesetests, and (III) after the out-of-plane shaking tests. The objective was to evaluate the intrin-sic damping ratio at the three stages of damage (no damage, in-plane, in-plane plus anydamage from the out-of-plane shaking) and whether the damping ratio was affected by thedamage level. The free vibration tests were conducted by pulling the top of the wall inthe in-plane direction with a tension cable and cutting the cable at a load of 9.0 kN (cal-culated not to cause in-plane flexural cracking) to allow the wall to vibrate. The responseof the wall was monitored with two accelerometers (one for each stone wythe at the top)and the results averaged as no twisting was observed. During the vibration, the wall actedas a cantilever with no vertical compressive stresses except self-weight, i.e., the axial loadwas removed before commencing the free vibration. Further details on the sequence of thetesting and loading procedures as well as the effect of damage on the static and dynamicproperties of the walls can be found in Elmenshawi et al. [2010a] and Sorour et al. [2011].

3. Hysteretic Behavior and Failure Mode of the Stone Walls

URM walls are able to resist seismic-induced forces through their in-plane shear strengthand stiffness, if out-of-plane failure is prevented. The shear strength of URM depends onthe failure mode obtained, which in turn depends on the imposed axial compression, theaspect ratio of the wall, and the boundary conditions. For a block/brick URM wall withthe same aspect ratio as in these tests, λ = 1.38, and imposed compressive stress (σ v =0.3 MPa), the wall would be classified as a slender wall, and a flexural rocking failuremechanism could be obtained if the shear strength was not reached [FEMA 356, 2000].Vasconcelos et al. [2006] reported that a single-wythe, dry stone wall with an aspect ratioof λ = 1.2, subjected to an axial compressive stress of 0.5 MPa and cyclic displacementexcursions, showed a flexural response up to the ultimate strength and a rocking failuremechanism beyond that. A similar rocking mechanism was also obtained for a stone wallwith an aspect ratio of 0.67 when subjected to in-plane dynamic loading. However, for thecurrent three-wythe stone walls, regardless of the typology, it was observed that no crackingoccurred until the drift ratio of 0.18% (average of both loading directions) was reachedin the in-plane static tests, as shown in Fig. 5. The shear strength of the walls degraded

FIGURE 5 Diagonal cracks after the in-plane cyclic tests in limestone (left) and sandstone(right) wythes.

sharply beyond this limit; however, continued racking at this drift ratio emphasized thecracking pattern. The cracking pattern was fundamentally diagonal with cracking in thehead and bed joints. However, due to the heterogeneity of the stone units in terms of size,the pattern was not the regular stair-stepped form often seen in URM of brick or block[Elmenshawi et al., 2010b]. Also, the diagonal cracking in the sandstone wythe was notreproduced exactly in the limestone wythe as shown in Fig. 5. The bonding pattern andsize of the stones influences considerably the precise path of the cracking in the respectivewythes. The walls made of batch II had to be racked more than those made of batch I toaccentuate the cracking pattern. This sheds some light on the role of the thickness of themortar joints on cracking of the walls as opposed to the strength of the mortar (walls ofbatch I had thicker mortar joints of stronger mortar than walls of batch II).

The lateral load-displacement response of the walls during the quasi-static in-planecyclic tests were very similar in shape and amplitude regardless of the strengthening schemeused as presented in Elmenshawi et al. [2010b]. This may be seen in the four samples pro-vided in Figure 6. Reductions in lateral strength typically began after the drift ratio of0.18% had been reached, so the corresponding shear strength is identified as the strengthlimit state. The ratios of the experimental shear strength for each wall, Vu, to the shearstrength of a plain wall, wall 1, Vu,W1, are listed in Table 2. The hysteretic energies, Et,dissipated by each wall normalized with respect to that of wall 1, Et,W1, are also listed.The hysteretic energy is the area enclosed by the hysteretic loops and represents the wallcapacity to mitigate the imposed load through the inelastic behavior of the walls, whichcauses cracking and permanent deformations. The level of variation in the results shown inTable 2 for the shear strength and dissipated energy reveals (up to the level of maximumshear strength) that none of the strengthening schemes had a significant effect. Therefore,cross-wall metal anchors improve neither the lateral shear strength according to this work,

–200

–100

–0.22 –0.11 0 0.11 0.22

(a) Wall 1

–200

–100

–0.22 –0.11 0 0.11 0.22

(b) Wall 3

–200

–100

–0.22 –0.11 0 0.11

(c) Wall 7

–200

–100

0.22 –0.26 –0.13 0 0.13 0.26

Lateral drift ratio (%)

(d) Wall 8

FIGURE 6 Hysteretic behavior of four of the stone walls under quasi-static in-planeexcursions.

TABLE 2 Strength, dissipated energy, and stiffness degradation of the stone walls

Wall No. W1 W3 W4 W5 W6 W7 W8

Vu/Vu,W1 1.0 1.11 1.07 0.94 0.90 1.12 1.16Et/Et,W1 1.0 0.85 0.91 1.04 0.81 1.12 1.01ku/ko 0.44 0.54 0.51 0.42 0.41 0.45 0.51

0 1 2 3 4 5 6 7

δe δuLat

Lateral displacement, δ (mm)

× Experimental data

Elasto-plastic model

1 − 0.5V ko

δ= δ δu

⎛ ⎞⎜ ⎟⎝ ⎠

FIGURE 7 Modeling of the experimental results by an equivalent elasto-plastic system.

nor the compressive strength according to Valluzzi et al. [2004]. The observation of diag-onal cracks at the drift ratio of 0.18% and the commencement of strength degradationbeyond that point are in agreement with observations in other URM wall specimens (notstone), where the load that causes diagonal cracking is very close to the maximum shearforce, which is in the vicinity of 85–100% of the maximum shear for URM [Magenes andCalvi, 1997]. The results for wall W2 are not shown as that wall was subjected to a differentaxial stress resulting in its strength exceeding the actuator capacity, and thus not cracking.The relationship between the lateral shear strength, V , and lateral displacement, δ, was non-linear with a continuous decrease in the tangent stiffness, as shown in Fig. 7. The stiffnessdegradation ku/ko at the strength limit is shown in Table 2, where it may be seen that thesecant stiffness ku is almost half of the initial stiffness ko under this small drift. ko is the ini-tial tangent stiffness of the regression line to the experimental data, and ku (=Vu,exp/δu,exp:Vu,exp and δu,exp are the experimental shear strength and corresponding lateral displacement,respectively) is the secant stiffness at the wall’s shear strength. An equivalent elasto-plasticmodel was achieved by equating the areas under the regression line of the experimentalenvelopes and the elasto-plastic curve [Elmenshawi et al., 2010b]. The two displacementindicators δe and δu are the elastic limit and the ultimate displacement, respectively, on theelasto-plastic curve.

4. Prediction of the Lateral Shear Strength of Stone Walls

Evaluation of the mechanical properties of multi-wythe unreinforced stone masonry is notan easy task. The wall is composed of different materials for each wythe and the wythesare of varying thickness along the length and up the height of the wall, increasing thecomplexity compared to single wythe URM walls. One may wonder if it is possible to

treat the wall as if it were a homogeneous material, despite the clear heterogeneity. It isdifficult to provide a comprehensive response from one set of experimental tests. For thebehavior of multi-wythe URM walls subjected to axial compression, attempts were con-ducted to evaluate the wall axial strength and elastic modulus of the whole wall once theindividual mechanical properties of each wythe were known [Binda et al., 1991, 2006;Egermann, 1993; Egermann and Neuwald-Burg, 1994]. Considering the wall as homoge-neous, regardless of the wythe composition, has also been used to estimate the mechanicalproperties of the masonry for mixed stone and brick walls [Sheppard, 1985]. This latterconcept is common for the idealization of rubble stone walls, where the randomness of thewall cross section is a maximum [Corradi et al., 2003]. Multi-wythe walls will behave asone element if strain compatibility is maintained between the different wythes. In the cur-rent work, the inner rubble core was not uniform in width and was confined by transversestones at the ends of the walls. Moreover, the walls were capped with reinforced concretebeams. These conditions simulate a stone wall in a very good environment regarding wallintegrity. No relative movement of the wythes was noticed during either static or dynamicexcursions. Therefore, the cross-sectional area A, of the wall is taken as the width, �, timesthe thickness, t for calculating average axial and shear stresses. This assumption wouldyield better results if the width of the middle core were small and the outer wythes hadsimilar mechanical properties.

The observed failure mode of the test specimens shows that shear was dominant,despite the high aspect ratio and light compressive stress applied. Thus, failure criteriaestimating the strength of URM walls failing in diagonal tension patterns are consideredherein. However, because the walls were not squat, the rocking strength is first evaluated tounderstand why rocking failure was not observed. For these walls to rock about the toe, thelateral shear strength Vu,r needs to be [FEMA 356, 2000]:

Vu,r = 0.9α1

λN, (1)

where α is a factor that considers the boundary conditions of the wall (equal to 0.5 fora fixed-free wall; and to 1.0 for a fixed-fixed wall), λ is the aspect ratio of the wall, andN is the imposed axial compression force including self-weight. With N = 395 kN, Vu,r =258.5 kN, which exceeds the experimental shear strength shown in Table 3 by a mean factorof 1.8. Thus, rocking failure would not occur. For rocking to have been the likely mode offailure in these test specimens, the aspect ratio would have to be greater than 2.45.

Generally, URM walls need to be checked against diagonal cracking, or sliding shearfailures when subject to in-plane lateral loading [Magenes and Calvi, 1997; Tomaževic,2009]. Although none of the existing shear failure criteria were based on the cyclic behav-ior of URM or stone walls, it was found that the experimental lateral strengths of dry stonewalls were similar whether they were exposed to cyclic or monotonic displacement ampli-tudes, which meant that the cyclic history had no effect on the shear strength of those walls[Vasconcelos et al., 2006]. Shear failure represented by diagonal tension cracking in URMwalls usually results in a stair-stepped crack pattern through mortar joints, but can follow astraight diagonal path through the units, depending on the relative strength of the masonryunits and the mortar. The former pattern is preferred as it provides greater “plastic” defor-mation, involving friction between the masonry units and mortar. The compressive stressperpendicular to the bed joints allows for the development of frictional forces that remainactive over higher lateral displacements. Therefore, the stepped failure mode is considereddeformation-controlled, while the straight line pattern is considered force-controlled due to

TABLE 3 Comparisons between the experimental and predicted values of wall shearstrength

Experiment Experiment/predicted

Wall no. Vu (kN)Vu/Vu,r

(Eq. 1)Vu/Vu,u

(Eq. 2)Vu/Vu,d

(Eq. 3)Vu/Vu,f

(Eq. 4)Vu/Vu,s

(Eq. 5)

W1 138.8 0.54 0.26 0.96 0.40 1.57W3 153.6 0.59 0.28 1.06 0.44 1.74W4 148.6 0.57 0.27 1.03 0.43 1.68W5 130.1 0.50 0.24 0.90 0.37 1.47W6 124.6 0.48 0.23 0.86 0.36 1.41W7 155.2 0.60 0.29 1.07 0.44 1.76W8 161.2 0.62 0.30 1.11 0.46 1.83

Mean 144.6 0.56 0.27 1.00 0.41 1.64∗SD 13.72 0.05 0.16 0.09 0.03 0.04

∗SD = Standard Deviation

its brittle nature [FEMA 356, 2000]. Hence, the feasibility of using the shear failure crite-ria for regular URM walls will be verified for the current unreinforced multi-wythe stonewalls.

4.1. Straight Diagonal Tension

Diagonal tension cracking through the stone units was not observed during the experimentalprogram due to the higher strength of the stone units compared to the mortar. Nevertheless,to evaluate the shear strength corresponding to this failure mode, the following equation isused:

Vu,u = 1

2.3 (1 + αv)

ft,uσv

√1 + σv

ft,uN, (2)

where ft,u is the direct tensile strength of the stone unit, σ v (= 0.3 MPa) is the imposedaxial compressive stresses (=N/(t.�)), and αv = 0.5λ (for a fixed-fixed wall) is the shearratio and accounts for the transition from local failure conditions to global strength of thewall. The lowest tensile strength was found to be ft,u = 1.8 MPa for the limestone [Bindaet al., 2006]. This value of ft,u is selected for the current comparison. Equation (2) is thatof Magenes and Calvi [1997] who modified the equation proposed by Mann and Müller[1982] by adding the correction factor of (1+αv). The ratios of the experimental shearstrength to that obtained by Eq. (2) are listed in Table 3.

The strength of diagonal tension cracking can also be obtained by assuming the stonewalls to be isotropic, elastic and homogeneous, and to depend only on the maximumprincipal tensile stress at the middle of the wall [Turnšek and Cacovic, 1970]. This shearstrength is:

Vu,d = 1

√1 + σv

ftN 1.0 ≤ λ ≤ 1.5, (3)

where λ is the aspect ratio of the wall. λ is used in Eq. (3) to account for the shear stressdistribution which depends on the wall aspect ratio and the ratio between shear and verticalstress, with the limits shown being proposed for fixed-fixed walls [Magenes and Calvi,1997]. ft is the referential tensile strength and is the maximum tensile stress correspondingto the lateral wall strength, being determined from experimental tests by inverting Eq. (3).However, as a simplification, FEMA 356 [2000] suggests that ft can be replaced by the bed-joint shear strength for non-stone URM walls. The assumption underlying Eq. (3) is thatthe diagonal cracking depends solely on the principal tensile stress and is not controlled byfriction theories. Sheppard [1985] suggested a value of ft = 0.08 MPa based on results fromtests on mixed stone-brick masonry walls. The best fit to the current results gives a value offt = 0.09 MPa, which is very close to the Sheppard’s value. The ratios of the experimentalshear strength to that obtained by Eq. (3) are listed in Table 3, and are all close to 1.

4.2. Stepped Diagonal Tension

The walls cracked in the mortar joints with irregular stair-stepped patterns, which weresometimes a bit blurred as shown in Fig. 5 for the limestone wythe. The patterns weredriven by the non-uniform sizes of the stone units [Elmenshawi et al., 2010b]. The shearstrength associated with this sort of cracking pattern can be evaluated with the Coulombcriterion as:

Vu,f = c + μsσv

1 + αv(�t) , (4)

where c is the cohesion strength, and μs is the friction coefficient of the masonry joints.Again, the equation is corrected by (1+αv) to account for the transition from local failureto the global strength of the masonry [Magenes and Calvi, 1997]. In the case of sliding fail-ure along a horizontal plane or dry joints in a deteriorated heritage structure, the cohesionstrength can be neglected [Magenes and Calvi, 1997; Vasconcelos and Lourenço, 2009a].The values of c and μs found in the literature vary considerably, as they depend on thetype of stone and joints being tested [Binda et al., 1994; Lourenço and Ramos, 2004;Vasconcelos and Lourenço, 2009a,b]. Given the wide ranges in these references, valuesof 0.35 MPa, and 0.65 were selected herein for c and μs, respectively. The ratios of theexperimental shear strength to that obtained by Eq. (4) are listed in Table 3.

The shear strength of stepped diagonal tension can also be predicted by Eq. (5),which is based on the behavior of a single-wythe dry joint stone wall under the actionsof combined normal and shear stresses [Lourenço et al., 2005]:

Vu,s = tan φ

[1 − 0.5λ tan φ

1 − v

)]N; v = σv

tan φ = 0.65 (= μs), and fm is the compressive strength which was taken as 1.3 MPa forthe current walls; fm was the average value of the peak compressive strengths of six ofthe eight walls tested to determine the ultimate capacity at the end of the testing program.Equation (5) was based on the assumption that a diagonal strut forms like a fan, partly inparallel at the wall toe. The maximum slope of the struts with respect to the vertical islimited by the friction angle of the joint-stone interface [Lourenço et al., 2005]. The ratiosof the experimental shear strength to those obtained with Eq. (5) are listed in Table 3.

4.3. Discussion

As may be seen in Table 3, Eq. (3) predicts the shear strength of the stone walls very wellsuggesting that the lateral shear strength of the wall is related to the principal tensile stressat the middle of the wall. The good prediction occurred despite the fact that the multi-wythestone walls are neither elastic, nor isotropic, nor homogeneous—all assumed in the deriva-tion of Eq. (3). Although the other equations recognize that the masonry is heterogeneousand anisotropic, they poorly predict the lateral shear strength of these stone walls. Thissuggests that plain stone masonry has a tendency to behave as an isotropic and homoge-neous material when the irregularity of the texture is high and the sample is large enoughfor its behavior not to be governed by localized texture [Calderini et al., 2009]. The inabil-ity of Eq. (4), in particular, to predict the shear strength of the walls despite the steppedcracking pattern is perplexing. This may be due to the resisting mechanism observed inthe walls being much more related to the tensile strength of masonry (due to the tensileprincipal stresses) than to the shear friction resistance of the unit-mortar interfaces. In fact,the friction between the mortar and stone units can add a secondary resisting mechanismafter the diagonal cracking pattern develops through sliding along the crack. Nevertheless,this secondary mechanism does not control the lateral strength of the walls. In addition, thecohesion and friction coefficient assumed were based on well-defined stone patterns, whichis not the case in the current stone walls, and a lower friction coefficient can be expected inirregular URM walls [Calderini et al., 2009]. The poor prediction with Eq. (2) is not sur-prising as the stones did not fracture. Thus, the failure was not related to the tensile strengthof the stones—the behavior of these stone walls in in-plane shear depended on the behaviorof the stone-mortar interface. Equation (5) underestimated the shear strength of the currentwalls because of the lack of dependence of the shear strength on the compressive strengthof the stone masonry and the apparent lack of dependence on the friction properties of theconstituent materials. Certainly the stone walls tested do not represent all the typologies(bond pattern) that exist in heritage structures. However, others have also reported that theshear strength of stone walls does not depend on the bond pattern for compressive stressesranging from 0.5–0.875 MPa, and that the shear strength decreases as the randomness ofthe masonry bond increases, for higher compressive stress [Vasconcelos and Lourenço,2009b].

The objective of knowing the lateral shear strength analytically is to enable identifica-tion of the equivalent elasto-plastic system that describes the in-plane behavior of the stonemasonry walls. With k/ko = 0.8, the corresponding elastic drift δe/h = 0.1% was obtainedbased on the idealization of stiffness degradation [Elmenshawi et al., 2010b]. This pro-posed elasto-plastic equivalence is useful for nonlinear static or dynamic analyses of stonemasonry walls.

5. Linear and Nonlinear Damping Mechanisms and Ratios

Damping is a way of representing the dissipation of seismic-imposed energy. Duringa seismic event, URM structures can dissipate earthquake-induced energy through dis-tinct damping mechanisms, namely viscous damping, hysteretic damping, and impactdamping. Viscous damping is the simplest way to introduce energy dissipation math-ematically in elastic analysis, and is thus a linear damping. The other two dampingmechanisms are mainly due to nonlinear behavior, but can be transferred to equivalentvalues of viscous damping. Obtaining viscous damping ratios that are equivalent to non-linear damping mechanisms is an essential requirement in seismic analysis and evaluationfor displacement-based approaches [Priestley, 1998], capacity spectrum analysis [ATC-40,1996], or the substitute structure approach [Shibata and Sozen, 1976].

5.1. Viscous Damping

A viscous damping ratio is usually assumed for stone masonry structures. The informa-tion available on this subject however, is scarce and contradictory [Benedetti et al., 1998;Mazzon et al., 2009]. The effective viscous damping ratio of a masonry structure can beevaluated if the viscous damping ratios of the individual walls are known (e.g., Priestley,1998; Shibata and Sozen, 1976). Free vibration tests were conducted on the current wallsbefore and after the in-plane static and dynamic loadings and again after the shake tabletests, so that the effect of damage on the damping mechanisms and ratios could be assessed[Elmenshawi et al., 2010a, 2010b]. A typical result is shown in Fig. 8a where the in-planeacceleration a is plotted against time t. The frequency content and dominant frequency f(Hz) obtained from the Fast Fourier Transformation (FFT) of the vibration is shown inFig. 8b.

The viscous damping ratio ζ can be measured by the well-known logarithmicdecrement χ from the acceleration response as [Elmenshawi et al., 2010a]:

χ = ln

[a (ti)

a (ti + 1/f )

]= 2π

ζ√1 − ζ 2

, or ζ = χ√4π2 + χ2

Theoretically, if the stone walls behaved like an elastic-isotropic material, the frequencyf would be a unique value for the stone walls and represent the fundamental frequency,since only the first mode of vibration can be excited by a free vibration test [Beards,1996]. However, as shown in Fig. 8b, other frequencies with small amplitudes do existdespite the dominance of one frequency. This means that there is not a unique dampingratio for the successive cycles. To overcome this obstacle, regression analysis was used todefine a damping function, Y(t), for each test to signify the degradation of the wall response(acceleration in the current study) [Elmenshawi et al., 2010a]:

Y (t) = A exp(−χ

), (7)

where A is the amplitude of the function and T (=1/f ) is the fundamental period of vibra-tion based on the dominant frequency for each phase from the results of FFT. For theundamaged stone walls, the damping function is shown in Fig. 9, from which the value ofχ = 0.19 is obtained. This, in turn, gives ζ = 3% from Eq. (6). Similarly, the dampingratios for the walls post in-plane loading and post the shake table tests are 4% and 5%,

–0.25

–0.15

–0.05

Time, t – sec.

(a) Relationship of acceleration vs. time for wall 3.

Prior to in-plane loading

Post in-plane loading

Post shake–table tests 0

0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25

Prior to in-plane loading Post in-plane

loading

Post shake-table

Frequency, f – Hz

(b) Fast Fourier Transformation (FFT) for each phase for wall 3.

FIGURE 8 Free vibration results of wall 3.

0 5 10 15 20

tY(t) = 0.96 exp

⎛ ⎞−0.19⎜ ⎟

⎝ ⎠

× Experimental data

FIGURE 9 Illustration of the damping function for the walls prior to in-plane loadings.

respectively. These ratios show that the inherent viscous damping ratio of the multi-wythestone masonry in the current walls is less than that used for other structural systems, eval-uated by others [Benedetti et al., 1998] or used by design codes (5%). It is worth notingthat the metal anchors used to tie the wythes across the walls had no effect on the dynamicproperties of the walls, in contrast to the effect of grouting as reported by Mazzon et al.[2009].

Although viscous damping was assumed to be the major contributor to energy dissipa-tion in the foregoing analysis, it was shown that Coulomb friction damping was also presentin the specimens tested and had a greater influence in the damaged states (i.e., post the in-plane loadings and post the out-of-plane tests) than in the undamaged state [Elmenshawiet al., 2010a]. However, although Coulomb friction damping influences the behavior ofstone masonry, it is impractical to consider Coulomb friction damping in the dynamic anal-ysis of such structures. Viscous damping is much easier to use in structural analysis withoutimpairing the accuracy of energy dissipation, despite its dependence on the amplitude ofvibration and the induced damage.

If the fundamental mode of vibration is assumed as the dominant mode in stiff her-itage structures, the effect of damage on the viscous damping ratio can be expressed as[Elmenshawi et al., 2010a]:

ζi = 1.89

)0.185

ζo, (8)

where ζ o is the viscous damping ratio in the undamaged state (= 3%). In Eq. (8), thedamage is represented by the in-plane drift ratio of the wall. For example, for a drift ratioof 0.18% at the strength limit state of the stone wall, the corresponding viscous dampingratio ζ i is 1.376ζ o, and if ζ o = 0.03, then ζ i = 0.041. This formulation is appealing if theconcepts of capacity spectrum analysis [ATC-40, 1996] or substitute structure [Shibata andSozen, 1976] are employed.

5.2. Hysteretic Damping

The stone masonry walls exhibited another type of damping through their hysteretic behav-ior shown in Fig. 6. In contrast to the viscous damping, hysteretic damping represents thecapability of dissipating energy in the nonlinear stage, and this type of damping could be

ViEsiδi=1

ζh,i = π

ng, ζ

Drift ratio, δ/h (%)

(b) Hysteretic damping ratio vs. drift ratio

0 0.05 0.1 0.15 0.2 0.25

Regression trend

Lower-bound value ζh = 4%

(a) Evaluation of the hysteretic

FIGURE 10 Relationship between hysteretic damping and drift ratio for stone walls.

the dominant mechanism at failure. However, an equivalent viscous damping ratio, ζ h, tothe hysteretic damping can be obtained by assuming that the viscous damping system dis-sipates the same energy per cycle as the nonlinear system [Bandstra, 1983; Chopra, 2006].For a hysteretic cycle i, Fig. 10a, ζ h is:

ζh,i = 1

Esi, (9)

where Ei is the energy dissipated (the area enclosed by the hysteretic loop) in cycle i, andEsi is as defined in Fig. 10a. The relationship between the equivalent viscous dampingratios of the specimens vs. the drift ratios is shown in Fig. 10b: there is no clear math-ematical relationship. Nevertheless, the general trend of the linear regression line showshysteretic damping increasing with drift ratio but with a poor correlation (R2 = 0.04). Thisbehavior is in contrast to the behavior of other structural systems such as reinforced con-crete, where the value of equivalent damping increases clearly as the damage increases[Elmenshawi and Brown, 2010]. Even the behavior of stone masonry differs from that ofother URM (e.g., brick) failing in shear as presented by Magenes and Calvi [1997]. In gen-eral, for URM walls, the value of the equivalent viscous damping is dependent upon theexpected failure mode; giving higher values for shear failure mechanisms and lower val-ues for flexural failure mechanisms. In other words, the equivalent viscous damping ratioincreases as the effect of shear increases in masonry walls [Magenes and Calvi, 1997]. Forrocking behavior, where the hysteretic shape is characterized by the well-known S-shape,hysteretic damping is minimal because no damage would occur and neither stiffness norstrength would degrade. Nonetheless, when rocking is combined with other flexural failuremodes (e.g., toe crushing), the hysteretic damping of URM walls is about 5% [Magenesand Calvi, 1997]. As shown in Fig.10b, for stone masonry walls failing in shear, a lower-bound constant value of 4% can be assumed as conservative. This is very close to theviscous damping ratio obtained from the free vibration tests. The difference between stonemasonry walls and other URM walls can be ascribed to the fact that stone masonry exhibitsvery limited plastic deformation compared to other URM walls. Also, the hysteric dampingobtained for the stone walls is even lower than that of other URM walls achieving the samefailure mode (diagonal tension) as described by Magenes and Calvi [1997].

To apply the concepts presented above in a design method based on displacement-based approaches, the effective viscous damping ratio is:

ζeff = ζi + ζh . (10)

The values of effective viscous damping ratios for stone masonry walls according to thecurrent study are between 7% and 9%. The lower value can be used as a conservative limitin a force-based design approach, since it will lead to a higher seismic demand.

6. Elastic Moduli of Stone Masonry Walls

As a part of the current project, elastic moduli of stone masonry walls were evaluated bystatic procedures including axial compression and shear tests [Sorour et al., 2011]. As acomparative study herein, the ratio of the shear modulus to the elastic modulus (G/E) forthe walls prior to the in-plane loadings, will be evaluated using the results of the quasi-staticand free vibration tests. The values of the initial tangent stiffness ko, Fig. 7, is determinedfor each wall as listed in Table 4 using regression analysis. The effective elastic stiffnessk = 0.8ko presented earlier can be approximated for walls with fixed-ends as:

k = 0.8ko = Et

λ3 + λ(

1.2G/E

) , (11)

where E is the elastic modulus based on static axial compression tests [Sorour et al., 2011].The value of G/E was calculated for each wall (including W2) from the quasi-static testsresults using Eq. (11) and reported in Table 4. An average value of G/E = 0.09 wasobtained, which may be compared with the value of G/E = 0.4 currently used in regu-lar design of URM. The ratio obtained agrees very well with the recent recommendationsthat a value of G/E = 0.1 should be used [Tomaževic, 2009]. There is an inherent impli-cation that G and E are not related through Poisson’s ratio as in continuum mechanics forisotropic homogeneous materials.

The G/E ratio can also be evaluated by using the results of free vibration tests.To consider the effect of shear deformation as well as flexural deformation during thefree vibration of a cantilevered stone wall, the wall is assumed to behave as a uniformshear beam and the translational vibration is calculated by one-dimensional wave theory.In order to extract the free vibration characteristics, the wall is assumed to be undamped:accordingly, for the wall shown in Fig. 11a, the applied shear force at an instant time t anda height y is:

TABLE 4 Mechanical properties of stone walls based on static and dynamic tests

Wall no.

(kN/mm)Eq.(11) f (Hz)

E (MPa)[Sorour et al.,

2011]G/E

Eq.(11) c (m/sec)

k(kN/mm)Eq.(17)

G/EEq.(18)

W1 62.1 13.5 1956 0.09 148.5 21.2 0.04W2 92.1 12.7 1636 0.18 139.6 18.7 0.04W3 55.7 12.5 2304 0.07 137.0 18.0 0.03W4 57.9 11.8 1874 0.09 130.2 16.3 0.03W5 58.4 12.2 2151 0.07 134.3 17.3 0.03W6 61.1 14.4 — — 158.7 24.2 —W7 65.1 13.4 2027 0.09 147.7 21.0 0.04W8 53.7 10.4 2135 0.07 113.9 12.5 0.02

Mean 2012 0.09 0.03

(a) Wall geometry and deformation (b) Effective wall stiffness used in shear beam analogy

u(y,t)V(t)

FIGURE 11 Shear beam analogy used to analyze the stone walls.

V (t) = k · u (y, t) , (12)

where k·u represents the restoring force of the wall prior to the elastic limit (defined as δe

in Fig. 7). k is the effective wall stiffness (the slope of the elastic line in the elasto-plasticmodel as shown in Fig. 7) as in Fig. 11b and u is the lateral displacement at time t andheight y. Also, at any time, the total time-varying force acting on the wall, V(t), equals thewall’s inertia force (mass, m × acceleration):

V (t) = m∂2u

∂t2. (13)

For the geometry shown in Fig. 11a, and at instant time t, we can assume that:

u (y, t) = ∂u

∂yh and V (t) = ∂V

∂yh . (14)

By substituting the first assumption into Eq. (12), differentiating it with respect to y andsubstituting into the second assumption, we get:

V (t) = kh2 ∂2u

∂y2. (15)

Equations (13) and (15) are equal, giving:

∂y2− 1

∂t2= 0; c2 = kh2

m. (16)

Equation (16) represents the propagation of shear waves in the wall, with c being thewave speed. Iwan [1997] obtained the value of c = 4h·f , which is within the range of100–200 m/s. Therefore,

m. (17)

The values of c corresponding to the fundamental frequencies, f , are listed in Table 4, andare within the expected range. Equation (17) can also be used to calculate the wall stiffness,

k, for a given f or c, and the results are shown in Table 4. One can observe that the values ofk obtained from Eq. (17) are lower than those obtained by quasi-static tests—Equation 11.Additionally, the stiffness of the wall (for the fixed-free boundary condition) is:

k = Et

4λ3 + λ(

1.2G/E

) (18)

Again, E represents the elastic modulus under static compression. The G/E ratios obtainedby Eq. (18) are also shown in Table 4 with an average value of 0.03. Although this averageratio of G/E is low compared to the value obtained from quasi-static test results (Eq. (11)),it seems that modelling stone walls as shear beams is reasonable and confirms that therelationship between G and E can not be tied to Poisson’s ratio. The difference betweenstatic and dynamic results could be due to the inelasticity and heterogeneity of the stonewalls.

7. Conclusions

The work presented here is an analysis of results of different static and dynamic tests onthe behavior of multi-wythe stone masonry walls. Two of the walls were plain while otherscontained different metal anchors in the transverse direction and one was constructed withtraditional stone interlocking. Based on the analyses the following remarks can be made.

● Under the loading conditions used, up to the wall shear strength, neither the metalanchors nor the traditional stone interlocking increased the strength, dissipatedenergy, or stiffness of the walls.

● The wall shear strength can be predicted successfully by assuming that the wall willcrack at the middle from the effect of principal tensile stress. Therefore, an analyticalmodel to describe the lateral force-deformation behavior can be determined.

● For stone masonry walls, the viscous damping is drift- and damage-dependent, andthere is little correlation between the hysteretic damping and the lateral drift. Thus,a lower-bound has been suggested to limit the hysteretic damping of the stone wallsto 4%, which is very close to the viscous damping ratio. The total damping ratio asrevealed by this study is within 7–9% for walls failing in diagonal tension.

● The use of static and dynamic results to evaluate the wall stiffness and ratio of shearmodulus to elastic modulus (G/E) yielded different results. The values obtainedwere considerably lower than the ratio of G/E = 0.4 being used in masonry designcodes.

Funding

The authors would like to acknowledge the support of Public Works and GovernmentServices Canada, in particular the Parliamentary Precinct Branch and the HeritageConservation Directorate, and the ISIS Canada Network of Centres of Excellence.

References

ATC-40 [1996] Seismic Evaluation and Retrofit of Concrete Buildings. Report No. SSC 96-01,Applied Technology Council, Redwood, California.

Atkinson, G. [2009] “Earthquake time histories compatible with the 2005 national building code ofCanada uniform hazard spectrum,” Canadian Journal of Civil Engineering 36(6), 991–1000.

Bandstra, J. [1983] “Comparison of equivalent viscous damping and nonlinear damping in discreteand continuous vibrating systems,” Journal of Vibration, Acoustics, Stress, and Reliability inDesign 105(3), 382–392.

Beards, C. [1996] Structural Vibration – Analysis and Damping. Arnold, London.Benedetti, D., Carydis, P., and Pezzoli, P. [1998] “Shaking table tests on 24 simple masonry

buildings,” Earthquake Engineering and Structural Dynamics 27(1), 67–90.Binda, L., Fontana, A., and Anti, L. [1991] “Load transfer in multi leaf masonry walls,” Proc. 9th

International Brick and Block Masonry Conference, 3, Berlin, Germany, pp. 1488–1497.Binda, L., Fontana, A., and Mirabella, G. [1994] “Mechanical behaviour and stress distribution in

multiple-leaf stone walls,” Proc. 10th International Brick and Block Masonry Conference, 1,Calgary, AB, Canada, pp. 51–59.

Binda, L., Pina-Henriques, J., Anzani, A., Fontana, A., and Lourenço, P. [2006] “A contributionfor the understanding of load-transfer mechanisms in multi-leaf masonry walls: testing andmodelling,” Engineering Structures 28(8), 1132–1148.

Brookes, C. and Swift, R. [2000] “Numerical modelling of masonry to explore the performanceof anchor based repair systems and the repair of monuments in Cairo,” Proc. EarthquakeSafe-Lessons to be Learned from Traditional Construction, UNESCO/ICOMOS InternationalConference, Istanbul, Turkey.

Brookes, C. and Tilly, G. [1999] “Novel method of strengthening masonry arch bridges,” Proc.Structural Faults and Repair – 99, 8th International Conference, London.

Calderini, C., Cattari, S., and Lagomarsino, S. [2009] “In-plane strength of unreinforced masonrypiers,” Earthquake Engineering and Structural Dynamics 38(2), 243–267.

Chopra, A. [2006] Dynamics of Structures, Prentice Hall, Englewood Cliffs, NJ.Corradi, M., Borri, A., and Vignoli, A. [2003] “Experimental study on the determination of strength

of masonry walls,” Construction and Building Materials 17(5), 325–337.Costa, A. [2002] “Determination of mechanical properties of traditional masonry walls in dwellings

of Faial Island, Azores,” Earthquake Engineering and Structural Dynamics 31(7), 1361–1382.Earthquake Engineering Research Institute (EERI) [2005] “Intensities and damage distribution in the

June 2005 Tarapacá, Chile, earthquake,” EERI News Letter, November.Egermann, R. [1993] “Investigation on the load bearing behaviour of multiple leaf masonry,” IABSE

Symposium, Structural Preservation of the Architectural Heritage: IABSE Report, 70, Rome,Italy, pp. 305–312.

Egermann, R. and Neuwald-Burg, C. [1994] “Assessment of the load bearing capacity of historicmultiple leaf masonry walls,” Proc. 10th International Brick and Block Masonry Conference, 3,Calgary, AB, Canada, pp. 1603–1612.

Elmenshawi, A. and Brown, T. [2010] “Hysteretic energy and damping capacity of flexural elementsconstructed with different concrete strengths,” Engineering Structures 32(1), 297–305.

Elmenshawi, A., Sorour, M., Mufti, A., Jaeger, L., and Shrive, N. [2010a] “Damping mechanismsand damping ratios in vibrating unreinforced stone masonry,” Engineering Structures 32(10),3269–3278.

Elmenshawi, A., Sorour, M., Mufti, A., Jaeger, L., and Shrive, N. [2010b] “In-plane seismicbehaviour of historic stone masonry,” Canadian Journal of Civil Engineering 37(3), 465–476.

Elmenshawi, A., Sorour, M., Parsekian, G., Duchesne, D., Paquette, J., Mufti, A., Jaeger, L., andShrive, N. [2010c] “Out-of-plane dynamic behaviour of unreinforced stone masonry,” Proc. 8th

International Masonry Conference, Dresden, Germany.FEMA 356 [2000] Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Federal

Emergency Management Agency, Washington, D.C.Foo, S. and Davenport, A. [2003] “Seismic hazard mitigation for buildings,” Natural Hazards

28(2–3), 517–535.Iwan, W. [1997] “Drift spectrum: measure of demand for earthquake ground motions,” Journal of

Structural Engineering 123(4), 397–404.Jordan, J. and Brookes, C. [2004] “The conservation and strengthening of masonry structures,” Proc.

7th Australasian Masonry Conference, Newcastle, New South Wales, Australia.

Lizzi, F. [1981] The Static Restoration of Monuments: Basic Criteria-Case Histories, Strengtheningof Buildings Damaged by Earthquakes, Sagep Publisher, Genoa.

Lourenço, P., Oliveira, D., Roca, P., and Orduna, A. [2005] “Dry joint stone masonry walls subjectedto in-plane combined loading,” Journal of Structural Engineering 131(11), 1665–1673.

Lourenço, P. and Ramos, L. [2004] “Characterization of cyclic behaviour of dry masonry joints,”Journal of Structural Engineering 130(5), 779–786.

Magenes, G. and Calvi, G. [1997] “In-plane seismic response of brick masonry walls,” EarthquakeEngineering and Structural Dynamics 26(11), 1091–1112.

Mann, W. and Müller, H. [1982] “Failure of shear-stressed masonry – an enlarged theory, tests andapplication to shear walls,” Proc. British Ceramic Society, pp. 223–235.

Mazzon, N., Valluzzi, M., Aoki, T., Garbin, E., De Canio, G., Ranieri, N., and Modena, C. [2009]“Shaking table tests on two multi-leaf stone masonry buildings,” Proc. 11th Canadian MasonrySymposium, Toronto, Canada.

Meyer, P., Ochsendorf, J., Germaine, J., and Kausel, E. [2007] “The impact of high-frequency/low-energy seismic waves on unreinforced masonry,” Earthquake Spectra 23(1), 77–94.

NBCC [2005] National Building Code of Canada, National Research Council, Ottawa, Ontario,Canada.

Priestley, M. [1998] “Displacement-based approaches to rational limit states design of new struc-tures,” Proc. Eleventh European Conference on Earthquake Engineering, Balkema, Rotterdam.

Sheppard, P. [1985] “In-situ test of the shear strength and deformability of an 18th century stone-and-brick masonry wall,” Proc. 7th International Brick Masonry Conference, Melbourne, Australia,pp. 149–160.

Shibata, A. and Sozen, A. [1976] “Substitute-structure method for seismic design in R/C,” Journalof the Structural Division 102(ST1), 11824–11831.

Sorour, M., Elmenshawi, A., Parsekian, G., Mufti, A., Jaeger, L., Duchesne, D., Paquette, J., andShrive, N. [2011] “An experimental programme for determining the characteristics of stonemasonry walls,” Canadian Journal of Civil Engineering 38(11), 1204–1215.

Tomaževic, M. [1999] Earthquake-Resistant Design of Masonry Buildings, Imperial College Press,London.

Tomaževic, M. [2000] “Seismic redesign of existing stone-masonry buildings,” European EarthquakeEngineering 3, 59–66.

Tomaževic, M. [2009] “Shear resistance of masonry walls and Eurocode 6: shear versus tensilestrength of masonry,” Materials and Structures 42(7), 889–907.

Turnšek, V. and Cacovic, F. [1970] “Some experimental results on the strength of brick masonrywalls,” Proc. Second International Brick Masonry Conference held in Stoke-on-Trent, England,The British Ceramic Research Association, pp. 149–156.

Valluzzi, M., Porto, F., and Modena, C. [2004] “Behaviour and modeling of strengthened three-leafstone masonry walls,” Materials and Structures 37(3), 184–192.

Vasconcelos, G. and Lourenço, P. [2009a] “Experimental characterization of stone masonry in shearand compression,” Construction and Building Materials 23(11), 3337–3345.

Vasconcelos, G. and Lourenço, P. [2009b] “In-plane experimental behaviour of stone masonry wallsunder cyclic loading,” Journal of Structural Engineering 135(10), 1269–1277.

Vasconcelos, G., Lourenço, P., Mouzakis, H., and Karapitta, L. [2006] “Experimental investiga-tions on dry stone masonry walls,” Proc. 1st International Conference on Restoration of HeritageMasonry Structures, Cairo, Egypt.

Vintzileou, E. and Tassios, T. [1995] “Three-leaf stone masonry strengthened by injecting cementgrouts,” Journal of Structural Engineering 121(5), 848–856.

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