Seismic Earth Pressures on Flexible Cantilever Retaining Walls With

8/10/2019 Seismic Earth Pressures on Flexible Cantilever Retaining Walls With

1/11

Full length article

Seismic earth pressures on exible cantilever retaining walls withdeformable inclusions

Ozgur L. Ertugrul a , * , Aurelian C. Tranda r ba Department of Civil Engineering, Mersin University, Ciftlikkoy 33343, Turkeyb Fugro GeoConsulting, Inc., Houston, TX 77081, USA

a r t i c l e i n f o

Article history:Received 10 April 2014Received in revised form9 July 2014Accepted 15 July 2014Available online 26 August 2014

Keywords:Cantilever retaining wallDeformable geofoam panel1- g shaking table testsDynamic earth pressurePolystyreneFlexibility ratioAnalytical approach

a b s t r a c t

In this study, the results of 1- g shaking table tests performed on small-scale exible cantilever wallmodels retaining composite back ll made of a deformable geofoam inclusion and granular cohesionlessmaterial were presented. Two different polystyrene materials were utilized as deformable inclusions.Lateral dynamic earth pressures and wall displacements at different elevations of the retaining wallmodel were monitored during the tests. The earth pressures and displacements of the retaining wallswith deformable inclusions were compared with those of the models without geofoam inclusions.Comparisons indicated that geofoam panels of low stiffness installed against the retaining wall modelaffect displacement and dynamic lateral pressure pro le along the wall height. Depending on the in-clusion characteristics and the wall exibility, up to 50% reduction in dynamic earth pressures wasobserved. The ef ciency of load and displacement reduction decreased as the exibility ratio of the wallmodel increased. On the other hand, dynamic load reduction ef ciency of the deformable inclusionincreased as the amplitude and frequency ratio of the seismic excitation increased. Relative exibility of the deformable layer (the thickness and the elastic stiffness of the polystyrene material) played animportant role in the amount of load reduction. Dynamic earth pressure coef cients were compared withthose calculated with an analytical approach. Pressure coef cients calculated with this method were

found to be in good agreement with the results of the tests performed on the wall model having lowexibility ratio. It was observed that deformable inclusions reduce residual wall stresses observed at the

end of seismic excitation thus contributing to the post-earthquake stability of the retaining wall. Thegraphs presented within this paper regarding the dynamic earth pressure coef cients versus the wall

exibility and inclusion characteristics may serve for the seismic design of full-scale retaining walls withdeformable polystyrene inclusions.

2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

1. Introduction

Studies on the reduction of dynamic earth pressures of retaining

walls have gained signi cant importance during this decade.Within these studies, utilization of geofoam inclusions appears asan innovative approach to reduce the earth pressures on retainingwalls. Several studies focused on the potential load reduction ef -ciency of geofoam inclusions, indicating that the reduction per-formance of the geofoam inclusions depends on characteristics of

the dynamic excitation, and mechanical characteristics of theback ll and deformable material.

Athanasopoulos et al. (2007), Bathurst et al. (2007), Zarnani and

Bathurst (2009) , and Ertugrul and Tranda r (2011) investigated thereduction of dynamic earth pressures of yielding rigid walls bycompressible inclusions. Subsequently, Tranda r and Ertugrul(2011) discussed the in uence of geofoam inclusions on reducinglateral dynamic earth pressure and displacements of a yieldinggravity retaining wall subjected to a real earthquake excitation.Athanasopoulos-Zekkos et al. (2012) used deformable inclusions toreduce the seismic incremental earth pressures and displacementsof yielding gravity type earth retaining walls.

In a recent study, Ertugrul and Tranda r (2013) discussed theresults of 1- g static loading tests performed on cantilever retainingwalls with EPSand XPSgeofoam inclusions. In this study, only staticload reduction ef ciency of geofoam was investigated. Based on thestatic test results, a nite element model was analyzed and the

outputs of the numerical model were validated using test data.Parametric analyses were performed to investigate the effect of

* Corresponding author. Tel.: 90 533 393 70 66.E-mail addresses: [email protected] , [email protected]

(O.L. Ertugrul).Peer review under responsibility of Institute of Rock and Soil Mechanics, ChineseAcademy of Sciences.1674-7755 2014 Institute of Rock and Soil Mechanics, Chinese Academy of

Sciences. Production and hosting by Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jrmge.2014.07.004

Contents lists available at ScienceDirect

Journal of Rock Mechanics andGeotechnical Engineering

j ou rna l homepage : www. rockgeo tech .o rg

Journal of Rock Mechanics and Geotechnical Engineering 6 (2014) 417 e 427
mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.jrmge.2014.07.004http://www.sciencedirect.com/science/journal/16747755http://www.rockgeotech.org/http://dx.doi.org/10.1016/j.jrmge.2014.07.004http://dx.doi.org/10.1016/j.jrmge.2014.07.004http://dx.doi.org/10.1016/j.jrmge.2014.07.004http://dx.doi.org/10.1016/j.jrmge.2014.07.004http://www.rockgeotech.org/http://www.sciencedirect.com/science/journal/16747755http://crossmark.crossref.org/dialog/?doi=10.1016/j.jrmge.2014.07.004&domain=pdfhttp://dx.doi.org/10.1016/j.jrmge.2014.07.004mailto:[email protected]:[email protected]


2/11

different back ll and geofoam characteristics as well as structuralperformances of the cantilever walls. Formulas were proposed toestimate the static load reduction ef ciency of geofoam inclusionsplaced against retaining walls with different characteristics. In thecurrent investigation, dynamic response of cantilever earthretaining walls with deformable inclusions subjected to dynamicloads are discussed based on 1- g shaking table test results.

2. Methodology of the study

The present study focuses on the reduction of dynamic earthforces of yielding cantilever retaining walls caused by deformablegeofoam inclusions. Deformable inclusion properties, exibility of the retaining wall, granular back ll characteristics and the excita-tion parameters signi cantly increase the complexity of themechanism of dynamic load reduction mechanism induced by thedeformable panels of geofoam. Under such circumstances, physicaltesting with shaking table serves as a versatile tool to investigatethis complex soil-geofoam-structure interaction. In the presentstudy, the results of 1- g shaking table tests performed on small-scale exible cantilever wall models using either the granular

back ll or the deformable geofoam panel-granular back ll systemare presented and discussed. Tests were conducted in a state-of-the-art laminar container to reduce the disturbance of the modelresponse from wave re ections encountered in dynamic tests

performed in the rigid containers. In uences of wall stiffness,geofoam type, inclusion thickness and seismic excitation charac-teristics (frequency and amplitude) on the dynamic earth pressuresand wall displacements were investigated.

Results of the current study were also compared with those of analytical Steedman e Zeng methodology ( Steedman and Zeng,1990 ), which was validated using data obtained from physicaltests performed on centrifuge facility.

3. Physical tests

The 1- g physical tests performed on small-scale geotechnicalmodels, an inexpensive and ef cient way to investigate thebehavior of the prototype qualitatively. However, these tests havetheir own disadvantages, e.g. the requirements of the dimensionalsimilitude theory may not be fully ful lled in 1- g physical modeltests. Some published papers ( Hazarika et al., 2003; Bathurst et al.,2007 ) also discussed 1- g shaking table test results withoutmentioning prototype dimensions and the dimensional similituderelationships. In content, dynamic centrifuge tests are more suc-cessful in satisfying the similitude relationships between the pro-

totype and the model ( Wang et al., 2005; Wang, 2012 ).Nevertheless, dynamic 1- g tests can provide a source of reliabledata for supporting numerical modeling and back analysis ( Wood,2004 ).

Fig. 1. Cross-sectional view of the model con gurations. (a) Control test; (b) Wall with geofoam inclusion.

O.L. Ertugrul, A.C. Tranda r / Journal of Rock Mechanics and Geotechnical Engineering 6 (2014) 417 e 427 418


3/11

Physical tests were conducted using a rectangular laminar sandcontainer available in the Department of Civil Engineering at the

Middle East Technical University. The uniaxial container with di-mensions of 1.0 m 1.5 m 1.0 m (length width height)consists of laminar frames, low friction linear and ball bearings,guide walls to limit vertical dilatational movements of the frames

and a thin membrane made of rubber to prevent material leakagewhen the laminar frames are moving.

Pressureand displacement transducers weremounted along thewall height to monitor pressures and displacements of the wallstem. Accelerometers were placed at different heights within theback ll and on the wall to monitor horizontal and vertical accel-erations. A cross-sectional view of the test set-up and positions of the transducers are depicted in Fig. 1. The model walls arecomposedof steel with dimensions of 700 mm 980 mm (2-4-5-8) mm (height length thickness) rigidly welded to a steelbase with dimensions of 980 mm 500 mm 8 mm(length width thickness). The connection of the wall stem tothe wall foundation was achieved by welding. Signals from thetransducers were recorded by a digital data acquisition hardwarecapable of 100 kHz sampling at each channel and signal condi-tioning elements for the required channels.

4. Material characteristics

The geotechnical properties of the dry cohesionless back llmaterial used in the tests was described by Ertugrul and Tranda r(2011) . Thegranular material is classi ed as poorlygraded sand (SP)which consists of highly angular grains. The maximum and mini-mum void ratios of the model sand were determined as 0.745 and0.436, respectively, according to the procedure described by Head(1992) . Speci c gravity ( Gs) was determined as 2.66 fromthe tests performed following ASTM D854-83 procedures.Consolidated-drained triaxial tests yielded an internal frictionangle and dilatancy angle of 43.5 and 22.5 , respectively, for aneffective con ning stress range of 5 e 15 kPa.

The densities of EPS and XPS geofoam materials used asdeformable panels in the physical tests were determined as 15 kg/m 3 and 22 kg/m 3, respectively. Low-density geofoam products werecarefully selected for this study in order to provide a low stiffnessbuffer between thewall and the cohesionlessback ll, thus allowingfor soil lateral displacements induced by the compression of thedeformable zone at very low con ning stresses.

Static and cyclic triaxial tests were carried out on geofoamsamples to determine the stress e strain relationship. Cylindricalspecimens having a height to diameter ratio of 2 were extractedfrom EPS and XPS panels by computer-controlled laser cutters atACH Foam Technologies LLC, Salt Lake City, Utah. The uniaxialcompression tests on geofoam for EPS15 and XPS22 provided yieldstresses of 39 kPa and 131 kPa, respectively, at a strain rate of 10 4 min 1. The strain rate was consistent with the loading rate of the geofoam panels during the back lling process of the 700-mmhigh retaining wall models in the physical tests.

According to the triaxial test results, EPS geofoam basically ex-hibits bi-linear stress e strain behavior with strain hardeningoccurring at 2% axial strain. Elastic modulus ( E i) representing the

linear elastic portion was determined as 1500 kPa from monotonic

Fig. 2. Typical cyclic stress e strain loops for EPS15 ( f 3 Hz; N 10 cycles). (a)D (s 1 s 3)cyclic 3 kPa, (b) D (s 1 s 3)cyclic 12 kPa.

Fig. 3. Normalized Young s modulus ( E /E 0) in relation to the cyclic axial strain

amplitude ((s

1 s

3)static 15 kPa and D

(s

1 s

3)cyclic 3e

14 kPa).

Table 1A summary of the test parameters.

Walltype

Wallexibility

ratio, dw

Inclusionmaterial

Inclusionthickness ratio,t i/H

Excitationfrequency, f (Hz)

Accelerationamplitude, amax( g )

I* 128 E: EPS15,X : XPS22orN: noinclusion

7: 0.07or14 : 0.14

4e 10 0.1 e 0.7II 524III 1024IV 8197

Note: *Bold letters are used to express test series in abbreviated form (e.g. Type-II-E7 is the abbreviated form to indicate the wall model having dw 524 and EPS15

geofoam inclusion possessing t i/H of 0.07).



4/11

loading tests. The measured elastic modulus of the EPS used in thecurrent study is signi cantly lower than that estimated by therelationship suggested by Horvath (1995) . One important cause of the low elastic modulus reported in the current study is the lowstrain rate (10 4 min 1) that has been adopted in the compressiontests performed. Most of the relationships in the literature betweenthe elastic modulus and the density of the geofoam were based onthe monotonic test results performed with a customary strain rateof 10 1 min 1 (Koerner, 2005 ). Duskov (1997) reported that loadingrate signi cantly affects the stiffness of the EPS geofoam.

XPS geofoam exhibits a well-de ned yield point in associationwith strain softening after yielding. Elastic modulus representingthe linear elastic portion was determined as 5580 kPa. The triaxialtest results also revealed that an increase in the con ning stressescausesa decrease in the elastic modulus and yields deviatoric stressof geofoam.

Stress-controlled cyclic triaxial tests were performed on EPS15and XPS22 samples to determine the dynamic modulus ( E dyn ) andthe maximum axial strain ( max ) under dynamic loads. During thetests, cyclic component of the axial stressremained below the staticcon ning stresses initially applied to the samples. Fig. 2 shows theviscoelastic stress e strain response of EPS geofoam at different cy-clic deviatoric stress levels. Based on the data obtained from cyclictriaxial tests, the Young s moduli ( E ) of the geofoam at differentaxial strains were normalized with initial modulus ( E 0) to developE /E 0 degradation curves for EPS and XPS geofoams in relation to thecyclic axial strain amplitude, as shown in Fig. 3.

In the tests, cyclic axial strain amplitudes ( ac) up to about 0.50%were observed. According to the results proposed by Tranda r andErickson (2012) , geofoam exhibits visco-elasto-plastic behaviorafter exceeding threshold of axial strain amplitude of 0.54%. Hence,the dynamic properties of the EPS and XPS geofoams reportedin this study are representative for the viscoelastic behavior of these materials. The initial Young s moduli of EPS15 and XPS22

corresponding to a cyclic strain amplitude ac 0.01% were esti-mated as 4745 kPa and 8907 kPa, respectively, using the followingequation proposed by Tranda r and Erickson (2012) :

E 0 59 :93 r 2 1622 :8r 15602 (1)

where E 0 and r are expressed in kPa and kg/m 3, respectively. Theinitial Young s moduli estimated by Eq. (1) were found to be inagreement with the results of the laboratory tests performed in thisstudy. Tranda r and Erickson (2012) indicated that results fromcyclic uniaxial compression tests performed on EPS geofoam revealinsigni cant variation in the Young s modulus for cyclic axial strainamplitudes of up to 5 10 4. Thus, the measured Young s modulusvalues at cyclic axial strain amplitudes not greater than 5 10 4 incyclic uniaxial compression tests may be appropriate to describethe small strain elastic behavior of geofoam.

5. Test procedure

The instrumented retaining wall models were placed on the 20-cm thick compacted layer of sand. During the back lling process,the wall model was kept xed against horizontal movements bymeans of lateral supports. Back ll was constituted of 10-cm lifts bydry pluviation, a commonly used method to reconstitute granularmaterials representative of some initial state ( Okamoto and Fityus,2006 ). To make use of dry pluviation technique, a steel shutter anddiffuser screen having the same dimensions with the laminarcontainer were manufactured. Based on the test results presentedby Okamoto and Fityus (2006) , hole spacing of the shutter anddiffuser screen were selected as 60 mm and 2.36 mm, respectively,in order to obtain relative densities between 70% and 75% byraining procedure. At the end of the back lling process, the dataacquisition equipment was used to monitor wall pressures on thenon-yielding wall (lateral restraints were presented). The data

Fig. 4. Retaining wall model ( dw 524) without deformable inclusion; (a) Before the dynamic phase; (b) After 0.1 g -4 Hz excitation; (c) After 0.4 g -8 Hz excitation; (d) After 0.7 g -

10 Hz excitation.



5/11

acquisition continued during the removal of the restraints accom-plished by the slow unloading of the mechanical jack located be-tween the wall model and the sides of the container. Lateral earthpressures and wall movements were monitored until no furtherwall movements and pressure redistribution occurred. The testsinvolving compressible geofoam inclusions were carried outfollowing the same procedure. However, EPS and XPS geofoampanels were installed between the wall model and the back ll priorto the pluviation. Direct shear tests were performed to determinethe interface friction between the geofoam and the granular ma-terial. The friction coef cient of the contact plane between thegeofoam and the granular back ll was found as 0.13 since thesurfaces of the geofoam panels used in the current study werecovered with plastic tape to reduce the friction between the soiland the geofoam. With decreasing frictional force at the geofoam eback ll interface, the loading axis of the earth thrust becomescloser to horizontal. In the shaking table tests, harmonic displace-ments matching the following target sinusoidal acceleration-timehistory were applied to the base of the laminar container bymeans of dynamic actuator:

ah t 8>>>>>>>>>>>>>>>:

amax4

ft sin 2p ft t < 4 f

amax sin 2p ft 4 f

t < 5

amax4

5 4 f

t f sin 2p ft 5 t 5 4 f

(2)

where t is the time, f is the frequency of the excitation, and amax isthe acceleration amplitude. Although the application of random

earthquake excitations in physical modeling studies is consideredmore realistic, Bathurst and Hatami (1998) and Matsuo et al. (1998)reported that simple harmonic base excitations can cause moreaggressive impact on the physical model when compared with theeffect of a real earthquake excitation with similar predominantfrequency and amplitude. Additionally, application of harmonicbase motion allows the physical models to be excited in the samecontrolled way by enabling more accurate comparisons to be maderegarding the effect of different input parameters investigated inthis study. A summary of the test parameters is listed in Table 1 .

Retaining wall models having different stem thicknesses wereused to investigate the in uence of relative exibility of theretaining structure on the seismically induced earth pressures andthe performance of deformable geofoam inclusions. Plane strainrelative exibility ratio ( dw ) of a retaining wall is considered as theprimary parameter affecting the response of the cantilever wall-back ll system ( Veletsos and Younan, 1997 ) and is expressed in adimensionless form as

dw 12 1 n2w GE w

H t w

3(3)

where G is the shear modulus of the back ll, H is the wall height, E wis the Young s modulus of the wall, t w is the wall thickness, and nwdenotes the Poisson s ratio of the material. Relative exibility ratiosfor four model walls were determined as 128, 524, 1024 and 8197when calculated using Eq. (3) .

6. Discussion of the test results

Residual wall displacements and surface settlements of theback ll at the end of different seismic excitation phases are

Fig. 5. Retaining wall model ( dw 524) with EPS15 deformable inclusion having t i/H 0.14. (a) Before the dynamic phase; (b) After 0.1 g -4 Hz excitation; (c) After 0.4 g -8 Hz

excitation; (d) After 0.7 g -10 Hz excitation.



6/11

depicted in Figs. 4 and 5 . It is indicated that horizontal displace-ments and back ll settlements increase as the excitations withhigher amplitude and frequency were applied to the model. EPS15

geofoam panel having a relative thickness (i.e. ratio of panelthickness, t i, to wall height, H ) t i/H 0.14 caused a signi cant in-crease in the back ll settlement as a result of the compressivedeformations of the geofoam panel.

In the test series without geofoam panels, the surface settle-ments at the end of the test were signi cantly lower whencompared with those of the geofoam tests. It was observed that the

exural wall deformations and the reduction in the back ll volumedue to dynamic densi cation are the primary factors causing set-tlement for the tests without geofoam. However, installation of acompressible element between the wall stem and the granularback ll introduces another factor, i.e. compressible deformations of the geofoam layer, which causes additional surface settlements.Horvath (2010) de ned a dimensionless parameter ( l ) called thenormalized compressible inclusion stiffness:

l EH t iP atm

(4)

where P atm is the atmospheric pressure, in the same units as E , usedto make l dimensionless. Parameter l is dependent on H /t i as canbe observed from the given formula. In the current investigation,the authors de ned t i/H as the relative thickness and used thisparameter in the discussions. During the tests, it was observed thatthe settlement in the vicinity of the wall increases as t i/H increases.

In the dynamic tests, the granular back ll subjected to dynamicbase excitation was densi ed, causing higher lateral stresses in theback ll compared with the initial condition. As the lateral loads of the geofoam buffer increases permanently due to soil densi cation,compressive deformations of the geofoam panels continuouslyincrease, causing progressive vertical back ll settlements in thevicinity of the wall. While the compressive deformations in thegeofoam panels increase, higher volume of granular back ll movesin the horizontal direction towards the wall. This causes additionalvertical back ll settlements concentrated in the vicinity of the wall.As the relative thickness ratio ( t i/H ) of the geofoam inclusion in-creases, the additional vertical settlements are induced by

compressive deformations of the geofoam.

6.1. Dynamic wall pressures and lateral displacements

In Fig. 6, the total dynamic earth pressures at the depth z H (i.e. wall base) were compared for Type-III wall models ( dw 524)subjected to a base excitation characterized by a max 0.3 g and f 4 Hz. Initial static stresses as well as the dynamic incrementalstresses for the walls with EPS15 geofoam inclusions were found tobe lower than those of the model without deformable inclusion.The increments of dynamic stresses for Type-III-E7 and Type-III-E14 models (EPS15 inclusion with t i/H 0.07 and t i/H 0.14,respectively) were signi cantly lower compared with the controlcase of the wall without geofoam inclusion (Type-III-N).

Fig. 6. Evolution of the dynamic wall pressures monitored at the wall base(amax 0.3 g, f 4 Hz).

Fig. 7. Evolutions of wall displacements for (a) Type-I-N; (b) Type-I-E14 ( dw 128); (c) Type-IV-N; (d) Type-IV-E14 ( dw 128).



7/11

The evolutions of lateral displacements at the wall top duringdynamic phase ( amax 0.3 g and f 4 Hz) for the most rigid(Type-I,dw 128) and the most exible models (Type-IV, dw 8197) arecompared in Fig. 7. The horizontal displacements monitored at thetop (indicated with bold lines) of the model Type-I ( Fig. 7a) aresigni cantly lower than those observed for the more exible modelwall Type-IV ( Fig. 7c). Residual wall displacements ( dres ) increase aswall exibility ratio increases. EPS15 geofoam inclusions with t i/

H 0.14 signi cantly reduce the dynamic incremental and residualwall displacements ( Fig. 7b and d).Based on the comparisons of the lateral dynamic pressure and

wall displacements with different exibility ratios, it can be noted

that the earth pressure against the rigid walls was reduced by thewithin-back ll deformations induced by the lateral compression of the low stiffness inclusion. The widespread back ll settlementswere considered to be an indicator of the compressive de-formations of the geofoam panel. This positive effect of thedeformable geofoam panels also reduces the exural displace-ments of the wall stem in association with the load reductionbehavior. Pressures and displacements of the walls with XPS geo-

foam panel were not presented in Figs. 6 and 7 . However, it can besaid that the XPS deformable panels have slightly low ef ciencycompared with the performance of the EPS geofoam panels.

The evolution of the total dynamic lateral force of model wallsType-I and Type-IV is depicted in Fig. 8 . Wall exibility has an effecton the residual earth force ( P res ) as well as on the dynamiccomponent ( D P dyn ) of the total thrust( Fig. 8a andc). EPS15 geofoamwith t i /H 0.14 provides signi cant reduction in P res and D P dyn forboth of the models ( Fig. 8b and d).

Fig. 8. Evolution of the total dynamic thrust for (a) Type-I-N; (b) Type-I-E14 ( dw 128); (c) Type-IV-N; (d) Type-IV-E14 ( dw 8197).

Fig. 9. The parameters used in the calculation of the dynamic earth forces according to

Steedmane

Zeng method (1990) .

Fig. 10. Normalized earth pressure pro les calculated with Steedman e Zeng method

(amax 0.3 g and f 5 Hz).



8/11

6.2. Comparisons of the test data with the results obtained bySteedman e Zeng method

One of the important studies addressing the evaluation of dy-namic lateral earth pressures of xed base cantilever retainingwalls was presented by Steedman and Zeng (1990) . In this study,the authors proposed an analytical methodology which took into

account the shear wave velocity distribution within the back ll,thus allowing for a phase difference and variable accelerationpro le in a prototype. Centrifuge test data exhibited a goodagreement with the results obtained by the analytical methodologywell known as Steedman e Zeng (S e Z) method.

The parameters used in the calculation of seismic forces withthe analytical approach suggested by Steedman and Zeng (1990)are presented in Fig. 9. The harmonic base excitation is written as

A z ; t kh g sin u t H z

V s (5)

where kh is the horizontal acceleration amplitude, V s is the shearwave velocity of the back ll, u is the angular frequency of the baseshaking, and z is the elevation measured from the wall top. For atypical xed base cantilever wall, the horizontal inertia force Q hacting on a horizontal element (thickness of d z ) of the failurewedgewithin the back ll is given by

Q h Z H

0

rH z tan a

A z ; t d z (6)

where r is the density of the back ll, and a is the inclination angleof wedge with the horizontal direction. The total dynamic thrust iscalculated with the following equation considering the equilibriumof the forces acting on the wedge shown in Fig. 9:

P ae Q h cos a 4 W sin a 4

cos d a 4 (7)

where W is the weight of the soil wedge, 4 is the angle of soil shearresistance, and d is the angle of wall friction. The total lateral earthpressure coef cient is thus obtained as

K ae 2P aegH 2

(8)

The distribution of the total lateral pressure pae ( z ) is expressedas

pae z v P ae z

v z cosa 4 kh g z cos d a 4 tan a

sin u t z V s

g z tan a

sin a 4 cos d a 4

pae z pad z pas z

9>>>>>>=>>>>>>; (9)where pad ( z ) and pas ( z ) are the dynamic and static components of the total lateral pressure, respectively. The loading point of thedynamic thrust can be expressed by

H d M d z H

P ad cos d Z

H

0

pad z cos dH z d z P ad cos d

(10)

where M d (z H) is the total bending moment at the xed base, andP ad is the dynamic component of the total thrust. Earth pressurepro les calculated with the analytical method and those obtainedfrom physical tests are presented in Figs.10 and 11 , respectively. The

Fig. 11. Normalized pressure pro les (amax 0.3 g and f 5 Hz). (a) dw 1024, without geofoam panel; (b) dw 524, without geofoam panel; (c) dw 1024, EPS15 with t i/H 0.14;

(d) dw 524, EPS15 with t i/H 0.14.



9/11

total earth pressures observed along the wall height are in goodagreement with those calculated with the analytical procedure.

However, the initial static and dynamic components were found tobe signi cantly different from those estimated by the analyticalmethod. According to the test results presented in Fig. 11, it can beinferred that the lateral arching behavior of the granular back llleads to the formation of nonlinear pressure pro les along the wall.Regarding the static and dynamic components of the total earthforce, the discrepancy between the test data and the results of theanalytical study could be explained with the arching effects pre-sented in the physical model. Pressures estimated with theanalytical methodology were found to be more representative forthe Type-I with low exibility ratio, dw 128 (comparison of Figs. 10 and 11 b).

The ratio of the dominant excitation frequency to the funda-mental frequency of the wall e back ll system plays a major role in

the magnitude of seismic pressures and wall displacements. Inorder to make comparisons of the seismic forces in relation to thefrequency ratio achieved in the tests, the rst fundamental fre-quency ( f n) of an equivalent one-dimensional linear elastic soilcolumn can be estimated by a known height ( H ), shear modulus ( G)and back ll density ( r ) as follows:

f n ffiffiffiffiffiffiffiffiG=rp 4H (11)The modi ed natural frequency f

*

n of a back ll-retaining wallsystem wasapproximated as 32 Hz using the following shape factorsuggested by Wu (1994) :

f *

n Sf n

S ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 12 ns H B2 9>>=>>;

(12)

where B is the width of the two-dimensional model. Consideringthe back ll height and the fundamental frequency of the back ll-retaining wall system for the tests carried out within this study,phase differences within the back ll could not be observed. How-ever, ampli cation of the base motion within the back ll could beobserved for the range of investigated excitation characteristics.Since this study was performed on small-scale wall models in 1- g environment, back ll phasing effects were out of the scope of the

investigation.

Loading points ( h t/H ) of the total dynamic thrust for differentexcitation characteristics are presented in Fig. 12. According to the

test data, the loading point of total thrust is estimated between0.4 H and 0.6 H from the wall base. However, the loading pointcalculated with the analytical method is lower. This discrepancyoriginates from the shape of the total dynamic pressure pro les of the physical tests and those calculated with analytical method.

6.3. Dynamic earth pressure coef cients (K ae )

In Figs. 13 e 15 , the lateral earth pressure coef cients ( K ae ) aredepicted for wall models with different exibility ratios anddeformable inclusion characteristics. According to Fig. 13 , increaseof amax causes a nonlinear increase in K ae values. A good agreementcan be noted between the coef cients calculatedwith the analytical

method and the test data corresponding to the wall withoutdeformable buffer. The earth pressure coef cients shown in Fig. 13were calculated from test data obtained from the rigid wall modelType-I ( dw 128). On the other hand, wall exibility has a prom-inent role in the dynamic earth pressures as demonstrated inFig.14 . According to the test results, the total lateral dynamic forcesdecrease as the exibility ratio of the wall increases. Deformablegeofoam inclusions reducing earth pressure coef cients dependson the inclusion characteristics and exural attributes of the wall.As observed in Fig. 14, the inclusion with the smallest stiffnessratio ( E i/t i) provides the highest reduction. Forthe wall model Type-I (dw 128), EPS15 inclusion having t i/H 0.14 provides

Fig. 12. Location of maximum thrust in relation to (a) Acceleration amplitude, amax (for f = f *

n 0:32); (b) Frequency ratio, f = f *

n (for amax 0.7 g ).

Fig. 13. Variation of dynamic earth pressure coef cient ( K ae ) with amax f = f *

n 0:15

for the Type-I model ( dw 128).



10/11

approximately 50% decrease in K ae . The same geofoam inclusionprovides only 33% decrease in dynamic earth pressure coef cientfor the model Type-IV ( dw 8197). The in uence of frequency ratio

f = f *

n on K ae values for Type-III wall ( dw 1024) is shown in Fig.15 .It can be observed that K ae values signi cantly increase as f = f *

n increases.

7. Conclusions

In this study, results of small-scale physical tests on exiblecantilever earth walls with deformable geofoam inclusions werepresented. Wall models having different exibility ratios weresubjected to harmonic base excitations. Deformable inclusionspossessing different stiffness and thickness characteristics wereinstalled between the model walls and the cohesionless granularback ll to serve as the deformable layer. Test results indicated thatthe wall exibility has a signi cant in uence on the dynamic earth

pressures. The dynamic earth forces and displacements of the walls

with deformable panels were compared with those of the modelswithout geofoam inclusions. Comparisons indicate that geofoampanels of low stiffness installed against the model retaining wallsaffect displacement and lateral pressure pro le along the wallheight. The ef ciency of dynamic load and displacement reductiondecreases as the exibility ratio of the model wall increases. On theother hand, load reduction ef ciency of the geofoam increases asthe amplitude and frequency ratio of the seismic excitation in-creases. Relative exibility of the deformable layer (the thicknessand the elastic stiffness of the polystyrene material) plays animportant role in reducing seismic earth forces. Depending on theinclusion characteristics and the wall exibility, up to 50% reduc-tion in dynamic lateral earth pressures may occur. According to thetest results, the model retaining walls without geofoam inclusionsexperienced high residual stresses when subjected to the earth-quake effect due to densi cation of the granular material.Deformable inclusions reduced residual wall stresses observed atthe end of seismic excitation, thus contributing to the post-earthquake stability of the retaining wall. Loading point of themaximum dynamic thrust varies between 0.4 H and 0.6 H ,depending on the inclusion type, exibility ratio of the wall and thecharacteristics of the harmonic motion applied to the base of themodels. Dynamic earth pressure coef cients were compared withthose calculated by the proposed analytical approach. Pressurecoef cients calculated with this method were found to be in a goodagreement with the testing results of the model walls with low

exibility ratio.The presented graphs concerning the earth pressurecoef cients

versus the wall exibility and inclusion characteristics may servefor the seismic design of full-scale retaining walls with deformablepolystyrene inclusions.

Con ict of interest

We wish to con rm that there are no known con icts of interestassociated with this publication and there has been no signi cant

nancial support for this work that could have in uenced itsoutcome.

References

Athanasopoulos-Zekkos A, Lamote K, Athanasopoulos GA. Use of EPS geofoamcompressible inclusions for reducing the earthquake effects on yielding earthretaining structures. Soil Dynamics and Earthquake Engineering 2012;41:59 e71.

Athanasopoulos GA, Nikolopoulou CP, Xenaki VC. Seismic Isolation of earth-retaining structures by EPS geofoam compressible inclusions d dynamic FEanalyses. In: Proceedings of the 4th International Conference on EarthquakeGeotechnical Engineering; 2007. Thessaloniki, Greece, Paper No. 1676 .

Bathurst RJ, Hatami K. Seismic response analysis of a geosynthetic reinforced soilretaining wall. Geosynthetics International 1998;5(1/2):127 e 66 .

Bathurst RJ, Zarnani S, Gaskin A. Shaking table testing of geofoam seismic buffers.Soil Dynamics and Earthquake Engineering 2007;27(4):324 e 32 .

Duskov M. Materials research on EPS-20 and EPS-15 under representative condi-tions in pavement structures. Geotextiles and Geomembranes 1997;15(1 e 3):147 e 81.

Ertugrul OL, Tranda r AC. Lateral earth pressures on exible cantilever retainingwalls with deformable geofoam inclusions. Engineering Geology 2013;158:23 e33 .

Ertugrul OL, Tranda r AC. Reduction of lateral earth forces acting on rigid non-yielding retaining walls by EPS geofoam inclusions. Journal of Materials in CivilEngineering 2011;23(12):1711 e 8.

Hazarika H, Okuzono S, Matsuo Y. Seismic stability enhancement of rigid non-yielding retaining walls. In: Proceedings of the 13th International Offshoreand Polar Engineering Conference, vol. 2. Cupertino, USA: International Societyof Offshore and Polar Engineers (ISOPE); 2003. p. 697 e 702 .

Head KH. Manual of soil laboratory testing. Soil classi cation and compaction tests.2nd ed, vol. 1. London: Pentech Press; 1992 .

Horvath JS. Geofoam geosynthetic. New York: P.C. Scarsdale; 1995 .Horvath JS. Lateral pressure reduction on earth-retaining structures using geo-

foams: correcting some misunderstandings. In: ASCE ER2010: Earth Retention

Conference 3, Bellevue, USA; 2010 .

Fig.15. Variation of dynamic earth pressure coef cient ( K ae ) for wall Type-III with f = f *

n(amax 0.3 g , dw 1024).

Fig. 14. Variation of dynamic earth pressure coef cient ( K ae ) with dw (base motion f = f

*

n 0 :13, amax 0.3 g ).

http://refhub.elsevier.com/S1674-7755(14)00070-5/sref1http://refhub.elsevier.com/S1674-7755(14)00070-5/sref1http://refhub.elsevier.com/S1674-7755(14)00070-5/sref1http://refhub.elsevier.com/S1674-7755(14)00070-5/sref1http://refhub.elsevier.com/S1674-7755(14)00070-5/sref1http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref3http://refhub.elsevier.com/S1674-7755(14)00070-5/sref3http://refhub.elsevier.com/S1674-7755(14)00070-5/sref3http://refhub.elsevier.com/S1674-7755(14)00070-5/sref3http://refhub.elsevier.com/S1674-7755(14)00070-5/sref4http://refhub.elsevier.com/S1674-7755(14)00070-5/sref4http://refhub.elsevier.com/S1674-7755(14)00070-5/sref4http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref9http://refhub.elsevier.com/S1674-7755(14)00070-5/sref9http://refhub.elsevier.com/S1674-7755(14)00070-5/sref9http://refhub.elsevier.com/S1674-7755(14)00070-5/sref9http://refhub.elsevier.com/S1674-7755(14)00070-5/sref10http://refhub.elsevier.com/S1674-7755(14)00070-5/sref11http://refhub.elsevier.com/S1674-7755(14)00070-5/sref11http://refhub.elsevier.com/S1674-7755(14)00070-5/sref11http://refhub.elsevier.com/S1674-7755(14)00070-5/sref11http://refhub.elsevier.com/S1674-7755(14)00070-5/sref11http://refhub.elsevier.com/S1674-7755(14)00070-5/sref11http://refhub.elsevier.com/S1674-7755(14)00070-5/sref10http://refhub.elsevier.com/S1674-7755(14)00070-5/sref9http://refhub.elsevier.com/S1674-7755(14)00070-5/sref9http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref8http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref7http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref6http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref5http://refhub.elsevier.com/S1674-7755(14)00070-5/sref4http://refhub.elsevier.com/S1674-7755(14)00070-5/sref4http://refhub.elsevier.com/S1674-7755(14)00070-5/sref4http://refhub.elsevier.com/S1674-7755(14)00070-5/sref3http://refhub.elsevier.com/S1674-7755(14)00070-5/sref3http://refhub.elsevier.com/S1674-7755(14)00070-5/sref3http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref2http://refhub.elsevier.com/S1674-7755(14)00070-5/sref1http://refhub.elsevier.com/S1674-7755(14)00070-5/sref1http://refhub.elsevier.com/S1674-7755(14)00070-5/sref1http://refhub.elsevier.com/S1674-7755(14)00070-5/sref1


11/11

Koerner RM. Designing with geosynthetics. 5th ed. Upper Saddle River, USA:Prentice Hall; 2005 .

Matsuo O, Tsutsumi T, Yokoyama K, Saito Y. Shaking table tests and analysis of geosynthetic-reinforced soil retaining walls. Geosynthetics International1998;5(1/2):97 e 126 .

Okamoto M, Fityus SG. An evaluation of the dry pluviation preperation techniqueapplied to silica sand samples. In: Geomechanics and Geotechnics of ParticulateMedia. London: Taylor and Francis Group; 2006. p. 33 e 9.

Steedman RS, Zeng X. The in uence of phase on the calculation of pseudo-staticearth pressure on a retaining wall. Geotechnique 1990;40(1):103 e 12 .

Tranda r AC, Erickson BA. Stiffness degradation and yielding of EPS geofoamunder cyclic loading. Journal of Materials in Civil Engineering 2012;24(1):119 e 24 .

Tranda r AC, Ertugrul OL. Earthquake response of a gravity retaining wall withgeofoam inclusion. In: Geo-frontiers 2011: Advances in Geotechnical Engi-neering. Reston, USA: American Society of Civil Engineers; 2011 .

Veletsos AS, Younan AH. Dynamic response of cantilever retaining walls. Journal of Geotechnical and Geoenvironmental Engineering 1997;123(2):161 e 72 .

Wang MW, Iai S, Tobita T. Numerical modelling for dynamic centrifuge model testof the seismic behaviors of pile-supported structure. Chinese Journal of Geotechnical Engineering 2005;27(7):738 e 41 (in Chinese) .

Wang MW. Dynamic centrifuge tests and numerical modelling for geotechnicalearthquake engineering in lique able soils. Beijing: Science Press; 2012 (inChinese) .

Wood DM. Geotechnical modeling. 1st ed. New York: Spon Press; 2004 .Wu G. Dynamic soil structure interaction: pile foundations and retaining structures.

PhD Thesis. Vancouver: The University of British Columbia; 1994 .

Zarnani S, Bathurst RJ. Numerical parametric study of expanded polystyrene (EPS)geofoam seismic buffers. Canadian Geotechnical Journal 2009;46(3):318 e 38 .

Dr. Ozgur L. Ertugrul is an assistant professor and grad-uate student supervisor in Department of Civil Engineer-ing, University of Mersin. He obtained his M.S. and Ph.D. inMiddle East Technical University. He earned GraduateStudies Performance Award in 2005 from Institute of Natural and Applied Sciences, Middle East Technical Uni-

versity. He made research on the dynamic characterizationof geofoam in Department of Geology and Geophysics,University of Utah in 2009. His studies mainly concentrateon the seismic response of retaining walls, reduction of earth stresses with compressible inclusions, sesmic designof tunnels and underground structures. He has expertiseon physical and numerical modeling of geotechnicalproblems. He has been involved in research projects fun-

ded by Turkish State Planning Organization, Middle East Technical University andMersin University. He served as a consultant for ground improvement and deep ex-cavations projects to the Turkish Government. He has published several papers on theseismic response of retaining walls and reduction of lateral earth stresses withdeformable geofoam inclusions. He is a member of Turkish Society of Civil Engineers,Turkish National Committee of Soil Mechanics and Foundation Engineering, Interna-tional Society for Soil Mechanics and Geotechnica Engineering. He makes paper re-views for journals such as Journal of Geotechnical and Geological Engineering,Lanslides and ASCE Journal of Materials in Civil Engineering.

http://refhub.elsevier.com/S1674-7755(14)00070-5/sref12http://refhub.elsevier.com/S1674-7755(14)00070-5/sref12http://refhub.elsevier.com/S1674-7755(14)00070-5/sref13http://refhub.elsevier.com/S1674-7755(14)00070-5/sref13http://refhub.elsevier.com/S1674-7755(14)00070-5/sref13http://refhub.elsevier.com/S1674-7755(14)00070-5/sref13http://refhub.elsevier.com/S1674-7755(14)00070-5/sref14http://refhub.elsevier.com/S1674-7755(14)00070-5/sref14http://refhub.elsevier.com/S1674-7755(14)00070-5/sref14http://refhub.elsevier.com/S1674-7755(14)00070-5/sref14http://refhub.elsevier.com/S1674-7755(14)00070-5/sref14http://refhub.elsevier.com/S1674-7755(14)00070-5/sref15http://refhub.elsevier.com/S1674-7755(14)00070-5/sref15http://refhub.elsevier.com/S1674-7755(14)00070-5/sref15http://refhub.elsevier.com/S1674-7755(14)00070-5/sref15http://refhub.elsevier.com/S1674-7755(14)00070-5/sref15http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref17http://refhub.elsevier.com/S1674-7755(14)00070-5/sref17http://refhub.elsevier.com/S1674-7755(14)00070-5/sref17http://refhub.elsevier.com/S1674-7755(14)00070-5/sref17http://refhub.elsevier.com/S1674-7755(14)00070-5/sref17http://refhub.elsevier.com/S1674-7755(14)00070-5/sref17http://refhub.elsevier.com/S1674-7755(14)00070-5/sref18http://refhub.elsevier.com/S1674-7755(14)00070-5/sref18http://refhub.elsevier.com/S1674-7755(14)00070-5/sref18http://refhub.elsevier.com/S1674-7755(14)00070-5/sref19http://refhub.elsevier.com/S1674-7755(14)00070-5/sref19http://refhub.elsevier.com/S1674-7755(14)00070-5/sref19http://refhub.elsevier.com/S1674-7755(14)00070-5/sref19http://refhub.elsevier.com/S1674-7755(14)00070-5/sref20http://refhub.elsevier.com/S1674-7755(14)00070-5/sref20http://refhub.elsevier.com/S1674-7755(14)00070-5/sref20http://refhub.elsevier.com/S1674-7755(14)00070-5/sref20http://refhub.elsevier.com/S1674-7755(14)00070-5/sref20http://refhub.elsevier.com/S1674-7755(14)00070-5/sref21http://refhub.elsevier.com/S1674-7755(14)00070-5/sref22http://refhub.elsevier.com/S1674-7755(14)00070-5/sref22http://refhub.elsevier.com/S1674-7755(14)00070-5/sref23http://refhub.elsevier.com/S1674-7755(14)00070-5/sref23http://refhub.elsevier.com/S1674-7755(14)00070-5/sref23http://refhub.elsevier.com/S1674-7755(14)00070-5/sref23http://refhub.elsevier.com/S1674-7755(14)00070-5/sref23http://refhub.elsevier.com/S1674-7755(14)00070-5/sref23http://refhub.elsevier.com/S1674-7755(14)00070-5/sref22http://refhub.elsevier.com/S1674-7755(14)00070-5/sref22http://refhub.elsevier.com/S1674-7755(14)00070-5/sref21http://refhub.elsevier.com/S1674-7755(14)00070-5/sref20http://refhub.elsevier.com/S1674-7755(14)00070-5/sref20http://refhub.elsevier.com/S1674-7755(14)00070-5/sref20http://refhub.elsevier.com/S1674-7755(14)00070-5/sref19http://refhub.elsevier.com/S1674-7755(14)00070-5/sref19http://refhub.elsevier.com/S1674-7755(14)00070-5/sref19http://refhub.elsevier.com/S1674-7755(14)00070-5/sref19http://refhub.elsevier.com/S1674-7755(14)00070-5/sref18http://refhub.elsevier.com/S1674-7755(14)00070-5/sref18http://refhub.elsevier.com/S1674-7755(14)00070-5/sref18http://refhub.elsevier.com/S1674-7755(14)00070-5/sref17http://refhub.elsevier.com/S1674-7755(14)00070-5/sref17http://refhub.elsevier.com/S1674-7755(14)00070-5/sref17http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref16http://refhub.elsevier.com/S1674-7755(14)00070-5/sref15http://refhub.elsevier.com/S1674-7755(14)00070-5/sref15http://refhub.elsevier.com/S1674-7755(14)00070-5/sref15http://refhub.elsevier.com/S1674-7755(14)00070-5/sref14http://refhub.elsevier.com/S1674-7755(14)00070-5/sref14http://refhub.elsevier.com/S1674-7755(14)00070-5/sref14http://refhub.elsevier.com/S1674-7755(14)00070-5/sref14http://refhub.elsevier.com/S1674-7755(14)00070-5/sref13http://refhub.elsevier.com/S1674-7755(14)00070-5/sref13http://refhub.elsevier.com/S1674-7755(14)00070-5/sref13http://refhub.elsevier.com/S1674-7755(14)00070-5/sref13http://refhub.elsevier.com/S1674-7755(14)00070-5/sref12http://refhub.elsevier.com/S1674-7755(14)00070-5/sref12

Documents

Seismic Earth Pressures on Flexible Cantilever Retaining Walls With