945

i) Assistant senior researcher, Earthquake and Structural Engineering Laboratory, Structures Technology Division, Railway Technical ResearchInstitute, Japan (izawa＠rtri.or.jp).

ii) Professor, Geosphere Research Institute, Saitama University, Japan (jkuwano＠mail.saitama-u.ac.jp).The manuscript for this paper was received for review on November 30, 2009; approved on June 8, 2011.Written discussions on this paper should be submitted before May 1, 2012 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku,Tokyo 112-0011, Japan. Upon request the closing date may be extended one month.

945

SOILS AND FOUNDATIONS Vol. 51, No. 5, 945–958, Oct. 2011Japanese Geotechnical Society

EVALUATION OF EXTENT OF DAMAGE TOGEOGRID REINFORCED SOIL WALLS SUBJECTED TO EARTHQUAKES

JUN IZAWAi) and JIRO KUWANOii)

ABSTRACT

The aim of this study is to establish a simple method for evaluating the extent of damage to geogrid reinforced soilwalls (GRSWs) subjected to earthquakes. Centrifuge tilting and shaking table tests were conducted to investigate theseismic behaviour of GRSWs, with special focus on the eŠects of the tensile stiŠness of the geogrids, the pullout char-acteristics and the backˆll materials. As a result, it was found that GRSWs showed large shear deformation in the rein-forced area after shaking, that such deformation was in‰uenced by the tensile stiŠness of the geogrids, the pulloutresistance and the deformation modulus of the backˆll material, and that ˆnally slip lines appeared. However, theGRSWs maintained adequate seismic stability owing to the pullout resistance of the geogrids, even after the formationof slip lines. It is considered that such slip lines appeared due to the failure of the backˆll material. Since the maximumshear strain occurring in the backˆll can be roughly estimated from the inclination of the facing panels, using a simpleplastic theory, it is possible to evaluate whether the backˆll has reached its peak state or not. The formation of sliplines observed in the centrifuge model tests could be well explained by this method. Finally, the method is proposed toestimate the failure sections in the GRSWs using a Two Wedge analysis.

Key words: earthquake, geosynthetics, reinforced soil, retaining wall, slip line (IGC: E8/H2)

INTRODUCTION

Earth structures reinforced with geosynthetics arewidely used and contribute towards the improvement ofthe stability of many kinds of earth structures. In particu-lar, steep embankments and soil walls can be constructedmore easily and more economically with geogrids thanwith other conventional methods. Besides these two ad-vantages, it is well known that geogrid reinforced soilwalls (GRSWs) have a much better seismic performancecompared to that of other conventional retaining walls.Tatsuoka et al. (1996) reported damage to some types ofretaining walls after the 1995 Hyogo-ken Nambu Earth-quake. According to their report, the GRSWs having afull-height rigid facing wall, used for railways, showedvery small displacement, although they were located inareas which experienced severe shaking, where many con-ventional gravity types of retaining walls fully collapsed.Nishimura et al. (1996) also investigated the damage toGRSWs having divided facing panels after the earth-quake. They reported that the GRSWs subjected to a seis-mic intensity of 6 or more showed no apparent failure,and maintained adequate stability during/after the earth-quake. Due to these experiences, the total number ofGRSWs being constructed has been increasing sig-niˆcantly since the Kobe earthquake, even though con-

struction works in general in Japan have been decreasingyear by year due to economic problems (Koseki et al.,2006).

However, it is natural that GRSWs show some extentof deformation during/after earthquakes, because theirreinforcing eŠect can be mobilized after a certain amountof deformation to the GRSWs themselves. In particular,there is a possibility that the deformation of GRSWscould be signiˆcant due to bad weather conditions, inade-quate construction techniques and so on. In fact, someGRSWs showed relatively serious deformation during/after the 2004 Niigata-ken Chuetsu Earthquake. One ofthe possible reasons for such severe damage is the heavyrain which hit the same area right before the earthquakeand caused saturation to most of the backˆll (Yoshida etal., 2005; The Japanese Geotechnical Society, 2007). It isobvious that damaged GRSWs with some deformationhave a factor of safety greater than one under ordinaryconditions. However, the factor of safety against the nextevent, e.g., a large earthquake or heavy rain, is not clear.In such cases, it is necessary to evaluate the residual sta-bility of the damaged GRSWs and to assess the necessityof repairing or reconstructing them for the quick recov-ery of infrastructures. Such assessments should usuallybe made based only on surface deformation, such as walldisplacement or the settlement at the crest, without a de-

946

Fig. 1. Particle size distributions of Toyoura sand and Silica sandNos. 5 and 3

946 IZAWA AND KUWANO

tailed investigation into the damaged GRSWs. Atpresent, there is only one empirical method for assessingthe failure risk of reinforced cuttings (e.g., Japan High-way Public Corporation, 2002). Thus, the purpose of thisstudy is to establish a simple and reasonable method forevaluating the extent of damage to GRSWs subjected toearthquakes based on surface deformation.

For the above purpose, it is essential to know thefailure and the deformation behaviour of GRSWsduring/after earthquakes in detail. Many studies havebeen undertaken on the seismic stability of GRSWs,focusing on the eŠects of the slope, the surface gradient,the spacing, the kind of facing, the length and the type ofreinforcement(s) (e.g., Koga et al., 1988; Koga andWashida, 1992; Sakaguchi et al., 1992; Sato et al., 1995;Takahashi et al., 1999; Watanabe et al., 2003; El-Emanand Bathurst, 2004, 2005, 2007). However, they did notmention the extent of damage to the geogrid reinforcedsoil walls subjected to earthquakes. In addition, little at-tention has been paid to the eŠect of the properties ofgeogrids (e.g., tensile strength, stiŠness and shape) or tothe soil–geogrid interaction on the seismic stability ofGRSWs, although the seismic behaviour of GRSWs maybe signiˆcantly in‰uenced by them. Therefore, in order toobserve the seismic behaviour of GRSWs and to inves-tigate the eŠect of the properties of geogrids and thesoil–geogrid interaction, a series of centrifuge shakingtable tests was conducted using some kinds of model geo-grids and backˆll material. In addition, centrifuge tiltingtable tests were conducted with the same centrifugemodels to observe in detail the failure and the deforma-tion behaviour of GRSWs subjected to a horizontal bodyforce.

It is necessary to deˆne some criteria for evaluating theextent of damage to GRSWs, which has to be evaluatedbased only on the surface deformation of the GRSWs, asmentioned above. Since GRSWs are composed of backˆllmaterial and geogrids, the failure or the extent of damagecan be determined by ruptures or pullouts of the geo-grids, the failure of the backˆll material and so on.However, the meaning of damage to the backˆll shouldbe clariˆed, because GRSWs are soil structures that aremainly composed of backˆll material. Thus, damage tothe backˆll is selected as an index to evaluate the extent ofdamage to the GRSWs, and the relationship between thesurface deformation of GRSWs and damage to the back-ˆll is discussed based on the test results. Finally, thispaper proposes a simple and rational method, using sur-face deformation, to evaluate the extent of damage toGRSWs subjected to earthquakes.

CENTRIFUGE MODEL TESTS

The purpose of centrifuge model tests is to determinethe relationship between the surface deformation ofGRSWs and the extent of damage to the GRSWs broughtabout by earthquakes. Although shaking table tests areusually conducted to establish the seismic behaviour ofsoil structures, it is di‹cult to observe the deformation in

detail during shaking, because a seismic phenomenonhappens too quickly, especially in centrifugal gravityˆelds. Besides centrifuge shaking table tests, centrifugetilting table tests were also conducted on the same cen-trifuge models used in the centrifuge shaking table tests.Centrifuge tilting table tests can apply a horizontal bodyforce to the model statically, which is the same conditionas that assumed in the pseudo static analysis used for or-dinary aseismic designs. And, the deformation of themodel can be observed in more detail than in centrifugeshaking table tests. This advantage can greatly help to de-termine the relationship between the surface deformationof GRSWs and the degree of damage to GRSWs subject-ed to a horizontal body force.

The seismic behaviour of GRSWs is probably aŠectedby the types of geogrids and backˆll material used. There-fore, the eŠects of such materials are also discussed byconducting some centrifuge tests with two types of modelgeogrids and three types of backˆll material. Particularfocus is placed on the stiŠness and the pullout character-istics of geogrids and on the particle size of the backˆll.Model setups and a test procedure will be presented belowin brief, but details of the tests may be found in Izawa(2008).

Backˆll Material and Model GeogridsToyoura sand and Silica sand Nos. 5 and 3 were select-

ed for the centrifuge tests in order to establish the eŠectof particle size, because it is well known that particle sizeaŠects the mechanical properties of backˆll (e.g., Yoshi-da and Tatsuoka, 1990). These materials are mainly com-posed of silica, but have diŠerent particle sizes, which arelarger in the order of Toyoura sand, Silica sand No. 5 andSilica sand No. 3. Particle size distribution curves areshown in Fig. 1. Each average particle size, D50, is 0.190,0.520 and 1.40 mm, respectively. All the materials wereused with a relative density of 80z in the centrifugemodels. The physical and the mechanical properties ofthe soils are summarized in Table 1. The internal friction-al angle, q?, was determined from the peak deviatorstress, (s1-s3)peak, and the conˆning pressure, s?c, was ob-tained from drained triaxial tests under conˆned pressure

947

Table 1. Properties of backˆll materials

Toyoura SilicaNo. 5

SilicaNo. 3

Average particle size: D50 (mm) 0.190 0.520 1.40

Maximum void ratio: emax 0.973 1.107 1.009

Minimum void ratio: emin 0.609 0.720 0.697

Void ratio at Dr＝80z: e 0.682 0.797 0.759

Dry unit weight atDr＝80z: gd (kN/m3) 15.4 14.3 14.5

Internal friction angle atDr＝80z: q? (9) 40.4 45.0 46.0

Deformation modulus atDr＝80z: E50 (MN/m2) 0.944*s0.726

c 0.985*s0.728c 3.329*s0.524

c

*sc: conˆning pressure (kPa)

Fig. 2. Shape of model geogrids

Table 2. Properties of model geogrids

Name CS CS2

Thickness (mm) 0.5 1.0

Tensile strength (kN/m) 7.01 20.2

Tensile strain at rapture (z) 4.21 4.72

Tangential tensile stiŠness (kN/m) 197 557

Secant tensile stiŠness (kN/m) 166 428

Fig. 3. Pullout resistance vs Pullout displacement

Fig. 4. Pullout strength vs Vertical stress

947DAMAGE IN GRSWS

levels, s?c, of 49, 98 and 147 kPa. E50 was determined asthe secant Young's modulus at half of the peak deviatorstress. The approximate equations listed in Table 1 weredetermined from the relationship between E50 and s?c.Clearly, backˆll soil with a larger particle size has a largerinternal friction angle and a higher deformation modu-lus.

Two types of model geogrids, referred to as CS andCS2, were used. Type CS was made of polycarbonateplates with a thickness of 0.5 mm. Type CS2 was made ofpolycarbonate plates with a thickness of 1.0 mm toproduce a higher tensile stiŠness than and the same sur-face friction as Type CS. The two types of geogrids hadthe same shape, as shown in Fig. 2. The shape and thematerials were selected to obtain su‹cient tensile stiŠnessand pullout resistance. The tensile properties of the geo-grids are summarized in Table 2; they were obtainedfrom tensile tests. The tensile stiŠness of Type CS2 wasabout 2.5 times higher than that of Type CS. Additional-ly, pullout tests were conducted to investigate the pulloutcharacteristics between each type of backˆll material andeach geogrid. Figures 3(a) and (b) show typical pulloutbehaviour at vertical stress levels, sv, of about 50 kPa and80 kPa, respectively. The pullout strengths are plottedagainst sv in Fig. 4, where the pullout strength was deter-

mined as the peak pullout resistance or the pulloutresistance at the maximum pullout displacement of 20mm. The apparent cohesion, cp, and the pullout frictionangle, qp, which are the interception and the gradient ofthe pullout strength and the vertical stress relation, re-spectively, were obtained from Fig. 4, as is summarized

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Table 3. Pullout characteristics

Model geogrid CS CS2 CS2 CS2

Backˆll material Toyoura SilicaNo. 5

SilicaNo. 3

Apparent cohesion: cp (kPa) 0.930 7.90 16.7 30.2

Pullout friction angle: qp (9) 21.4 40.5 44.5 46.1

Pullout strength ratio:tan qp/tan q? 0.451 0.983 0.983 1.003

Table 4. Test cases

Case Geogrid Backˆll

CS-T CS Toyoura sand

CS2-T CS2 Toyoura sand

CS2-S5 CS2 Silica sand No. 5

CS2-S3 CS2 Silica sand No. 3

Fig. 5. Model setups

948 IZAWA AND KUWANO

in Table 3. The pullout friction angle of Type CS withToyoura sand was almost half of that of Type CS2. ThisdiŠerence is attributed to the diŠerence in thickness, be-cause the surface friction between them is the same. Theapparent pullout cohesion and the pullout friction anglesof Type CS2 increased in the order of the particle size ofthe three types of sand. However, the pullout strength ra-tio, tan qp/tan q?, was almost the same for all three ofthem.

Similarity for Centrifuge ModellingThe similarity for model geogrids should be carefully

considered in centrifuge model tests on GRSWs. Manyresearchers have reported studies on the similarities (e.g.,Springman et al., 1992; Zonberg et al., 1997; Viswanad-ham and Konig, 2004; Viswanadham and Mahajan,2007). It is di‹cult to fulˆl the geometric properties be-tween the model and the real geogrid. It is more im-portant to satisfy the mechanical and the soil-geogrid in-teraction properties than to make just a miniature. Theˆrst requirement is to use a model geogrid with 1/Nreduced stiŠness compared to a real geogrid, where N in-dicates the centrifugal acceleration. To satisfy the secondsimilarity, the model geogrid must have the same frictionangle as that of a real geogrid.

Kuwano et al. (1999) investigated some mechanical andpullout characteristics of 11 kinds of geogrids used inJapan. They reported that the tensile stiŠness of real geo-grids ranged mainly from 200 kN/m to 3000 kN/m,although there was a very stiŠ geogrid with a tensile stiŠ-ness of about 11950 kN/m. The levels of tensile stiŠnessfor CS and CS2 were 166 kN/m and 428 kN/m, respec-tively, which correspond to about 8000 kN/m and 21400kN/m in centrifugal acceleration of 50 G. Although themodel geogrids were somewhat stiŠ, such high stiŠnessand large strength were necessary to obtain the pulloutcharacteristics in the pullout tests. In fact, as indicated inFig. 3, even CS2 ruptured in the pullout test conducted inthis study at a vertical pressure of 80 kPa. Past studieshave revealed that a high pullout resistance is eŠective inthe seismic stability of reinforced soil structures (e.g.,Huang et al., 2008a, b). Thus, relatively high stiŠness isnecessary to model geogrids reasonably in centrifugemodeling. Kuwano et al. (1999) also reported, in regardsto the pullout friction angle, that pullout strength ratiostan qp/tan q were about 0.5 to 1.5. As indicated in Table3, although the pullout strength ratios for CS seem to be a

little bit lower, CS2 had su‹cient pullout resistance forall three types of backˆll material. Therefore, the ge-ogrids seem to be modeled reasonably well in this study.

Outline of the Tests and Model SetupTokyo Tech Mark 3 Centrifuge (Takemura et al., 1999)

was used for both the centrifuge tilting and the shakingtable tests. Four cases were conducted with two types ofmodel geogrids and three types of backˆll material, aslisted in Table 4. The ˆrst and second parts of each casename indicate the geogrid type and the backˆll material,respectively. All the tests were conducted at a centrifugalacceleration of 50 G. The model GRSWs had a dividedfacing panel system, which is usually used for roads inJapan. Model setups for the centrifuge tilting and shak-ing table tests are shown in Figs. 5(a) and (b), respec-tively. The models were made by the air pluviationmethod to achieve a relative density of 80z in each

949

Fig. 6. Typical time histories of input waves

949DAMAGE IN GRSWS

strong box. Although a laminar container is recommend-ed for use in dynamic centrifuge model tests, especially inthe case of a level ground, it is not suitable for model testswith asymmetric models, such as retaining walls andslopes. If a laminar container were used for the shakingtable tests on GRSWs, the walls would deform towardthe backˆll. This is because the backˆll does not receiveany reaction force from the laminar wall, while it doesreceive reaction force from the facing and the relativelystiŠ reinforced zone. Residual deformation toward thebackˆll is not realistic. Thus, we used a rigid containerwith cushions on both sides of the box. For the cushions,10-mm thick urethane with a stiŠness of 210 kN/m2 wasselected. The height of the models was 150 mm, whichcorresponded to 7.5 m in prototype scale. Five layers of90-mm long geogrids were laid in the backˆll at 30-mmintervals, where the same geogrids were used along heightto clarify the behaviour of the model and the eŠect of thematerial properties. Pre-cast concrete facing panels,which are commonly used in Japan, were modelled withpolycarbonate plates with a thickness of 5 mm and trian-gular channels, as shown in Fig. 5. One geogrid was rigid-ly attached to the mid-height of one facing panel withepoxy adhesive. They were not ˆxed to each other andcould rotate relatively freely. Surface displacements weremeasured with displacement transducers. In the cen-trifuge shaking table tests, accelerometers were set in thebackˆll to measure the response acceleration. Pre-failuredeformation in the backˆll was observed from digital im-ages obtained from a CCD-TV camera. Optical targetswere set on the glass side to form a grid with an intervalof 15 * 15 mm and 10 * 10 mm for CS-T and the othercases, respectively. As optical targets, small nails, 5 mm *5 mm in length, and an OHP sheet were used. The dis-placement of the optical targets, which were set on the g-lass side wall, was determined from the images using theimage processing technique (Tayler et al., 1998). The dis-placement vectors and the strain distributions of themodels were calculated using the results of the imageanalysis.

Centrifuge Tilting Table TestsThe tilting table for the geotechnical centrifuge used in

this research was developed by Nikken Sekkei NakaseGeotechnical Institute (Saitoh et al., 1995; Ohishi et al.,1995). This system can apply static horizontal body forceto a model, as assumed in a pseudo static analysis, by tilt-ing the table with an electric motor. In this research, theGRSWs were tilted at a tilting velocity of 1.0 degree/minuntil the GRSWs collapsed at a centrifugal accelerationof 50 G. As the GRSWs did not collapse even when thetilting angle reached 209, which is the maximum tiltingangle of this system, additional tables with inclined an-gles of 109and 159were set on the tilting table for CS-Tand the other cases, respectively, and the model GRSWswere put on the inclined tables. Then, the GRSWs couldbe tilted to 309and 359, which were su‹cient tilting an-gles to observe the failure behaviour of the GRSWs.

Centrifuge Shaking Table TestsThe centrifuge shaking table tests were conducted with

a Horizontal-Vertical 2D shaker for the Tokyo TechMark 3 Centrifuge (Takemura et al., 2002). Althoughthis shaker can operate horizontal and vertical accelera-tions independently, only the horizontal acceleration wasapplied to the GRSWs in this study. As indicated in Fig.6, 20 cycles of sinusoidal waves at a frequency of 100 Hz(2 Hz in the prototype) were applied to the GRSWs dur-ing the ˆrst three shaking steps. Maximum accelerationswere approximately 5 G, 15 G and 20 G for the 1st, 2ndand 3rd shaking steps, respectively. In the followingsteps, sinusoidal waves with 40 cycles and a maximum ac-celeration of 20 G were applied to the model several timesuntil the model showed signiˆcantly large deformation.

SEISMIC BEHAVIOUR OF GRSWS

Behaviour of GRSWs Subjected to Pseudo Static Load-ing

Figure 7 shows the relationship between the horizontaldisplacement at the top facing panel and horizontal seis-mic coe‹cient kh, which is calculated by the followingequation.

kh＝tan h (1)

where h is the tilting angle. All cases showed almost thesame behaviour, as follows. The GRSWs did not showany deformation during the spinning up of the centrifugeand at the early tilting stage. Then, the GRSWs began todeform at a particular seismic coe‹cient. After that, thedeformation rate rapidly increased and the GRSWs fullycollapsed. Failure points were determined as the horizon-tal displacement began to increase inˆnitely, as shown inFig. 7. For example, in the case of CS2-T, the GRSW be-

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Fig. 7. Horizontal displacements at the top panels

Fig. 8. Distributions of maximum shear strain gmax

Fig. 9. Vertical distributions of horizontal displacements of facingpanels in centrifuge tilting table tests

950 IZAWA AND KUWANO

gan to deform at about kh＝0.38, and showed very largedisplacement due to the sliding of the reinforced area atabout kh＝0.45. In comparison with CS-T, CS2-Tshowed higher stability. This is because the CS2 typecould restrict the deformation of the reinforced area ow-ing to its higher tensile stiŠness against the pseudo statichorizontal force. CS2-S5 and S3 show relatively high sta-bility compared to that of CS2-T, because backˆll materi-al with a larger particle size has a higher internal frictionangle and a higher deformation modulus. These resultsclearly show that GRSWs having geogrids with highertensile stiŠness and backˆll material with a larger particlesize can show higher seismic stability.

Figures 8(a)–(d) show the distributions of maximumshear strain gmax around the time the GRSWs failed. Thestrain levels were calculated from the displacement of theoptical targets set on the model. The concentrated area ofgmax is considered to denote a slip line in these ˆgures.Thus, it is found that clear slip lines with a two-wedgeshape appeared in the cases of CS-T, CS2-T and CS2-S5when the GRSWs failed, as shown in Fig. 7. Further-more, these slip lines were not observed until just beforethe failure. For example, in the case of CS2-T, althoughthere is no concentrated area at kh＝0.445 (h＝24.09), aclear slip line can be seen at kh＝0.455 (h＝24.59) atwhich time the GRSW almost collapsed. In other words,the GRSWs failed immediately after the formation of sliplines. That is, failure of GRSWs can be deˆned as the mo-ment when the backˆll material reaches failure with theformation of slip lines. On the contrary, such a clear slipline was not observed in the case of CS2-S3, as is shownin Fig. 8(d). In other words, the GRSW of CS2-S3 failedwithout showing a clear slip line at a higher horizontalseismic coe‹cient.

It is thought that the formation of such slip lines resultsfrom the failure of the backˆll material due to the defor-mation of the reinforced area. In order to grasp thedeformation mode before failure, distributions ofhorizontal displacement along the height are indicated inFig. 9, which were displacements of the targets next tothe panels. The displacement of the lowest target and theinclination of the horizontal displacement distributiondenote sliding displacement and shear deformation, re-spectively, as indicated in Fig. 9. Almost the same defor-mation mode was observed in all cases. The GRSWs

showed a relatively large shear deformation. In addition,such shear deformation was signiˆcant in the lower part.That is, it is thought that the backˆll material collapsedto form slip lines due to the shear deformation. Then, thefacing panel inclinations in the lower part, uw, are plottedagainst the horizontal seismic coe‹cient in Fig. 10. Thefailure points shown in Fig. 7 are also indicated in Fig.10. This ˆgure clearly shows that the slip lines appearedand the GRSWs collapsed when the facing panel inclina-tion in the lower part reached about 3.0z for CS-T, CS2-T and CS2-S5. In the case of CS2-S3, although clear sliplines were not found, kh for a uw of 3z corresponds to thekh at failure, as shown in Fig. 7.

951

Fig. 10. Facing panel inclination at lower part vs Horizontal seismiccoe‹cient

Fig. 11. Typical time histories of horizontal displacement at middleheight of GRSWs

Fig. 12. Horizontal displacements at top facing panel vs Accelerationpower

951DAMAGE IN GRSWS

In summary, the GRSWs show large shear deforma-tion in the lower part for pseudo static horizontal load-ing. When the facing panel inclinations, due to such sheardeformation, reached about 3.0z, the backˆll materialfailed and slip lines appeared. The GRSWs collapsed im-mediately after the formation of slip lines. As mentionedearlier, the centrifuge tilting table tests can applyhorizontal body force to the GRSWs as an earthquakeload, whereby the loading conditions are the same asthose modelled in designs. The failure modes observed inthis study were almost the same as those assumed in thedesigns. This means that the concept of the present designregarding failure is valid. Although tilting table tests can-not simulate the real seismic behaviour of earth struc-tures, they are useful for observing the behaviour of theGRSWs subjected to the same horizontal body force asthat assumed in pseudo static method. We will discuss acomparison between the results of the centrifuge tiltingtable tests and the analysis with the pseudo static methodlater.

Behaviour of GRSWs during EarthquakesFigure 11 shows the time histories for the horizontal

displacement at the middle height of the GRSWs in thesecond shaking step together with the input accelerationtime history in the case of CS-T. It has been conˆrmedthat almost the same input motion could be applied ineach test. Similar deformation behaviour was observed inall the cases. Namely, horizontal displacement graduallyincreased with shaking, but the GRSWs became stableagain after the shaking ceased. In addition, the deforma-tion rate gradually decreased during the shaking. This isprobably because the tensile stress was eŠectively generat-ed in the geogrids due to the deformation of the rein-forced area, and the reinforced area could receive addi-tional conˆning pressure. This is typical deformation be-haviour for GRSWs, and such behaviour results in higherseismic stability of GRSWs in comparison to the otherconventional earth structures. In addition, no ruptureswere observed in any of the cases.

Similar to the results of the centrifuge tilting tabletests, Fig. 11 shows that higher seismic stability could beobtained in the case with stiŠer geogrids and a larger par-ticle size of the backˆll to some extent. However, the

eŠect of the maximum input acceleration as well as theshaking duration should be considered when comparingthe seismic stability of GRSWs, because GRSWs deformgradually with shaking, as described above, and the max-imum acceleration alone does not characterize the inputmotion. In order to consider both eŠects, accelerationpower IE is used here as follows:

IE＝fT

0a2dt (2)

where a is the input acceleration and T is the shaking du-ration. This index indicates the total power of the inputseismic wave like arias intensity (e.g., Kayen and Mitch-ell, 1997). Figure 12 shows the relationship between theresidual horizontal displacement after each shaking stepand the cumulative acceleration power. By using the ac-celeration power, the eŠect of the properties of the geo-grids and the backˆll material on the seismic stability ofthe GRSWs can be clearly seen.

Figure 13 shows the vertical distributions of thehorizontal displacement of the GRSWs along the height.Similar to the results of the centrifuge tilting table tests,the shear deformation in the lower part was signiˆcant.Thus, facing panel inclinations in the lower part, uw, areplotted against the cumulative acceleration power in Fig.14. For CS2-T and CS2-S5, the facing panel inclinationsexceeded 3.0z after shaking steps 3 and 2, respectively.Thus, it is assumed that slip lines had already appeared.In order to conˆrm this, the maximum shear strain distri-butions for CS2-T and CS2-S5, after some shaking steps,

952

Fig. 13. Vertical distributions of horizontal displacements of facingpanels in centrifuge shaking table tests

Fig. 14. Facing panel inclination at lower part vs Acceleration power

Fig. 15. Distributions of maximum shear strain gmax in CS2-T

952 IZAWA AND KUWANO

are shown in Figs. 15 and 16, respectively. In the case ofCS2-T, a very clear slip line can be seen in the backˆll af-ter Step 8 (Fig. 15(e)). However, it is found that gmax be-gan to concentrate around the clear slip line observed inFig. 15(b) after Step 3. Therefore, it is thought that thebackˆll material had already failed and a slip line had be-gun to appear during shaking in Step 3. Also, for CS2-S5,gmax began to concentrate around the slip line duringshaking in Step 2 (Fig. 16(b)), which can be clearly seenduring the shaking in Step 13 (Fig. 16(e)). That is, the slipline had already begun to appear during the shaking inStep 2, simultaneously with the failure of the backˆllmaterial. This result indicates that the slip lines appearedwhen the inclination of the facing panels in the lower parthad reached about 3.0z for CS2-T and CS2-S5, similarto the results of the centrifuge tilting table tests. In addi-tion, the failure mode was very similar to that in the cen-trifuge tilting table tests. On the other hand, no clear slipline appeared in CS2-S3, although the facing panel incli-nation was over 10 degrees, as shown in Fig. 17, whichshows the distributions of maximum shear strain after theshaking in Step 13. Unfortunately, a similar statementcannot be made about CS-T, because clear maximumshear strain distributions could not be obtained for it,probably due to a measurement problem.

It is thought that the seismic stability of GRSWs afterthe formation of a slip line depends on the pulloutresistance, while the stiŠness of geogrids and backˆllmaterial are mainly eŠective before the formation of a

slip line. Figure 18 shows an enlarged view of Fig. 12.CS2-T and CS2-S5 showed almost the same horizontaldisplacement before the shaking in Step 3. After that,larger displacement could be seen with the growth of aslip line in CS2-T. As mentioned earlier, CS2-S5 had alarger pullout resistance than CS2-T. This result supportsthe concept that the seismic stability of GRSWs with aslip line depends on the pullout resistance.

It should be noted that the GRSWs did not collapse inthe centrifuge shaking table tests, even after the appear-ance of slip lines. In the centrifuge tilting table tests, thedevelopment of slip lines proceeded rapidly, because thepseudo static horizontal force kept acting on the GRSWs.Thus, the GRSWs failed immediately after the formationof the slip lines. On the other hand, in the centrifugeshaking table tests, the slip lines were generated graduallywith the shaking, because the seismic horizontal force va-ried instantaneously and the models were not always sub-jected to the peak accelerations. In addition, the reinforc-ing eŠect of the geogrids could be eŠectively obtainedwith the increase in the gradual deformation of the rein-forced area in the centrifuge shaking table tests, and theGRSWs were able to reach a new stable state after eachshaking step. Therefore, the GRSWs in the centrifugeshaking table tests were able to sustain su‹cient stability,

953

Fig. 16. Distributions of maximum shear strain gmax in CS2-S5

Fig. 17. Distributions of maximum shear strain gmax in CS2-S3

Fig. 18. Horizontal displacement at top facing panel vs Accelerationpower

953DAMAGE IN GRSWS

even though the deformations were larger than those inthe centrifuge tilting table tests, as shown in Figs. 9 and13.

As mentioned earlier, the model geogrids used in thisstudy were modeled well on tensile stiŠness and pulloutresistance. The tensile strength of the model geogridsmight be higher than those of practical geogrids used forGRSWs with a height of 7.5 m. If an ideal geogrid withlower stiŠness were used in the centrifuge model tests, it isthought that similar deformation and failure behaviourwould be observed in the test series. This is because thestrain at failure is generally larger than 10z, and thebackˆll will fail before the rupture of the geogrids.

CRITICAL INCLINATION OF FACING PANELS OFGRSWS

As mentioned above, the formation of slip lines is con-sidered to be one of the most important factors which canindicate the degree of damage to GRSWs. It is very im-portant to deduce the formation of a slip line in the back-ˆll in order to evaluate the extent of damage to theGRSWs after earthquakes. The centrifuge test resultsconducted in this study clearly indicate that slip lines mayappear due to the failure of the backˆll material when theinclination of the facing panels of the GRSWs reaches aparticular value. Such an inclination is deˆned as the crit-ical facing panel inclination, ucr. Here, the relationshipbetween the inclination of the facing panels and the ex-tent of damage to the backˆll is discussed in order to re-late ucr and the failure of the backˆll. Bransby and Milli-gan (1975) proposed a simple method to evaluate the gmax

occurring in the backˆll behind a sheet pile wall using thefacing panel inclination of the wall with the followingequation:

gmax＝2uw sec n (3)

where gmax is the maximum shear strain in the backˆll, uw

is the facing panel inclination of the wall and n is thedilatancy angle of the backˆll material. This relation wasderived from a simple plastic theory (Bransby and Milli-gan, 1975). Furthermore, they conˆrmed that theproposed equation could provide a good agreement withthe test results conducted by Bransby (1972). This equa-tion is very useful for determining the gmax occurring inthe backˆll, because the facing panel inclination and theproperties of the backˆll material are the only informa-tion required. However, it is not a daily practice to deter-mine the dilatancy angle of the backˆll material from ele-ment tests. Figure 19 shows the relationship between thefacing panel inclination and the maximum shear straincalculated by the proposed equation with some possibledilatancy angles. The results show that the eŠect of thedilatancy angle on the calculated maximum shear strain issmall enough to be considered negligible. Thus, theproposed equation can be simpliˆed as follows, assumingthat the dilatancy angle is zero:

gmax＝2uw (4)

954

Fig. 19 Maximum shear strain in the backˆll vs Inclination of the wall

Fig. 20. Results of drained tri-axial tests under s?c＝98 kPa

954 IZAWA AND KUWANO

Using this equation, the maximum shear strain induced inthe backˆll of GRSWs may be approximately determinedfrom the inclination of the facing panels.

In both the centrifuge tilting and the shaking tabletests, the slip lines appeared when the facing panel incli-nation reached about 3.0z in the case of CS-T, CS2-Tand CS2-S5. At that time, the maximum shear strain oc-curring in the backˆll was estimated to be about 6.0z us-ing Eq. (4). Figure 20 shows the relationships between thedeviator stress and the maximum shear strain for Toy-oura sand and Silica sand Nos. 5 and 3. They were ob-tained from drained triaxial compression tests at the con-ˆning pressure of 98 kPa, which is almost the same pres-sure as the vertical pressure in the lower part of theGRSWs used in this study. As shown in this ˆgure, Toy-oura sand and Silica sand No. 5 show their peak deviatorstress levels at the maximum shear strain of 6.2z and5.7z, respectively. These values obviously correspond tothe calculated maximum shear strain levels at failure.This means that the slip lines appeared when the maxi-mum shear strain in the backˆll reached their peak states.That is, the maximum shear strain in the backˆll can beevaluated using Eq. (4) with only the inclination of thefacing panels of the GRSW. Therefore, the critical facingpanel inclination of GRSWs, ucr, at which a slip line ap-

pears, can be determined by the following equation:

ucr＝12

gpeak (5)

where gpeak is the maximum shear strain at the peak stateof the backˆll material. In the case of CS2-T and CS2-S5,slip lines appeared at almost the same facing panel incli-nation. This is because Toyoura sand and Silica sand No.5 show their peak values at almost the same maximumshear strain. CS-T also showed the slip line at almost thesame facing panel inclination, which had the same back-ˆll material but a diŠerent geogrids from those of CS2-T.On the other hand, the GRSW of CS2-S3 did not show aclear slip line, as silica sand No. 3 did not show a clearpeak in its stress-strain relationship, as shown in Fig. 20.As shown in Eq. (5), ucr can be determined only with theproperties of the backˆll. Test results conˆrmed the factthat slip lines appeared at almost the same inclination ofthe facing panel in cases of CS-T and CS2-T, which hadthe same backˆll but diŠerent geogrids. This is becausethe formation of a slip line is attributed to the failure ofthe backˆll. It is noted that the seismic stability ofGRSWs are aŠected by the properties of the geogrids be-fore the formation of a slip line, and the deformation ofGRSWs can be eŠectively conˆrmed using geogrids withhigh tensile strength and a large pullout resistance.

The extent of damage to geogrid reinforced soil wallssubjected to earthquakes can be evaluated by deducingthe formation of a slip line in the backˆll with Eq. (5). Inaddition, it is possibile to use ucr as the limit value in per-formance based designs.

LOCATION OF SLIP LINE IN GRSWS

The formation of slip lines in GRSWs can be evaluatedwith the proposed equation and the facing inclination ofthe GRSWs if the stress-strain relationship of the backˆllmaterial is known. Furthermore, if the location of theslip lines can be obtained, this information will be veryuseful for evaluating the residual stability of the damagedGRSWs. It can produce quite useful information forquick assessments of the necessity for repair or recon-struction. Therefore, a method for evaluating the loca-tions of slip lines is discussed in the following.

Two Wedge AnalysisThe Two Wedge method is widely used for evaluating

the seismic stability of GRSWs (e.g., Cai and Bathurst,1996; Ling et al., 1997), which gives the horizontal seis-mic coe‹cients at failure and the locations of the sliplines. Since the GRSWs showed the Two Wedge type offailure sections in the centrifuge tests, the Two Wedgemethod is applicable to seismic stability analyses ofGRSWs.

Figures 21(a) and (b) show the failure sections ofGRSWs assumed in the Two Wedge analysis and theforce equilibrium between Wedge A and Wedge B, re-spectively. In the analysis, the minimum factor of safetyagainst the sliding of Wedge B is determined by changing

955

Fig. 21. Failure section and equilibrium of forces assumed in Two Wedge analysis

Fig. 22. Relationship between safety factor against sliding andhorizontal seismic coe‹cients at failure with peak pulloutresistance

955DAMAGE IN GRSWS

va and vb, which are the angles of the slip lines forWedges A and B, respectively. The driving force for thesliding of Wedge B, SF, is calculated as follows:

SF＝khWB cos vB＋(1－kv)WB sin vB

＋PAE cos (qw－vB) (6)

where kh and kv are the horizontal and the vertical seismiccoe‹cient, WB is the weight of the Wedge B, PAE is thedynamic active earth force acting on Wedge B and qw isthe friction angle between Wedge A and Wedge B. Thedynamic active earth pressure is calculated using theMononobe-Okabe earth pressure theory (Mononobe,1924), and qw is deˆned as being equal to q? in this analy-sis. The resistance force, SR, contains the shearresistance of the backˆll soil and the pullout resistance, asfollows:

SR＝s－khWB sin vB＋(1－kv)WB cos vB

＋PAE sin (d－vB)＋Rp sin vBttan q＋RP cos vB＋clB. (7)

where RP is the pullout resistance, c is the cohesion of thebackˆll material and lB is the length of the slip line ofWedge B. Accordingly, a factor of safety against the slid-ing of Wedge B, Fs, can be expressed as follows:

Fs＝SRSF

. (8)

Results and DiscussionFigure 22 shows the relationship between the factors of

safety against sliding and the horizontal seismiccoe‹cient at failure. In this analysis, peak pulloutresistances were used, as listed in Table 3. The horizontalseismic coe‹cients at failure, obtained in the centrifugetilting table tests, are also indicated in the ˆgure. It isclear that Two Wedge analyses, with the peak pulloutresistances, produce too high of a safety factor. Figures23(a)–(d) show the calculated failure sections. There arevery deep calculated slip lines behind the reinforced area,although the slip lines in the reinforced area are almostthe same as those in the test results. In the Mononobe-Okabe theory, the inclination of a slip line behind thewall increases with the seismic coe‹cient. An unrealisti-cally large sliding block was observed behind the rein-forced area, when the reinforced soil walls did not col-

lapse against the very high seismic coe‹cient in the calcu-lation with the peak pullout resistance. It is probably be-cause excessively large pullout resistances were used forthe calculations. As shown in Fig. 24, a large pullout dis-placement is necessary to obtain the peak pulloutresistance for all geogrids. For example, a pullout dis-placement of about 6 mm is necessary for obtaining thepeak pullout resistance in case CS2-T. Such pullout dis-placement is too large for the model GRSWs, because thehorizontal displacement at the lower facing panel couldbe estimated to be about 1 mm when the GRSW showedclear slip lines and failed in the centrifuge tilting tabletests. That is, it is considered that the pullout resistance ata pullout displacement of about 1 mm was mobilized atthe failure of the GRSW as a whole, as indicated in Fig.24. Then, the mobilized pullout resistances at failure wereevaluated properly based on the results of the pullout testresults and Two Wedge analyses were carried out again.The pullout parameters used for this analysis are summa-rized in Table 5.

Figure 25 shows the relationship between the horizon-tal seismic coe‹cients and the factors of safety obtainedfrom the Two Wedge analyses with the mobilized pulloutresistances. It is clear that the mobilized pulloutresistances were able to yield give reasonably goodresults. These results reveal that the Two Wedge methodcan adequately simulate the force equilibrium in GRSWssubjected to pseudo static loading, which is used in aseis-

956

Fig. 23. Failure sections obtained from Two Wedge analysis with peakpullout resistance

Fig. 24. Peak and mobilized pullout resistance

Table 5. Pullout characteristics used for Two-Wedge analysis withmobilized pullout resistance

Geogrid CS CS2 CS2 CS2

Back ˆll soil Toyoura Silica 3 Silica 5

Internal friction angle:q? (deg.) 41.0 46.0 51.0

Apparent pullout cohesion:cp (kPa) －0.221 15.2 16.6 16.4

Pullout friction angle:qp (deg.) 11.0 13.0 17.7 22.5

Pullout strength ratio:tan qp/tan q? 0.224 0.265 0.309 0.335

Fig. 25. Relationship between safety factor against sliding andhorizontal seismic coe‹cients at failure with mobilized resistance

956 IZAWA AND KUWANO

mic designs. Figure 26 shows the slip lines obtained bythe stability analyses. They are very similar to those ob-tained in centrifuge tilting and shaking table tests. Thismeans that the Two Wedge method can give potential slip

lines in GRSWs subjected to earthquakes if the mobilizedpullout resistance is properly used in the analysis.

As mentioned before, in another series of tests, aGRSW with extremely soft geogrids (Izawa and Kuwano,2010), whose tangential and secant tensile stiŠness wasabout 300 kN/m and 100 kN/m in prototype, respec-tively, failed when the backˆll failed with slip lines, and itwas far before the deformation with which a peak pulloutresistance was mobilized.

CONCLUSIONS

This paper has discussed how to evaluate the extent ofdamage to geogrid reinforced soil walls (GRSWs) sub-jected to earthquakes. For this purpose, centrifuge tiltingand shaking table tests were conducted, with special fo-cus on the eŠects of the tensile stiŠness of the geogrids,the pullout characteristics and the particle size of thebackˆll material. As a result, the following conclusionswere obtained.(1) GRSWs subjected to pseudo static horizontal loading

show large shear deformation in the lower part of thereinforced area. Such deformation can be in‰uencedby the tensile stiŠness of the geogrids and the defor-mation modulus of the backˆll material. That is,large seismic stability can be obtained by using stiŠergeogrids and backˆll material. Due to such deforma-tion, clear slip lines appear in and behind the rein-

957

Fig. 26. Failure sections obtained from Two Wedge analysis withmobilized pullout resistance

957DAMAGE IN GRSWS

forced area; they are triggered by the failure of thebackˆll material. Eventually, GRSWs fully collapseddue to the sliding of the reinforced area.

(2) GRSWs subjected to seismic loading show almost thesame deformation mode as those subjected to pseudostatic horizontal loading. That is, the large sheardeformation in the lower part is signiˆcant and suchdeformation can be in‰uenced by the tensile stiŠnessof the geogrids and the deformation modulus of thebackˆll material as well. Finally, clear slip lines mayappear due to the failure of the backˆll material.However, GRSWs do not fully collapse. They main-tain adequate seismic stability owing to the pulloutresistance of the geogrids even after the formation ofslip lines. Seismic stability after the formation of sliplines greatly depends on the pullout resistance be-tween the geogrids and the backˆll material.

(3) The maximum shear strain in the backˆll, gmax, can beestimated from the inclination of the facing panels ofthe GRSWs, uw, and the following equation:

gmax＝2uw

which was derived from a simple plastic theory.When the maximum shear strain in the backˆll, cal-culated by the equation, reaches the maximum shearstrain at the peak state, gpeak, the backˆll materialfails and slip lines appear simultaneously, which de-velop with deformation due to earthquakes. There-fore, the critical facing panel inclination of GRSWs,ucr, can be given as follows:

ucr＝12

gpeak.

Using this equation, the formation of a slip line inGRSWs can be evaluated with only the facing panelinclination of the GRSW. As a slip line appears dueto the failure of the backˆll, the formation of a slipline can be evaluated with only the properties of thebackˆll.

(4) The location of a slip line can be obtained by the TwoWedge method. In the analysis, however, the mobi-lized pullout resistance should be used instead of thepeak pullout resistance. The former is the pulloutresistance at the displacement inducing a failure ofthe backˆll; it is achieved at a much smaller displace-ment than the latter. The results obtained from theTwo Wedge analysis help to evaluate the remainingstability of GRSWs after an earthquake.

ACKNOWLEDGEMENTS

The authors would like to express special thanks to Mr.Sakae Seki (Tokyo Institute of Technology), Mr. YoshiroIshihama (Nippon Steel Corporation) and Mr. KosukeOkano (Bridgestone Corporation) for their great contri-butions to the centrifuge tests and data analysis. Theywould also like to oŠer heartfelt thanks to ProfessorOsamu Kusakabe (Ibaraki National College of Technolo-gy), Professor Hideki Ohta (Chuo University), Dr. JiroTakemura (Tokyo Institute of Technology) and Dr. Aki-hiro Takahashi (Tokyo Institute of Technology), whoprovided invaluable comments and warm encourage-ment.

NOTATIONS

kh: Horizontal seismic coe‹cientkv: Vertical seismic coe‹cienth: Tilting angle (9)n: Dilatancy angle (9)

q?: Internal friction angle of soil (9)tp: Pullout resistance (kPa)qp: Pullout internal friction angle (9)cp: Pullout apparent cohesion (kPa)uw: Surface inclination of the wall (z)ucr: Critical surface inclination (z)

gmax: Maximum shear straingpeak: Maximum shear strain at peak state of backˆll

958958 IZAWA AND KUWANO

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