1 INTRODUCTION. t max. Tie-back method Figure 1 Internal stability analysis of geogrid-reinforced retaining wall in tie-back method

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1 ABSTRACT: The reiforig effets of geogrid-reifored soil are geerall evaluated b the tesile effet due to the tesile fore of a geogrid. However, we have experimetall examied the existee of the ofiig effet, whih is oe ompoet of the reiforig effets ad is idepedet o the tesile fore of a geogrid. A evaluatio method i whih the reiforig effet a be divided ito tesile effet ad ofiig effet is proposed related to the dilata rate of reifored soil mass. The mobilized ofiig effet is give b a futio of the dilata rate, i whih the basi idea is i the assumptio of the dissipated eerg doe b uit volume of the reifored soil mass. The ofiig effet is itrodued ito the tie-bak wedge method of geogrid-reifored retaiig walls i a pratial desig. A ew formula for alulatig the maximum tesile fore of geogrid mobilized o the slidig plae was derived o the basisi of Rakie s ative earth pressure theor. INTRODUCTION The reifored effets of geogrid-reifored soil are geerall evaluated b the tesile effet aloe due to the tesile fore of a geogrid. Some researhers reported, based o the i-situ measuremets, that the tesile fore of a geogrid, whih should be mobilized for the stabilit of a struture, was ot full mobilized i soil, although the struture maitaied the suffiiet stabilit. The other researhers reported that a strog earthquake iflited little damage o a reifored struture. These studies suggest the existee of a additioal reiforig effet other tha the tesile effet due to tesile fore of a geogrid. I a previous stud, the reiforig effets of geogrid-reifored soil were experimetall examied. As a importat result, the existee of a additioal reiforig effet i laborator ad model tests was ofirmed, ad the additioal effet was defied as the ofiig effet (Ohiai et al., 996, 998; Kawamura et al, 2;Yasufuku et al., 22). Critial slidig plae t max Reiforemet θ P R P R siθ Tie-bak method Figure Iteral stabilit aalsis of geogrid-reifored retaiig wall i tie-bak method P R osθ Figure 2 Diret shear test o reifored soil 385

2 Shear stregth, s + T Reifored No-reifored taφ taφ Tesile effet Shear stregth, s + T Reifored (+β)taφ No-reifored taφ taφ Cofiig effet Tesile effet σ (+β)σ Normal stress, σ Normal stress, σ Cofiig effet Figure 3 Relatioship betwee shear stregth, s ad ormal stress o slidig plae, σ, osiderig ol tesile stress Figure 4 Relatioship betwee s ad σ, osiderig both of tesile ad ofiig effets It has bee foud from a series of laborator tests that the ofiig effet mobilized i the reifored soil mass exists, whih is idepedet o the tesile fore of a geogrid. The quatitative evaluatio is requested to appl the ofiig effets to the geeral geogrid-reifored soil struture. I the preset stud, the ofiig effet was evaluated quatitativel b experimetal ad theoretial osideratios. A parameter for estimatig the ofiig effet is derived as a futio of the dilata agle of the reifored soil mass i whih the importat ke idea is i a assumptio of the dissipated eerg doe b uit volume of reifored soil mass. It was itrodued ito the tie-bak wedge method, whih is oe of the most widel used method i the world, based o Rakie s earth pressure theor as show i Figure. A ew formula that takes ito aout the ofiig effet related to the soil dilata behaviour is proposed for hekig the safet of eah laer of a geogrid. Fiall, ritial height of geogrid reifored retaiig wall, whih are alulated b tie-bak wedge method with ad without osideratio of the ofiig effet, are disussed. 2 REINFORCING EFFECTS IN GEOGRID-REINFORCED SOIL The reiforig effets of geogrid-reifored soil are ofte evaluated b ol the tesile effet due to the tesile fore of a geogrid. Jewell ad Wroth (987) arried out diret shear tests o reifored soil, as show i Figure 2, ad the showed that the shear resistae of reifored soil ireased b τ EXT = PR AS ( si θ taφ + osθ ) () where τ EXT is the iremet of shear resistae, P R is the mobilized tesile fore of the reiforemet, A S is the area of the slidig plae, φ is the iteral fritio agle of soil ad θ is the agle betwee the reiforemet ad the slidig plae. Equatio () a be osidered as the tesile effet due to the tesile fore of a geogrid. As show i Equatio (), τ EXT does ot deped o the ormal stress o the slidig plae ad it is equal to the iremet of apparet ohesio of soil, T, i Figure 3. Cosiderig this tesile effet, the relatioship betwee the shear stregth of reifored soil, s R, ad the ormal stress, σ, a be expressed as s R = + T P = + A R S + σ taφ ( siθ taφ + osθ ) + σ taφ (2) Fukushima et al. (988) arried out the large-sale triaxial ompressio tests usig geogrid-reifored sad, ad their results learl showed the iteral fritio agle ireases. 386

3 Geogrid Critial slidig plae Agle : θ Shear stregth, s (kpa) (a) Tooura sad T=.96kN θ=4 R=.57 D r=85%.98kn.373kn No-reifored Normal stress, σ (kpa) Vertial load : P Soil Upper shear box Fixed ed θ Lower shear box Shear stress : τ Overburde pressure : σ Slidig plae Tesile fore : T Geogrid Shear stregth, s (kpa) (b) Masado θ =4 R=.57 ρ d=.83kn/m 3.98kN T=.96kN No-reifored.373kN Normal stress, σ (kpa) Figure 5 Sketh of shear box i test apparatus Figure 6 Tpial test results relatioship betwee shear stregth, s, ad ormal stress σ, uder the oditio of various tesile fores of geogrid We have defied the ofiig effet, whih will reflet a apparet iremetal ofiig stress i reifored soil mass, as a effet that is idepedet o the tesile effet, ad also we have proposed a evaluatio method that takes ito aout both the tesile effet ad the ofiig effet, as show i Figure 4. βtaφ i Figure 4 is the iremet of the slope of the reifored lie of the s-σ relatioship. However, i order to simpl itrodue the ofiig effet ito a desig method, the shear stregth of reifored soil should be evaluated ot as the iremet of the iteral fritio agle, βtaφ, but as the iremet of the ormal stress, βσ, as follows (Ohiai et al.,996, 998): P s = + R ( siθ taφ + osθ ) + ( + β ) σ taφ (3) A S The ofiig effet is believed to be the effet of restritio of soil aroud the geogrid b the geogrid, ad the ofiig stress aroud the geogrid apparetl ireases. I other words, this idea idiates that the ofiig effet is losel oeted with the dilata behaviour of reifored soil mass. 3 EXPERIMENTAL OBSERVATIONS OF CONFINING EFFECTS A ew shear test apparatus was developed to ivestigate the reiforig effets o the slidig plae of geogridreifored soil mass, as show i Figure 5 (Ohiai et al., 996). The shear box is retagular i shape ad is 2 mm wide, 2 mm log ad 38 mm high. The shear box is divided ito two equall sized upper ad lower parts b slidig plae ilied b a agle of θ. Oe ed of the geogrid is fixed to the upper part of the shear box, so that the slidig soil mass with geogrids moves as a rigid blok. This is the etral feature. A o- 387

4 T3 T2 Shear stregth, s + T3 + T2 + T Reifored (+β)taφ No-reifored taφ T ( + β) σ βσ θ Slidig plae σ Geogrid Normal stress, σ Figure 7 Method for evaluatig shear stregth of reifored soil Figure 8 Coditio of ormal stress o the slidig plaes i geogrid-reifored soil mass stat tesile fore of the geogrid is provided so that the ofiig effet a be estimated separatel from the tesile effet. Two kids of soil, dr Tooura Sad, whih is a tpial silia sad, ad Masado, whih is a deomposed graite soil with optimum water otet (w opt =2.6%), were used i a series of tests. After applig a ostat value of tesile fore of the geogrid, T, ad a overburde pressure, σ, all the tests were arried out uder the vertial loadig at a ostat speed of.35 mm/mi. The test oditios are summarized i Table. The shape idex, R, for evaluatig the otat area betwee the soil ad the geogrid was previousl proposed b the authors (Ohiai et al., 996). Figures 6 (a) ad (b) shows the tpial relatioships betwee shear stregth, s, ad ormal stress, σ, obtaied from the results of a series of tests oduted uder the oditio of various tesile fores of the geogrid. The shear stregth, s, is defied as the maximum value of shear stress, τ=(p/a)siθ, util the shear displaemet reahes mm. P is the vertial load, A is the area of the slidig plae ad θ is the slidig agle. The ormal stress, σ, is the ormal ompoet of the overburde pressure, σ, agaist the slidig plae ad is expressed as σ =σ osθ. The relatioships betwee s ad σ for both o-reifored ad reifored soils are expressed b straight lies. Similar relatioships were obtaied uder differet oditios of the slidig agle, θ, shape idex, R, relative desit of Tooura sad, D r, ad dr uit weight of Masado, γ d. The relatioships a therefore shematiall be modeled as show i Figure 7. For Tooura sad, the iterept of the relatioship of o-reifored sad is zero. The evaluatio method that takes ito aout both the tesile effet ad the ofiig effet was verified b laborator tests i whih the slidig plae i the geogridreifored soil mass was simulated (see Figure 7). Cosiderig the stress oditio ear the slidig plae of a reifored retaiig walls as show i Figure 5, Eq.(3) a be rewritte as Eq.(4). T sr = + ( siθ taφ + osθ ) + σ taφ + β σ taφ (4) A The fourth term i Eq.(4), βσ taφ, is the ofiig effet idepedet of the tesile fore of the geogrid. This term meas that the ormal stress o the slidig plae, σ, apparetl ireases due to the ofiig effet, as illustrated i Figure 8. The oeffiiet β is a parameter for evaluatig the ofiig effet whih is osidered to be depedet o the dilata behaviours of the reifored soil mass. 4 EVALUATION OF CONFINING EFFECT RELATED TO SOIL DILATANCY The ofiig effet of reifored soil mass is supposed to be the effet of restritio of soil aroud the geogrid b the geogrid, ad thus the ofiig stress aroud the geogrid apparetl ireases show i Figure 8.I other words, it is osidered that the ofiig effet of reifored soil mass is losel related to the soil dilata behaviours durig shearig. I tur, i order to ratioall evaluate the ofiig effet parameter β i 388

5 Eq.(4), the work equatios applied to a simple shear test sample are disussed for reifored ad oreifored soil mass. We shall suppose that a small shear stress irease dτ auses a shear deformatio, so that the shear strai > ad likewise a small ormal stress dσ auses a vertial ompressio so that the diret strai dε >. Aoordig to the stress-strai sstem i Figure 9, we ow a dedue the magitude of the plasti work whih is fed ito the elemet ad presumabl dissipated suh that dw = σ dε + τ x (5) We assume that this work has bee dissipated b fritio ad dilatio due to shearig. The, the geeral form of the dissipatio eerg equatio for reifored soils, whih does t diretl ilude the ofiig effet parameter β, is supposed to be give b dw 2 ( taφ ) ( dε ) 2 o r = σ x + (6) where φ is defied as a iteral fritio agle at ritial state, ad ote that this equatio is similar to that of modified Cam-la i whih both fritio ad volumetri terms are iluded. O the other had, whe osiderig that the ofiig effet, that is, a apparet iremetal diret stress is geerall mobilized b the restritio of smooth movemet of soils aroud the geogrid, it is essetial to uderstad that the ofiig effet a be mobilized b beig restritive of soil dilative behaviour due to shearig. Assumig that the reifored soil mass a be homogeized i average, it is believed that the dissipated work i reifored soils, whih diretl reflet the ofiig effet, a be expressed as dw r ( σ + σ ) ( taφ ) 2 = (7) x where, σ is a apparet iremetal ormal stress orrespodig to the ofiig effet. It is lear that this tpe of equatio is similar to that of Cam-la. Furthermore whe rememberig that σ is equal to βσ as show i Eq.(4), Eq.(7) is rewritte as dw r ( σ + βσ ) ( taφ ) 2 = (8) x dx d extesio B W σ C τ 2 ψ X o dx x = d dε = d taψ = = dx dx dε dε A ompressio x τ ψ x Y d x Figure 9 Dilata agle at peak stregth state i diret shearig, ad the orrespodig Mohr irle of strai iremet 389

6 We presumed that the work doe b the stresses at the boudaries i Eq.(5) must have bee iterall dissipated. Thus, Eqs.(7) ad (8) represet a iteral eerg dissipatio equatio whih otais ) a iteral fritio agle φ for o-reifored soil, 2) the ormal stress with a ofiig effet for reifored soil mass ad 3) a iteral shear strai whih defies the magitude of the hage of the shape of the elemet. After assumig that the dissipated work equatios at peak stregth state i Eq.(6) is equivalet to that i Eq.(8), so that dw o-r =dw r ad b mergig Eq.(6) with Eq.(8) we obtaied the followig equatio 2 2 ( taφ ) ( dε ) = ( σ βσ ) ( taφ ) 2 σ + x + x (9) After brief alulatios i terms of the ofiig effet parameter β, we a get the followig equatio Thus, 2 ( σ ) ( ta ) ( ) + βσ φ x + dε = σ ( taφ ) 2 x 2 () 2 2 ta dε ψ β = + = + ta () ta φ x φ It is lear that β is give as a futio of the dilata rate defied b dε / x at peak diret shear stregth for the speime. For simpliit, we assume that dε / x at peak stregth state a be obtaied from the simple diret shear tests of the o-reifored soil mass assoiated with a reifored soil mass. Eq.() represets that β beomes greater with the ireasig dilata rate at peak state. It is oted that, based o the defiitio of dilata agle ψ show i Figure 9, dε / x is easil oeted with ψ, that is, taψ=-dε / x. Further the dilata rate dε v /dε s uder plai strai oditio is ofte used to idiate the dilata behaviours where dε v =dε +dε 3 ad dε s =dε -dε 3. I this ase, osiderig the harateristis of Mohr irle of strai show i Figure 9, the dilata agle ψ is also related to dε v /dε s, suh that siψ= dε v /dε s. Therefore, the mutual relatioship betwee dε / x ad dε v /dε s is oeted through the dilata agle ψ suh that ε d dε = = ψ γ ta si ε (2) d x d s Figure shows the harateristis of β agaist the dilata agle ψ diretl liked with dε / x ad/or dε v /dε s i terms of iteral fritio agle φ at peak stregth state for the simple shear uder the plai strai oditios whih are alulated b Eqs () ad (2). It is foud that β roughl hages from to.3 with ireasig the dilata agle ψ from to 3 degrees as a futio of φ whih are believed to be a expeted.3 β.2. φ C = 3 φ C = 34 φ C = Dilata agle ψ Figure Chages of ofiig effet idex β with dilata agle 39

7 Surharge load : q Tesile fore otributed b oe laer of geogrid z S V T max 45 +φ/2 K a γz K a q Figure Tie-bak wedge method for iteral stabilit aalsis (Caadia Foudatio Egieerig Maual, 992) rage of ψ ad also that the ireasig rate of β beomes higher with the ireasig dilata agle. This tede asserts that the ompatio of reifored soil mass is importat to obtai the proper ofiig effet. It is further poited out that the predited rage of β gives a good agreemet with the experimetal results whih have bee reported b the authors (Ohiai et al. 996; Kawamura et al., 2; Yasufuku et al., 22). 5 INTRODUCTION OF CONFINING EFFECT INTO CURRENT DESIGN GUIDELINE I this setio, the ofiig effet is itrodued ito the tie-bak wedge method reommeded i the Caadia Foudatio Egieerig Maual(992: see Figure ), whih is haraterized to be simple to use for appliatios. Iteral stabilit iludes the failure mehaism suh that ) rupture of the geogrid due to tesile overstressig, 2) pullout of the geogrid withi the reifored soil mass ad 3) failure of the faig oetio. Amog those, we foused o the first of the above mehaisms, thus, the ofiig effet mobilized i the reifored soil mass is itrodued ito the iteral stabilit aalsis related to the rupture of the geogrid. I the ase of the exteral stabilit i whih the reifored soil mass is regarded as a rigid blok, the ofiig effet ma ot be mobilized. I the tie-bak wedge method, the safet of eah laer of the geogrid is refereed to a iteral Rakie ative plae propagatig from the toe of the wall at a agle of 45 + φ/2 degrees to horizotal. The essetial features are summarized i Figure. The maximum tesile fore of the geogrid, T max, is mobilized at the slidig plae i the reifored soil mass. Rakie s earth pressure theor gives the horizotal earth pressure as a triagular distributio. Horizotal ative earth pressure, σ h (z), at the depth of z from the top of the wall a be expressed as σ ( z) = K γz K q (3) h a + a where K a is the oeffiiet of Rakie s ative earth pressure, γ is uit weight of soil ad q is the surharge load. The tesile fore of the geogrid is thought to resist the horizotal earth pressure diretl, ad the sum of tesile fores of eah laer of the geogrid must be larger tha that of the horizotal earth pressure. The maximum tesile fore, T max, of the geogrid at the depth of z from the top of the wall is expressed as the area of the gra zoe i Figure ad it is omputed as max = σ h ( z) Sv = ( K aγz + K aq Sv (4) T ) where S v is the otributor area about eah geogrid laer. As a geeral treatmet, S v is ofte regarded as the legth of the vertial spae of geogrid. The allowable desig tesile fore of the geogrid, T A, must exeed the maximum tesile fore, T max, as follows: 39

8 Surharge load : q Redutio of maximum tesile fore Iremet of ultimate earth pressure due to ofiig effet : K a βγz z S V T max 45 +φ/2 (-β)k a γz K a q Figure 2. Tie-bak wedge method for iteral stabilit aalsis osiderig the ofiig effet (proposed method) ( K aγz + Kaq) SV T A Tmax = (5) Equatio (5) is used to hek the safet of eah laer of the geogrid, ad the vertial spaig of eah laer of geogrid is determied. The legth of eah laer of the geogrid is thus obtaied b osiderig the pullout resistae of the geogrid. However, the determiatio of the legth is ot disussed i this paper. The ofiig effet a be expressed as βσ taφ, as show i Eq.(4), ad also it reflets the effet of a additioal ormal stress, βσ, apparetl idued o the slidig plae. Thus, the overburde pressure o the horizotal surfae of the geogrid, σ, whih a be omputed as σ o =σ /osθ, apparetl ireases b the amout of βσ due to the ofiig effet. It is assumed that the ultimate earth pressure of the reifored retaiig wall uder plasti equilibrium oditios ould be haged b the amout of K a βσ =K a βγz due to the ofiig effet. This assumptio is based o the followig simple idea. The slidig agle of the ultimate slip failure, 45+φ/2 degrees, ad the oeffiiet of Rakie s ative earth pressure, K a, is regarded as a ostat, beause the ofiig effet is evaluated idepedetl agaist the iteral fritio agle, φ, as show i Figure 4. Therefore, the maximum tesile fore that diretl resists to the horizotal earth pressure a be redued b the amout of K a βγz as shematiall show i Figure 2. Fiall, osiderig the ofiig effet, Eq.(5) of the desig method reommeded i the Caadia Foudatio Egieerig Maual (992) a be rewritte as [( β ) Kaγz + K aq SV T A Tmax = ] (6) where β is diretl related to the dilata agle ψ whe itroduig Eq.(2) ito Eq.(), suh that: 2 ta ψ β = + (7) ta φ 392

9 Surharge load, q Geogrid Table 2 Desig parameters used Uit weight of soil, γ t Iteral fritio agle, φ Allowable tesile stregth of geogrid, T A 7.7kN/m 3 3 degrees 39.8kN/m 2 9 Surharge load, q 9.8kN/m 2 Vertial spaig Dilata agle, ψ,, 2, 3degrees Figure 3 Cross-setioal diagram for desig 25 Critial hight of wall, H r (m) ψ= ψ= ψ=2 ψ=3.5.5 Vertial spaig of geogrids, S V (m) Figure 4 Critial height of geogrid-reifored wall, H r agaist vertial spae of geogrid at various dilata agles refletig the ofiig effet A ross-setioal diagram of a geogrid-reifored retaiig wall ad the parameters for desig are show i Figure 3 ad Table 2, respetivel. The values of the ofiig effet parameters, β, used for the omputatio are estimated b usig Eq.(7), where, the dilata agles with β are hose from to 3 degrees as the expeted values i pratie. Figure 4 shows omparisos of alulated values of the ritial height of the retaiig wall, H r, uder the oditio of various ofiig effet parameters ad the various vertial spaigs of geogrids. I the ase of β= whih reflets that ψ=, the ofiig effet is ot osidered i the desig method. The ritial height, H r, ireases with the dereases of the vertial spaig of geogrids ad the ireases of the ofiig effet parameter, β whih is diretl liked with the dilata agles of reifored soil mass. I the proposed desig method, the ritial height of wall, H r, ireases b roughl 5-2% i the expeted pratial rages of the vertial spae of geogrids from.5m to.m, depedig o the magitude of the ofiig effet parameter, β, whih was liked with the dilata behaviours of the reifored soil mass. 393

10 6 CONCLUSIONS A evaluatio method i whih the reiforig effets a be divided ito tesile effet ad ofiig effet is proposed related to the dilata behaviour of reifored soil mass, i order to itrodue the ofiig effet ito desig methods. The mobilized ofiig effet was give b a futio of the dilata rate, i whih the ke idea is i the assumptio of the dissipated eerg doe b the uit volume of the soil mass. The proposed model idiated that the ofiig effet parameter, whih defies the degree of the apparet iremetal ofiig stress to the urret ormal stress o the expeted slidig plai, was i the rage of to.3 agaist the supposed dilata agles from to 3 degrees. The expeted rage had a good agreemet with the experimetal oes whih have bee reported b the authors. The ofiig effet losel liked with the dilata agle of reifored soil mass was itrodued ito the tie-bak wedge method of geogrid-reifored retaiig wall based o Rakie s ative earth pressure theor. For istae, i the proposed desig method, the ritial height of the reifored wall ireased b roughl 5-2% i the expeted pratial rages of the vertial spae of geogrids from.5m to.m, depedig o the magitude of the ofiig effet parameter, β, whih was liked with the dilata behaviours of the reifored soil mass. REFERENCES Bastik, M. ad Segresti, P., Use of Double Wedge Equilibrium for Reifored Earth Struture Desig, Pro. of It. Smp. o Earth Reiforemet Pratie (IS Kushu 96), Fukuoka, Balkema, Vol., pp39-34(996). Caadia Geotehial Soiet, Caadia Foudatio Egieerig Maual 3rd Editio, pp (992). Fukuda, N., Yamaouhi, T. ad Miura, N., Comparative Studies of Desig ad Costrutio of a Steep Reifored Embamkmet, Geotextiles ad Geomembraes, Vol. 4, pp (986). Fukuda, N. Takashi, Y., Ohuhi, J. Nishimura, J., Kioshita, E. ad Yoshizawa, M., Comparative Studies of Desig Method of Geotextile Reifored Steep Embakmet, 24 th JSSMFE, pp. 5-9(989) (i Japaese). Fukushima, S., Yokomahi, F. ad Kagawa, K., Stregth Charateristi of Reifored Sad i Large Sale Triaxial Compressio, Pro. of the It. Geoteh. Smp. pp. 99-4(988). Jewell, R. A. & Wroth, C. P, Diret shear test o reifored sad, Geotehique, 37, No. pp.53-68(987). Kawamura, T. Ohiai, H. Yasufuku, N. ad Hirai, T., Itrodutio of Cofiig Effet of Geogrid-Reifored Soil ito Desig Method, Geosthetis Egieerig Joual, Vol. 4, pp. 2-22(999a) (i Japaese). Kawamura, T. Ohiai, H. Yasufuku, N. Omie, K. ad Hirai, T., Cofiig Effet i Geogrid-Reifored Soil, Poster Sessio Proeedigs of Theth Asia Regioal Coferee o Soil Mehais ad Geotehial Egieerig, pp (999b). Ohiai, H., Yasufuku, N. Yamaji, T., Guag-Li Xu ad Hirai, T., Experimetal Evaluatio of Reiforemet i Geogrid-soil Struture, Pro. of It. Smp. o Earth Reiforemet (IS Kushu 96), Vol., pp (996). Ohiai, H., Yasufuku, N. Kawamura, T., Hirai, T. & Yamaji, T., Effet of Ed-Restrait i Geogrid-Soil Strutures, Pro. of 6 th It. Cof. o Geosthetis, Atlata, pp (988).. Pema, J. ad Austi, R. A., A. Compariso of Desig Approahes for Geostheti Reifored Soil Strutures i Europe, Pro. 6th It. Cof. o Geosthetis, Atlata, pp. 5-56(998). Publi Works Researh Ceter, Desig ad ostrutio maual of geotextile-reifored embakmet, Tehial memoradum of Pubri Works Researh Ceter, pp.44(993) (i Japaese). Tatsuoka, F., Koseki, J. Tateama, M., Performae of reifored soil strutures durig the 995 Hogo-ke Nabu Earthquake, Pro. of It. Smp. o Earth Reiforemet (IS Kushu 96), Fukuoka, Balkema, Vol. pp.973-8(996). Yasufuku,N., Ohiai,H., Omie, K., Niomia, Y., ad Kawamura, T., Evaluatio of Cofiig Effet i Geogrid-Reifored Retaiig Wall related to the Pratial Appliatio, Pro. of the 7th Iteratioal Coferee o Geosthetis, Vol.4, pp (22). 394