SCE Journal of Civil Engineedr Geetechnical Engineering I VoL 5, No / June 0 l pp 175-183 Application of Constitutive Model to Predict the Behavior of EPS-Geofoam By Byung-Sik Chun*, Hae-Sik Lim** and Young-Wan Shin*** Abstract EPS (Expanded Polystyrene)-geofoam, a super light weight material, has the unit weight of 20-~30 kg/m~ and is used as one of the methods acquiring the safety for settlement and bearing capacity There are a few constitutive models for the selection of the EPS-geofoam fill which is essential to the determination of the fill configuration and the settlement calculation, However, it is difficult to determine the parameters of its model In this paper, therefore, a practical nonlinear constitutive model developed fi'om the results of drained triaxial compression tests was proposed The proposed nonlinear numerical constitutive model was applied to a large scale model test and to a field constmction in Japan The predictions agree well with the measurements Keywords: EPS-geofoam, cons~'tu~ive model, triaxial compression test, nonlinear numerical constitutive model Introduction Super light Expanded Polystyrene blocks (EPS blocks) have been used in the road conswaction industry as a light weight material for nearly three decades, The literature indicates that the Norwegian Road Research Laboratory has successfully used EPS-geofoam on more than 100 projects, it has been reported that the EPS-geofoam produces almost "Zero" lateral pressure on the bridge abutment walls (Bang, S.C., 1995) EPS-geofoam has also been used extensively as frost proofing layer in highways in Europe and N o a h America (BASF, 1995) When EPS-geofoam needs to be used, it should have appropriate strength and stress-strain behavior so that EPSgeofoam can endure overburden stress and deformation The exact behavior of EPS-geofoam has to be predicted in In general, the linear elastic model using initial tangent modulus has been used to predict the behavior of EPS-geofoam But, it doesn't represent the nonlinear behavior of EPS-geofoam, The nonlinear model was developed by Cho, Y~K (1992) as shown in Fig, 1, But, this constitutive model for the stress-s~rain of EPS-geofoam is not practical because it is difficult to obtain the exact values of its parameters, The time dependent model using Findiey equation proposed by Horvath J,S (1998) assumes that the immediate strain has only an elastic component although not necessarily linear It neglects plastic strain T Taka~ra and K order to decide installation shape and replacement area since the effectiveness of EPS-geofoam varies depending on the installation shape EPS-geofoam behaves differently from soils, and the strength and stress-strain behavior of EPS-geofoam show large differences based on the density of EPS-geofoam Therefore, it needs to develop the practical numerical constimtive model predicting the behavior when EPS-geofoam is employed as light weight filling material 50 , !/-,,q !nitial Tangent Line 40 0v U) UJ O~ I- 3O o o.a2 o.~ i o.o6 0.08 o.~ o.12 o.14 AXIAL STRAIN Fig Parameters to Depict Stress-strain Relation The manuscript for this paper was submitted for review on November 2, 2000, - 175- / :::::::::::::::::::::::::: ::::::::i"i 2o *Member, Professor, Dept of Civil Engrg of Hanyang Univ (E-mail: hengdang@unitel.co.kr) **Member, Senior Researcher, Office of Korea National Housing Co (E-mail: haisik@hitel.net) ***Member, Graduate student, Dept of Civil Engrg of Hanyang Unbz (E-mail: geoeng@unitel.co.kr) Vol 5, No 2/June 2001 i Byung-Sik CT~un,Hae-Sik Lira and Young- Wun Shin Miura, 1995 are analyzed EPS-geofoam by DEM So, the objects of this paper are two One is to propose the practical stress-strain model of EPS-geofoam as a function of overburden stress so that it is employed as light weight filling material And the other is to convict the adaptability of proposed constitutive model comparing the predictions with the measurements in the laboratory test and the field construction Review of EPS-geofoam characteristics Anisotropy of EPS-geofoam is one of the most important properties, but it is easily neglected The stress-strain behavior of EPS-genfoam varies with producing direction (Kutara et a/., 1990) The direction of stress on the EPSgeofoam perpendicular to producing is more effective The EPS-geofoam typically shows elasto-plastic behavior showing linear behavior in the strain range from 1% to 1.5% As the density of EPS-geofoam increases, the modulus and axial stresses increase without showing clear apex According to Hamada and Yamanouchi (1989), the volrune of EPS-geofoam decreases linearly during compression Namely, the volume change rate is constant, and depends on the density of EPS-geofoam and lateral pressure applied Another important property of EPS-geofoam is time dependent stress-strain behavior According to previous researches (Chun et al., 1996, EPS CMDO, 1993, Horvath, 1998), the strain of EPS-geofoam increases with applied stress that maintains for long duration at the same stress level The amount and duration of creep depend on the density of EPS-geofoam and the level of applying stress (Horvath, 1998) Therefore, these 'facts indicate that EPSgeofoam has to be used under adequate stress level in practical situations E~ l ln~ lX-o Xd L Y0 (1 + Ejfo)J (lc) G - (-4180 + 39000 t9 + (-6.2 - 53 Z) or3 (1 d) Ep = ( + 4 t ) + ( - - ) c (le) Y0 = (1.4+90519+( + D c cr3 /1= 0.2 ~ for 0< c73 i ~ z; ~ ~ ] ', ~oo-~ I ~-, ~ / / oo0ti iltl iIiiiiiiiiii iiiiiiii!iiii:iiiit 121 i I 0.00 4, O0 1200 m 0,00 4.00 axial strain ( % ) (b) density k g / m ~ 1000 10.00 i Dconfining~ pressure f / 8.00 i o l ii ll i, z~ I ' " 6.00 K= io; ~ ,' ~ a o ~ , % > ~1 ~ u~ressure-~'~ ~ , a~ 600 - m - [ [ 800 ~" ~ ' " ~ " ~" ~ ~ ~ ~ ~ ~ ~ ~" K'~'" "1 ~'"~" ~ i (30 6/s 12.00 axial strain ( % ) (a) density k g / m =_ 8.00 R - 0.310 (5c) d : density o f E P S - g e o f o a m (kg/m 3) The derivative o f Eq (4), which is the tangential modulus at each stress level, can be expressed as Eq (6) E, - (Y3: confining stress (kPa) abcs 2b s + 2cs R : correlation coefficient where, R : coefficient o f determination m u m correlation coefficient is 0.99 Therefore, Eq (4) (6) G : tangential modulus s The statistic analyses o f various tests show that the mini- b : Axial strain a, b, c : Parameters concerned with density and confining stress describes axial stress-strain behavior o f EPS-genfoam suc- The relationsNp between Poissons ratio and the density cessfully (Table 1) The parameter a and b have multi-linear and the confining pressure o f E P S - g e o f o a m can be express- - 178 - KSCE Journal of Civil Engineering Application of Constitutive Model to Predict the Behavior of EPS-Geofoam Table The Statistic Analysis of Triaxial Test Data of EPS on Stress-strain Relation Curve fitting of test results on proposed ftmction " equation (3) Conelation b c Coefficient Prediction of parameter a,b,c by equation (4) Density (t/m3) Confining Stress kPa a b c 0.294 238.584 2.2 0.537* 0.9985 234.347 2.394 0.814 0.294 248.515 2.17 0.684 0.9988 234.347 2.394 0.814 0.294 248.044 2.06 0.901 0.9978 234.347 2.394 0.814 0.294 20 246.71 2.86 0.985 0.9978 241.127 2.234 0.794 0.294 20 261.202 2.18 1.190' 0.9968 241.127 2.234 0.794 0.294 20 258.959 2.12 0.726 0.9977 241.127 2.234 0.794 0.294 40 252.528 2.01 0.900 0.9986 247.907 2.074 0.773 0.294 40 255.185 2.48 0.864 0.9973 47.907 2.074 0.773 0.294 40 236.599 2.45 0.567 0.9978 247.907 2.074 0.773 0.294 60 263.031 1.88 0.629 0.9977 254.687 1.914 0.753 0.294 60 265.07 1.95 0.829 0.9958 254.687 1.914 0.753 0.245 174.611 2.01 0.875 0.9985 185.13 2.184 0.857 0.245 167.971 2.01 0.69 0.9985 185.13 2.184 0.857 0.245 173.444 2.30 1.114' 0.9989 185.13 2.184 0.857 0.245 20 196.215 1.84 0.637' 0.9972 191.91 2.024 0.875 0.245 20 197.153 1.94 0.972 0.9984 191.91 2.024 0.875 0.245 20 187.599 1.92 0.726 0.9984 191.91 2.024 0.875 0.245 40 179.574 2.13 1.031 0.9961 198.69 1.864 0.893 0.245 40 179.972 1.807 0.95 0.9949 198.69 1.864 0.893 0.245 40 185.094 1.75 0.811 0.9958 198.69 1.864 0.893 0.245 60 196.225 1.42 1.062 0.9937 205.47 1.704 0.912 0.245 60 183.996 1.542 0.599' 0.9912 205.47 1.704 0.912 0.245 60 195.417 1.739 0.715 0.9910 205.47 1.704 0.912 0.196 127.718 2.2 0.967 0.9974 135.913 1.974 0.799 0.196 121.901 2.203 0.928 0.9969 135.913 1.974 0.799 0.196 20 142.91 1.591 0.737 0.9989 142.693 1.814 0.856 0.196 20 132.287 2.281 0.823 0.9983 142.693 1.814 0.856 0.196 40 134.355 1.805 0.584* 0.9947 149.473 1.654 0.913 0.196 40 150.003 1.565 1.007 0.9989 149.473 1.654 0.913 0.196 40 142.382 1.873 0.716 0.9949 149.473 1.654 0.913 0.196 60 161.188 0.966 1.062 0.9986 156.253 1.494 0.970 0.196 60 174.163 0.945 1.257 * 0.9982 156.253 1.494 0.970 0.147 91.812 1.435 0.739 0.9983 86.696 1.765 0.640 0.147 92.381 1.805 0.624 0.9994 86.696 1.765 0.640 0.147 20 97.642 1.487 0.786 0.9963 93.476 1.605 0.736 0.147 20 100.209 1.749 0.693 0.9967 93.476 1.605 0.736 0.147 20 99.255 1.674 0.584 0.9958 93.476 1.605 0.736 0.147 40 104.817 1.568 0.696 0.9940 100.256 1.445 0.833 0.147 40 108.622 1.528 0.773 0.9962 100.256 1.445 0.833 0.147 40 105.837 1.37 0.896 0.9902 100.256 1.445 0.833 0.147 60 108.696 1.346 0.938 0.9957 107.036 1.285 0.929 0.147 60 112.109 1.489 1.190' 0.9955 107.036 1.285 0.929 0.147 60 115.817 1.25 1.042 0.9855 107.036 1.285 0.929 0.147 60 108.786 1.300 0.958 0.9944 107.036 1.285 0.929 a 9excluded data in regression analysis o f t Vol 5, No 2/June 2001 - 179 - Byung-Sik Chun, Hue-Sik Lira ard Young- Wan Shin ed as Eq (7) The volumetric strain of EPS-geofoam has a Table Statistic Analysis Results of Poisson's Ratio linear relation with the axial compression strain as shown in Fig 3, and the slope of the carwe has a correlation with the Density Confining Vol Strain/ (t/m3) Stress axialstrain Calculation PreNctionof ofpoisson ~oissonratio ratio by Eq (6) by Eq (7) density and the confining stress of EPS-geofoam The regression analysis of the relation between the volumetric strain and the axial compression strain conceming the density and the confining stress of EPS-geofoam in Fig shows that correlation coefficient is 0.9934 at least (Table 2) r 0.0023xcr R = = (7) 0.03 0.59 0.03 0.6533 0.9934 0.2050 0.189332 0.9995 0.1733 0.189332 0.03 0.6478 0.9983 0.1761 0.189332 0.03 20 0.7339 0.9985 0.1326 0.142977 0.03 20 0.7735 0.9985 0.1133 0.142977 0.03 30 0.8446 0.9997 0.0777 0.119800 where, p : Poisson's ratio d : density ofEPS-gcofoam (kg/m 3) 0.03 40 0.8235 0.9991 0.0883 0.096623 0.03 40 0.8323 0.9986 0.0838 0.096623 crs : confining pressure (kPa) 0.03 40 0.8686 0.9995 0.0674 0.096623 R : coefficient of determination 0.03 60 0.8713 0.9996 0.0644 0.050268 0.03 60 0.8072 0.9993 0.0964 0.050268 0.03 60 0.8873 0.9995 0.0564 0.050268 0.025 0.5443 0.9996 0.2278 0.173900 The proposed nttmerical model was applied to two cases One is the full scale model test which was performed in 0.025 0.4316 0.9982 0.2842* 0.173900 0.025 0.4262 0.9998 0.2869* 0.173900 Public Works Research Institute, Ministry of Construction of Japan, (1990), and the other is the retaining wall constmction site to verify its applicability 0.025 0.413 0.9994 0.2935* 0.173900 0.025 20 0.737 0.999 0.1331 0.127546 0.025 20 0.7698 0.9993 0.1151 0.127546 Numerical analysis of proposed model 5.1 Comparison with laboratory experimental tests After the EPS-geofoam is built on as shown in Fig 4, horizontal pressure and settlement were measured The 0.025 20 0.8615 0.9997 0.0692* 0.127546 0.025 40 0.8323 0.9993 0.0839 0.081191 0.025 40 0.8321 0.9999 0.0840 0.081191 EPS-geofoam has a density of 20 kg/m and the size of 2.0 m• m• m, and the backfill material is river sand The soil parameters are shown in Table and 0.025 40 0.861 0.9997 0.0695 0.081191 0.025 60 0.8929 0.9997 0.0535 0.034837 0.025 60 0.9242 0.9997 0.0379 0.034837 The proposed nonlinear elastic model and linear elastic 0.025 60 1.0847 0.9997 0.0423* 0.034837 0.02 0.655 0.9996 0.1725 0.158469 0.02 20 0.7591 0.9982 0.1204 0.112115 0.02 20 0.7532 0.9993 0.1234 0.112115 0.02 20 0.7534 0.9996 0.1233 0.112115 0.02 40 0.8568 0.9999 0.0716 0.065760 0.02 40 0.8415 0.9995 0.0793 0.065760 0.02 40 0.8467 0.9998 0.076 0.065760 model using initial tangential modulus axe used to analysis EPS-gcofoam, linear elastic model to concrete and MohrCoulomb elasto-plastic model soil respectively The comparisons of results between linear elastic model and proposed nonlinear model are shown in Fig 5, and face panel unit : mm SCREW JACK side wall Oil JACK coo o JUl Eps / IIit le ,; II!1 25tv I ~ l *excluded data in regression analysis of Poisson's ratio t ,and r -.-I c~ ) ,~ooo I for horizontal pressure and settlement It shows that they correspond 5.2 Comparison with field measurements The two additional retaining structures were built on the slope of existing retaining wall as shown in Fig Since the bearing capacity of retaining wall was not enough, EPS- Fig Outline of Laboratory Model Test - 180 - KSCE Journal of Civil Engineering Application of Constitutive Model to Predict the Behavior of EPS-Geofoam t.0 2',0 6m NO.3 03 settlement Plate I i , , I - ~ ~ g 2.0 i E ~ 2m " *~,~,k~ ,i, ~t.,.~ ~ ' r ,~, [ -5 0 I I " ( ~ r~ - "~ EPS model linear elastic measured value [ I I I E=~S nlodel " lineal elast c rllSgsJred calue I ~ I horizontal position (m) horizontal pressure (tim 2) Fig Settlement after Banking of Height rn Fig Horizontal Pressure Before Banking 1.0 retaining wall el I = E d3 t- ,'5 J 2m ~11,_,~ retaining wall Fig Outline of Test Construction ,.~ ~ EPS model linearelastic measured value road lOm O I I I inclinometer horizontal pressure (tim 2) settlement upper plate con'c slab f- Fig Horizontal Pressure after Banking of Height rn I i l I ~ ~ concrete anchoring head geofoam was used in backfill material The slope in the rear o f the EPS-geofoam filling is made at a slope of l : 1.5 to reduce earth pressure EPS-genfoam has a density of 20 kg/ m 3, and the size of EPS-geofoam is 1.8 m• mx0.4 m (Fig 9) Wire mesh is installed on the concrete slabs which are placed in the surl~ace and the middle point o f EPS-genfoam filling section The concrete slabs are extended to the ground as a role o f anchorage The soils contacted on the imental test analysis obtained tiom triaxial tests EPS-geofoam are classified as GM and SM by USCS, and soil properties are shown in Table and In mmaerical analysis, nonlinear elastic model and linear elastic using initial tangent modnlns are employed for EPSgeofoam, linear elastic model was used for the concrete slab boundary o f EPS blocks and concrete plate, and MohrCoulomb elasto-plastic model is used for soils as shown in Fig 10 The soil parameter values used in analysis were determined through the same routine as in laboratory exper- Boundary conditions in analysis are as follows; the analysing scope was proposed as shown in Fig 10, the displacements of X and Y directions are fixed at the bases, and the displacements o f X direction are allowed at vertical faces Since the site is road, the traffic load o f 5.1 t/m (DB 240, 3.8 t/m2(DB 18t)are applied on the road surface A t the locations o f the road surface, top concrete base, and mid-layer concrete slab in the width o f road surface 10 m, the measurements and the predicts o f set- Vol 5,No 2/June2001 - 181 - r d I r middle H ~iI 3m 8m W earth i pressurement Fig Outline of Installing Measurements Byung-Sik Chun, Hae-Sik Lira and Young-Wart Shin Table Test Results of Applied Soil Type of soil Natural water Unit weight T(t/m3) Backfilled soil of model test 1.46 Field soil of application site 1.68 o), (%) Friction angle (degree) Cohesion c (t/m2) Max dry density ym (t/m 3) Opt Moistur content 6.3 31.3 0.5 1.606 10.9 30 1.5 1.967 9.5 content COop~(%) Table Material Parameters Used in Analysis Type of soil Unit weight Friction angle, Cohesion c Elastic modulus Poisson's ratio Bulk modulus /(t/m 3) ~ (degree) (t/m2) g(Kpa) v K(Kpa) Shear modulus G(Kpa) lackfilled soil of model tesl 1.46 31.3 0.5 1.5x 104 0.25 1.0x 104 6.0x 104 ;ield soil of application site 1.78 30 1.5 1.96x 104 0.30 1.63x 104 7.5x 10~ ~PS as nonlinear elastic 0.02 Eq (5) Eq (6) 5.10x103 0.12 2.24x103 2.28x103 2.04x 106 0.15 ~PS as linear elastic 0.02 ;oncrete 2.5 material model rnohr-coulomb elastic - unit : rn - ~alysing scope L J_ 7.69x 106 axial stress and strain can be expressed as a function o f parameters a, b, c concerned with the density o f EPS-geofoam and the confining stress In the proposed model, the parameter a and b have multi-linear relation, and parameter c has a nonlinear relation with the density o f EPS-geofoam and the confining stress (2) The first derivative of stress-strain function, which can represent the tangential modulus, can be expressed as a function o f density and confining stress (3) The volumetric strain and axial strain have a linear relation, and its slope is related to the density and the confining stress The Poisson's ratio, which can be calculated by dividing volumetric strain by axial strain, has a multilinear relation with density and confining stress, and its relation can be described as a certain fimction (4) In the case o f the horizontal earth pressure comparisons, the predicted results by the proposed nonlinear elastic model does not show a considerable difference with the results o f linear elastic model and the measurements However, the settlement predicted by the proposed constitutive model shows larger values than the results by the linear elastic model, and gives approximately the same values as measurements Therefore, the proposed model predicts ~ eps & elastic L 9.52x 106 50~ Fig 10 Applicated Material Medel in Analysis tlements using elastic model and proposed model were compared in Fig 11 The predictions using proposed nonlinear model are larger than those using linear elastic model, and agree well with the measurements C o n c l u s i o n s nonlinear compressibility of EPS-geofoam better than existing linear elastic model In this study, the numerical model to predict behavior o f EPS-geofoam was proposed In order to estimate validity o f the proposed model, numerical analyses for the large scale laboratory test and the field measurements were performed The conclusions o f this study are as follows; (1) The EPS-geofoam has an elasto-plastic behavior, and its behavior has close relations to density and confining stress Through the analysis o f drained triaxial test results for the density of EPS-geofoam o f 15 kg/m3-30 kg/m 3, the References S.C Bang (1995) "Experimental and Analytical Study of Expanded Polystyrene Blocks in Highway Application," Proceedings of International Seminar on the Application of EPS Jbr Embankment Construction, Seoul, pp 105-133 BASF (1995), "Code of Practice Using Expanded Polysty- 182 KSCE Joumat of Civil Engineering Application of Constitutive Model to Predict the Behavior ofEPS-Geofoam O iB bottom of EPg(analysed) -El- aid con'c slab(analysed) -4 upper con'c slab(analysed) road surface(analysea) - - ~ roa~ surface(measureed) F : ~ upper con'c slab(~easured) mid conic slab(measured) o Er E o) (P E zl] r u3 -4 LJ -C 16 18 20 22 24 26 ~e 28 horizontal position of E P S filling (m) , , , , - i , , r ~8 20 2~ ~4 z~ horizontal position of E P S filling (m) , zB tl)) settlement by linear elastic model(DB 24t) (a) settlement by proposed EPS model(DB 24t) c ~D E E o ~D ,4 -C~ , p , , t6 horizontal position of E P S filling (m) (c) settlement by proposed EPS model(DB 18t) ~8 20 22 24 2~ horizontal position of E P S filling (m) z8 (d) settlement by linear elastic model(DB 18t) Fig 11 The Comparison of Settlements with Surface Load and Numerical Model rene for the Construction of Road Embankments," Technical Information from BASF, pp 7-9 YK Cho (1992) Behavior ojT~etaining Wallwith EPS Blocks as Baclffill, Thesis of Master Course, University of South Dakota, pp 1-29 B.S Chun, M.S Jang and H.S Lim (1996) "A Study on Engineering Characteristics of Load Reducing Material EPS," Journal of the Korean Geoteehnical Society, Vol 12, No 2, pp 59-69 EPS Construction Method Development Organization (1993) EPS Construction Methods, pp 1-58 Hamada, E andYamanouchi, T (1989) "Mechanical Properties of Expanded Polystyrene as a Lightweight Fill Material, Soils and foundations," Japanese Geotechnical Society, Vol 37, No 2, pp 13-18 Horvath J.S (1996) "Geofoam Gensynthetic: Past, Present and Future," Electronic Journal of Geotechnical Engineering, Vol 1,No 1, 1996 Vol 5,No 2/June2001 - 183- Hoiwath J.S (1998) "Mathematical Modeling of the Sl~essStrain-Time Behavior of Geosynthetics Using the Findley Equation: General Theory and Application to EPS-Block Geofoam," Manhattan College Research Report No CE/GE98-3, U.S.A Kutara, K., Aoyama, N., Takenchi, 12 and Takechi O (1990) Prototype Model test on Earth Pressure Reducing by EPS of Block Filling Structures, Public Works Research Institute in Japan, pp 4-55 10 Preber, T., Bang, S.C and YK Chung (1994) '~ehavior of expanded polystyrene blocks," Transportation Research Record No 1462, Transportation Research Board, Washington, D.C., U.S.A., pp 36-46 11 T Takahara and K Miura (1998) 'SMechanical Characteristics of EPS Block Fill and its simulation by DEM and FEM, Soils and Foundations," Japanese Geotechnical Society, Vol 38, No.l, pp 97-110 ... And the other is to convict the adaptability of proposed constitutive model comparing the predictions with the measurements in the laboratory test and the field construction Review of EPS-geofoam. .. express- - 178 - KSCE Journal of Civil Engineering Application of Constitutive Model to Predict the Behavior of EPS-Geofoam Table The Statistic Analysis of Triaxial Test Data of EPS on Stress-strain... material parameter with dimension of stress cr : the applied stress KSCE Journal of Civil Engineering Application of Constitutive Model to Predict the Behavior of EPS-Geofoam mv, nv :a dimensionless