LIQUEFACTION CHARACTERISTICS EVALUATION THROUGH DIFFERENT STRESS-BASED MODELS: A COMPARATIVE STUDY

Transcription

1 Journal of Engineering Research and Studies E-ISSN Research Article LIQUEFACTION CHARACTERISTICS EVALUATION THROUGH DIFFERENT STRESS-BASED MODELS: A COMPARATIVE STUDY P. Raychowdhury 1* and P. K. Basudhar 2 Address for Correspondence 1* Department of Civil Engineering, Indian Institute of Technology, Kanpur 2816, India 2 Department of Civil Engineering, Indian Institute of Technology, Kanpur 2816, India prishati@iitk.ac.in ABSTRACT The paper presents a comparative study of the predicted response of a liquefiable saturated sand deposit of Nigata city under different seismic ground motion using three different stress based analytical models due to Finn et al. (1977), Liou et al. (1977), and Katsikas and Wylie (1982). The results are also compared with simplified methods that are adopted in the current design practice. It has been found that the models by Finn et al. (1977) and Katsikas and Wylie (1982) result in close predictions, whereas the predictions by Liou et al. (1977) are significantly different, particularly for predicting the rate of partial liquefaction for the chosen soil deposit and earthquake motions. INTRODUCTION Liquefaction is an earthquake-induced ground failure phenomenon observed in saturated loose sand deposits. Liquefaction involves generation of excess pore pressure, loss of shear strength and excessive volume contraction with associated settlement. Although the simple methods based on SPT and CPT results are most commonly used in practice and also recommended in the design provisions (FEMA- 356 and NEHRP, 2), nonlinear site response analysis and dynamic time history analyses are recommended for design of high risk infrastructures such as dams and nuclear power plants. If the sand deposit is densely packed, repeated shearing causes dilation instead of contraction, helping the excess pore pressure to be redistributed. The liquefaction potential of a soil deposit depends on several factors, such as: void ratio and relative density of soil, depth of water table, effective confining stress, and coefficient of lateral earth pressure, seismic and geologic history of the site and intensity, duration and other characteristics of ground shaking. As such, a proper understanding of their effects for evaluating the liquefaction characteristics is essential. Seismic response of saturated sand deposits and liquefaction phenomenon has gained significant attention after 1964 Niigata earthquake. Other significant earthquakes, such as 1964 Alaska, 1989 Loma- Prieta, 1995 Kobe and 21 Bhuj earthquake, have also demonstrated severe damaging potential of soil liquefaction on buildings, bridges, railways, ports and other infrastructures. A qualitative understanding of the mechanism of liquefaction of saturated sands subjected to cyclic loading can be explained by critical void ratio approach (Castro, 1975). Critical void ratio is the void ratio of any sand, for which there will be no volume change during drained shear. A sand deposit having a void ratio above the critical value tends to contract during shear, and develops positive pore pressure under undrained conditions, and has a potential to experience liquefaction. Conversely, deposits having an initial void ratio below critical value tend to dilate during shear, producing a decrease in porewater pressure and a corresponding increase in effective stress under undrained conditions. Till date significant analytical, experimental, numerical and post-earthquake field investigations have been carried out to understand the mechanism and predict the potential of liquefaction and related consequences. Analytical models are developed to predict liquefaction characteristics by Martin et al. (1975), Liou et al. (1977), Finn et al. (1977), Katsikas and Wylie (1982), Desai (2), Liyanapathirana and Poulos (22), to name a few. Some of the analytical models adopted effective stress-based approach (e.g. Liou et al. (1977), Finn et al. (1977), Katsikas and Wylie JERS/Vol.II/ Issue II/April-June,211/

2 Journal of Engineering Research and Studies E-ISSN (1982), Liyanapathirana and Poulos (22)), while few of them adopted energy-based approach (e.g. Desai, 2). Experimental studies including cyclic triaxial tests, shaking table tests and centrifuge tests have been conducted for the last four decades (e.g. Seed and Lee (1966) Elgamal et al. 1996, Ashford et al. 2) to validate the theories and better understand the mechanism. Simplified methods to evaluate liquefaction characteristics from SPT and CPT test results are developed by Seed and Idriss (1982), Tokimatsu and Seed (1987), Robertson and Wride (1998), Youd et al. (21) and Idriss and Boulanger (28). Although simplified total stress-based methods are used in general practice for the ease of computation to evaluate the liquefaction potential and associate settlement, these methods are unable to account for the progressive stiffness degradation of soil due to repeated shearing and pore-pressure rise during an earthquake event. As a result, nonlinear site response analysis and dynamic time history analyses are recommended for design of high risk infrastructures such as dams, bridges and nuclear power plants (Idriss and Boulanger, 28). In this study, three different analytical models by Finn et al. (1977), Liou et al. (1977), and Katsikas and Wylie (1982) are studied to compare the response of saturated sand deposit under earthquake motions. The reason behind choosing these models for comparison study are as follows: (a) these models are pioneering and fundamental for theoretical assessment of liquefaction phenomenon, (b) they can account for nonlinear stress-strain behavior of soil, (c) progressive rise in excess pore pressure and associated degradation of soil strength with time are well captured in these models, and (d) these models are widely used in the current design practice. Moreover, a number of new numerical liquefaction models have been derived based on these models. For example, the model developed by Finn et al. (1977), alternatively known as DESRA model, has been widely used for nonlinear site response analysis and liquefaction characterization. Later on, this model is modified and implemented in widely used software FLAC (Itasca, 25) and has been validated against other software such as SHAKE (Schnabel et al., 1972). In this study, for the purpose of comparison, a liquefiable saturated sand deposit of Niigata city is considered. A nonlinear shear stress-strain relationship and a gradual degradation of the shear modulus are considered for all three models. Cyclic stress ratio, excess pore pressure generation, effective stress reduction and development of shear strain are considered as four most important parameters characterizing liquefaction potential. Dynamic time history analysis is carried out to obtain the time history of the above-mentioned liquefaction parameters for earthquake motions from the 1964 Niigata and 1995 Kobe earthquakes. Finally, the responses from these models are compared with recent simplified methods summarized in Youd et al. (21). Adopted Numerical Models For the sake of completeness and proper appreciation a brief description of the considered models is provided in this section. Model#1: Finn, Lee and Martin (1977) This model includes formulation of constitutive relations incorporating nonlinear methods to predict the important features of the dynamic response of saturated sand deposits that generally occur when the pore-water pressure rises in the sand deposit during earthquake shaking. The model takes into account the important factors that affect the dynamic response of a sand layer, such as transient pore pressure rise, soil damping, hardening, variation of shear modulus with shear strain and changes in effective mean normal stress. The stress-strain behavior of sand in this model is formulated using hyperbolic relationship adopted by Hardin and Drnebvich (1972) as shown in Equations 1 through 3. τ Gmγ Gm 1+ γ τ = (1) m JERS/Vol.II/ Issue II/April-June,211/

3 Journal of Engineering Research and Studies E-ISSN (2) pore pressure generation, shear stress, and shear strain are obtained for any layer of a sand deposit. A flowchart indicating the procedure adopted by the model is provided in Figure 1 (a). Discretization of soil medium (3) where, G m and τ m are initial maximum shear modulus and maximum shear stress, respectively; K is coefficient of earth pressure at ' rest, e is the void ratio, σ v is vertical effective stress in pound/sq. ft.; and ε ' is the effective angle of shearing resistance. The maximum shear modulus and shear stress (G mn and τ mn ) at the n th loading cycle are determined from the initial peak values using the following expressions: Earthquake input motion Calculation of initial G, τm, shear wave velocity Vs, initial pressure wave velocity, VP1 and VP2, time step for shear wave model and time step for pressure wave model Calculation of shear strain and shear stress from shear wave submodel C c Calculation t G s from t Calculation of w, w, σ, S from pressure wave sub-model Calculation of w, w, σ, S from pressure wave submodel (4) (5) ' where, σ v is the effective vertical stress at the beginning of n th ' loading cycle, σ v is the initial effective vertical stress, ε vd is the accumulated volumetric strain; and H 1, H 2, H 3, and H 4 are constants, that were determined using calibrations against experiments carried out in simple shear apparatus. The volumetric strain, ε vd is again related to the rate of change in pore pressure (generation or dissipation) in the following manner: (6) where, u is the pore pressure and E r is the onedimensional rebound modulus of sand at an effective stress of σ v '. The steps are repeated for each cycle of an earthquake event using numerical techniques, and responses including Calculation of new G and Vs from effective stress Figure 1(a): Flow charts showing steps adopted in Model #1 Model#2: Liou, Streeter, and Richart (1977) The model by Liou et al. (1977) considered the soil deposit as one dimensional, two-phase medium composed of water and soil skeleton. The model is constituted by coupling two submodels, namely, shear wave sub-model and pressure wave sub-model. The component of ground motion parallel to ground surface is treated as shear wave sub-model, whereas the component perpendicular to the ground surface is treated as pressure wave sub-model. The rate of change of in the constrained compressibility is computed from modulus reduction. The shearing strain causes the increase of constrained compressibility, and the soil tends to settle. In undrained condition, this leads to rise of pore water pressure and reduction in effective stress. The dependence of the constrained modulus of the skeleton upon the dynamic shear modulus and the dependence of the shearing properties on the transient effective stress provide the coupling between the two parts of the model. A brief JERS/Vol.II/ Issue II/April-June,211/

4 Journal of Engineering Research and Studies E-ISSN discussion on each sub-model and their coupling is provided herein. Shear Wave Submodel The shear wave sub-model is used to calculate shearing stress, shearing strain, and modulus reduction caused by the motion bedrock. The propagation of the shear waves in onedimensional unsaturated soil deposits is modeled by Ramberg-Osgood relationship (Ramberg and Osgood, 1943) (shown in Equations 7 and 8). For initial loading: For reloading and unloading: (7) where, Cw= compressibility of water, P * = excess pore pressure, n = porosity of soil, w and w * are displacements defined in such a way, that volume of solid and volume of water that pass through a unit area fixed in space are, (1-n)w and nw *. The quantity np * represents the excess tensile force acting on the portion of a unit area of soil occupied by water, is denoted by S *. (12) If S is initial hydrostatic value of tensile force and S is the current value of the same quantity, then, (8) Where, τ i, and γ i represent the coordinates of the strain reversal point on the τ-γ plane. α, R, and C 1 are constants describing a given soil. G m and τ m are determined after Hardin and Drnebvich (1972) as shown in Equations 1 through 3. The dynamic equation of motion for the shear wave propagating through the solid matrix of the soil column in x-direction can be written as: And (9) (13) Stress-strain relation for the soil skeleton is: (14) In the theory of linear poro-elasticity, C c is related to G and the compressibility of the skeleton, C b, by, (15) Where, G s is the secant shear modulus of the soil skeleton. Finally, propagation of the plane shear waves in saturated deposits is represented as: (1) where, ρ = mass density of saturated soil, g = acceleration of gravity, θ = surface slope of the constant thickness of soil layer, u x = horizontal particle displacement in x-direction, U = velocity of the soil skeleton in x-direction. Pressure Wave Submodel By assuming the solid grains to be incompressible and by neglecting small terms, the relationship can be obtained. (16) Coupling Between Two Sub-models The numerical model for liquefaction is constituted by coupled shear wave and pressure wave motions. In the model, the deposit below water table is divided into a number of equal distance intervals and both sub-models are applied to them. Since in saturated soils volumetric disturbances travel at a speed much greater than the shear wave speed, N time steps are needed in the pressure wave sub-model for every time step in shear wave sub-model. (11) JERS/Vol.II/ Issue II/April-June,211/

5 Journal of Engineering Research and Studies E-ISSN (17) The shear wave sub-model is first used to calculate shearing stress, shearing strain, and reductions in G s caused by the motion of the bedrock. The rate of change of in the constrained compressibility, C c / t is then computed from G s / t. The pressure wave motions generated by changes in C c are then calculated from the pressure wave sub-model. The shearing strain causes the increase of C c, and the soil tends to settle. In undrained condition, this leads to rise of pore water pressure and reduction in effective stress. The steps are summarized in Figure 1 (b). the means of coupling the shear and pressure waves during motion. Specific features of this one-dimensional model are the preservation of the inelastic soil character during shearing, coupling between shear wave propagation and pore-water pressure development and seepage, and the association of excess pore-water pressure development with the inelastic volumetric deformation of the solid matrix and reasonable validation of the model against shaking table tests. The modeling approach is discussed briefly here. Under cyclic straining the structure change of the soil is given by, (18) Earthquake input motion Discretization of soil medium Calculation of initial G, τ m, shear wave velocity V s and time step for shear wave sub-model Calculation of shear strain and shear stress from shear wave submodel Calculation soil densification from shear wave sub-model Calculation pore water pressure and seepage velocity from pressure wave sub-model where, ε v = net solid matrix deformation, ε vs = volume reduction (densification) due to particle rearrangement, ε vr = volume expansion(rebound) due to relaxation of soil matrix. Based on a number of experimental studies, elastic rebound of the soil can be described as: (19) where, ε vr is corresponding soil rebound, σ is mean effective stress, and A and σ are constants. From experimental results an empirical expression is developed by Katsikas (1979) for the soil rebound: Calculation of effective stress from pore water pressure and total stress (2) σ is mean effective stress in pounds/sq. ft. Then Calculation of new G and V s from effective stress Figure 1(b): Flow charts showing steps adopted in Model #2 Model#3: Katsikas, and Wylie (1982) This model is also an effective stress-based numerical model that provides the interaction between shearing deformation and transient pore-water pressure development. Onedimensional propagation of shear waves through the solid matrix of the soil and pressure waves through the pore water is the principal part of the model. The volumetric soil deformation provides the soil densification increment, ε vs, corresponding to a time increment t, during straining may be given as: (21) where N c = Number of cycles from the beginning of straining, γ(%)= instantaneous shear strain at the end of a time increment t, γ(%) = change in shear strain over time t, and A1, A3 = parameters that depend on soil properties. The following expressions were derived by the first JERS/Vol.II/ Issue II/April-June,211/

6 Journal of Engineering Research and Studies E-ISSN writer, Christos A. Katsikas, based on the experimental results: (22) displacement time histories along with Fourier amplitude spectra are shown in Figure 4 and 5. These acceleration time histories are applied at the bottom of the deposit as input excitation. Discretization soil medium in form of a MDOF shear building (23) where,d r = relative density of the soil and D 5 = grain diameter in mm corresponding to 5% finer. The in elastic volumetric deformation of the solid matrix is associated with the generation of excess pore water pressure through the coupling between the shear wave propagation through soil skeleton and the pressure wave propagation through pore water. The numerical analysis is done by method of characteristics. The steps are shown through a flowchart in Figure 1(c). Input Earthquake Motions Considered in the Study In this study, two ground motion time histories from 1964 Niigata Earthquake and 1995 Kobe earthquake have been used. The detail information of the ground motions are given in Table 1. The acceleration, velocity and Acceleration (g) Velocity (cm/s) Displacement (cm) Earthquake input motion Table 1 Details of ground motion time history used Calculation of initial G, τm and then soil spring stiffness. Calculation of initial mass, stiffness and damping matrices Calculation acceleration, velocity, displacement for each DOF and then shear strain and shear stress for each layer: shear wave sub-model Generation of pore pressure from volumetric compaction Dissipation of pore pressure and thus calculation of resultant pore pressure Calculation of effective stress from pore water pressure and total stress Calculation of new G and therefore stiffness matrix from effective stress Figure 1(c): Flow charts showing steps adopted in Model #3 Earthquake Magnitude Station Component PGA (g) PGV cm/sec) PGD (cm) 1964 NIIGATA B1F SMAC-A EW Kobe 6.9 JMA EW (a) (b) (c) Frequency (Hz) Figure 4: (a) Acceleration time history, (b) velocity time history, (c) displacement time history and (d) Fourier amplitude spectrum for E-W component of 16th June 1964 Niigata Earthquake Fourier Amplitude (cm/sec) (d) JERS/Vol.II/ Issue II/April-June,211/

7 Journal of Engineering Research and Studies E-ISSN Acceleration (g) Velocity (cm/s) Displacement (cm) (a) (b) (c) Fourier Amplitude (cm/sec) Frequency (Hz) Figure 5: (a) Acceleration time history, (b) velocity time history (c) displacement time history, and (d) Fourier amplitude spectrum for E-W component of 16th January 1995 Kobe Earthquake, station JMA Soil Profile Considered in the Study For this study, a liquefiable soil profile, zone B of Niigata city (Seed and Idriss, 1982) has been considered. The subsoil at Niigata city consists of mainly thick alluvial sand deposits, which have been overlaid along the coast by deposits of dune sand. The sand deposits are relatively loose at ground surface and become denser with (Equations 6-7). The values of G m and τ m at different depths in the soil deposit are given in a tabular form (Table 2). Figure 2 (a) shows the standard penetration blow counts for the chosen The depth of alluvial sand site (Seed and Idriss, 1987). Before performing the dynamic analyses, simplified method as summarized in Youd et al. (21) is used to calculate the liquefaction potential of the deposit. The methods summarized in Youd et al. (21) are widely used by the design practice and are recommended by most of the current design codes such as Federal Emergency Management Agency (FEMA, 1996) and National Earthquake Hazard Reduction Program (NEHRP, 2). According to Youd et al. (21), a deposit is considered to be potentially liquefiable when the cyclic stress ratio (CSR) induced by an earthquake is greater that the cyclic resistance ratio (CRR) of that deposit. Equation (3) to (5) is used to derive CSR and CRR for a deposit and a potential earthquake in that region. Table 2 Initial G and m estimated for zone B of Niigata sand increasing depth. exceeds 1 meters. Niigata sand is fine sand consisting of grains that are subangular to subrounded. The specific gravity is G s =2.67, the maximum void ratio is e max =.99, the minimum void ratio is e min =.55 the mean diameters are D 5 =.23mm and D 1 =.13mm, and coefficient of uniformity U c = The grain size distribution curve reported by Ishihara and Koga (1981) is an average curve of the Niigata sand. The water table was approximately at.9 m below the ground surface (Seed and Idriss, 1982). The unit weight of the sand above water table and the submerged unit weight below water table were estimated as 17.5 kpa, and 8. kpa, respectively. Poisson s ratio for Niigata Zone B sand is approximated as.4 and the coefficient of horizontal earth pressure is estimated as.46 (from Seed and Idriss, 1982). A nonlinear relationship is adopted for shear stress-strain relationship after Ramberg and Osgood (1943) Layer Number G m (MPa) τ m (Pa) (d) JERS/Vol.II/ Issue II/April-June,211/

8 Journal of Engineering Research and Studies E-ISSN Niigata (M=7.5, pga=.21g) Kobe (M=6.9, pga=.82g) Depth (ft) 4 Depth (m) Depth (ft) 4 Depth (m) Blows/ft Liq Non-liq CRR/CSR (a) (b) Figure 2: (a) Standard penetration resistance of zone B, Niigata City and (b) Liquefaction potential calculated after Youd et al. (21) where, τ av = average cyclic stress, ' vo = total vertical stress before shaking, ' vo = effective vertical stress before shaking, a max = peak ground acceleration, r d = reduction factor due to depth, (N 1 ) 6 = corrected blow count, CRR 7.5 = cyclic resistance ratio for an earthquake with magnitude 7.5, MSF = magnitude scaling factor. In this study, for the Niigata soil profile zone B, CSR and CRR are calculated for both Niigata and Kobe motion. Figure 2(b) shows the profile of the ratio of CRR to CSR, in which the liquefaction zone (when CRR<CSR) and nonliquefaction zone (when CRR>CSR) are identified. It can be observed that for the Niigata motion, the site is liquefiable up to a depth of 35 ft (11.5m), whereas for the Kobe motion, the entire deposit is potentially liquefiable according to the methods after Youd et al. (21). Results and Discussion Considering the representative soil profile of Niigata city zone, B and using the earthquake excitation mentioned above, the comparison of responses from three models are studied. Figures 3 through 6 show the results of the time history analyses in terms of cyclic stress ratio, excess pore pressure, normalized effective stress, and shear strain, respectively. The above mentioned response parameters are most important to evaluate the liquefaction potential of a deposit. The results shown here correspond to the response of soil layer at a depth of 1 m. It is important to note that based on simplified analysis after Youd et al. (21), for both the earthquake motions the soil is liquefiable at depth 1m. Figures 4a and 4b show the cyclic stress ratio time history for Niigata EW motion and Kobe JMA motion, respectively, calculated using all the three models considered herein. Cyclic resistance ratio calculated after Youd et al. (21) is also noted here. It can be observed from Figure 3a that prediction of model 1 and model 3 indicates that the deposit liquefies at about 8.5 sec for Niigata motion. The liquefaction triggering is defined as the condition when cyclic stress ratio (i.e. the demand) exceeds the cyclic resistance ratio (i.e. the capacity). Figure 4b, similarly shows that model 1 and 3 indicates liquefaction occurrence at 7.2 sec for the Kobe motion. Model 2 prediction does not indicate any liquefaction in both the cases. It should be noted that ~7-1sec in Niigata motion and 7-12 sec in Kobe motion is approximately the duration of the strong motions. JERS/Vol.II/ Issue II/April-June,211/

9 Journal of Engineering Research and Studies E-ISSN Cyclic Stress Ratio CRR (Youd et al., 21) Model #1 (a) Model #2 (b) Model # CRR (Youd et al., 21) Figure 3: Cyclic stress ratio: (a) Niigata motion and (b) Kobe motion Another important feature of the liquefaction is the generation of excess pore water pressure and consequent reduction in effective stress. Figure 4a and 4b show the time histories for excess pore water pressure normalized by total static vertical stress predicted through the different models as adopted. It is observed that for Niigata motion, all three models predict liquefaction at about 1 sec, considering that liquefaction is defined when excess pore pressure is 1% of the total stress. However, it can be seen that the rise of excess pore pressure with time varies significantly from model to model. Especially model 2 indicates a very steep curve compared to other two models. This variation leads to significant difference in prediction of partial liquefaction characteristics. For example, at time = 6sec, excess pore pressure ratio is 22%, 9% and 3% using model 1, 2 and 3, respectively. For Kobe motion, similar responses are observed. Note that simplified methods summarized by Youd et al. (21) based on SPT and CPT data are unable to predict the pore-water pressure built up. The effective stress responses also show the similar result (Figure 5a and 5b). Shear strain induced by liquefaction is one of the most critical consequences of liquefaction. Liquefaction is often defined as a situation when shear strain is increased to ±5% (Seed and Idriss, 1987). Figure 6a and 6b show the comparative predictions of liquefaction induced shear strain for Niigata and Kobe motions, respectively. Excess Pore Pressure (%) (a) Model #1 Model #2 Model #3 8 (b) Figure 4: Excess pore pressure ratio: (a) Niigata motion and (b) Kobe motion JERS/Vol.II/ Issue II/April-June,211/

10 Journal of Engineering Research and Studies E-ISSN Normalized Effective Stress (a) Figure 5: Effective stress ratio: (a) Niigata motion and (b) Kobe motion It can be seen that model 2 indicates liquefaction occurrence (shear strain = 5%) at about 9 sec for Niigata motion, whereas other two models indicates shear strain well below 5% for this motion. On the other hand, for Kobe motion, according to model 2, liquefaction occurs (shear strain = -5%) at 9.5 sec, whereas model 3 indicates liquefaction occurrence at 11 sec. Model 1 shows that shear strain does not reach 5% for this case. Note that the simplified method suggested by Tokimatsu and Seed (1987) which is also adopted in the design practice such as FEMA-356 (FEMA, 2) and NEHRP (NEHRP, 2), indicates, indicate that the shear strain of this layer does not reach 5% shear strain under these earthquake motions. The overall observation from the comparative study indicates that model 1 and 3 predictions are similar and are close to that by simplified methods summarized Shear Strain (%) Model #1 Model #2 Model #3 5% shear strain Model #1 Model #2 Model # (b) in Youd et al. (21), whereas model 2 prediction is significantly different from that by the other two models. Since model 1 (Finn et al, 1977, alternatively known as DESRA model) is widely accepted in the earthquake engineering community and is well-validated against several case studies and other dynamic response evaluation software such as SHAKE (Schnabel et al., 1972), it may be assumed that this model s prediction is somewhat accurate. Based on the above assumption, it may be concluded that model 2 is under-predicting the cyclic stress ratio, but over-predicting the rate of excess pore pressure generation and the rate of effective stress reduction significantly. In addition, model 2 is also over-predicting the induced shear strain in the soil deposit. This over-prediction is significantly high after 7 sec for Niigata motion and 9.5 sec for the Kobe motion Figure 6: Shear strain: (a) Niigata motion and (b) Kobe motion JERS/Vol.II/ Issue II/April-June,211/

11 Journal of Engineering Research and Studies E-ISSN CONCLUSIONS In this study, a comparative analysis involving three effective stress-based analytical models, Finn et al. (1977), Liou et al. (1977) and Katsikas et al. (1982) is carried out for predicting the response of a liquefiable saturated sand deposit of Niigata city under different earthquake ground motions. All three models assume nonlinear shear stress-strain relationship, and a gradual degradation of the shear modulus. The strength degradation is coupled with pressure wave propagation through the pore water and consequent volume change. Comparison results are shown in terms of four most important parameters characterizing liquefaction potential: cyclic stress ratio, excess pore pressure generation, effective stress reduction and development of shear strain. Dynamic time history analysis is carried out to obtain the time history of the above-mentioned parameters for earthquake motions from the 1964 Niigata and 1995 Kobe earthquakes. The results are also compared with simplified methods that are adopted in current design provisions such as FEMA (1996) and NEHRP (2). It has been found that the prediction by the models of Finn et al. (1977) and Katsikas et al. (1982) matches well, whereas the prediction by Liou et al. (1977) is significantly different for the chosen soil deposit and ground motions. This difference of response involving Liou s model is particularly significant for the excess pore pressure generation and consequent strength loss as indicated by higher rate of partial liquefaction (Figure 4a-b and 5a-b). This may be due to the difference in considering the excess pore pressure generation used in Liou s model. In general, however, the time indicating full liquefaction (pore pressure =1%) is close for all three models (~1-12 sec). REFERENCES Ashford S. A., Rollins, K. M., and Lane, D. (24). Blast-Induced Liquefaction for Full Scale Foundation Testing, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 13(8), Castro, G. (1975). Liquefaction and Cyclic Mobility of Saturated Sand, Journal of Geotechnical Engineering Division, ASCE, 11 (6), Desai, C. (2). Evaluation of liquefaction using disturbed state and energy Approaches. Journal of Geotechnical Engineering Division, ASCE, 126(7), Elgamal A. W, Zeghal M, Parra E. (1996) Liquefaction of reclaimed island in Kobe, Japan. Journal of Geotechnical Engineering Division, ASCE, 122(1), FEMA 356, Prestandard and Commentary for the Seismic Rehabilitation of Buildings, American Society of Engineers, Virginia., 2. Finn, W. D. L., Lee, K. W., Martin, G. R. (1977) An effective stress model for liquefaction. Journal of Geotechnical Engineering Division, ASCE, 13(GT6), Itasca (25). Fast Lagrangian Analysis of Continua. Itasca. FLAC manual, 25. Idriss, I. M. and Boulanger, R. W. (28). Soil Liquefaction during Earthquakes, Engineering Monograph, Earthquake Engineering and Research Institute (EERI), Oakland, California. Ishihara, K. and Koga, Y. (1981). "Case Studies of Liquefaction in the 1964 Niigata Earthquake," Soils and Foundations, Japanese Society of Soil Mechanics and Foundation Engineering, 21(3), Sept 1981, Katsikas, C. A. and Wylie, E. B. (1982). Sand Liquefaction: Inelastic Effective Stress Model. Journal of the Geotechnical Engineering Division, ASCE, 18(1), Liou, C. P., Richart, F. E. and Streeter, V. L. (1977). Numerical Model for Liquefaction. Journal of the Geotechnical Engineering Division, ASCE, 13 (6), Liyanapathirana, D. S. and Poulos, H. G. (22). A numerical model for dynamic soil liquefaction analysis. Soil Dynamics and Earthquake Engineering, 22 (22), Martin, G. R., Finn, W. D. L. and Seed, H. B. (1975). Fundamentals of Liquefaction under Cyclic Loading. Journal of the Geotechnical Engineering Division, ASCE, 11 (5), NEHRP, Recommended Provisions for Seismic Regulations for New Buildings, Building Seismic Safety Council, Washington, D.C., 2. Ramberg, W. and Osgood, W. T. (1943). Description of Stress-strain Curves by Three Parameters, Technical Notes 92, NASA, Washington D. C. JERS/Vol.II/ Issue II/April-June,211/

12 Journal of Engineering Research and Studies E-ISSN Robertson, P. K., and Wride, C. E. (1998). Evaluating cyclic liquefaction potential using the cone penetration test. Canadian Geotechnical Journal, 35(3), Schnabel, P. B., Lysmer, J. and Seed, H. B. (1972). SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites, Report No. EERC 72-12, Earthquake Engineering Research Center, University of California, Berkeley. Seed, H. B. and Idriss, I. M. (1982). Soil Liquefaction during Earthquakes, Engineering Monograph, Earthquake Engineering and Research Institute (EERI), Oakland, California. Seed, H. B. and Lee, K. L. (1966). Liquefaction of Saturated Sands During Cyclic Loading, Journal of Geotechnical Engineering Division, ASCE, 92 (SM6), Tokimatsu, K. and Seed, H. B. (1987). Evaluation of Settlement in Sand due to Earthquake Shaking. Journal of the Geotechnical Engineering Division, ASCE, 113 (8), Youd, T. L. et al. (21). Liquefaction resistance of soils: Summary report from the 1996 NCEER and 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 127(1), JERS/Vol.II/ Issue II/April-June,211/