NON-LINEAR SOIL MODELS FOR SITE RESPONSE ANALYSIS
Reference
Dim.
Total or
Effective
Stress
Joyner and Chen (1975)
1-D,
2-D
Taylor and Larkin (1978),
Larkin and Marsh (1991)
1-D
2-D
Streeter et al. (1974)
1-D
Pyke (1979)
1-D
Total
Lee and Finn (1978, 1991)
Finn et al. (1986)
1-D,
3-D
Both
Martin and Seed (1982)
?
?
Matasovic and Vucetic
(1993)
1-D
Prevost 1977
3-D
Mroz, et al. (1979),Mroz
et al. (1978, 1981)
Dafalias and Hermann
(1982), (Dafalias and
Popov 1977)
Li et al. (1992)
Wang et al. (1990)
Bardet (1989)
Borja and Amies (1994);
Borja, Lin et al. (2000)
3-D
3-D
Eff.
3-D
Total
Seed and Idriss (1969),
Schnabel et al. (1972),
Idriss and Sun (1992)
Hudson et al. (1994)
?
?
1-D
2-D
Mechanical
1-D: array of elasto-plastic elements with
Coulomb slider
2-D: Nested yield surfaces (Iwan 1967)
Similar to Joyner and Chen (1975)
Empirical
Uses a Ramberg-Osgood (1943) model
with Masing (1926) rules. Equations are
solved using method of characteristics
Good review of mechanistic and empirical
models, including Iwan (1967). Presents a
modified set of Masing rules.
Hyperbolic loading curve coupled with
Masing criterion. Uses pore pressure
generation model of Martin et al. 1975)
Similar to above, plus Davidenkov model
Modification to Lee and Finn (1978)
model
Plasticity Based
Total
Nested yield surfaces (original concept I
Mroz 1967)
3-D
Dafalias (1986)
Zienkiewicz et al. (1999)
Finn (1988)
Scott (1985)
Bazant and Krizek (1976)
?
Notes
Multiple yield surfaces. Mroz et al (1981)
introduces the concept of infinite surfaces.
Bounding surface plasticity with
vanishing elastic region. Independently
proposed also by Krieg (1975)
Bounding surface plasticity model
Bounding Surface Plasticity Model
Bounding surface plasticity model with
vanishing elastic region
Bounding surface plasticity model, also
uses concept of hypoplasticity
Hypoplasticity model
?
?
?
?
Endochronic Model
Equivalent Linear
Total
Original equivalent linear concept and
code. Most used model
Total
Finite element solution in the frequency
domain using an equivalent linear
approach
Code
DENSOR
(Larkin 1978)
CHARSOIL
TESS (Pyke
1992)
DESRA-2 (1-D)
DESRA-2C
TARA-3 (3-D)
MASH (Martin
and Seed 1978)
D-MOD
DYNA1D
(Prevost 1998,
1-D only)
SUMDES
SPECTRA
(Borja and Wu
1994)
?
?
SHAKE,
SHAKE91
QUAD4-M
1
Notes: Most of the table above is compiled from the thesis of Thomas Lok (2000) and Rodriguez-Marek (2000)
Bardet, J.P. (1989). "Prediction of deformations of Hostun and Reid Bedford sands with a simple bounding plasticity
model," in Constitutive Equations for Granular Non-cohesive Soils, A. Saada and G. Bianchini, Eds., 131-148,
Balkema.
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Mechanics Division, ASCE 102(EM2) 225-238.
Borja, R. I., Chao, H. Y., Sama, K. M., and Masada, G. M. (2000). "Modelling non-linear ground response of nonliquefiable soils." Earthquake Engineering and Structural Dynamics, 29, 63-83.
Borja, R.I., and Amies, A.P. (1994). "Multiaxial cyclic plasticity model for clays." Journal ofGeotechncial Engineering,
120(6) 1051-1070.
Dafalias, Y. F. (1986). "Bounding surface plasticity, I: Mathematical foundation and hypoplasticity." Journal of
Engineering Mechanics, ASCE, 112 966-987.
Dafalias, Y. F. and Herrmann, L. R. (1982). "Bounding surface formulation of soil plasticity," in Soil Mechanics –
Transient and Cyclic Loads, Pande, G. N. and Zienkiewicz, O. C., Eds., John Wiley and Sons, New York, NY.
Dafalias, Y. F., and Popov, E. P. (1977). “Cyclic loading for materials with a vanishing elastic region.” Nuclear
Engineering and Design, 41, 2, Apr. 1977, pages 293-302.
Finn, W. D. L. (1988). "Dynamic analysis in geotechnical engineering." Proceedings, Earthquake Engineering and Soil
Dynamics II – Recent Advances in Ground Motion Evaluations. Geotechnical Special Publication 20, ASCE 523591.
Hudson, M., Idriss, I.M., and Beikae, M. (1994) “QUAD4M: A Computer Program to Evaluate the Seismic Response of
Soil Structures using Finite Element Procedures and Incorporating a Compliant Base,” Center for Geotechnical
Modeling, Dep. of Civil & Env. Engng, University of California, Davis.
Idriss, I. M. and Sun, J. I. (1992). "User's Manual for SHAKE91, A computer Program for Conducting Equivalent Linear
Seismic Response Analyses of Horizontally Layered Soil Deposits Program Modified based on the Original SHAKE
Program Published in December 1972 by Schnabel, Lysmer and Seed."
Iwan, W,. D. (1967). "On a class of models for the yielding behavior of continuous and composite systems." Journal of
Applied Mechanics, 34, 612-617.
Joyner W. B., and Chen, A. T. F. (1975). "Calculation of nonlinear ground response in earthquakes." Bulleting of the
Seismological Society of America, 65(5) 1315-1336.
Krieg, R. D. (1975). "A practical two-surface plasticity theory." Journal of Applied Mechanics, 42, 641-646.
Lee, M. K. W. and Finn, W. D. L. Finn (1978). "DESRA-2, Dynamic effective stress response analysis of soil deposits
with energy transmitting boundary including assessment of liquefaction potential." Soil Mechanics Series No. 36,
Department of Civil Engineering, University of British Columbia, Vancouver, Canada.
Lee, M. K. W. and Finn, W. D. L. (1991). "DESRA-2C: Dynamic effective stress response analysis of soil deposits with
energy transmitting boundary including assessment of liquefaction potential." University of British Columbia, Faculty
of Applied Science.
2
Li X. S., Shen, C. K., Wang, Z. L. (1998). "Fully-coupled inelastic ground response analysis for 1986 Lotung Earthquake
Events." Journal of Geotechnical Engineering, ASCE, 124(7).
Li. X.S., Wang, Z. L, and Shen, C. K. (1997). “SUMDES. A nonlinear procedure for response analysis of horizontally
layered sites subjected to multi-directional earthquake loading. Department of Civil Engineering, University of
California at Davis.
Lok, M. H. (1999). "Numerical modeling of seismic soil-pile-superstructure-interaction in soft clay." A dissertation
submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Civil Engineering of the
University of California at Berkeley.
Martin, P. P., and Seed, H. B. (1982). "One-dimensional dynamic ground response analyses." Journal of Geotechnical
Engineering Division, ASCE, 108(7), 935-952.
Mróz, Z. (1967). "On the description of anisotropic work-hardening." Journal of Mech. Phys. Solids, 15, 163-175.
Mróz, Z., Norris, B. A., and Zienkiewicz, O. C. (1978). "Application of an anisotropic hardening modeling in the analysis
of elasto-plastic deformation.", Geotechnique, 29(1), 1-34.
Mróz, Z., Norris, B. A., and Zienkiewicz, O. C. (1981). "An anisotropic critical state model for soils subjected to cyclic
loading." Geotechnique, 31, 451-469.
Prevost, J. H. (1977). "Mathematical modeling of monotonic and cyclic undrained clay behavior." International Journal
of Numerical Analysis Methods in Geomechanics, 1, 195-216.
Prevost, J. H. (1989). "DYNA1D: A computer program for nonlinear site response analysis, technical documentation."
Technical Report No. NCR-89-0025, National Center of Earthquake Engineering Research, Sunny at Buffalo, NY.
Pyke, R. M. (1979). "Nonlinear models for irregular cyclic loadings." Journal of Geotechnical Engineering Division,
ASCE, 105(GT6) 715-726.
Pyke, R. M. (1992). "TESS: A computer program for nonlinear ground response analyses." TAGA Engin. Systems and
Software, Lafayette, CA.
Ramberg, W. Osgood, W. T. (1943). "Description of stress-strain curves by three parameters." Tech. Note 902, National
Advisory Committee of Aeronautics.
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 at Berkeley, Berkeley, CA.
Scott, R. F. (1985). "Plasticity and constitutive relations in soil mechanics." Journal of Geotechnical Engineering, ASCE
111(5) 563-605.
Seed, H. B. and Idriss, I. M. (1969). "The influence of soil conditions on ground motions during earthquakes." Journal of
the Soil Mechanics and Foundation Engineering Division, ASCE, No. 94, 93-137.
Streeter, B. L., Wylie, E. B., and Richart, F. E. (1974). "Soil motions computations by characteristics methods." Journal
of the Geotechnical Engineering Division, ASCE, 100(GT3) 247-263.
Taylor, P. W. and Larkin, T. J. (1978). "Seismic response of nonlinear soil media." Journal of the Geotechnical
Engineering Division, ASCE, 104(GT3) 369-183.
3
Wang, Z. L., Dafalias, Y. F. and Shen, C. K. (1990). "Bounding surface hypo-plasticity model for sands." Journal of
Engineering Mechanics, ASCE, 116(5) 993-1001.
Zienkiewicz, O. C., Chan, A. H. C., Pastor, M., Schrefler, B. A., Shiomi, T. (1999). Computational Geomechanics with
Special Reference to Earthquake Engineering. John Wiley and Sons, New York, NY.
Zienkiewicz, O. C., Chang, C. T., and Hinton, E. (1978). "Nonlinear seismic response and liquefaction." International
Journal of Numerical Analysis Methods in Geomechanics, 2, 381-404.
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