Non-linear soil models for site response analysis

NON-LINEAR SOIL MODELS FOR SITE RESPONSE ANALYSIS

Reference	Dim.	Total or Effective Stress	Notes	Code
Mechanical
Joyner and Chen (1975)	1-D, 2-D	?	1-D: array of elasto-plastic elements with Coulomb slider 2-D: Nested yield surfaces (Iwan 1967)
Taylor and Larkin (1978), Larkin and Marsh (1991)	1-D 2-D		Similar to Joyner and Chen (1975)	DENSOR (Larkin 1978)
Empirical
Streeter et al. (1974)	1-D		Uses a Ramberg-Osgood (1943) model with Masing (1926) rules. Equations are solved using method of characteristics	CHARSOIL
Pyke (1979)	1-D	Total	Good review of mechanistic and empirical models, including Iwan (1967). Presents a modified set of Masing rules.	TESS (Pyke 1992)
Lee and Finn (1978, 1991) Finn et al. (1986)	1-D, 3-D	Both	Hyperbolic loading curve coupled with Masing criterion. Uses pore pressure generation model of Martin et al. 1975)	DESRA-2 (1-D) DESRA-2C TARA-3 (3-D)
Martin and Seed (1982)	?	?	Similar to above, plus Davidenkov model	MASH (Martin and Seed 1978)
Matasovic and Vucetic (1993)	1-D		Modification to Lee and Finn (1978) model	D-MOD
Plasticity Based
Prevost 1977	3-D	Total	Nested yield surfaces (original concept I Mroz 1967)	DYNA1D (Prevost 1998, 1-D only)
Mroz, et al. (1979),Mroz et al. (1978, 1981)	3-D		Multiple yield surfaces. Mroz et al (1981) introduces the concept of infinite surfaces.
Dafalias and Hermann (1982), (Dafalias and Popov 1977)	3-D		Bounding surface plasticity with vanishing elastic region. Independently proposed also by Krieg (1975)
Li et al. (1992) Wang et al. (1990)	3-D	Eff.	Bounding surface plasticity model	SUMDES
Bardet (1989)			Bounding Surface Plasticity Model
Borja and Amies (1994); Borja, Lin et al. (2000)	3-D	Total	Bounding surface plasticity model with vanishing elastic region	SPECTRA (Borja and Wu 1994)
Dafalias (1986)			Bounding surface plasticity model, also uses concept of hypoplasticity
Zienkiewicz et al. (1999)			Hypoplasticity model
Finn (1988)	?	?	?	?
Scott (1985)	?	?	?	?
Bazant and Krizek (1976)			Endochronic Model
Equivalent Linear
Seed and Idriss (1969), Schnabel et al. (1972), Idriss and Sun (1992)	1-D	Total	Original equivalent linear concept and code. Most used model	SHAKE, SHAKE91
Hudson et al. (1994)	2-D	Total	Finite element solution in the frequency domain using an equivalent linear approach	QUAD4-M

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.

Bazant, Z. P. and Krizek, R. J. (1976). "Endochronic constitutive law for liquefaction of sands." Journal of Engineering 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 non-liquefiable 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 523-591.

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.

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.

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.