Application of a Critical State Model for Cyclic Loading of Sands

Document Type : Research Article


Department of Civil and Environmental Engineering, Amirkabir Uuniversity of Technology, Tehran, Iran


The purpose of the current paper is to extend a critical state constitutive model presented previously for sand behavior under monotonic loading such that it can predict behavior under cyclic loads as well. Due to the use of the critical state soil mechanics framework, the original model was able to predict sand behavior over a wide range void ratios and confining pressures, and take into account various aspects of behavior of loose and dense sands, including inherent and stress-induced anisotropies, softening and liquefaction of sands under monotonic loads. Extension of the base model for cyclic loading is accomplished through the use of bounding surface plasticity. Yield surface of the original model is used as the bounding surface of the new model, and also its loading surface using a deviatoric mapping rule. A new hardening modulus is used that enables predicting the behavior during loading and unloading. Flow rule of the original model is also modified in order to enable better prediction of the loading-unloading behavior, especially after phase transformation. Predictions based on this model showed satisfactory match with observed behavior of sands over a wide range of void ratios and confining pressures in drained and undrained monotonic and cyclic loading.


Main Subjects

[1] K.H. Roscoe, A. Schofield, C. Wroth, On the yielding of soils, Geotechnique, 8(1) (1958) 22-53.
[2] A. Schofield, P. Wroth, Critical state soil mechanics, McGraw-Hill London, 1968.
[3] M. Pastor, O. Zienkiewicz, K. Leung, Simple model for transient soil loading in earthquake analysis. II. Non-associative models for sands, International Journal for Numerical and Analytical Methods in Geomechanics, 9(5) (1985) 477-498.
[4] C. di Prisco, R. Nova, A constitutive model for soil reinforced by continuous threads, Geotextiles and Geomembranes, 12(2) (1993) 161-178.
[5] K. Been, M.G. Jefferies, A state parameter for sands, Géotechnique, 35(2) (1985) 99-112.
[6] S.R. Imam, N.R. Morgenstern, P.K. Robertson, D.H. Chan, A critical-state constitutive model for liquefiable sand, Canadian geotechnical journal, 42(3) (2005) 830-855.
[7] S.R. IMAM, N.R. Morgenstern, P.K. Robertson, D.H. CHAN, Yielding and flow liquefaction of loose sand, Soils and Foundations, 42(3) (2002) 19-31.
[8] S.R. IMAM, D.H. Chan, P.K. Robertson, N.R. MORGENSTERN, Effect of anisotropic yielding on the flow liquefaction of loose sand, Soils and foundations, 42(3) (2002) 33-44.
[9] D.M. Wood, K. Belkheir, Strain softening and state parameter for sand modelling, Geotechnique, 44(2) (1994) 335-339.
[10] M.T. Manzari, Y.F. Dafalias, A critical state two-surface plasticity model for sands, Geotechnique, 47(2) (1997) 255-272.
[11] Z. Mroz, On the description of anisotropic workhardening, Journal of the Mechanics and Physics of Solids, 15(3) (1967) 163-175.
[12] W.D. Iwan, On a class of models for the yielding behavior of continuous and composite systems, Journal of Applied Mechanics, 34(3) (1967) 612-617.
[13] O. Zienkiewicz, Generalized plasticity formulation and application to geomechanics, Mech. Eng. Materials, (1984) 655-679.
[14] Y. Dafalias, On cyclic and anisotropic plasticity, A General model, (1975).
[15] Y. Dafalias, E. Popov, A model of nonlinearly hardening materials for complex loadingEin Modell für Werkstoffe mit nichtlinearer Verfestigung unter zusammengesetzter Belastung, Acta mechanica, 21(3) (1975) 173-192.
[16] Y. Dafalias, A modell for soil behavior under monotonic and cyclic loading conditions, in: Structural mechanics in reactor technology. Transactions. Vol. K (a), 1979.
[17] J.-P. Bardet, Bounding surface modeling of cyclic sand behavior, in: Proceedings of the Workshop on Constitutive Laws for the Analysis of Fill Retention Structures. Edited by E. Evgin, Ottawa, 1987, pp. 1-19.
[18] Y. Dafalias, L. Herrman, A. Anandarajah, Cyclic loading response of cohesive soils using a bounding surface plasticity model, (1981).
[19] H.I. Ling, S. Yang, Unified sand model based on the critical state and generalized plasticity, Journal of Engineering Mechanics, 132(12) (2006) 1380-1391.
[20] M. Taiebat, Y.F. Dafalias, SANISAND: Simple anisotropic sand plasticity model, International Journal for Numerical and Analytical Methods in Geomechanics, 32(8) (2008) 915-948.
[21] Y. Dafalias, M. Taiebat, SANISAND-Z: zero elastic range sand plasticity model, Geotechnique, 66(12) (2016) 999-1013.
[22] M.E. Kan, H.A. Taiebat, A bounding surface plasticity model for highly crushable granular materials, Soils and Foundations, 54(6) (2014) 1188-1201.
[23] K. Hashiguchi, Cyclic plasticity models: critical reviews and assessments, in: Foundations of Elastoplasticity: Subloading Surface Model, Springer, 2017, pp. 235-256.
[24] D. Gallipoli, A. Bruno, A bounding surface compression model with a unified virgin line for saturated and unsaturated soils, Géotechnique, 67(8) (2017) 703-712.
[25] K. Ishihara, F. Tatsuoka, S. Yasuda, Undrained deformation and liquefaction of sand under cyclic stresses, Soils and foundations, 15(1) (1975) 29-44.
[26] Y. Javanmardi, Application of a Critical State Bounding Surface Model for Cyclic Response of Saturated Sand (in Persian), Amirkabir University of Technology, 2011.
[27] R.S. Crouch, J.P. Wolf, Y.F. Dafalias, Unified critical-state bounding-surface plasticity model for soil, Journal of engineering mechanics, 120(11) (1994) 2251-2270.
[28] Y.F. Dafalias, M.T. Manzari, Simple plasticity sand model accounting for fabric change effects, Journal of Engineering mechanics, 130(6) (2004) 622-634.
[29] S. Nemat-Nasser, Y. Tobita, Influence of fabric on liquefaction and densification potential of cohesionless sand, Mechanics of Materials, 1(1) (1982) 43-62.
[30] J.A. Yamamuro, P.V. Lade, Steady-state concepts and static liquefaction of silty sands, Journal of geotechnical and geoenvironmental engineering, 124(9) (1998) 868-877.
[31] Y. Vaid, E. Chung, R. Kuerbis, Stress path and steady state, Canadian Geotechnical Journal, 27(1) (1990) 1-7.
[32] K. Been, M. Jefferies, J. Hachey, Critical state of sands, Geotechnique, 41(3) (1991) 365-381.
[33] K. Ishihara, Liquefaction and flow failure during earthquakes, Geotechnique, 43(3) (1993) 351-451.
[34] R. Verdugo, K. Ishihara, The steady state of sandy soils, Soils and foundations, 36(2) (1996) 81-91.
[35] M. Yoshimine, K. Ishihara, Flow potential of sand during liquefaction, Soils and Foundations, 38(3) (1998) 189-198.
[36] X.-S. Li, Y. Wang, Linear representation of steady-state line for sand, Journal of geotechnical and geoenvironmental engineering, 124(12) (1998) 1215-1217.
[37] D. Sheng, Y. Yao, J.P. Carter, A volume–stress model for sands under isotropic and critical stress states, Canadian Geotechnical Journal, 45(11) (2008) 1639-1645.
[38] F.E. Richart, J.R. Hall, R.D. Woods, Vibrations of soils and foundations, (1970).
[39] X. Li, Y.F. Dafalias, Dilatancy for cohesionless soils, Geotechnique, 50(4) (2000) 449-460.
[40] R. Verdugo, Characterization of sandy soil behavior under large deformation, PhD Thesis. Tokyo, Japan, University of Tokyo, 1992.
[41] T.B.S. Paradhan, The behavior of sand subjected to monotonic and cyclic loadings, PhD Thesis. Kyoto, Japan, Kyoto University, 1990.