An endochronic-based approach to simulating pore water pressure variation during liquefaction of sand

Document Type : Article

Authors

Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

Abstract

Liquefaction is one of the consequences of earthquake in soil layers comprised of saturated loose sands. Various aspects of liquefaction have been investigated using different methods of field, laboratory, and numerical studies. Numerical simulation of liquefaction constitutes a major part of these researches. Application of a proper constitutive law in the numerical analysis is crucial for modeling the
complicated undrained behavior of saturated sands during dynamic loading. Simplicity of formulation, limited number of parameters, and good performance are the main features of a proper constitutive law. In this study, an Endochronicbased model for simulating liquefaction of sand is implemented into the finite element program, PISA. Coupled dynamic field equations of Biot’s theory with u-p formulation are used to determine pore fluid and soil skeleton responses. Generalized Newmark method is employed for integration in time. The developed code is capable of predicting the magnitude of the generated pore water pressure, coupled with advanced constitutive laws such as critical state twosurface plasticity as well as simple models such as Mohr- Coulomb. Simulating cyclic simple shear and centrifuge tests using Endochronic model showed favorable performance of this model for predicting the variation of pore water pressure in saturated soil layers subjected to earthquake excitations.

Keywords


1. Lopez-Querol, S. and Blazquez, R. Liquefaction, and  cyclic mobility model for saturated granular media",  International Journal for Numerical and Analytical  Methods in Geomechanics, 30(5), pp. 413{439 (2006).  2. Dafalias, Y.F. Overview of constitutive model used in  velacs", In Veri_cation of Numerical Procedures for the  Analysis of Soil Liquefaction Problems, 2, Rotterdam,  Balkema (1993).  3. Valanis, K.C. A theory of viscoplasticity without a  yield surface. Part 1: General theory", Arch. Mech.,  23, pp. 535{551 (1971).  4. Han, C.W and Yang, R.J. Application of the improved  endochronic theory of plasticity to loading with  multiaxial strain-path", International Journal of Nonlinear  Mechanics, 18(5), pp. 395{408 (1983).  5. Valanis, K.C. and Read, H.E. A new endochronic  plasticity model for soils", In: Soil Mechanics-  Transient and Cyclic Loads, Wiley, pp. 375{417 (1982).  6. Bazant Zdenek, P. and Krizek Raymond, J. Endochronic  constitutive law for liquefaction of sand",  550 A. Pak and M.A. Iranmanesh/Scientia Iranica, Transactions A: Civil Engineering 27 (2020) 541{550  Journal of The Engineering Mechanics Division,  102(2), pp. 225{238 (1976).  7. Zienkiewicz, O.C., Chang, C.T., and Hinton, E. Nonlinear  seismic response and liquefaction", International  Journal for Numerical and Analytical Methods in Geomechanics,  2(4), pp. 381{404 (1978).  8. Finn, W.L. and Bhatia, S.K. Endochronic theory of  sand liquefaction", In Proceedings of the 7th Word  Conference on Earthquake Engineering, Turkey: Istanbul  (1980).  9. Blazquez, R. and Lopez-Querol, S. Generalized densi  _cation law for dry sand subjected to dynamic  loading", Soil Dynamics and Earthquake Engineering,  26(9), pp. 888{898 (2006).  10. Cuellar, V. Rearrangement measure theory applied  to dynamic behavior of sand", PhD Thesis, Civil  Engineering Department, Northwestern University,  Evanston, IL, U.S.A. (1974).  11. Papadimitriou, A., Bouckovalas G., and Dafalias Y.  Plasticity model for sand under small and large cyclic  strains", Journal of Geotechnical and Geoenvironmental  Engineering, 127(11), pp. 973{983 (2001).  12. Blazquez, R. and Lopez-Querol, S. Endochronicbased  approach to the failure of the lower San Fernando  dam in 1971", Journal of Geotechnical and  Geoenvironmental Engineering, 133(9), pp. 1144{1153  (2007).  13. Lopez-Querol, S. and Blazquez, R. Validation of a  new endochronic liquefaction model for granular soil  by using centrifuge test data", Soil Dynamics and  Earthquake Engineering, 27(10), pp. 920{937 (2007).  14. Chan, D. and Morgenstern, N. SAGE: a _nite  element program for stress analysis in geotechnical  engineering", Technical report, Geotechnical Group.  The University of Alberta (1998).  15. Chan, D. PISA: Program for incremental stress analysis",  User Manual, version 1.0, PISA Inc (1997).  16. Pak, A. Numerical modelling of hydraulic fracturing",  Ph.D. Thesis, Department of Civil and Environmental  Engineering, University of Alberta (1997).  17. Shahir, H. Dynamic analysis of saturated porous  media for numerical simulation of liquefaction", M.Sc.  Thesis, Department of Civil Engineering, Sharif University  of Technology, Tehran, Iran (2001).  18. Rahmani, A., Ghasemi Fare, O., and Pak, A. Investigation  of the inuence of permeability coe_cient on the  numerical modeling of the liquefaction phenomenon",  Scientia Iranica : Transactions A, 19(2), pp. 179{187  (2012).  19. Shahir, H., Pak, A., Taibeat, M., and Jeremic, B.  Evaluation of variation of permeability in lique_-  able soil under earthquake loading", Computers and  Geotechnics, 40, pp. 74{88 (2012).  20. Biot, M.A. General theory of three dimensional consolidation",  Journal of Applied Physics, 12(2), pp.  155{168 (1941).  21. Zienkiewicz, O.C. and Shiomi, T. Dynamic behavior  of saturated porous media; the generalized biot  formulation and its numerical solution", International  Journal for Numerical Methods in Engineering, 8, pp.  71{96 (1984).  22. Katona, M.G. and Zienkiewicz, O.C. A uni_ed set of  single step algorithms part 3: The beta-m method, a  generalization of the newmark scheme", International  Journal of Numerical Methods in Engineering, 21, pp.  1345{1359 (1985).  23. Arulanandan, K. and Sybico, J. Post liquefaction settlement  of sand", In Proceeding of the Worth Memorial  Symposium England, Oxford University (1992).  24. Jafarzadeh, F. and Yanagisawa, E. Settlement of  sand models under unidirectional shaking", First International  Conference on Earthquake Geotechnical  Engineering, IS Tokyo (1995).  25. Shahir, H. and Pak, A. Estimating liquefactioninduced  settlement of shallow foundations by numerical  approach", Computers and Geotechnics, 37(3), pp.  267{279 (2010).  26. Arulmoli, K., Muraleetharan, K.K., Hossain, M.M.,  and Fruth, L.S. Velacs: Veri_cation of liquefaction  analyses by centrifuge studies-laboratory testing program",  Soil Data Report, Earth Technology Corporation  (1992).  27. Taboada, V.M. and Dobry, R. Experimental results of  model no. 1 at RPI, University of California, California  Institute of Technology (1993).  28. Manzari, M.T. and Dafalias, Y.F. A critical state  two-surface plasticity modelfor sands", Geotechnique,  47(2), pp. 255{272 (1997).