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

Document Type : Article


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


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.


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
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
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 in
uence of permeability coecient on the
numerical modeling of the liquefaction phenomenon",
Scientia Iranica : Transactions A, 19(2), pp. 179{187
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
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 model for sands", Geotechnique,
47(2), pp. 255{272 (1997).