Abstract
The phenomenon of liquefaction is one of the most important subjects in Earthquake Engineering and Coastal Engineering. In the present study, the governing equations of such coupling problems as soil skeleton and pore water are obtained through application of the two-phase mixture theory. Using au-p (displacement of the solid phase-pore water pressure) formulation, a simple and practical numerical method for the liquefaction analysis is formulated. The finite difference method (FDM) is used for the spatial discretization of the continuity equation to define the pore water pressure at the center of the element, while the finite element method (FEM) is used for the spatial discretization of the equilibrium equation. FEM-FDM coupled analysis succeeds in reducing the degrees of freedom in the descretized equations. The accuracy of the proposed numerical method is addressed through a comparison of the numerical results and the analytical solutions for the transient response of saturated porous solids. An elasto-plastic constitutive model based on the non-linear kinematic hardening rule is formulated to describe the stress-strain behavior of granular materials under cyclic loading. Finally, the applicability of the proposed numerical method is examined. The following two numerical examples are analyzed in this study: (1) the behavior of seabed deposits under wave action, and (2) a numerical simulation of shaking table test of coal fly ash deposit.
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References
Akai, K. and Tamura, T., Study of two-dimensional consolidation accompanied by an elastoplastic constitutive equation.Proc. JSCE 269 (1978) 98–104 (in Japanese).
Armstrong, P.J. and Frederick, C.O., A mathematical representation of the multiaxial Baushinger effect.C.E.G.B. Report RD/B/N 731 (1966).
Barends, F.B.J., Interaction between ocean waves and seabed.Proc. GEO-COAST '91 2 (1991) 1099–1100.
Bazant, Z.P. and Krizerk, R.J., Endochronic constitutive law for liquefaction of sand.Proc. ASCE 102-EM2 (1976) 225–238.
Bear, J. and Bachmat, Y.,Introduction to Modeling of Transport Phenomena in Porous Media. Dordrecht: Kluwer Academic Publishers (1990).
Biot, M.A., Mechanics of deformation and acoustic propagation in porous media.J. Appl. Phys. 33(4) (1962) 1482–1498.
Chaboche, J.L. and Rousselier, G., On the plastic and viscoplastic constitutive equations. Part 1: Developed with internal variable concept.J. Pressure Vessel Technology ASME 105 (1983) 153–158.
Dafalias, Y. and Popov, E.P., Plastic internal variables formulation of cyclic plasticity.J. Appl. Mech. ASME 98 (1976) 645.
Garg, S.K., On balance laws for fluid-saturated porous media.Mechanics of Materials 6 (1987) 219–232.
Ghaboussi, J. and Dikmen, S.U., Liquefaction analysis of horizontally layered sands.Proc. ASCE 104-GT3 (1978).
Hashiguchi, K., Elastoplastic constitutive model with a subloading surface.Proc. Int. Conf. Comput. Mech. 5 (Tokyo-Berlin: Springer Verlag) (1986) 65–70.
Henkel, D.J., The role of waves in causing submarine landslides.Geotechnique 20 (1970) 75–80.
Ishihara, K. and Okada, S., Yielding of overconsolidated sand and liquefaction model under cyclic stresses.Soils and Foundations 18 (1978) 57–72.
Kanatani, M., Nishi, K., Kawakami, M. and Ohmachi, M., Two-dimensional nonlinear response analysis during earthquakes based on the effective stress method.Proc. 6th Int. Conf. Numer. Meth. Geomech. 3 (1988) 1749–1754.
Madsen, O.S., Wave-induced pore pressures and effective stresses in a porous bed.Geotechnique 28 (1978) 377–393.
Martin, G.R., Finn, W.D.L. and Seed, H.B., Fundamentals of liquefaction under cyclic loading.Proc. ASCE 101-GT5 (1975) 423–438.
Mroz, Z., On the description of anisotropic hardening.J. Mech. Phys. Solids 15 (1967) 163.
Oka, F. Constitutive equations for granular materials in cyclic loadings.IUTAM Conf. on Deformation and Failure of Granular Materials. Delft: Balkema (1982) 297–306.
Oka, F., The validity of the effective stress concept in soil mechanics. In: Sataka, M. and Jenkins, J.T. (eds.)Micromechanics of Granular Materials. Amsterdam: Elsevier (1990) pp. 207–214.
Okusa, S., Wave-induced stresses in unsaturated submarine sediments.Geotechnique 32 (1985) 235–247.
Prevost, J.H., Nonlinear transient phenomena in saturated porous media.Computer Methods in Applied Mechanics and Engineering 20 (1982) 3–18.
Seed, H.B. and Rahman, M.S., Analysis for wave-induced liquefaction in relation to ocean floor stability.Report on Research Sponsored by NSF. Report No. UCB/TE-77/02 (1977).
Simon, B.R., Zienkiewicz, O.C. and Paul, D.K., An analytical solution for the transient response of saturated porous elastic solids.Int. J. Numer. Anal. Meth. Geomech. 8 (1984) 381–398.
Simon, B.R., Wu, J.S.S., Zienkiewicz, O.C. and Paul, D.K., Evaluation ofu-w andu-π finite element methods for the dynamic response of saturated porous media using one-dimensional models.Int. J. Numer. Anal. Meth. Geomech. 10 (1986) 461–482.
Truesdell, C., The rational mechanics of materials.On the Foundations of Mechanics and Energetics. New York: Gordon and Breach (1965) 293–304.
Yamamoto, T., Wave induced instability in seabeds.Proc. of the ASCE Special Conf. Coastal Sediments (1977) 898–913.
Zienkiewicz, O.C. and Bettes, P., Soils and other saturated media under transient, dynamic conditions. General formulation and the validity of various simplifying assumptions.Soil Mechanics-Transient and Cyclic Loads. New York: John Wiley & Sons (1982) 1–16.
Zienkiewicz, O.C. and Shiomi, T., Dynamic behavior of saturated porous media; The generalized Biot formulation and its numerical solution.Int. J. Numer. Anal. Meth. Geomech. 8 (1984) 71–96.
Zienkiewicz, O.C. and Taylor, R.L.,The Finite Element Method (fourth edition) 2. McGraw-Hill (1991) 518–522.
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Oka, F., Yashima, A., Shibata, T. et al. FEM-FDM coupled liquefaction analysis of a porous soil using an elasto-plastic model. Appl. Sci. Res. 52, 209–245 (1994). https://doi.org/10.1007/BF00853951
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DOI: https://doi.org/10.1007/BF00853951