×

zbMATH — the first resource for mathematics

Consolidation of elastic-plastic saturated porous media by the boundary element method. (English) Zbl 1194.74496
Summary: This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid.
Biot’s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme.
The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms.
MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] C.A. Brebbia, J.C.F. Telles, L.C. Wrobel, Boundary Element Techniques, Theory and Applications in Engineering, Springer-Verlag, Berlin, A984. · Zbl 0556.73086
[2] Bui, H.D., Some remarks about the formation of three-dimensional thermoplastic problems by integral equations, Int. J. solids struct., 14, 935-939, (1978) · Zbl 0384.73008
[3] Cleary, M.P., Fundamental solutions for a fluid-saturated porous solid, Int. J. solids struct., 13, 785-806, (1977) · Zbl 0367.73088
[4] M. Predeleanu, Boundary integral method for porous media, in: Proceedings of the Third International Seminar on Boundary Element Methods, 1981, pp. 325-334. · Zbl 0476.73069
[5] Kuroki, T.; Ito, T.; Onishi, K., Boundary element method in biot’s linear consolidation, Appl. math. model., 6, 2, 105-110, (1982) · Zbl 0487.73102
[6] Cheng, A.H.-D.; Liggett, J.A., Boundary integral equation method for linear porous-elasticity with applications to soil consolidation, Int. J. numer. methods engrg., 20, 255-278, (1984) · Zbl 0525.73124
[7] Cheng, A.H.-D.; Predeleanu, M., Transient boundary element formulation for linear poroelasticity, Appl. math. model., 11, 4, 285-290, (1987) · Zbl 0624.73024
[8] Cheng, A.H.-D.; Detournay, E., A direct boundary element method for plane poroelasticity, Int. J. numer. anal. methods geomech., 12, 551-572, (1988) · Zbl 0662.73056
[9] Cheng, A.H.-D.; Detournay, E., On singular integral equations and fundamental solutions of poroelasticity, Int. J. solids struct., 35, 4521-4555, (1998) · Zbl 0973.74653
[10] Nishimura, N.; Kobayashi, S., A boundary integral equation method for consolidation problems, Int. J. solids struct., 25, 1, 1-21, (1989) · Zbl 0676.73074
[11] Dargush, G.F.; Banerjee, P.K., A time domain boundary element method for poro-elasticity, Int. J. numer. methods engrg., 28, 10, 2423-2449, (1989) · Zbl 0726.73081
[12] Park, K.H.; Banerjee, P.K., Two- and three-dimensional soil consolidation by BEM via particular integral, Comput. methods appl. mech. engrg., 191, 3233-3255, (2002) · Zbl 1101.74371
[13] Cavalcanti, M.C.; Telles, J.C.F., Biot’s consolidation theory – application of BEM with time independent fundamental solutions for poro-elastic saturated media, Engrg. anal. bound. elem., 27, 145-157, (2003) · Zbl 1080.74558
[14] Pan, E.; Maier, G., A symmetric boundary integral approach to transient poroelastic analysis, Comput. mech., 19, 3, 169-178, (1997) · Zbl 0887.73076
[15] Biot, M.A., Theory of elasticity and consolidation for a porous anisotropic solid, J. appl. phys., 26, 182-185, (1955) · Zbl 0067.23603
[16] Biot, M.A., Theory of elasticity and consolidation for a porous anisotropic solid, J. appl. phys., 26, 182-185, (1955) · Zbl 0067.23603
[17] Biot, M.A., Theory of deformation of a porous viscoelastic anisotropic solid, J. appl. phys., 27, 459-467, (1956)
[18] Coussy, O., Mechanics of porous continua, (1995), Wiley New York
[19] Coussy, O., Poromechanics, (2004), John Wiley and Sons
[20] Coussy, O.; Dormieux, L.; Detournay, E., From mixture theory to biot’s approach for porous media, Int. J. solids struct., 35, 34-35, 4619-4635, (1998) · Zbl 0932.74014
[21] A. Benallal, C. Comi, Properties of the finite-step problem in numerical analysis of unstable saturated porous continua, in: Proceedings of the COMPLAS 5, Barcelona, Spain, Part 2, 1997, pp. 1611-1616.
[22] Lewis, R.W.; Schrefler, B.A., The finite element method in the deformation and consolidation of porous media, (1998), John Wiley & Sons Chichester, Great Britain · Zbl 0935.74004
[23] Loret, B.; Harireche, O., Acceleration waves, flutter instabilities and stationary discontinuities in inelastic porous media, J. mech. phys. solids, 39, 569-606, (1991) · Zbl 0749.76075
[24] Loret, B.; Prevost, J.H., Dynamic strain-localization in fluid-saturated porous media, ASCE J. engrg. mech., 117, 4, 907-922, (1991)
[25] Nur, A.; Byerlee, J.D., An exact effective stress law for elastic deformation of rock with fluids, J. geophys. res., 76, 6414-6419, (1971)
[26] Rice, J.R.; Cleary, M.P., Some basic stress diffusion solutions for fluid saturated elastic – plastic porous media with compressible constituents, Rev. geophys. space phys., 14, 227-241, (1976)
[27] J.R. Rice, Pore pressure effects in inelastic constitutive formulations for fissured rock masses, in: Advances in Civil Engineering through Engineering Mechanics, American Society for Civil Engineers, New York, 1977, pp. 360-363.
[28] Venturini, W.S., Boundary elements in geomechanics, (1983), Springer-Verlag Berlin · Zbl 0581.73096
[29] Soares, D.; Telles, J.C.F.; Mansur, W.J., A time-domain boundary element formulation for the dynamic analysis of nonlinear porous media, Engrg. anal. boundary elements, 30, 5, 363-370, (2006) · Zbl 1187.74248
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.