A simple BEM formulation for poroelasticity via particular integrals

Abstract A simple particular integral formulation is presented for poroelastic analysis. The elastostatics and steady-state potential flow equations are used as the complementary solution. A set of global shape functions is considered to approximate the pore pressure loading term in the poroelastic equation, the transient terms of pore pressure and displacements in the pore fluid flow equation to obtain the particular integrals for displacement, traction, pore pressure and flux. Numerical results for four plane problems of soil consolidation are given and compared with their analytical solutions to demonstrate the accuracy of the present formulation. Generally, agreement among all of those results is satisfactory if a few interior points are added to the usual boundary elements.

[1]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[2]  Emmanuel M Detournay,et al.  A direct boundary element method for plane strain poroelasticity , 1988 .

[3]  P. K. Banerjee,et al.  Boundary element methods in engineering science , 1981 .

[4]  P. K. Banerjee,et al.  A new boundary element formulation for two- and three-dimensional thermoelasticity using particular integrals , 1988 .

[5]  Alavandi Bhimaraddi,et al.  Free vibration analysis of doubly curved shallow shells on rectangular planform using three-dimensional elasticity theory , 1991 .

[6]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[7]  P. K. Banerjee,et al.  Two- and three-dimensional soil consolidation by BEM via particular integral , 2002 .

[8]  P. K. Banerjee.  The Boundary Element Methods in Engineering , 1994 .

[9]  A. Cheng,et al.  Boundary integral equation method for linear porous‐elasticity with applications to soil consolidation , 1984 .

[10]  P. K. Banerjee,et al.  A New Boundary Element Method for Three-Dimensional Coupled Problems of Consolidation and Thermoelasticity , 1991 .

[11]  P. K. Banerjee,et al.  Two- and three-dimensional transient thermoelastic analysis by BEM via particular integrals , 2002 .

[12]  G. Dargush,et al.  Boundary element method for dynamic poroelastic and thermoelastic analyses , 1995 .

[13]  P. K. Banerjee,et al.  A time domain boundary element method for poroelasticity , 1989 .

[14]  R. E. Gibson,et al.  PLANE STRAIN AND AXIALLY SYMMETRIC CONSOLIDATION OF A CLAY LAYER ON A SMOOTH IMPERVIOUS BASE , 1970 .

[15]  Gary F. Dargush,et al.  A boundary element method for axisymmetric soil consolidation , 1991 .

[16]  J. Mandel.  Consolidation Des Sols (Étude Mathématique) , 1953 .