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Boundary integral equation method for linear porous‐elasticity with applications to soil consolidation
Author(s) -
Cheng Alexander HD.,
Liggett James A.
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200206
Subject(s) - mathematics , discretization , mathematical analysis , finite element method , biot number , integral equation , elasticity (physics) , linear elasticity , compressibility , laplace transform , consolidation (business) , boundary value problem , boundary element method , mechanics , physics , accounting , business , thermodynamics
For physical phenomena governed by the Biot model of porous‐elasticity, a reciprocal relation, similar to the Betti's recoprocal theorem in elasticity, is constructed in Laplace transformed space. Integrating the reciprocal relation enables one to formulate boundary integral equations. The fundamental kernels for the integral equations are solved in closed forms for the case of isotropic material. Numerical implementation of two‐dimensional problems includes finite element ideas of discretization and polynomial interpolation, and numerical inversion of a Laplace transform. Practical applications of the method are found in consolidation problems in soils which contain compressible as well as incompressible pore fluids. Also, as a numerical experiment, consolidation of partially saturated soil is simulated and interesting phenomena are observed. The currently developed boundary integral equation method (BIEM) for porous‐elasticity may be viewed as an efficient and accurate alternative of existing finite element and finite difference methods. For linear consolidation problems, application of BIEM is always preferred to the other numerical methods whenever possible.