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A semi‐discrete procedure for dynamic response analysis of saturated soils
Author(s) -
Chohan Harpal S.,
Sandhu Ranbir S.,
Wolfe William E.
Publication year - 1991
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610150703
Subject(s) - discretization , laplace transform , biot number , mathematics , mathematical analysis , galerkin method , finite element method , inverse laplace transform , physics , mechanics , thermodynamics
Abstract Biot's equations of wave propagation through fluid‐saturated porous elastic media are discretized spatially using the finite element method in conjunction with Galerkin's procedure. Laplace transformation of the discretized equations is used to suppress the time variable. Introducing Laplace transforms of constituent velocities at nodal points as additional variables, the quadratic set of equations in the Laplace transform parameter is reduced to a linear form. The solution in the Laplace transform space is inverted, term by term, to get the complete time history of the solid and fluid displacements and velocities. Since the solution is exact in the time domain, the error in the calculated response is entirely due to the spatial approximation. The procedure is applied to one‐dimensional wave propagation in a linear elastic material and in a fluid‐saturated elastic soil layer with ‘weak’, ‘strong’ as well as ‘moderate’ coupling. With refinement of the spatial mesh, convergence to the exact solution is established. The procedure can provide a useful benchmark for validation of approximate temporal discretization schemes and estimation of errors due to spatial discretization.