A symmetric boundary integral approach to transient poroelastic analysis

Abstract

The problem of the transient quasi-static analysis of a poroelastic body subjected to a history of external actions is formulated in terms of four boundary integral equations, using time-dependent Green's functions of the ''free'' poroelastic space. Some of these Green's functions, not available in the literature are derived ''ad hoc''. The boundary integral operator constructed is shown to be symmetric with respect to a time-convolutive bilinear form so that the boundary solution is characterized by a variational property and its approximation preserving symmetry can be achieved by a Galerkin boundary element procedure. IntroductionPoroelasticity is concerned with heterogeneous media consisting of an elastic solid skeleton saturated by a diffusing pore fluid. Its range of application covers a variety of important real-life problems, such as design of nuclear reactor cores, exploitation of oil or gas deposits, simulations of living bone behaviour to orthopaedical surgery purposes, control of filtration leakage from reservoirs, and manufacturing process design for composite materials. Poroelasticity is now the subject of a fairly abundant literature, stemming from Terzaghi's concept of effective stress and Biot's linear consolidation theory (1941, 1957, 1962). From a computational mechanics point of view, poroelastic analysis has been conducted using either the finite element method or the traditional (collocation) boundary element method.The comprehensive state-of-the-art review by Cheng and Detournay (1993) provides abundant, clearly presented information, updated to 1991, on constitutive models, problem formulations, solution methodologies and geotechnical applications. Systematic presentations of coupled problems from the computational standpoint and of the phenomenological theory of porous media from the continuum mechanics standpoint are contained in Lewis and Schrefler (1987) and in the recent treatise by Coussy (1995), respectively. Among the noteworthy publications on poroelasticity, somehow related to the present study, we quote here those due to Manolis and

Formulação do método dos elementos de contorno para materiais porosos reforçados

“…Wilson Wesley Wutzow mais completo e abrangente sobre equações integrais e soluções fundamentais em poroelasticidade é apresentado por (CHENG e DETOURRNAY, 1998). (PAN e MAIER, 1997) apresentam uma formulação simétrica baseada em Galerkin para poroelasticidade. (PAN, 1999) utiliza as funções de Green para modelar o semiespaço poro-elástico subdividindo-o em camadas.…”