Dynamic fundamental solutions for compressible and incompressible modeled poroelastic continua

Abstract

In a two-phase material not only each constituent, the solid and the fluid, may be compressible on the microscopic level but also the skeleton itself possesses a structural compressibility. If the compression modulus of a constituent is much larger than the compression modulus of the bulk material this constituent is assumed to be materially incompressible. A common example is soil. Governing equations for such materials are found in the framework of Biot's theory either for the unknowns solid displacement and pore pressure or for the unknowns solid displacement and fluid displacement. For both formulations fundamental solutions are derived using the method of Hörmander. Unlike the u i s– p formulation, where the incompressible model can be obtained applying a limiting procedure directly to the compressible system of equations, a complete new derivation is necessary for the u i s– u i f formulation. This yields a model of incompressibility different from that of the u i s– p formulation which seems to be not suitable for poroelastodynamic problems.