A SPECTRAL ELEMENT METHOD FOR 2-DIMENSIONAL WAVE-PROPAGATION IN HORIZONTALLY LAYERED SATURATED POROUS-MEDIA

The general equilibrium equations describing the dynamic response of a porous saturated medium form a system of couples hyperbolic partial differential equations. Restricting to two-dimensional plane strain wave propagation, an analytical solution for the dilatational and shear wave contributions to the displacement vectors can be found by a transformation of the generalized coordinates (x, z, t) to (k(x), z, omega). A spectrally formulated element uses these frequency and horizontal wave number dependent eigenvectors as shape functions in a displacement formulation. The mass distribution is treated exactly without the need to subdivide an element into smaller elements and therefore, wave propagation is treated exactly. Saturated throw-off and layer elements are developed and enable-together with the dry elements as proposed by Rizzi and Doyle-the study of the harmonic and transient response of horizontally layered saturated and dry porous media. The benefits of the solution method are demonstrated by a numerical example.