Dynamic response of an elastic plate on a cross-anisotropic poroelastic half-plane to a load moving on its surface

Abstract

The dynamic response of a thin, isotropic and linear elastic plate on a half-space soil medium to a load moving on its surface is analytically obtained under plane strain conditions. The soil is assumed to be homogeneous, cross-anisotropic and water fully saturated linear poroelastic. Anisotropy manifests itself in the elastic skeleton, the pore water pressure and the permeability. The full Biot's equations of motion are employed. The load is assumed to be distributed over a finite length and moves with constant speed. The moving load is expanded in a complex Fourier series form involving the horizontal coordinate, time and speed. All the response quantities referring to the plate and the soil are also expanded in Fourier series in the same way. Thus, the governing partial differential equations of motion for the plate and the poroelastic soil (u-p formulation) are reduced to a system of ordinary differential equations with only one independent variable, the vertical coordinate. Use of compatibility and equilibrium at the plate-poroelastic soil interface as well as the boundary conditions of the problem, result in the solution of the above system of equations in analytic form. This solution is validated by comparing Its results against other analytic solutions referring to simpler cases (isotropic elastic with a plate and isotropic poroelastic soil without a plate). Finally, parametric studies are conducted to assess the anisotropy effect on the response of the system to moving loading for various values of porosity, permeability and load speed.