This note has the purpose of re‐formulating the finite dimensional dynamic friction problem with unilateral contact as a standard L1 differential inclusion when the data is such that contact persistently holds. Existence of solution to the problem is re‐established by using standard theoretical results for differential inclusions.

A direct approach of the boundary element method for treating 3-D boundary-value problems of poroelastodynamics is considered. Biot’s material model with four unknown base functions is used. Computational results for the surface responses of displacements and pore pressures as functions of a force acting on a half-space weakened by a cavity are presented.

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In the present paper, the solution of a finite one-dimensional column with Neumann and Dirichlet boundary conditions are deduced based on the theory of mixture. The solution is obtained in the Laplace domain and the time-step method is chosen to obtain the time domain solution. The material data of Massillion sandstone are used for calculations. The column response to the dynamic loading is examined in terms of displacement, pore water pressure, and pore air pressure.