In this paper, the authors propose a numerical investigation in the time domain of the mechanical wave propagation due to an impulsional load on a semi-infinite soil. The ground is modelled as a porous saturated viscoelastic medium involving the complete Biot theory. An accurate and efficient Finite Element Method using a matrix-free technique is used. Two parallel algorithms are used: Geometrical Domain Decomposition (GDD) and Algebraic Decomposition (AD). Numerical results show that GDD algorithm has the best time. Physical numerical results present the displacements of the fluid and solid particles over the surface and in depth.