Wave propagation of buried spherical SH-, P1-, P2- and SV-waves in a layered poroelastic half-space

Abstract

Few studies have investigated the wave propagation of spherical sources in a layered half-space. In this paper, based on Biot's theory of poroelastic media, the exact anti-axisymmetric (cylindrical SH-waves) and axisymmetric (cylindrical P1-P2-SV waves) stiffness matrices for a layered poroelastic half-space are derived. Then the dynamic responses due to buried spherical SH-, P1-, P2- and SV-waves in a layered poroelastic half-space are studied by using the direct stiffness method combined with the Hankel transform. The present solutions are in good agreements with those in a uniform pure elastic half-space as well as a uniform poroelastic half-space. These solutions have the advantages that all of the parameters in the solutions have explicit physical meanings and the thickness of discrete layers does not affect the precision of calculation; thus, the presented formulations are very convenient for engineering applications. Numerical calculations are performed in both the frequency and time domains by taking buried spherical SH-, P1- and SV- waves in a uniform poroelastic half-space and in a single poroelastic layer over a poroelastic half-space as examples. The numerical results show that wave propagation of spherical sources in a layered half-space can be significantly different from that in a uniform half-space; the dynamic responses are highly dependent on the saturated parameters, vibration frequency and the surface drained condition; the presence of the underlying half-space makes the time histories of the dynamic responses in a single layered half-space much more complicated with much longer duration.