Dynamic 2.5-D Green's function for a point load or a point fluid source in a layered poroelastic half-space

Abstract

The complete dynamic two-and-a-half-dimensional (2.5-D) Green's function for an internal point load or fluid source buried in a layered poroelastic half-space is derived and applied to the 2.5-D boundary element method (BEM) in this paper. Based on Biot's theory, the general solutions are derived using the potential decomposition method and the Fourier transform. Utilizing the boundary conditions of the free surface, interfaces and bottom half-space, as well as the general solutions, the complete 2.5-D Green's function for a layered poroelastic half-space is obtained using the transmission and reflection matrix (TRM) method. The solutions presented in this paper are free of numerical instability for the high frequency and large layer thickness. The proposed 2.5-D Green's function is verified by comparison with the existing solutions. A case study of calculating vibrations from a semi-circular tunnel embedded in a layered poroelastic half-space is presented using the 2.5-D BEM along with the proposed 2.5-D Green's function. The layer interfaces and the surface of the poroelastic half-space no longer have to be meshed, avoiding spurious reflections at mesh truncations. The boundary element mesh can be limited to the surface of the tunnel, significantly reducing the size of the boundary element mesh.