Dynamic impedance functions for a rigid strip footing resting on a multi-layered transversely isotropic saturated half-space

This paper is concerned with the dynamic impedance functions (force-displacement relationships) of a surface rigid strip footing resting on a multi-layered transversely isotropic (TI) saturated half-space. The rigid footing is perfectly bonded to the layered half-space and is subjected to time-harmonic vertical, horizontal and moment loadings. The half-space under consideration consists of a number of horizontal layers with different thicknesses and an underlying half-space, which are all governed by the Biot's poroelastodynamic theory. The surface of the half-space can be either fully permeable or impermeable. The dynamic interaction problem is solved by employing an indirect boundary element method (IBEM), which uses Green's functions for uniform strip loads acting on the surface of a multi-layered TI saturated half-space. The discretization of the method is restricted to the footing-subsoil interface because of the layered half-space kernel functions, and the accuracy of the method would not be affected by the thickness of the discrete layers because of the exact dynamic stiffness matrix. Comparison with the existing solutions for the TI elastic and isotropic saturated media is conducted to verify the method, which are special cases of the more general problems addressed. Selected numerical solutions are presented to portray the influence of material anisotropy, frequency of excitation, surfaced drainage condition and layering on the dynamic impedance functions. Numerical results show that the dynamic impedance functions for the TI material can be significantly different from those of the isotropic material. The variation of the TI parameters alters the resonant frequencies of the layer and further alters the dynamic interaction between the layer and the footing.