A unified approach for stress wave propagation in transversely isotropic elastic and poroelastic layered media

Abstract

A complete solution is presented for stress wave propagation in multi-layered alternatively saturated and dry transversely isotropic elastic media in the frequency domain, where hysteretic damping in the soil skeleton has also been considered. In this paper, a new representation is introduced for the transmission-reflection matrix method to deal with the problem. The u-p formulation of Biot’s poroelastodynamic theory is considered for the governing equations of the porous layers, while equations of motion of single-phase media are utilized for dry layers. The potential functions used in this research for saturated porous materials are degenerated to the ones for dry materials, by setting the porous-related parameters to be identically zeros. Thus, generally, uniform formulations are used for both saturated and dry layers. The continuity conditions at the interface of the dry and saturated adjacent layers are modeled exactly to investigate the qPSV-waves precisely. The proposed generalized reflection and transmission matrices are employed to satisfy the compatibility conditions. Some numerical evaluations for simpler cases are presented to show the validity of the solution. Physical aspects of surface permeability, hysteretic damping, anisotropy, and underground water level are studied parametrically to justify the behavior of the solutions, and to discover the physical effects of different parameters involved in the subject.