This paper is concerned with the study of a poroelastic soil layer under impulsive horizontal loading. Building upon Biot's general theory of poroelasticity, a comprehensive set of governing equations addressing three-dimensional transient wave propagation problem are established. Explicit general solutions for displacements and pore-pressures are derived by employing a sophisticated mathematical approach, incorporating decoupling transformation, Fourier series expansion, and Laplace-Hankel integral transform techniques. Subsequently, physical-domain components are numerically obtained by an enhanced Durbin method coupled with inverse Hankel transform. Comparisons the existing transient solutions for the ideal elastic half-space are made to validate the proposed formulations' reliability and precision. Through representative analyses for time-domain results, it is illustrated to study the influence of the soil thickness and types of loading pulse on the transient dynamic response of finite-thickness poroelastic soil layers. The results in comparative analysis show that the magnitudes of the horizontal displacement and pore water pressure can be affected and become more fluctuant when the thickness of the poroelastic soil layer decreases. The basic solutions may be attributed to a variety of wave propagation problems due to transient dynamic loading and illustrate the corresponding distinct wave features elegantly.

This work presents an analytical method for determining vertical dynamic impedance and displacement response factor of a rigid cylindrical foundation embedded in unsaturated poroelastic soils. The foundation is assumed to be perfectly boned to its surrounding soil and its overlying half-space of unsaturated poroelastic soil, subjected to harmonic vertical loadings. The soil surrounding the circumference of the cylinder is modeled as a number of infinitely thin horizontal soil layers. Based on the Biot-type soil constitutive model, the equations governing the interaction of unsaturated soils with the cylindrical foundation are derived. Solutions are obtained by solving ordinary differential equations transformed from partial differential governing equations using the Hankel transform. The proposed solutions are verified against existing solutions of benchmark elastodynamic problems for embedded cylindrical foundations in dry and saturated soils. Using the derived solutions, several influencing parameters defining the stiffness and mass of the foundation system are examined to investigate the dynamics of the foundation interacting with it adjacent soils. It is concluded that the dynamic displacement response factor is sensitive to soil saturation. It is believed that the proposed solution should be beneficial to dynamic design with cylindrical foundations embedded in unsaturated soils.

Three approximate analytical solutions for the problem of the seismic response of two rigid cantilever walls retaining a transversely isotropic poroelastic soil layer over bedrock are presented under conditions of plane strain and time harmonic ground motion. These approximate solutions come as a result of various reasonable simplifications concerning various response quantities of the problem, which reduce the complexity of the governing equations of motion. The method of solution in all the cases is the same with that used for obtaining the exact solution of the problem, i.e., expansion of response quantities in the frequency domain in terms of sine and cosine Fourier series along the horizontal direction and solution of the resulting system of ordinary differential equations with respect to the vertical coordinate in conjunction with the boundary conditions. The first approximate solution is obtained on the assumption of neglecting all the terms of the equations of motion associated with the fluid acceleration. The second approximate solution is obtained on the assumption that the fluid displacements are equal to the corresponding solid displacements. The third approximate solution is obtained as the sum of the second approximate solution for the whole domain plus a correction inside a boundary layer at the free soil. All three approximate solutions are compared with respect to their accuracy against the exact solution and useful conclusions pertaining the approximate range of the various parameters, like porosity, permeability and anisotropy indices, for minimization of the approximation error are drawn.