Three simplified models for the analytic determination of the dynamic response of a crossanisotropic poroelastic half-plane to a load moving with constant speed on its surface are presented and compared against the corresponding exact model. The method of analysis of the exact and approximate models uses complex Fourier series to expand the load and the displacement responses along the horizontal direction of the steady-state motion and thus reduces the partial differential equations of the problem to ordinary ones, which are easily solved. The three simplified models are characterized by reasonable simplifying assumptions, which reduce the complexity of the exact model and facilitate the solution. In the first simplified model all the terms of the equations of motion associated with fluid acceleration are neglected. In the second simplified model, solid displacements are assumed to be equal to the corresponding fluid ones, while the third simplified model is the second one corrected with respect to the fluid pressure at the free boundary (top) layer. All three simplified models are compared with respect to their accuracy against the exact model and the appropriate range of values of the various significant parameters of the problem, like porosity, permeability, anisotropy indices, or load speed, for obtaining approximate solutions as close to the exact solution as possible is thoroughly discussed.

In contrast to homogeneous soil deposits, stratified layering introduces vertical heterogeneity, resulting in not only greater spatial variability but also more complex structural responses. This complexity is further exacerbated by gravitational compaction, which gives rise to distinct fluid flow and solid deformation mechanics within each variably saturated layer and at the interfaces between layers-markedly differing from those observed in homogeneous, single-layer soils. The current study systematically addresses these key issues by developing a comprehensive flow-deformation formulation of poroelasticity that rigorously captures the conservation of mass and momentum within and between phases in a system of unsaturated, multi-layer unconsolidated sediments under time-invariant loading. A key innovation of this formulation is its robust incorporation of gravitational body forces, enabling the establishment of a physically-consistent boundary-value problem that ensures continuity-preserving conditions at layer interfaces. Furthermore, we derive two novel closed-form analytical expressions that, for the first time, quantify the final total stress and total settlement in such a soil system under the influence of gravitational body forces. To characterize the extent of this impact, we introduce a dimensionless parameter that provides a quantitative measure of gravitational effects. To further enhance our understanding of the theory, we conduct a series of numerical simulations on a duallayer soil system comprising sand overlying clay, with varying levels of water saturation. Our results demonstrate that, irrespective of the saturation levels examined, gravitational body forces exert a significantly greater influence on the lower clay layer than on the upper sand layer, particularly at lower water saturations. Neglecting gravitational body forces in a layered soil model leads to an underestimation of both the dissipation rate of excess pore water pressure and the total settlement. Notably, the discrepancy in final total settlement between models that include and exclude gravitational forces exhibits an approximately linear dependence on soil thickness.

In this paper, the findings presented by Barron (1948) have been corroborated by way of a hydraulic-mechanical coupled finite element analysis. Specifically, the FEM analysis was conducted using a poroelasticity approach in combination with a transient formulation that incorporates Darcy's law. This study highlights the fact that variations in pore pressure dissipation between the coupled FEM analysis of this study and Barron's theoretical analysis are minimal. The coupled FEM simulations confirm Barron's conclusions that, as the well diameter ratio (n) increases, the rate of pore water pressure dissipation decreases. Ultimately, for design purposes, a stress field is also required and consequently, a coupled FEM analysis is necessary. On this basis, results indicate high shear stress concentrations near the upper and lower boundaries, while the mean effective stress decreases from the well bore boundary.

This study examines the seismic behavior of a rigid wall in cross-anisotropic poroelastic layered soil, focusing on the frequency domain. Both analytical and numerical solutions are developed to tackle the problem. The analytical solution employs the finite Fourier transform, whereas the numerical solution uses the differential quadrature method. The proposed numerical solution considers various boundary conditions of the wall and base. The results are compared with those of existing studies on elastic soil, encompassing both homogeneous and heterogeneous cases, as well as poroelastic soil. The comparison demonstrates the accuracy of the proposed methods. Notably, the boundary conditions of the wall and base significantly affect the results at specific frequencies. In addition, the layered soil conditions have a relatively significant impact on the results across most frequencies.

Geo-materials naturally display a certain degree of anisotropy due to various effects such as deposition. Besides, they are often two-phase materials with a solid skeleton and voids filled with water, and commonly known as poroelastic materials. In the past, despite numerous studies investigating the vibrations of strip foundations, dynamic impedance functions for multiple strip footings bonded to the surface of a multi-layered transversely isotropic poroelastic half-plane have never been reported in the literature. They are first presented in this paper. All strip foundations are assumed to be rigid, fully permeable, and subjected to three types of time-harmonic loadings. The dynamic interaction problem is investigated by using an exact stiffness matrix method and a discretization technique. The flexibility equations are established by enforcing the appropriate rigid body displacement boundary conditions at each footing-layered soil interface. Numerical results for dynamic impedance functions of two-strip system are presented to illustrate the influence of various effects on dynamic responses of multiple rigid strip foundations.

We develop an analytical solution to the problem of one-dimensional consolidation of unsaturated soil subjected to cyclic loads with arbitrary waveforms. The solution predicts the excess pore water and pore air pressures and the accompanying vertical compression in a poroelastic, unsaturated soil material. Cyclic loading occurs in a variety of engineering applications and often generates higher excess pore fluid pressures and larger vertical compression than does a time-invariant load. In the present study, the loading function is allowed to take on any arbitrary waveform represented by a Fourier trigonometric series. Analytical solution to the boundary-value problem in one dimension is given in closed form describing the frequency-independent and frequency-dependent components of the poroelastic response. We verify the analytical solution through representative examples involving cyclic loads with square and triangular patterns. Apart from the shape of the forcing function, we also investigate the effects of initial water saturation, soil texture, and excitation frequency on the system response.