Abstract
As a dynamic response, the wave propagation phenomenon usually varies with different media. In this study, the dynamic response of unsaturated poroelastic materials to an impulse load has been analytically investigated. The governing equations, in the Laplace domain, of the unsaturated poroelastic soil in terms of the variables us (solid displacement), pf (pore fluid pressure), and pa (pore air pressure) will be derived. These equations will be simplified in a one-dimensional form. The solutions that include the dynamic response to the vertical displacement of solid particles and to the variations of fluid and air pressures will be provided which are applicable for an arbitrary loading form. The solutions were validated with the results for saturated soil presented in the literature. The effect of material parameters on dynamic response was analysed through a series of parameter studies. It was found that increasing the porosity or fluid saturation effectively increases the amplitude of fluid and air pressures as well as the wave velocity. Although increasing the fluid saturation leads to solid displacement gradually decreases gradually, it results in increasing the amplitude of fluid and air pressure. The fluid saturation increasing above 0.9 results in wave travels faster significantly. The variation of fluid intrinsic permeability has little influence on the soil dynamic response until it reaches a high level. The findings of this study can help for better understanding of one-dimensional wave propagation in unsaturated soil.
Highlights
In the past few years, the load-induced saturated soil response has been widely investigated by analytical method
Schanz and Cheng [17] presented the dynamic response expression of saturated soil column with infinite length under dynamic load using the integral transformation and convolution quadrature method. ese problems can be described in Figure 1. eir work had established a benchmark for numerical calculation solving dynamic response, namely, wave propagation, in saturated media
Summary and Conclusions is paper studies the dynamic response caused by an impulse load in unsaturated poroelastic materials for the case of onedimensional space using the analytical method. e governing equations in the form of us-pf-pa were derived, and the analytical solutions for a one-dimensional poroelastic column in the Laplace transform domain were calculated, which were transformed to the time domain via the inverse Laplace transform using a numerical method. e solution has a concise closed form. e solutions were verified by comparing to the degeneration results for saturated soil with those reported by Schanz and Cheng [17]; and the effects of three important parameters, i.e., fluid saturation, fluid permeability, and porosity, were investigated
Summary
A partially saturated porous medium is a three-phase material, composing of solid particles, pore fluid, and pore air. S, f, e a) is the absolute variables usi , ufi , mass density of each individual and uai represent the displacement vectors in the solid, fluid, and air phases, respectively. E relative displacement vectors of fluid and air with respect to solid can be defined as wfi nSrufi − usi ,. By applying the Laplace transform defined in equations (3) to (11a) and (11b), the relative displacement vectors of fluid and air with respect to solid can be written as w fi. (21b) erefore, the governing equations of motion for unsaturated soil with us-pf-pa (solid displacement-pore fluid pressure-pore air pressure) form in the Laplace domain are obtained as equations (15), (21a), and (21b). Substituting equation (24) into equations (23a), (23b), and (23c) leads to an eigenvalue problem in terms of ξ as
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