Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading

This paper introduces an exact analytical solution predicting variations in excess pore-air and pore-water pressures and settlement considering the two-dimensional (2D) plane strain consolidation of an unsaturated soil stratum subjected to different time-dependent loadings. Based on the proposed solution, the distributions of excess pore pressures along vertical and horizontal directions can be determined. The general solution is first expressed in a series of eigenfunctions of homogeneous partial differential equations (PDEs) and is then substituted into the governing flow equations. Using term-by-term differentiation and the orthogonality of the sine function, the governing equations become ordinary differential equations (ODEs). Once the complex domain is obtained by applying the Laplace transformation technique, the closed-form analytical solutions describing the dissipation of excess pore-air and pore-water pressures can be obtained by taking a Laplace inverse. In this study, four external loadings, including ramping, asymptotic, sinusoid and damped sine wave, are simulated and incorporated into the proposed solutions. For the data analysis, the 2D consolidation behavior is investigated against variations in the permeability ratio (ka/kw)ka/kw). Additionally, parametric studies regarding loading functions are presented in this paper.