One-Dimensional Consolidation Analysis of Unsaturated Soils Subjected to Time-Dependent Loading

Abstract

During consolidation, excess pore-air and pore-water pressures are forced to dissipate through permeable boundaries. This dissipation process inevitably results in the reduction of the soil volume, and thus settlement. Such a phenomenon can be mathematically described by inhomogeneous governing equations of flow according to Fick’s (with respect to air phase) and Darcy’s (with respect to water phase) laws. This paper discusses the dissipation of excess pore-air and pore-water pressures and settlement of an unsaturated soil layer subjected to various time-dependent external loadings. An analytical solution is derived from the governing flow equations with respect to air and water using eigenfunction expansion and Laplace-transform techniques. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained using one-way or two-way drainage boundary conditions. On the other hand, four types of external loadings, namely ramping, asymptotic, sinusoid, and damped sine wave, are mathematically simulated and incorporated in the mathematical procedure. Once the time variable (