Two-dimensional plane strain consolidation of unsaturated soils considering the depth-dependent stress

In practical engineering, the total vertical stress in the soil layer is not constant due to stress diffusion, and varies with time and depth. Therefore, the purpose of this paper is to investigate the effect of stress diffusion on the two-dimensional (2D) plane strain consolidation properties of unsaturated soils when the stress varies with time and depth. A series of semi-analytical solutions in terms of excess pore air and water pressures and settlement for 2D plane strain consolidation of unsaturated soils can be derived with the joint use of Laplace transform and Fourier sine series expansion. Then, the inverse Laplace transform of the semi-analytical solution is given in the time domain using a self-programmed code based on Crump's method. The reliability of the obtained solutions is proved by the degeneration. Finally, the 2D plots of excess pore pressures and the curves of settlement varying with time, considering different physical parameters of unsaturated soil stratum and depth-dependent stress, are depicted and analyzed to study the 2D plane strain consolidation properties of unsaturated soils subjected to the depth-dependent stress.