Analytical solution of soil deformation and fluid pressure change for a two-layer system with an upper unsaturated soil and a lower saturated soil under external loading

Natural soils often exhibit stratification, thus resulting in distinct flow and deformation patterns within each stratum as acted on by applied compaction stress or induced fluid pressure gradient. A comprehensive theoretical model of poroelasticity is rigorously established in the current study, which provides a detailed mathematical treatment of soil deformation and pore fluid pressure change through the upper unsaturated and lower saturated zones caused by time-invariant external loads. This double-layer system consists of an upper soil layer bearing air and water simultaneously, whereas a lower soil layer remains entirely saturated. A linear transformation that exactly separates our coupled model equations into analytically solvable coordinates is first achieved. Then, a boundary-value problem involving these equations under a semipermeable drainage scenario is formulated as a representative example, which complies with the physical constraint to ensure the continuity of pore water flux and pressure at the interface. The problem is solved analytically using Laplace transformation, and next computed numerically with hydraulic and elasticity parameters corresponding to a saturated clay overlain by an unsaturated sand to evaluate the excess pore fluid pressure and total settlement in each zone. A parametric study is also performed to examine the effect of initial water content and soil texture on the deformation behavior of the soil as well as on the development of the pore fluid pressure. The excess pore water pressure in each zone is mutually affected; therefore, if the upper unsaturated zone has a lower hydraulic conductivity, it would hinder, as compared to the opposite condition, the dissipation of the excess pore water pressure in the lower saturated zone as a consequence of water drainage blockage occurring in the former. Thus, a significant implication of our results is that change in thickness of the lower saturated zone created by land surface stress loads will always be overestimated when its interaction with the hydromechanical behavior of the upper unsaturated zone is neglected.