Semi-analytical solution for one-dimensional consolidation of a two-layered soil system with unsaturated and saturated conditions

Semi-analytical solutions to one-dimensional (1D) consolidation of the two-layered soils are developed in this paper that can consider a two-layered soil system with unsaturated upper soils and saturated lower soils. In this case, the upper soil layer remains the water-air two-phase flows, while the lower soil layer only involves the flow of the water phase. Based on the assumptions made in the 1D consolidation framework for saturated and unsaturated soils, the analytical solutions in the transformation space for the consolidation model are derived using a decoupling technique and the Laplace transformation. Subsequently, following the Crump algorithm, the numerical inverse Laplace transformation is carried for the related semi-analytical results that can analyze the consolidation characteristics of the two-layered soils in the time domain. Furthermore, two typical cases for saturated soils in the literature are shown to examine the methodology and final solutions. Finally, results of a case study in this paper indicate that the excess pore pressures within the unsaturated soil layer near the interface are significantly affected by the water flow in the saturated soil layer, and that the final primary consolidation settlement of soils would be overestimated if the unsaturated condition of upper soils is ignored.