Prefabricated vertical drains (PVDs) are highly effective in hastening the consolidation process of soil and enhancing the strength of the foundation. Enhanced computational precision is achieved by utilizing a twodimensional (2D) plane strain model throughout the analytical procedure. The pronounced layering characteristic of saturated soils, coupled with the obstruction of pore water drainage across interfaces, results in a pronounced flow contact resistance effect. A comprehensive investigation into the 2D plane strain consolidation behavior of layered saturated soils under continuous drainage boundary conditions is facilitated by the presentation of the interfacial flow contact model. Subsequently, semi-analytical solutions for pore water pressure and the degree of consolidation are derived using the Laplace transform and the Crump inverse method. The proposed solution is analyzed for its degradation and compared against the experimental results and numerical solutions, to ascertain the accuracy and reliability of the presented solution. The research delves into the effects of flow contact resistance on parameters, including the permeability coefficient ratio (kv / kh) and boundary coefficients (rt and rb) throughout the consolidation process. Additionally, the impact of the flow contact resistance on the degree of consolidation is discussed. The results indicate that both the permeability coefficient ratio and boundary parameters have a close association with the flow contact resistance effect. Ignoring this effect may lead to inaccurate predictions of pore water pressure distribution and an overestimation of the soil consolidation.

In this paper, the one-dimensional rheological consolidation characteristics of multilayered saturated soil foundations under time-dependent loading and heating are investigated by considering the semi-permeability and the interface thermal resistance. By introducing the fractional derivative model and the thermos-elastic theory, a thermo-mechanical coupling model is established to describe the rheological properties of saturated soils. Semi-analytical solutions for strain, temperature increment, pore water pressure and settlement were derived through the Laplace transform and its inverse. The accuracy of the solutions proposed in this paper has been verified by comparing with existing solutions. The effects of different thermal contact models of the interface on the rheological properties of saturated soils under semi-permeable boundary are discussed, and the effects of fractional derivative order, constitutive material parameters, and thermal conductivity of soil on the thermal consolidation process are investigated. The results show that: neglecting the thermal resistance effect can result in an overestimates of the impact of rheological properties on the thermal consolidation process of saturated soils under semi-permeable boundaries; As the thermal resistance coefficient increases, the influence of soil thermal conductivity on settlement decreases.