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.

Layered unsaturated soils exhibit complex mechanical and physical properties. Owing to the roughness between unsaturated soil interfaces and the presence of irregularly distributed micro-pores, this study explores the laminar flow of pore water and counter-cyclonic flow of pore air through these channels at low velocities. In response to the complex consolidation behavior of unsaturated soils influenced by the flow and air contact resistance, an improved model is developed. The model incorporates the flow contact transfer coefficient (R-omega), flow partition coefficient (eta(omega)), air contact transfer coefficient (R-a) and air partition coefficient (eta(a)). Semi-analytical solutions for pore water pressure, pore air pressure and settlement in layered unsaturated soils are derived by employing the Laplace transform and its inverse transform. The rationality of the model is validated through comparative analysis with existing solutions. Analysis of the improved model yields critical insights: the presence of flow and air contact resistance leads to the development of relative pore pressure and air pressure gradients at interfaces, which diminishes the influence of the permeability coefficients of the water phase (k(omega)) and air phase (k(a)) on the consolidation process. Moreover, neglecting the flow and air contact resistance effects may lead to an overestimation of settlement.

Laminar flow phenomena may occur when pore water flows at low velocities across the interfaces between soils of different properties, thus causing flow contact resistance. To explore the impacts of interfacial flow contact resistance and rheological characteristics on the thermal consolidation process of layered viscoelastic saturated soil foundation featuring semi-permeable boundaries. This paper established a new thermal consolidation model by introducing a fractional order derivative model, Hagen-Poiseuille law and time-dependent loadings. The semi-analytical solutions for the proposed thermal consolidation model are derived through the Laplace transform and its inverse transform. The reliability and correctness of the solutions are verified with the experimental data in literatures. The influence of constitutive parameters, flow contact resistance model parameters on thermal consolidation process and the interfacial flow contact resistance on foundation settlement, is further explored. The results indicate that the impact of the constitutive parameters and permeability coefficient on the thermal consolidation of viscoelastic saturated soil is related to the flow contact resistance. The enhanced flow contact resistance effect leads to a significant increase in pore water pressure and displacement during the consolidation process.

Due to the presence of tiny gaps at the interface of two layers of saturated soil, water seepage occurs at a slower rate within these gaps, resulting in laminar flow at the interface. Based on the Hagen-Poiseuille law, a general imperfect flow contact model was established for layered saturated soil interfaces by introducing the flow contact transfer coefficient R omega and the flow partition coefficient eta omega. The investigation focused on the thermal consolidation behavior of layered saturated soil foundations under variable loadings considering the flow contact resistance effect at the interface. By employing the Laplace transform and its inverse transform, a semi-analytical solution for the thermal consolidation of layered saturated soil foundations was derived. In the context of a two-layer soil system, the effects of R omega, eta omega, and permeability coefficient k on the consolidation process were examined. The obtained results were then compared with three other interfacial contact models, thereby confirming the rationality of the presented model. The study findings revealed that the flow contact resistance effect leads to a clear jump in the pore water pressure. Furthermore, an increase in R omega and a decrease in eta omega were found to significantly enhance displacement and pore water pressure, while having minimal impact on the temperature increment. These insights contribute to a more comprehensive understanding of the thermal consolidation behavior of layered saturated soil foundations and underscore the significance of accounting for the flow contact resistance effect in such analyses.