Adopting the non-Darcy flow presented by Hansbo and considering the nonlinear compression and permeability characteristics of soils, the one-dimensional nonlinear consolidation problem of soft clays is investigated by means of a continuous drainage boundary. The numerical solutions of average consolidation degrees defined by settlement and excess pore water pressure are derived by using the finite difference method, and the correctness of these solutions is verified by comparing them with existing analytical and numerical solutions. Based on the proposed solutions, a parametric study is conducted to study the influence of interface parameter, non-Darcy flow parameter and soil nonlinearity on the consolidation behavior of soft clays. The results show that the solutions based on the continuous drainage boundary can be degenerated into the solutions based on the Terzaghi drainage boundary if the interface parameter is taken as a reasonable value. The soil consolidation behavior considering both non-Darcy seepage and nonlinear characteristics of soil is very complex.

The thermal effect can significantly influence the consolidation of the soil, especially in the cold region. Previous studies have established to research that the drops in the ambient temperature would slow down the consolidation process, resulting in the slow dissipation of excess pore water pressure. In addition, the previous studies neglect the final settlement because consolidation is also influenced by thermal effect. In this paper, a closed-form solution to the one-dimensional nonlinear consolidation of soil considering the thermal effect is proposed. In the mathematical framework, the influences of the thermal effect on the compression index, the permeability, and the elastic modulus of the soil are considered. The solution is fully verified by comparing it with the FDM solution neglecting the thermal effect and the classic Terzaghi’s solution. An analysis has been carried out to assess the influence of temperature, stress ratios, consolidation time, the ratio of compression index to permeability index, and the interface parameters on the consolidation process. Different from many previous studies overlooking the thermal effect on the modulus of the soil, a model has been developed which points out that the final settlement due to consolidation would vary significantly with the ambient temperature. Therefore, the thermal effect must be considered in the consolidation calculation of the freeze–thaw cycle soil in the cold region.