Temperature changes affect the nonlinear consolidation process in soils, and there is limited associated theoretical research. In this study, the governing equations for nonlinear consolidation and thermal conduction are developed, and a mathematical model for one-dimensional nonlinear thermal consolidation in saturated clay under the impeded drainage boundary is established, where the temperature-dependent compressibility and permeability are considered. Meanwhile, the finite-difference solutions for nonlinear consolidation and the analytical solutions for thermal conduction are obtained, respectively. Furthermore, the proposed model's reasonableness is verified by comparison with other theoretical models. Based on this, the impact of several factors on nonlinear thermal consolidation behaviors is investigated. With a rise in temperature increment (Delta T), the dissipation rate of excess pore water pressure (EPWP) accelerates in the later consolidation stage, and the final settlement becomes larger. In addition, the EPWP dissipation rate grows remarkably with an increasing impeded drainage boundary parameter (mu). In particular, the impeded drainage boundary can be degraded into a drainage boundary when the value of mu becomes large (e.g., mu = 100 m-1). Increasing preconsolidation pressure (pcR) results in a reduction in settlement, and the maximum values of EPWP decline with a rising linear loading time (tc). Overall, this study contributes to the accurate prediction of the nonlinear consolidation process taking the thermal effect into account. This study might provide a basis for the analysis of soil consolidation features in geotechnical projects that involve thermal effects, which have been growing in number in recent decades. For instance, an approach that combines thermal treatment with surcharge preloading has started to be employed for soft soil reinforcement. When this method is used in practical engineering projects, the changes in EPWP and settlement can be predicted based on the model developed in this study. In addition, this study reveals that increasing the temperature by 60 degrees C can lead to an increase in the final settlement of saturated clay by approximately 25%, compared with ambient temperature treatment. Besides, compacted clay, which typically serves as a bottom engineering barrier, might be subject to consolidation deformation due to varied temperatures and external loading. The model presented could contribute to properly predicting the porosity change in compacted clay under this scenario.

A semi-numerical approach is proposed to estimate the dissipation of excess pore water pressure and the development of negative skin friction at the normal impervious pile and the permeable pile after piling. An impeded drainage boundary associated with the opening ratio and opening size is introduced to simulate the drainage condition at the soil-permeable pile interface. In the proposed mathematical framework, analytical approaches are adopted to solve the linear equations, and numerical techniques are utilized to address the nonlinear problems so that the adaptivity and efficiency of the mathematical framework can be well balanced. Through comparisons with the field tests, the model tests, and the theoretical answers, the correctness and rationality of the proposed method are validated. Through a parametric study, the key design parameters of the permeable pile are investigated, and the following design tips are obtained: 1. The opening ratio plays the most important role in the drainage efficiency of the permeable pile; 2. Increasing the number of openings is preferred rather than increasing the size of openings, especially when the opening ratio is determined.