General analytical solutions for one‐dimensional nonlinear consolidation of saturated clay under non‐isothermal distribution condition

The fluctuation of temperature leads to the changes of physical-mechanical properties of clayey soils. In some practical projects such as landfills, the compacted clay liner is usually subjected to a non-isothermal distribution state. For one-dimensional nonlinear consolidation process of saturated clay under non-isothermal distribution condition, the general analytical solutions considering time-dependent loading are derived for the first time, where the methods of algebraic transformation and separation variable are used. Moreover, two forms of boundary conditions are included according to engineering practice. Referring to the proposed general analytical solutions, the expressions for the analytical solutions under instantaneous loading pattern and single-stage linear loading pattern are developed. Besides, the correctness of the presented analytical solutions is validated by comparing with the existing analytical solutions and finite difference solutions. Based on the proposed analytical solutions, the influence of temperature gradient, final loading and loading time on the consolidation behaviors is analyzed. It is found that the increase in temperature gradient accelerates the consolidation rate, and the average volume compressibility coefficient decreases by 65.4% when final loading increases from 50 to 500 kPa. In conclusion, the analytical solutions proposed in this study are more comprehensive and can be applied in different engineering cases.