Exact solutions for one-dimensional thermal consolidation of single-layer saturated soil

The consolidation under the non-isothermal field has long been the research focus. Based on the governing equations which take seepage flow into consideration, a new method to obtain exact solutions for one-dimensional thermal consolidation of single-layer saturated soil with three types of arbitrary boundary conditions is proposed. Firstly, the aim to solve temperature and excess pore pressure is transformed to solve the function ϕ by introducing the function φ. The eigenfunctions of differential equations are achieved with boundary conditions by the method of separation of variables. The nonhomogeneous boundary conditions are then transformed into homogeneous ones. The series form exact solutions are put forward according to the method of undetermined coefficients and eigenfunctions of differential equations. Finally, the conclusions that the seepage and temperature boundary play an important role in the thermal consolidation of the soil are reached by case studies.