Analytical solution for 1-D thermo-consolidation process of semi-infinite saturated soil using similarity transformation method

For a 1-D thermo-consolidation process of semi-infinite saturated soil induced by external load and changing temperature at the surface, basic equations are presented to describe the coupled evolvement of temperature and excessive porewater pressure, and two types of heat transfer and seepage boundary conditions are considered. Combination variables are introduced to decouple the governing equations, and general solutions of combination variables under the boundary conditions in the form of half-integer power functions are developed by applying the similarity transformation method. After expanding the external load and the boundary conditions into power series, the analytical solution for the temperature and the excessive porewater pressure can be obtained using these general solutions directly. After verification of our solution by certain solution in the literature, our solution is then applied to calculate and analyze the coupled response characteristics of soil temperature and excessive porewater pressure for semi-infinite saturated soil under the effects of sinusoidal temperature and heat flux at the soil surface. The results show that, the term of soil deformation work contributes very little to the heat transfer equation, and its impact on the evolution of temperature and excessive porewater pressure can basically be ignored; when the coefficient for the term of temperature changing rate in the consolidation equation is positive, temperature changes will cause changes in excessive porewater pressure with the opposite trend, and when the coefficient is negative, temperature changes will cause changes in excessive porewater pressure with the same trend.