Analytical solutions 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 loads and changing temperature at the surface, basic equations are proposed to describe the coupled evolvement of temperature and excessive porewater pressure, and two types of heat transfer and seepage boundary conditions are considered. The combination variables are introduced to decouple the governing equations, and their general solutions under the boundary conditions in the form of half-integer power functions are developed by applying the similarity transformation method. After expanding the external loads and the boundary conditions into power series, the analytical solutions for the temperature and the excessive porewater pressure can be obtained using these general solutions directly. After their verification by certain solution in the literature, our solutions are then employed 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 the excessive porewater pressure with the opposite trend, and when the coefficient is negative, temperature changes will cause changes in the excessive porewater pressure with the same trend.