Abstract: Based on the one-dimensional consolidation theory of unsaturated soil developed by Fredlund, the consolidation equations under two-dimensional plane strain are established, and the analytical solution of single-layer unsaturated soil under plane strain is obtained. Based on relevant theories, it is assumed that the volume change and the permeability coefficients are both constant, and the second-order binary partial differential equations are established, considering uniform or linear distribution of initial super-porosity pressure along the depth of the soil under the condition of instantaneous loading. To solve the equations, we first introduce the function method to reduce the order of the equation, and then obtain the general solution of the equation by variable separation method. Based on the solution, a case of two-dimensional plane strain problem under single-sided drainage conditions is investigated, and the correctness of the method is verified by numerical solution. The isochronal line of excess pore water and gas pressures dissipated in the vertical and horizontal directions in the two-dimensional plane is calculated by the proposed method. The influence of initial excess pore pressure on the consolidation and dissipation processes under different linear distributions is analyzed by calculation and comparison. The results show that the different distribution of initial excess pore pressure has an almost negligible effect on the dissipation of excess pore gas pressure, and has a great influence on the dissipation of excess pore water pressure.

Key words: unsaturated soil, two-dimensional consolidation, plane strain, analytical solution, initial excess pore pressure