Theoretical analysis on soil deformation and pore pressure subjected to shield tunneling in unsaturated soil

The precise forecasting of soil displacement and pore pressure resulting from shield tunneling is crucial for evaluating construction quality and impacts on neighboring structures. Current research rarely accounts for soil unsaturation. This paper introduces an analytical initial-solution, distinct from the Mindlin solution, and a modified three-dimensional displacement solution to predict soil displacement and pore pressure due to work load and ground loss. Based on continuum mechanics, three-dimensional consolidation equations of unsaturated soil are established firstly. By assuming no volume change at the initial time, the initial solution for the half-space to a buried concentrated force is derived using the Hankel integral transform method. Thereafter, the displacement and pore pressure caused by work load are computed through the superposition method. The accuracy of the proposed solution is confirmed by comparing analytical findings with three field results and the Mindlin solution. The analysis indicates that as soil saturation increases, the displacement shows a decrease trend while pore water pressure initially increases then decreases. Compared to saturated condition, displacement and pore pressure can vary by 38% and 45%, respectively, under unsaturated conditions. Results based on the Mindlin solution underestimate shield tunneling displacement, potentially posing significant safety risks to shield construction and adjacent structures.