Upper Bound Analysis for Collapse Failure of Shield Tunnel Face Excavated in Unsaturated Soils Considering Steady Vertical Flow

Natural soils are mostly in an unsaturated state and the corresponding mechanical properties differ significantly from a saturated one. In traditional stability analysis for a shield tunnel face, the soil mass is typically assumed to be dry or saturated for convenience of analysis. In this work, based on the upper bound theorem of classical plasticity theory and the log-spiral failure mechanism, face stability of the shield tunnel excavated in unsaturated soils under vertical steady flow is studied. The profile of shear strength is determined by virtues of the unified effective stress approach and the analytical solution of matric suction under unsaturated steady flow. On this basis, the analytical expression for the supporting pressure is deduced and the sequential quadratic programming is employed to search for the optimal upper bound solution. Through parametric analysis it is found the fitting parameters of SWCC and the groundwater level affect the supporting pressure notably. Besides, the relevant influence of vertical discharge is also significant when clayey soils are concerned.