Abstract
When a shield tunnel is excavated in water-rich strata with soft upper and hard lower layers, the failure mode of the tunnel face may shift from an overall failure mode to a partial failure mode. To address this issue, three-dimensional discrete failure mechanisms for both partial and overall failure modes are established on the basis of the upper bound theorem and spatial discretization techniques. The influence of pore water pressure is also considered, leading to the development of a method for calculating the critical support force of tunnel faces in such strata, while taking into account both failure modes and the effects of groundwater. Through parameter analysis, factors such as the tunnel diameter, proportion of soft soil, stratum cohesion, and pore water pressure coefficient significantly influence the tunnel face failure mode. A comprehensive critical support force, which takes both partial and overall failure modes into account, is proposed. The parameter analysis reveals that this comprehensive critical support force exhibits complex variations under the influence of multiple parameters. At the same time, a method is proposed to determine the upper and lower bounds of the ultimate support force, based on the calculation results under no seepage and free seepage conditions at the excavation face. The entire method provides a valuable reference for the stability analysis of tunnel faces in water-rich strata with soft upper and hard lower layers.