Three-Dimensional Upper Bound Limit Analysis on the Collapse of Shallow Soil Tunnels considering Roof Stratification and Pore Water Pressure

Based on the plastic upper bound theorem, a three-dimensional kinematically admissible velocity field is constructed for the collapse of the soil masses above a shallow tunnel. In this field, this paper considers the influences of the roof stratification, pore water pressure, ground overload, and support pressure. This study deduced the upper bound solutions of the weight of the collapsed soil masses and the corresponding collapse surfaces by utilizing the nonlinear failure criterion, associated flow rule, and variation principle. Furthermore, we verified the validity of the proposed method in this paper by comparing this research with the existing work and numerical simulation results. This study obtains the influence laws of varying parameters on the area and weight of the collapsed soil masses. The results reveal that the area and weight of the collapsed soil masses increase with increasing support pressure and soil cohesion, but decrease with increasing thickness of the upper soil layer, nonlinear coefficient, pore water pressure, and ground overload. Among them, the roof stratification, pore water pressure, soil cohesion, and nonlinear coefficient have a significant influence on tunnel collapse, which should be given special consideration in engineering design.