Prediction of roof supporting pressure for shallow tunnels in layered soils incorporating the effect of pore water pressure

In this study, we propose a method for predicting the supporting pressure required for shallow tunnels in layered soils, based on a curved roof collapse mechanism with multi-failure surfaces. In this method, the effect of the number and thickness of soil layers, pore water pressure, arbitrary roof profile, and ground additional load is considered simultaneously. A nonlinear power-law failure criterion is employed to describe the failure characteristics of the roof soils. The internal energy dissipation rate and the work rates produced by external forces are obtained based on the associated flow rule and plasticity potential theory. The analytical expressions of the required supporting pressure and roof collapse surfaces are obtained with the upper bound method. Furtherly, a shallow rectangular tunnel in two soil layers is selected for parametric investigation. The change laws of the required supporting pressure and collapse curves under varying parameters are obtained. Furthermore, the corresponding engineering recommendations are given, which may potentially provide references for the support design and construction of shallow tunnels in layered strata.