Prediction of the Required Supporting Pressure for a Shallow Tunnel in Layered Rock Strata Based on 2D and 3D Upper Bound Limit Analysis

Determination of the required supporting pressure is the premise of tunnel support design. Only when the support design meets the requirements can the tunnel be safe and stable during construction and operation. This paper focuses on a shallow tunnel in layered rock strata and proposes a method for predicting the required supporting pressure. In this method, the 2D and 3D failure mechanisms are constructed, respectively. The analytical solutions of the supporting pressure corresponding to the two cases are derived on the basis of upper bound theorem and Hoek–Brown failure criterion. Then, the proposed method is validated by comparing with the results of existing research studies. Furthermore, a shallow tunnel in two-layer rock strata is chosen to illustrate the difference between the two solutions. The comparison shows that the supporting pressure in the 2D case is greater than that in the 3D case in general and it tends to be conservative for tunnel design. Conversely, the 3D solution may help to reduce the support cost. Furthermore, the change laws of the supporting pressure and failure range corresponding to varying parameters are obtained. These results may practically provide theoretical references for tunnel support design in layered rock strata.