Limit analysis of shallow tunnels collapse problem with optimized solution

Abstract

The aim of this study is to understand the collapse mechanism of a shallow tunnel based on the upper bound analysis method, considering the variational approach for the problem with variable endpoints. The virtual power equation of upper bound theorem and Hoek-Brown criterion are combined to analyze the overlying rock mass, and the expression of collapse curve is obtained. Compared with the collapse curves solved by the variational method of the fixed endpoints problem in other studies, the advantage of this method is to consider the effect of the variable endpoints on the collapse curve, which is able to model the problem in a more realistic manner. The results show that the collapse curves obtained by the variational method of the variable endpoints problem are smaller than that of the existing study which are solved by the variational method of the fixed endpoints problem. The results also indicate that the width of excavation needs to be sufficiently small and the support for the overlying rock mass needs to be sufficiently large to prevent collapse. In general, these results will help to provide safe design and construction guidance for engineering practice.