Collapse Analysis of Square Tunnels in Cohesive–Frictional Soils

ABSTRACT The stability of a long square tunnel in a Mohr-Coulomb soil with a uniform friction angle, cohesion, and self-weight is investigated. This problem corresponds to drained loading of a tunnel in clay or rock, is difficult to analyse, and has been addressed rarely in the literature. For a range of tunnel geometries and material properties, rigorous bounds on the internal tunnel pressure required to prevent collapse are obtained using two numerical methods which are based on the bound theorems of classical plasticity and finite elements. The results are presented in terms of dimensionless stability charts and closely bracket the true collapse load for most cases of practical interest. The bounding methods used in the analyses have recently been developed at the University of Newcastle, and lead to large nonlinear programming problems that can be solved very efficiently using special purpose algorithms. The formulations are natural successors to techniques based on linear programming, and are fast enough to be used for large scale stability problems in three-dimensions. The upper and lower bound finite element solutions differ by less than a few per cent for most of the cases studied and, as an additional check, are compared against the analytical upper bound estimates derived from several assumed rigid block collapse mechanisms.