UNDRAINED STABILITY OF A SQUARE TUNNEL IN A SOIL WHOSE STRENGTH INCREASES LINEARLY WITH DEPTH

Abstract This paper examines the undrained stability of a shallow square tunnel in a soil whose strength increases linearly with depth. Rigorous bounds on the loads needed to resist collapse are derived using two numerical techniques which are based on finite element formulations of the classical limit theorems. Both of the numerical procedures assume a linearized perfectly plastic soil model and require the solution of large sparse linear programming problems. For the range of tunnel geometries considered, the numerical results bracket the exact collapse loads closely. The solutions are presented in the form of stability charts which can be used by practising engineers for the purposes of design.