UNDRAINED STABILITY OF A PLANE-STRAIN HEADING

This paper examines the undrained stability of a shallow heading under conditions of plane strain loading. The soil is assumed to have a uni form shear strength and self weight. Rigorous bounds on the load neede d to support the heading against active failure are derived using two numerical techniques that employ finite elements in conjunction with t he limit theorems of classical plasticity. In both of these techniques , the collapse load is found by solving a linear programming problem. The solution to the lower bound linear programming problem defines a s tatically admissible stress field and a ''safe'' estimate of the colla pse load, whereas the solution to the upper bound linear programming p roblem defines a kinematically admissible velocity field and an ''unsa fe'' estimate of the collapse load. For the range of heading geometrie s considered, the upper and lower bound solutions bracket the exact co llapse load to within 20% or better.