Undrained stability of a plane strain heading

Abstract

This paper examines the undrained stability of a shallow heading under conditions of plane strain loading. The soil is assumed to have a uniform shear strength and self weight. Rigorous bounds on the load needed to support the heading against active failure are derived using two numerical techniques that employ finite elements in conjunction with the 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 statically admissible stress field and a "safe" estimate of the collapse load, whereas the solution to the upper bound linear programming problem defines a kinematically admissible velocity field and an "unsafe" estimate of the collapse load. For the range of heading geometries considered, the upper and lower bound solutions bracket the exact collapse load to within 20% or better. Key words : heading, stability, limit analysis, plane strain.