Undrained stability of rectangular tunnels where shear strength increases linearly with depth

Abstract

This paper investigates the stability of a plane strain rectangular tunnel under undrained conditions, where the shear strength profile increases linearly with depth. The undrained stability of tunnels for a range of geometries and soil conditions is found using rigid-block upper bound methods as well as finite element limit analysis (FELA). The latter procedures employ a discrete form of the bound theorems of classical plasticity to formulate an optimization problem that is solved using a bespoke conic programming scheme. Rigorous solutions, obtained using adaptive re-meshing of the finite element mesh, generally bracket the true collapse load with upper and lower bound solutions to within 2%. Results from the parametric study are summarized in the form of stability charts.