Three-dimensional face stability analysis of shallow tunnels using numerical limit analysis and material point method

Abstract

In this work, the collapse conditions of shallow tunnel faces are studied using the Numerical Limit Analysis (NLA) and the Material Point Method (MPM). A particular form (based on a mixed representation of velocities and stresses) of the lower bound formulation of numerical limit analysis was used. The solution using NLA is evaluated considering finite elements for the volume discretization in conjunction with the second order cone and semidefinite programming methodologies. Drucker-Prager and Mohr-Coulomb failure criteria have been used. In the case of MPM, the continuum media is discretized by a set of material points which store all the relevant properties and variables such as mass, stress, velocity, and energy. The objective of this paper is to evaluate the characteristics of both methods when applied to the determination of the tunnel face stability conditions of shallow tunnels, in particular to the determination of failure mechanisms and run-out analysis of the failed mass. Results obtained from experiments on a small-scale model (Sterpi et al., 1996) are used as a reference for the study. The results obtained showed that both MPM and NLA can predict the global failure mechanism and the minimum tunnel face pressure required for stability.