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.

在这项工作中，使用数值极限分析（NLA）和材料点方法（MPM）研究了浅埋隧道工作面的坍塌状况。使用数值限制分析的下限公式的一种特殊形式（基于速度和应力的混合表示）。对使用NLA的解决方案进行了评估，并结合二阶锥和半定规划方法，考虑了用于体积离散化的有限元。使用了Drucker-Prager和Mohr-Coulomb失效准则。对于MPM，连续介质由一组材料点离散化，这些材料点存储了所有相关的属性和变量，例如质量，应力，速度和能量。本文的目的是评估两种方法在确定浅埋隧道的隧道面板稳定条件时的特性，尤其是在确定破坏机理和对失稳质量进行跳动分析时。从小规模模型的实验中获得的结果（Sterpi等，1996）被用作研究的参考。获得的结果表明，MPM和NLA都可以预测整体破坏机制和稳定所需的最小隧道工作面压力。