Limit Analysis of Active and Passive Mechanisms of Shallow Tunnels in Nonassociative Soil with Changing Water Table

Abstract

The evaluation of the failure mechanism of a shallow tunnel is very significant in geotechnical engineering. In this literature an analytical methodology for determining the plane strain limit failure mechanism for a shallow tunnel with an arbitrary cross section is presented. The paper presents active and passive failure modes for the shallow tunnels in linear and nonlinear soils. By variation calculus, the effects of dilation on the failure mechanism of the shallow tunnel are explored based on the nonassociative flow rule in the present work. Within the upper bound theorem different curve functions are obtained to describe the different failure mechanisms up and down the water level. Good agreement is demonstrated in both active and passive failure mechanisms with the lower bound solution solved in the similar trapdoor/anchor problem in linear Mohr-Coulomb soils. To analyze the influence of the dilatancy coefficient and position of the water table on the potential failure range, some examples and sensitivity analysis are conducted, which shows great consistency with existing research findings.