Application of Caquot's solution to the analysis of stability of shallow circular cavities in Tresca material

Abstract

The primary objective of this study is to expand upon and investigate a stress field solution for the stability of shallow cavities proposed by Caquot in 1934. Despite its relevance, this solution appears to have been overlooked in the literature. In this thesis, Caquot's analytical model is re-formulated to express the stability condition of a shallow cavity (a section of long cylindrical tunnel or a spherical opening) in terms of a factor of safety using the strength reduction technique, as commonly done in the evaluation of stability of slopes, embankments and levees. Caquot's analytical model is also extended to account for the presence of a mechanical surcharge on the ground surface, water pressure in the ground, and two conditions of water presence inside the cavity, namely, dry or flooded cavities. For the purpose of this study, the plastic constitutive model assumed for the ground is the Tresca shear failure criterion. This material model is a particular case of the Mohr-Coulomb material model with zero internal friction angle and cohesive strength only. Closed-form solutions for computation of factor of safety under dry and saturated ground conditions are presented and the effect of input variables involved in the problem are evaluated. Results of factor of safety obtained with the closed-form solutions presented here are shown to compare well with those obtained with the commercial finite difference software FLAC, a program that is widely used in the practical design of underground structures. All this suggests that the extended Caquot's solution presented in this thesis could be a valuable tool for practical evaluation of stability conditions of circular cavities, such as sections of long cylindrical tunnels or spherical openings, excavated near the ground surface.