Ground Movements due to Shallow Tunnels in Soft Ground. I: Analytical Solutions

Abstract

This paper presents simplified closed-form analytical solutions that can be used to interpret and predict ground movements caused by shallow tunneling in soft ground conditions. These solutions offer a more comprehensive framework for understanding the distribution of ground movements than widely used empirical functions. Analytical solutions for the displacement field within the ground mass are obtained for two basic modes of deformation corresponding to uniform convergence and ovalization at the wall of a circular tunnel cavity, based on the assumption of linear, elastic soil behavior. Deformation fields based on the superposition of fundamental, singularity solutions are shown to differ only slightly from analyses that consider the physical dimensions of the tunnel cavity, except in the case of very shallow tunnels. This work demonstrates a simplified method to account for soil plasticity in the analyses and illustrate closed-form solutions for a three-dimensional (3D) tunnel heading. A companion paper describes applications of these analyses to interpret field measurements of ground response to tunneling.