Plasticity solutions for ground deformation prediction of shallow tunnels in undrained clay

Elastic-plastic contraction solutions of a cavity within an infinite soil mass are widely used to estimate ground response curves of deep tunnels. The pressure-convergence response of soil around shallow tunnels, however, tends to vary with tunnel embedment ratio. To account for the embedment ratio effect, this paper presents a general solution procedure for undrained contraction analysis of a thick-wall cylinder or spherical shell of isotropically hardening soils, by which a set of analytical and semi-analytical large strain solutions for several Cam-Clay soil models is derived. Results obtained with the new solutions show that the cavity contraction response highly depends on the soil stress history (overconsolidation ratio) and the radial thickness of the surrounding soil. A limit ratio of the outer to the inner radii exists, beyond which the thickness ratio effect becomes negligible. The limit ratio for a spherical shell is smaller than that for a hollow cylinder, and it decreases with the overconsolidation ratio of soil. Based on the analogy between cavity contraction and tunnel convergence, theoretical methods for predicting ground response curves of shallow plane-strain tunnels in clays are proposed and validated by comparing with relevant experimental and numerical simulation results. The solutions can also provide valuable benchmark methods for verifying various numerical programmes.