Drained and undrained analyses of cylindrical cavity contractions by bounding surface plasticity

Abstract

This paper develops a rigorous semi-analytical approach for drained–undrained cylindrical cavity contraction problems in bounding surface elastoplastic geomaterials. For undrained situations, the effective radial, tangential, and vertical component stresses can be solved directly from the constitutive governing differential equations as an initial value problem, the excess pore pressure subsequently being determined from the radial equilibrium equation. In contrast, for the drained case the Eulerian radial equilibrium equation must be first transformed into an equivalent one in a Lagrangian description via the introduction of an auxiliary variable, then solved together with the elastoplastic constitutive relation for the three stress components as well as the specific volume. It is observed that during drained–undrained contraction processes, plastic deformations occur immediately as a direct result of employing the bounding surface model, so outside the cavity there exists no purely elastic zone. The computed stress distributions and in particular the stress path prediction through an example analysis capture well the anticipated elastoplastic and failure behaviour of the geomaterials surrounding the cavity. The validity and accuracy of the proposed semi-analytical elastoplastic solutions are justified through comparison with ABAQUS numerical results, and their applicability to the tunnel excavation and wellbore drilling problems is also demonstrated.