A semi-analytical solution for cylindrical cavity expansion in elastic–perfectly plastic soil under biaxial in situ stress field

Abstract

This paper presents an elastic–plastic semi-analytical solution for cylindrical cavity expansion in undrained soil (incompressible material) under the biaxial in situ stress condition. The soil around a cylindrical cavity is assumed to behave as elastic–plastic perfectly plastic material, as characterised by Tresca yield strength with the associated flow rule. Based on Galin's solution, the stress and the elastic–plastic boundary around the cylindrical cavity can be determined using the conformal mapping technique and complex variable theory. Then, by considering incompressible and small strain–displacement conditions, the problem of kinematics is reduced to solving a system of the second-order ordinary differential equations, which results in the general solution for the radial and circumferential displacements in the plastic zone around the cylindrical cavity. Subsequently, the constant coefficients of the general solution can be determined by the displacement continuity condition at the elastic–plastic boundary using the least-squares method. The new elastic–plastic analytical solution presented in this paper extends Galin's solution, particularly by giving a closed-form equation for the kinematics around the cylindrical cavity, which could reflect the ‘non-circular effect’ of the cylindrical cavity during the expansion in a biaxial in situ stress field. The new solution completes the theoretical framework for addressing the fundamental problem of cylindrical cavity expansion, and also provides a useful theoretical tool for potential application in geotechnical engineering problems such as in situ testing (pressuremeter tests in a biaxial in situ stress field).