A non-linear elastic/perfectly plastic analysis for plane strain undrained expansion tests

Abstract

INTRODUCTION This note presents the solution for the undrained expansion of a cylindrical cavity in a non-linear elastic/perfectly plastic soil, using a power law characteristic to describe the decay of stiffness with strain. Two additional soil parameters are required to implement the solution, a stiffness constant a and an elastic exponent â. Both parameters are obtained from pressuremeter tests incorporating cycles of unloading and reloading. A typical undrained self-bored pressuremeter test with unload/reload cycles is shown in Fig. 1. This test will be used as an example throughout the following text. The curvature of the initial part of the expansion and the unload/reload cycles show the elastic response of the ground is non-linear, becoming less stiff with increasing strain. Nevertheless, it is common practice to reduce such data to fundamental strength and stiffness properties using analyses that assume the ground response to loading is simple elastic/perfectly plastic. The solution presented in this note is a small step in the direction of more realistic soil models. Even so, it is capable of explaining much that has been puzzling users of pressuremeter data. Figure 2 gives the idealized shear stress versus shear strain response for the loading of a nonlinear elastic/perfectly plastic soil. The shear strain when a fully plastic response is achieved is denoted a y, and at this strain there is a corresponding secant shear modulus G y, which is a minimum value. At shear strains smaller than a y the secant shear modulus is higher than G y. A power law function is often found to ®t data of reducing stiffness with strain (Gunn, 1992; Bolton et al., 1993), so the variation of shear stress with strain shown in Fig. 2 can be written