Analytical solution of undrained cylindrical cavity expansion in saturated soil under anisotropic initial stress

This paper presents an analytical solution for undrained elasto-plastic cylindrical cavity expansion in saturated soil under anisotropic initial stress. The problem is formulated by assuming small-strain deformation in the elastic zone and large-strain deformation in the plastic zone. Plastic yielding is determined by the Tresca failure criterion and an associated flow rule. Two stress functions are used to describe the stress state in the two zones around the cavity. The elasto-plastic boundary can subsequently be determined by solving the two stress functions under the stress boundary conditions. Additionally, the cavity pressure-expansion relationship, the total stress and the excess pore pressure around the cavity wall under anisotropic initial stress can be easily obtained by application of a numerical integration. The results show that the cavity pressure and excess pore pressure under the isotropic initial total stress (K = 1) are larger than those under the anisotropic initial stress (K > 1 and K < 1), which is true at all states of the expansion. The higher value of K develops lower stress and pore pressure around the cavity wall at the ultimate states. However, the stress and excess pore pressure are not sensitive to the value of K. The present solution may be used for analyzing the uplift capacity of plate anchors in soils and Horizontal Directional Drilling (HDD) problems such as the tunneling, and pipeline installation.