Analytical solutions of combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam-Clay

This paper presents an analytical solution for combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam-Clay. The governing partial differential equations for the cylindrical cavity are established in the polar coordinate. The problem is formulated as a set of first-order differential equations by using the axisymmetric condition, equilibrium equations, and elastic-plastic constitutive relationship. The influence of the second shear loading on the initial shear strain is considered in the plastic state. Then the stress-strain distributions can be calculated by integrating within the elastic and plastic zones around the cavity. A finite element method simulation of the cavity under combined shear loading is established to verify the proposed approach, and the results are in good agreement with the proposed analytical solution. Parametric analyses are carried out on the effects of clay overconsolidation ratios and in situ stress coefficients under different loading paths and loading ratios. The results show that the combined shear loading on the cavity wall has a significant effect on the stress distribution of the surrounding soil, and the influence of the loading path cannot be neglected.