Elasto-plastic solution for drained cavity expansion in over-consolidated soil incorporating three-dimensional unified hardening model

The current solutions to cavity expansion cannot properly consider the stress-strain relationship and three-dimensional strength of the over-consolidated soil, thus there is some discrepancy between the solution and the practical situation. The existing researches show that the three-dimensional unified hardening (UH) model can well describe the mechanical properties of over-consolidated soil. Therefore, the model is used to develop a rigorous semi-analytical approach for drained cylindrical and spherical cavity expansion problems in over-consolidated soil. By introducing an auxiliary variable and combining the UH model, stress transform method and large strain theory, the cavity expansion problem is converted to solving a system of nonlinear differential equations as an initial value problem. There is no elastic zone around the cavity in the solution and the geomaterial parameters needed for the solution process are the same as for the Cam clay model. Compared with the modified Cam clay model-based solutions, the predicted results capture the stress-strain relationships, shear dilatancy, attenuation of over-consolidated ratio and potential failure stress ratio and three-dimensional stress states of the over-consolidated soil surrounding the cavity reasonably. Therefore, the proposed solution can be widely applied to the geotechnical problems in over-consolidated soil areas, such as the cone penetration tests and the pile installation.