Analytical Solution for Cavity Expansion in Rate-Dependent and Strain-Softening Clay and Its Application for CPT Tests

Abstract

This paper incorporated two important characteristics of clay, namely its rate-dependent and strain-softening behavior, into a theoretical framework based on cavity expansion. The modified Tresca model for clay proposed by Einav and Randolph was selected to describe the effects of the rate dependency and gradual softening of clay as it is sheared and remolded. First, the modified Tresca model was reduced to a strain-softening model without considering the rate effect. The exponential degradation (ED) function of the strength reduction proposed by Einav and Randolph was simplified further to a bilinear degradation (SBD) function. This step allowed an approximate closed-form solution to be obtained for the cavity expansion response, including the plastic zone radius, stress distribution, and cavity pressure-expansion relation, of the SBD model. The approximate closed-form solution for the SBD model was compared with the numerical integration solution for the ED model, and the comparison showed that the approximate closed-form solution is relatively accurate. Subsequently, the rate effects were incorporated into the SBD and ED strain-softening models, which are referred to as the rate-dependent (RD)-SBD and RD-ED models. Numerical integration solutions for cavity expansion in the RD-SBD and RD-ED models were obtained. A series of parametric analyses was conducted to investigate the effects of the cavity expansion velocity, strength reduction, and rate-dependent parameters on the cavity expansion responses. A closed-form solution for the limit expansion pressure (LEP) of the cavity expansion was obtained through a simple regression analysis based on the parametric results. The LEP solution was used to interpret the results of the cone penetration test (CPT) test, and a modified expression for the cone penetration resistance factor that incorporates the rate effect and strain softening was given. This simple modification provides a convenient way to evaluate the influence of the two factors on the CPT test results and allows the clay properties to be captured appropriately.