Cavity expansions in partially drained soils and a comparison to CPT results

Abstract

Cylindrical and spherical cavity expansions in soils are of interest, especially when interpreting cone penetration tests (CPTs) and pressuremeter tests (PMTs). Here the cavity expansion problem is solved semi-analytically, considering partial drainage of the soil, when the cavity wall velocity is constant. The solutions may assist with the interpretation of CPTs and PMTs when partially drained conditions prevail in the surrounding soils. The solution procedure involves writing the governing partial differential equations in dimensionless form. The modified Cam-clay constitutive model is adopted for the soil to demonstrate the solution procedure, due to its wide familiarity, although other models could be used by making simple modifications. The variables in the partial differential equations are functions of a dimensionless time, T, and a dimensionless radial coordinate, H. T depends on cavity radius, the time after expansion began and a coefficient of consolidation. The equations are solved for when T is fixed, simultaneously as an initial value problem, as the partial differential equations become ordinary differential equations. Important features captured by the analyses include pore water pressure variations with soil volume changes, as well as the differential of the pore water pressure satisfying the no-flow cavity wall boundary condition. Results for a cavity expansion reveal that initially, when T and the cavity are small, drained conditions prevail. As T and the cavity become larger the soil becomes partially drained and eventually undrained. T is analogous to the dimensionless cone penetration velocity used in CPT studies. Normalised cavity wall pressures vary with T similar to that of normalised cone penetration resistances, demonstrated using experimental data. Plots of the normalised cavity wall pressures against the state parameter show that the two key fitting constants are heavily influenced by partial drainage. A similar dependence must exist when plotting a normalised cone penetration resistance against the state parameter when partially drained conditions prevail. The practical ramifications of not dealing with this partial drainage may be huge, especially when assessing liquefaction susceptibility through estimations of the state parameter using correlations developed for when drained conditions prevail. Significant underestimations of state parameter, liquefaction susceptibility and post-liquefaction strengths may result.