Finite Strain Analysis for Expansion of Cavities in Granular Soils

Formulations based on finite strain theory are introduced to develop an analytical procedure for determining volume changes and volumetric strains in the elastic and plastic zones, and average volumetric strain, Δ, in the plastic zone during expansion of the cylindrical and spherical cavities. Vesic's cavity-expansion theory requires the value of Δ to be determined from triaxial shear tests. This requirement can be relaxed by use of an analytical procedure proposed herein. Δ significantly decreases with increase of the rigidity index, I_r, and slightly decreases with increase of friction angle, Φ. The analysis shows that volumetric strains are about 5 to 7 percent near the face of the cavity and rapidly reduce to less than 0.1 percent at the interface of the elastic and plastic zones. Dimensionless cavity expansion factors (F'_q, F'_c, F_q, F_c) versus Φ curves for various values of I_r and Poisson's ratio, v, are prepared on the basis of analytically calculated value of Δ. Depending on I_r and Φ values, these factors increase by about 2.5 to 12.5 percent with increase of v from 0.2 to 0.4.