Unloading and reverse yielding of a finite cavity in a bounded cohesive–frictional medium

Cavity expansion in finite or infinite media has important practical implications in many engineering areas. In this study, we investigate the elastic unloading and reverse yielding behaviours of cylindrical and spherical cavities in a bounded cohesive–frictional medium. Of particular interest is the critical state when reverse yielding in the hollow cylinder/sphere is imminent in relation to the cavity pressure, the cavity dimensions, as well as the material properties. The critical pressure and optimal thickness that lead to strengthening of the hollow cylinder/sphere by so-called “overstrain” have been determined analytically. Both quantities are found to be explicit functions of the frictional angle of the material. The study considers the Mohr–Coulomb criterion and the bounded medium, which include both Tresca and purely frictional materials as special cases and, at the same time, can be readily extended to the case of an infinite medium. Finally, the results are applied to the interpretation of pressuremeter tests in soils, weak rocks and cemented sands.