Loading and unloading of a thick-walled cylinder of critical-state soils: large strain analysis with applications

Thick-walled cylinder (TWC) tests are widely used to obtain soil properties and investigate wellbore instability problems in laboratory-controlled conditions. This paper presents analytical cavity expansion and contraction solutions for modelling undrained TWC tests under three typical loading and unloading programs. Both cylindrical and spherical cavities in critical-state soils with a finite radial extent subjected to monotonic loading or unloading under undrained conditions are considered. The solutions are developed in terms of finite strain formulations, and the procedure is applicable to any isotropically hardening materials. Parametric studies show the boundary effect may significantly affect the cavity expansion/contraction response. A limit outer-to-inner diameter ratio of the soil sample exists, beyond which the boundary effect becomes negligible. The limit ratio varies with the cavity geometry, soil stress history (OCR) and cavity deformation level. For undrained TWC tests, a diameter ratio over 20 should normally be adequate to remove the possible boundary effect. Predicted expansion and contraction curves by the new solutions are compared with published data of TWC tests in the literature, and good agreement is shown in each loading/unloading program. This indicates that the boundary effect, which greatly limits the application of conventional cavity expansion/contraction solutions into TWC problems, is successfully captured by the present solutions. The solutions can also serve as valuable benchmark for verifying various numerical methods involving critical-state plasticity models.