Many geotechnical scenarios involve cavity unloading from a loaded state, particularly in pressuremeter tests, and the unloading data of pressuremeter tests has exceptional attraction as it is less disturbed by the insertion process. However, the analyses for continuous cavity loading and unloading (i.e., cavity initially experiences expansion and then contracts) in critical state soils are rarely studied. To this end, a novel semi-analytical solution based on the unified state parameter model for clay and sand (CASM) is proposed for the whole expansion-contraction of spherical and cylindrical cavities under undrained conditions. The problem assumes that the cavity is unloaded after a monotonic loading stage, leading to plastic regions during both loading and unloading periods. The cavity response for the whole expansion-contraction process is investigated, with the total pressure and stress paths at the cavity wall presented and validated against numerical simulation. The developed solution is successfully implemented to interpret both loading and unloading data of pressuremeter tests. The undrained shear strength, in situ effective horizontal stress and initial overconsolidation ratio are back analyzed by using a curve fitting method based on the proposed solution.

Cylindrical cavity exhibits non-self-similarity during contraction process following expansion. Previous studies solve this problem with total strain approach and simple constitutive models, but the approach is not applicable when using an advanced constitutive model. This paper presents a semi-analytical solution for a cylindrical cavity undergoing expansion-contraction in undrained soils with auxiliary variable approach, incorporating the Modified Cam-Clay (MCC) model. The stress states around the cavity are formed by the superposition of initial and superimposed stress states. By treating superimposed effective stresses as self-similar, a semi-analytical solution is derived for solving the cavity expansion-contraction problem. The elastoplastic stress-strain relationship is formulated as a set of first-order differential equations, which can be solved as an initial value problem though Runge-Kutta (RK) method. Then the stress distribution around the cavity during expansion-contraction process can be determined. To validate the proposed approach, a series of well-conduced self-boring pressuremeter (SBP) tests are used to verify the proposed approach, which shows good agreements. Additionally, a FEM simulation incorporating the MCC model is performed, and the simulation results are presented to carry out parametric studies on soil parameters. A significant influence on the range of the plastic and reverse plastic zones is shown for overconsolidation ratio, while the in-situ coefficient of the earth pressure only quantitatively affects the stress distribution.

The contraction behavior of monotonically expanded cavities is intriguing as it offers insights into certain geotechnical scenarios, especially for pressuremeter tests, where the unloading data is equally informative as the loading data. Despite many solutions for cavity expansion, attempts for the analyses of cavity contraction from an expanded state were rarely made. To extend previous solutions to include contraction, this paper presents a novel semianalytical solution for drained contraction of spherical and cylindrical cavities from an initially expanded state in soils characterized by a unified state parameter model for clay and sand (CASM). Given the nonself-similar nature of the contraction after expansion problems, the hybrid Eulerian-Lagrangian (HEL) approach is employed to derive distributions and evolutions of stresses and strains around the cavities during the unloading process. Combined with the previous expansion solution, the complete loading-unloading cavity pressure curves and stress paths at the cavity wall are presented and verified against numerical simulations. Following validation through comparisons with calibration chamber pressuremeter tests conducted in Stockton Beach sand, a new method for the interpretation of pressuremeter testing data is developed based on the proposed solution. This method demonstrates its capability in the back-calculation of the effective horizontal stresses and state parameters for four distinct types of sands.