Closed-form solutions for large strain analysis of cavity contraction in a bounded Mohr-Coulomb medium

Abstract

This paper presents rigorous analytical solutions for cavity contraction analysis of a thick-walled cylinder/sphere after an arbitrary magnitude of expansion. Closed-form solutions are given for the distribution of stress and displacement within the cylinder/sphere of soil that is subjected to constant external pressure and monotonically decreasing internal pressure. The soil is modelled as an elastic-perfectly plastic material obeying the Mohr-Coulomb yield criterion and a non-associated flow rule. Large strain effects are taken into account by adopting the logarithmic strain definition in the plastic deformation analysis. The new solutions are validated with published results at first, then parametric studies are carried out. It is shown that the reference stress state (e.g. in-situ, elastic, partially plastic and fully plastic) and the cavity geometry ratio may greatly affect the unloading behaviour, in particular, when the cavity geometry ratio is smaller than a limit value. Finally, three typical applications of the solutions are demonstrated, including (i) design of the thickness of frozen cylinder walls accounting for large deformation effects, (ii) interpretation of laboratory pressuremeter tests with consideration of effect of the constant stress boundary, and (iii) shakedown analysis of a soil cylinder/sphere considering its geometry changes upon cyclic loading and unloading.

Keywords:

• Cavity contraction
• boundary effect
• shakedown
• pressuremeter
• frozen earth wall

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work presented in this paper has been supported by the ‘Taishan’ Youth Scholar Program of Shandong Province, China (No. tsqn201909016, No. tsqn201909044) and ‘Qilu’ Scholar Program of Shandong University.