Modified Kastner formula for cylindrical cavity contraction in Mohr-Coulomb medium for circular tunnel in isotropic medium

Abstract

The Kastner formula for cavity contraction is one of the commonly used formulae for the cavity contraction problem in tunnel excavation, and it is based on the assumption of small displacement around the cavity with no volume change in the plastic zone. In this paper, the errors arising from these assumptions are discussed, and the volume change of the plastic zone is considered. It can be seen that this assumption is reasonable for normal situations, but for rock with weak shear strength, the Kastner formula should be used with care, especially in situations where there will be relatively large volume changes in the plastic zone.