Question Kastner Formulae of Circular Tunnel

Abstract

Stress and deformation of surrounding rock are basic issues in tunnel engineering, directly affecting the safety evaluation and the support or lining measures to a tunnel. Kastner formulae proposed in 1950s describe the plastic zone range of a circular tunnel and the stress distribution in plastic zone, and have served as the theoretical basis of tunnel analysis in past decades. Supposing the surrounding rock is ideal elastic-plastic material with Mohr-Coulomb or Mises criterion, we proved that the support process to a circular tunnel is an unloading process in terms of plastic mechanics. The conclusion was verified by FLAC calculation. Both the stress increment and the displacement increment of surrounding rock in support stage are consistent with the elasticity theory. Therefore, Kastner formulae are only applicable to the excavation stage of tunnel, not to the support stage.