A simple gradient model for zonal disintegration of the surrounding rock around a deep circular tunnel

Abstract

Abstract Zonal disintegration phenomenon around a deep circular opening under hydrostatic pressure is investigated within the theoretical framework of gradient theory in the present paper. The simplest possible gradient constitutive model (including only one extra gradient coefficient) is adopted by adding Laplacian of volumetric strain into Hooke’s law. The gradient model can account for the influence of microstructures on macroscopic mechanical behaviors in many solid materials and rocks. The closed-form analytical solutions to stresses, strains and displacements around the tunnel are presented and compared with the results of classical elastic theory. The influences of microstructure on macroscopic mechanical behaviors are analyzed. It is indicated that the stresses and deformation distribution around the tunnel are fluctuant with consideration of microstructure effects. The number and size of fractured and non-fractured zones are determined by using the Mohr-Coulomb criterion. The effects of gradient coefficient and initial geo-stress of the rock masses on the prediction of zonal disintegration phenomenon are investigated by numerical analysis. In order to check the applicability of the proposed model, the predictions from the formulations are compared with the laboratory-scale test results. It is noted from the comparisons between predicted and measured values that the results of gradient model provides the comparable approximations for the radial displacement of surrounding rock very well. The results in this paper will be a benchmark for further investigations of zonal disintegration phenomenon.