Theory and Numerical Simulation of Deep Rock Mass Based on a Non-Euclidean Model

Abstract

Rock masses existing in nature may experience closed internal stress under the action of geological structures. This closed internal stress makes the deformation of the rock mass incompatible, so classic continuum theory is not suitable for analyzing the stress and deformation of rock masses. In this study, a non-Euclidean model for rock masses was established based on differential geometry. By choosing the non-Euclidean parameter as the internal variable, a thermodynamic model was constructed. Then, numerical computation based on the non-Euclidean model was applied to a circular tunnel in a deep rock mass. The distribution of internal stress and the effects of rock parameters on the distribution of internal stress were analyzed. Through our research, we conclude that the stress field of the deep rock mass consists of classical stress and internal stress and that the internal stress shows a distinct wavy behavior. The radius of the fractured zone decreases with an increasing Young’s modulus E and Poisson’s ratio $v$ , but increases with increasing non-Euclidean parameter ξ.