Abstract

Non-Euclidean continuum model is used for construction of the stress field for different problems. The general idea of the model is to introduce the parameter which allows us to describe incompatible deformation of rock masses in the terms of the non-Euclidean geometry. The non-Euclidean continuum model is applied for description of the zonal stress field around a cylindrical opening. The phenomenological parameters of the model are determined on the basis of comparison with experimental data. The anomalous deformation behavior in the cylindrical rock sample is analyzed on the foundation of the non-Euclidean continuum model as well. The problem of the non-Euclidean continuum model application to the mesocracking structures description on the different hierarchical rocks and rock massifs levels is discussed.

1 Introduction

The excavation of underground openings at great depths is a challenging issue for mining engineers. Deep rock masses are characterized by zonal disintegration which is referred as a zonal quasi-periodic structure around an excavated rock. The zonal failure structures were widely observed in deep gold mines in South Africa (Adams & Jager 1980). Similarly, the zonal disintegration phenomena have also been discovered in the Taimyrskii and Mayak mines in Russia (Shemyakin et al. 1986).

The zonal structure is characterized by the occurrence of irreversible strains ije in a rock and leads to the incompatibility condition for eij. In the classical theory of elasticity, the strain deformations satisfy the Saint-Venant compatibility conditions. So a novel theoretical idea is founded on abandoning the kinematics hypothesis of the classical continuum model. From the mathematical viewpoint it means that the internal geometrical structure of the rock does not coincide with the geometry of the observer's Euclidean space (Guzev 2010). The standard formalism of non-equilibrium thermodynamics was used to obtain the constitutive equations for the non-Euclidean model. However from a physical perspective, its geometric characteristics cannot be directly measured. Therefore, practical results of the model can be verified by a comparison with experimental data.

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