Rock behaviour frequently does not fit the classical theory of continuum mechanics because of rock aggregated granular structure. Particularly, rock fracturing may be accompanied by zonal disintegration formation. The key to building the nonclassic model of rock fracturing is the granulated structure. Deformations of solid bodies with microscopic flaws can be described within the scope of non-Euclidean geometry, and non-trivial deformation incompatibility can be referred to as a fracture parameter. The new continuum model presented in this paper enables the prediction of the zones initializing and developing as a periodic structure. The non–Euclidean description of phenomenon initiates an appearance of two new material constants. The coupled model must comprise the fourth–order parabolic equation on disintegration thermodynamic parameter be solved with the classical hyperbolic system of equations for the dynamics of continuous media. The 2D model of formation of disintegration zone was solved numerically. The zone magnitude and site that can be described by the term ‘disintegration scale’ are determined by values of new constants. Therefore, the numerical model based on the new non-Euclidean continuum model is capable of predicting formation of a disintegration field periodic structure.


Zonal disintegration in the mining industry began in the 1980s. The first observation of the phenomena in South Africa was made by Adams and Jager [1] at 1980. Later, Shemyakin et al. [2, 3, 4] observed and described the same phenomena. Glushikhin et al. [5] described a model experiment in a lab that reproduced the in–situ phenomena.

The periodic changes of the fractured zone cannot be clearly explained by classic approaches of solid mechanics. The linear theory of elasticity enables the stresses for cylindrical excavation to be calculated. Any of stress tensor components is a monotone function on an excavation boundary offset that provides the only possible fractured zone if certain rock-failure criteria is applied. To achieve the observed periodic structure using a classic approach, some redundant factors like the presence of specific hydrostatic pressure field must be available.

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