13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Fig. 1 [4, p. 33] Fig. 2 [4, p. 33] 2. Statement of the problem on regular cracks grid around oil and gas wells In [17-20] the energy approach was used to propose a model of symmetric brittle crack formation in a thin plate (and a wedge) under bending by a point indenter. The main purpose of that idealized minimal model was to quantify the study of some possible mechanisms determining the number of the cracks arising. In this paper, similar approach is used to model the formation of a regular grid of cracks around a circular cavity under hydrostatic pressure [21-22]. The basic idea is that cracks are formed due to the accumulation in the system of elastic energy of compression (or rather, the shear energy). As the material strength is exhausted, in the most stressed layer, adjacent to the interior of the body, a regular network of cracks appears, which formation takes all the elastic energy of that layer. In this case, of all the possible grids the minimum-energy-consuming fracture scheme occurs, that is, a system with such a number n and length L of the cracks, that the energy needed for its creation, is minimal. Unlike the case of plate bending here cracks go from the surface of the hole not perpendicular to it, but at an acute angle (though not necessarily at 450, ie in the direction of slip lines). In other words, they are not tensile cracks, though perhaps not quite shear ones. More precisely, in [2, p. 21, 37-38] "usual for rocks Coulomb-Mohr type criterion, according to which the failure on these planes occurs when the shear stress achieves some limit value [τ] = k – σntg ρ, where k and ρ are cohesion modulus and internal friction angle of rock respectively, which are the strength characteristics of the rock" is taken as a failure criterion. Aimed to clarify the fundamental possibility of constructing a simple model of cracks ordered systems of such type and calculation of cracks number, as well as
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