Institute of Mining SB RAS

Abstract

Introduction. The article considers a variant of a straight finite fracture modeled by a mathematical cut in the elastic plane. Aim. The new model proposed differs from the existing models by the damage zone bounded by the elastic material at the fracture tip up to the moment of the fracture growth. The process of fracturing is essentially nonlinear. Methodology. The model is based on the full-scale tension experiments with a reference sample of rocks enclosing a fracture and having the characteristic stress points, namely, proportionality limit, elasticity limit, plasticity domain and the domain in the vicinity of destructive stresses. Results. The problem with fracture is considered as an experiment to determine deformation with growing pressure in the fracture. The problem has no correct analytical solution. The problem on hydrofracture 20 "Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal". No. 4. 2020 ISSN 0536-1028 assumes the presence of the initial stress field in rock mass, which is essentially used in formulation of boundary conditions. Conclusions. All such problems belong to the class of Cauchy’s problems with an infinitely distant point in the computational domain. This article proposes the correct formulation of the fracture theory problem in the static, kinematic and dynamic framework.