Mechanical characteristics analysis of coal around borehole based on three-stage constitutive model and its numerical validation

The stress and deformation characteristics of coal around borehole have an important impact on the accuracy of stress monitoring in deep mining engineering. This study aims to analyze the stress and deformation of coal around borehole under different stress conditions and the influences of various parameters on deformation distribution by applying an analytical method. Firstly, the linearization of complete stress-strain model of coal is curried out according to the field observation data, and the simplified constitutive model is divided into three stages, i.e., elastic, plastic and broken stage. Secondly, based on the elastic-plastic theory, an analytical solution of coal around borehole includes stress and deformation of the elastic, plastic softening, and broken region is deduced, and the effects of parameters such as lateral pressure coefficient, intermediate principal stress coefficient, vertical stress, borehole radius, cohesion, and internal friction angle on radii of different regions are discussed in detail. Thirdly, the analytical results show that only the lateral pressure coefficient affects the deformation shape of coal around borehole, and other parameters have almost no influence on the deformation shape; A large lateral pressure coefficient corresponds to a small radius of the broken and plastic softening region; The radii of broken and plastic softening regions increase significantly with an increase in vertical stress but decrease clearly with an increase in cohesion and internal friction angle; Similarly, the larger the borehole radius, the greater the deformation ranges; The radii of two regions are not monotonous with the intermediate principal stress coefficient, there is almost an inflection point for the intermediate principal stress coefficient corresponding to the minimum radii of two regions, and the value is about 0.7. Finally, a two-dimensional numerical solution of coal around borehole is also employed by using the finite element method, and the radial and tangential stress calculated by FEM are essentially consistent with the results of the analytical method, and the maximum error is approximately 10.56%. Numerical results prove the rationality of the analytical method proposed in this study.