Abstract: Rock burst is one of the most serious dynamic disasters in coal mines,which is recognized as a world-class problem.The theoretical formula describing the occurrence mechanism of rock burst is the first premise to realize the prevention and control of rock burst quantitatively.In view of the fact that there is no explicit theoretical formula of rock burst,this paper has established a mechanical analysis model of roadway rock burst which was directly related to ground stress,physical parameters of coal and rock mass,support strength and engineering structural parameters,and obtained a set of theoretical formulas for rock burst.Firstly,the geometric model,boundary conditions,constitutive relation of deformation and failure of coal and rock mass and the mechanical criterion of rock burst were systematically studied.Secondly,combined with the “bilinear”and “trilinear”constitutive relations of deformation and failure of coal and rock mass,the structural model with two zone “elastic zone and plastic softening zone”and the model with three zone “elastic zone,plastic softening zone and fracture zone”were established,respectively.The stress analysis of surrounding rock of roadway was carried out,and the equilibrium system equation of roadway was obtained. Finally,according to the system equation and mechanical criterion of rock burst,the critical load,critical radius of fracture zone,critical radius of softening zone and their theoretical calculation formulas were obtained. The theoretical formulas was used to quantitatively explain some important scientific problems about rock burst,mainly including the relationship between the bursting ability of coal mass and the risk of rock burst,the theoretical determination of the critical mining depth of rock burst,the role of support in the initiation of rock burst and the safety factor design method of roadway support.The critical load,critical mining depth and rock burst prevention ability of roadway support of nearly 30 rock burst mines in China were calculated and analyzed to verify the correction of the theoretical formulas.The research results show that there is a clear theoretical relationship between these three index parameters-critical load,burst energy index and uniaxial compressive strength.The theoretical indicators of bursting ability of coal mass are bursting energy index and uniaxial compressive strength,and the theoretical indicator of risk of rock burst is the ratio of actual stress and critical load.Based on the theoretical formula of critical load of rock burst,the theoretical determination method of critical mining depth of rock burst in coal mines can be obtained,and the critical load of rock burst can be effectively enhanced with the improvement of support strength.The research results aim to inherit and break through the existing qualitative or statistical quantitative theory of rock burst,and lay a foundation for quantitative research on the mechanism and application of rock burst in coal mines.