冲击地压是煤矿最严重的动力灾害之一，是公认的世界级难题。刻画冲击地压发生机理的理论公式是实现冲击地压定量防治的第一前提。针对目前尚未有直接明了的冲击地压发生理论公式的现状，本文建立了与地应力、煤岩物性、支护强度和工程结构参数直接相联系的巷道冲击地压发生力学分析模型，得到了一套冲击地压发生的理论公式。首先，系统探究了冲击地压解析分析所涉及的几何模型、边界条件、煤岩体变形破坏本构关系和冲击地压发生的力学判据；其次，结合煤岩体变形破坏的“双线性”本构关系和“三线性”本构关系，分别建立了巷道“弹性区、塑性软化区”两分区结构模型与“弹性区、塑性软化区、破碎区”三分区结构模型，对巷道围岩展开应力分析，得到了巷道平衡系统方程；最后，由系统方程与冲击地压发生力学判据，得到了冲击地压发生的临界载荷、临界破碎区半径与临界软化区半径指标及其理论计算公式。采用理论公式定量解答了冲击倾向性与冲击危险性的理论关系、矿井冲击地压发生临界开采深度的理论界定和支护在冲击地压启动过程中的作用及支护安全系数设计方法等科学问题，并对我国近30座冲击地压矿井的冲击启动临界载荷、临界开采深度和支护防冲安全能力进行了计算或验算。研究结果表明，临界载荷、冲击能指数和单轴抗压强度三个指标参量间具有明确的理论关系；表征冲击倾向性的理论指标为冲击能指数和单轴抗压强度，表征冲击危险性的理论指标可为实际应力与临界载荷比值；基于冲击地压发生的临界载荷，可以得到矿井冲击地压发生临界开采深度的理论确定方法；支护强度的提高能够有效提升冲击地压发生的临界载荷。研究成果旨在继承并突破现有定性或统计定量的冲击地压理论，为实现煤矿冲击地压机理及应用的定量化研究奠定基础。

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.