目前，冲击地压理论研究已经完成了从定性分析到定量分析的转变。巷道围岩临界应力计算是巷道安全性评价的重要依据。鉴于冲击地压问题的极度复杂性，在理论上继续取得突破极为困难。基于理论公式的巷道围岩临界应力计算，无法考虑更复杂的实际情况，例如非圆形巷道、非静水压力和复杂岩层结构。冲击地压理论和数值计算相结合具有更加广阔的应用前景，能使冲击地压理论进一步走向实际应用，这是极有价值的发展方向。这方面研究成果的成功取得依赖于数值计算技术的快速发展。研究将当今较先进的岩层运动并行计算系统StrataKing(一种自主开发的以拉格朗日元与离散元耦合方法为基础的非线性断裂力学GPU并行计算方法)与冲击地压扰动响应失稳理论相结合，首次提出了圆形巷道扰动响应失稳理论的数值模拟方法。该方法的思想是将非线性断裂力学数值分析方法中的Ⅱ型断裂能设定为中间变量，从而建立了静水压力条件下圆形巷道围岩临界应力与冲击能指数之间的关系。为了获取冲击能指数的数值解，采用了仅出现一个剪切面的理想岩样进行单轴压缩数值试验，以排除其他因素对应力−应变曲线峰后倾向于直线部分斜率的影响。对于高角度剪切破裂，提出了将非标准岩样的计算结果转换成标准岩样的结果的折算方法。折算后冲击能指数的范围为0.17～13.52，位于全国131个冲击地压矿井的调研数据之内。巷道围岩临界应力的计算结果是理论结果的0.4～2.5倍，这与针对全国20个冲击地压矿井的调研数据(临界应力的修正系数普遍大于1，甚至接近8)定性相符，从局部化破坏围岩比均匀破坏围岩的承载力高的角度进行了解释。冲击地压与局部化的关系过去有讨论，扰动响应失稳理论与局部化过去并无关系。通过局部化，扰动响应失稳理论与冲击地压之间在破坏机理上产生了密切的关联。StrataKing可为冲击地压矿井巷道安全性评价提供强大的算力支撑。

At present, theoretical analyses of rockbursts have entered into the quantitative analysis stage from the qualitative analysis stage. The critical stress of the roadway surrounding rock has become the important basis for safe assessment of the roadway. Theoretical breakthrough becomes extremely difficult due to the extreme complexity of rockbursts. Calculation of the critical stress of the roadway surrounding rock based on the analytical formula is not applicable for the complex situation, such as non-circular roadway, non-hydrostatic pressure and complex strata structures. Combination of theories of rockbursts and numerical simulation possesses a broad application prospect, promoting theories of rockbursts to a further actual application. This is an extremely valuable development direction. Achievement of this aspect depends on the rapid development of the numerical technologies. In this paper, the self-developed advanced parallel computing system of strata movement (StrataKing, a parallel computing method in nonlinear fracture mechanics base on a hybrid Lagrangian and discrete element method) and the disturbance response instability theory of rockbursts was combined. A numerical method for the disturbance response instability theory of rockbursts for the circular roadway was proposed firstly. The idea of the method is that the Ⅱ-type fracture energy in nonlinear fracture mechanics is seen as a moderate variable. Thus, the relation between the critical stress of the circular roadway surrounding rock under hydrostatic pressure and the burst energy index was established. To obtain the numerical solution of the burst energy index, an ideal numerical test for a rock specimen in uniaxial compression, which is subjected to a single shear fracture, was conducted so that effects of other factors on the relative straight portion of the post-peak stress-strain curve can be neglected. For a high-angle shear fracture, the result for the non-standard rock specimen was converted into that for the standard rock specimen. The converted burst energy index is in the range of 0.17−13.52, falling into the survey data of 131 rockburst coal mines in China. The numerical critical stress of the circular roadway surrounding rock is 0.4−2.5 times of the analytical result, qualitatively consistent with the survey data (the modified coefficient of the critical stress of the circular roadway surrounding rock is usually greater than 1, even reaching 8) of 20 rockburst coal mines in China. We believe that the roadway surrounding rock subjected to the localized failure has a higher load-carrying capacity than subjected to the uniform failure. Thus, the phenomenon that numerical results are higher than analytical results can be explained. The relation between rockbursts and localization has been discussed, and not for the relation between the disturbance response instability theory and localization in the past. In the present paper, localization was acted as a medium so that a closed relation between the disturbance response instability theory and rockburst was established in terms of the fracture mechanism. StrataKing can provide a powerful support of computing power for safe assessment of roadway surrounding rock in rockburst coal mines.