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相似材料模拟试验结果表明,地下煤炭开采引起上覆节理岩体沉陷出现偏态特征。通过建立考虑节理倾角、迹长和迹宽的地质数学模型,运用随机介质理论,推导了地下煤炭开采引起上覆节理岩体沉陷的概率分布函数,认为单元岩块开采引起的地表沉陷概率分布符合n重Bernoulli试验概率分布规律;当n≥10时,采用Poisson分布来代替n重Bernoulli试验概率分布规律;考虑到地表沉降的连续性,采用Poisson分布实数域拓展后的Gamma分布代替Poisson分布,提出了考虑节理几何特征的上覆节理岩体沉陷预计方程。通过该模型计算的地表沉陷预计结果与相似材料模拟试验监测结果相比较,该模型能较好地预计地下煤炭开采引起上覆单组节理岩体沉陷,为开采沉陷预计和岩层移动监测提供了技术参考。
Simulation results of similar materials show that underground coal mining causes the overlying jointed rock mass subsidence to appear skewed. The probability distribution function of overlying jointed rock mass induced by underground coal mining is deduced by establishing the geological mathematical model considering the inclination, trace length and trace width of joints, and using the stochastic medium theory. The probability distribution of surface subsidence caused by unit rock mining is in accordance with n is the Bernoulli test probability distribution; when n≥10, the Poisson distribution is used instead of the n-Bernoulli test probability distribution; considering the continuity of surface subsidence, the Poisson distribution is used to replace the Poisson distribution Prediction equation of overlying jointed rock mass settlement considering geometrical characteristics of joints. The prediction results of surface subsidence calculated by this model are compared with the monitoring results of simulation test of similar materials. This model can predict the subsidence of overlying single group jointed rock mass well under the condition of underground coal mining, and provide the technology for the prediction of mining subsidence and the monitoring of rock movement reference.