考虑节理几何特征的地表沉陷预计方法

The prediction method for surface subsidence considering the geometrical characteristics of joints

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。

The similar material simulation test results show that the overlying joint rock mass subsi-dence caused by underground coal mining appears skewness characteristics. The geological and mathe-matical model considering the joint angle, trace length and the trace width is established and the proba-bility distribution function of the overlying joint rock mass subsidence caused by the underground coal mining is deduced by using the random medium theory. At the same time, the probability distribution of surface subsidence caused by mass mining is assumed to be in accordance with the n-Bernoulli trial dis-tribution. The n-Bernoulli trial distribution is equivalent to Poisson distribution when n is equal to or larger than ten. The overlying joint rock mass prediction equations considering the continuity of surface subsidence are proposed based on Gamma distribution （expanded version of Poisson distribution）. The comparison between the results of surface subsidence computed by the model calculation and those measured by the similar material simulation experiment has shown that the presented model can predict a single set of joint rock mass subsidence caused by the underground coal mining with relatively good accuracy, which provides technical support for mining subsidence forecasting and strata movement monitoring.