任意形状工作面沉陷预测的概率积分法及其应用

概率积分法是煤矿开采沉陷预测的重要方法，可适用于缓倾斜、倾斜煤层开采地表移动分布曲线符合正态分布规律的地表移动和变形计算。针对原方法对任意形状工作面存在的不足，在原有走向和倾向概率积分函数的基础上，以走向和倾向为基准划分积分函数区域，在该区域内剖分非结构化的三角形单元作为二重积分的基本单位；通过坐标旋转变换的二重积分换元法，转化为以直线为上、下限的二重积分，计算旋转后的影响半径，对新的二重积分采用复合辛普森数值积分公式，积分得出地表任意点在基本三角形开采单元下的积分下沉值；最后，通过叠加计算完成任意点、任意形状工作面概率积分法的沉陷预测计算。算法在GIS系统下实现，实例应用效果良好，可为“三下”采煤提供地表移动预测计算的支持。

Probability integral method of arbitrary shape face to predict mining subsidence and its application

The probability integral method is an important approach to predicting mining subsidence, which can be used to calculate surface movement and deformation with normal distribution profile in the gently inclined and inclined coal seams. To overcome the shortcoming of the original method for arbitrary shape face, the integral regions of mining are defined by the strike and dip directions with different integral functions, and divided into several unstructured triangular elements as the basic unit of double integrals. By the double integral conversion method with coordinate rotation transformation, the integral of the basic unit can be converted into double integrals with two lines for the upper and lower limits. When the influence radius of rotation is given, the new double integrals can be calculated using the numerical compound Simpson method to obtain the subsidence at any point on the surface due to the mining of basic triangular element. Finally, the superposition calculation of all basic triangular elements is used to finish the probability integral at any point to predict mining subsidence for arbitrary shape face. The proposed algorithm is implemented in the GIS platform with good results in the case study, providing the support for “under three” coal mining with surface movement prediction.