基于正态分布时间函数地表动态沉陷预测研究

为了研究地表动态沉陷规律，基于正态分布时间函数，结合地表沉陷预测公式，构建了能够进行任意点任意时刻地表动态沉陷预测的函数模型，分析曲线形态系数对时间函数和计算误差的影响，讨论正态分布时间函数的时空完备性，建立了基于时间函数的地表动态下沉计算公式。以辛置煤矿五采区开采为例，利用空间曲面拟合方法求取了地表动态沉陷预测参数，并对特征点的下沉趋势进行了预测。结果表明，地表沉陷预测时曲线形态系数δ > 2为其合理取值，理论预测相对中误差不会超过±4.55%，且随着δ的增大，预测误差逐渐减小；正态分布时间函数在地表下沉、下沉速度以及加速度方面均体现了地表沉陷时空分布的完备性。基于叠加原理的空间曲面拟合求参方法能够进行预测参数的自动求取，地表特征点下沉趋势预测最大中误差为±64 mm，相对中误差为±5.7%，理论值与实测值相吻合，基于正态分布时间函数的预测模型能够体现地表动态下沉的时空分布特征。

Progressive subsidence prediction of ground surface based on the normal distribution time function

With the aim of researching the law of dynamic surface subsidence, based on normal distribution time function, mathematical models utilized to predict progressive surface subsidence at any point and any moment are derived combining surface subsidence predictive formulas. The influence of curve pattern coefficient and calculation error of normal time function is analyzed. Besides, space-time completeness of normal distribution function is also discussed. Predictive formulae to predict surface dynamic subsidence are established based on normal time function. Furthermore, taking coal extraction of the fifth panel in Xinzhi coal mine, Shanxi province for example, predictive parameters of surface dynamic subsidence are deduced by means of dimensional curve surface fitting. According to those parameters the subsided tendency of surface key points is predicted. The results of this research indicate that the acceptable magnitude of curve pattern coefficient δ should be greater than 2 as predicting surface subsidence. In this way relative mean error of theoretical predictive magnitude will not exceed ±4.55%; and the error will decrease gradually as the increase of δ. Normal distribution function represents the completeness of space-time distribution in response to surface subsidence, subsided speed and accelerated velocity. The methodology of curve surface fitting based on superposition theory can automatically calculate predictive parameters of surface subsidence. And maximum mean error of subsided tendency prediction of key points is ±64 mm, relative one is ±5.7%, which is better fitted with what actual occurs. Subsidence predictive models of normal distribution time function can represent time-spatial distribution characteristics of progressive surface subsidence.