关键词: 时间函数, 正态分布, 动态下沉, 预测模型, 曲面拟合

Abstract: 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.

Key words: time function, normal distribution, progressive subsidence, predictive model, curve surface fitting