矿山开采沉陷理论发展历程综述

Summary and Development of Mining Subsidence Theory

介绍了开采沉陷研究起源及主要研究成果,阐述了克诺特影响函数法、李特维尼申的随机介质理论与概率积分法的历史渊源。指出克诺特影响函数法(1951年)是根据实测资料提出的;随机介质理论(1954年)是利用随机游动模型,将概率关系模型泰勒级数展开到二阶项,求解偏微分方程得出下沉概率;概率积分法(1965年)是采用了李特维尼申应用随机统计方法研究岩层移动的观点,建立了基于概率密度函数关系式的微分方程,求解微分方程得出概率密度函数。3种地表下沉预计方法原理相互独立,但三者的研究结论完全一致,即地表下沉影响函数均服从正态分布。3种预计方法都是对地表下沉现象进行描述,均无法解释开采引起的地表下沉机理。在上述分析的基础上,进一步指出,目前还没有一种预计模型可以对每个沉陷问题做出完全正确的预计,需要应用先进的测绘技术对沉陷过程进行更加精细的观测研究,将经典预计理论与现代数学及力学理论相融合,建立更加科学实用的预计模型是未来的发展方向。

The origin and main research results of mining subsidence are analyzed,the historical origin of Knothe influence function method,Litwiniszyn random medium theory and probability integration method are introduced.It is indicated that Knothe influence function method(1951)is on the basis of the actual observation data;random medium theory(1954)uses the random walk model to expand the Taylor series of the probabilistic relation model to the second order term,and solves the partial differential equation to get the sinking probability;probability integral method(1965)adopted Litwiniszyn’s viewpoint of applying random statistical method to study rock strata movement,established the differential equation based on the relationship of probability density function,and solved the differential equation to obtain the probability density function.Theprinciples of the three methods are independent from each other,and the conclusions of the three methods are completely consistent,the influence functions of surface subsidence are normal distribution.However,none of the three prediction methods can explain the mechanism of surface subsidence caused by mining,and they are all descriptions of surface subsidence phenomena.Therefore,at present,there is no prediction model that can make a completely correct prediction for each subsidence problem.It is necessary to apply advanced surveying and mapping technology to research more detailed observation data on the subsidence process,and combine the classical prediction theory with modern mathematical and mechanical theories,and establish a more scientific and practical prediction model is the further research direction.