采矿工程中的基础数学研究及其工程应用

Research on pure mathematical problems in mining engineering and their applications

本文介绍近年来关于矿井复杂地质动力系统的几项数学研究及其工程应用.主要内容包括:通过采矿工程、地质动力区划理论和基础数学的交叉融合,提出矿井复杂地质动力系统模型.考虑采矿工程一线急需研究的动力灾害治理问题,把巷道围岩稳定性问题转化为复动力系统的结构稳定性问题.通过研究花瓣定理的逆问题,得到巷道围岩稳定性的花瓣预警判据;关于矿井采场压力重分布问题,用复分析方法证明了矿压峰值点极限定理,继而揭示采矿工程中“切顶”“控高”“调速”等多项工程技术方法背后的数学原理;同时介绍以其为指导研发的矿井工作面末采技术,以及动力灾害的预警、治理和预防技术,阐述数学研究驱动的采矿工程中有关技术的原理性革新.

Herein,we present some pure mathematical problems associated with mining engineering and the engineering applications of their solutions.Mining engineering,geodynamic division theory,and pure mathematics are combined to create a model of the complicated geological dynamic system of mines.Motivated by the urgent need for dynamic disaster management in the mining industry,we consider the inverse problem of the petal theorem.We address the issue and suggest an early-warning criterion for the stability of rocks around the mining tunnels.Concerning the redistribution of mine stope pressure,we established a limit theorem of peak points of ground pressure.The theorem explains the mathematical principles of some prevailing techniques in mining engineering,such as roof-cutting and mining height and speed control.Furthermore,we establish a series of mining techniques,including a novel endmining method and a comprehensive system for dynamic disaster early warning,governance,and prevention.This research encourages the innovation of the principle of relevant mining technical methods.