Physical modeling on mining-induced energy release of crack propagation in overlying strata based on Steiner Minimum Tree Problem

Xue Dongjie●Zhou Hongwei●Ren Weiguang●Li Dongping.

Abstract

There are some difficulties in studying the law of mining-induced crack propagation and distribution in overlying strata, which directly influence the safety and efficiency of underground work including gas drainage for high-gas coal mine. The relationship between crack propagation and released energy was modeled based on the Steiner Minimum Tree Problem (SMTP for short). The modeling pointed out that the cracks initially expanded along the fastest path with minimum energy. Then the problem can be determined as constrained SMTP based on the comparison of real and mathematical crack modeling. The failure mode of overburden followed the bed-separated crack forms model of four points. Furthermore laboratory tests show that the theoretical and real rupture angles has no obvious relationship with depth. From the mechanical mechanism, the partial destruction of the rock surface can be explained by the Mohr-Coulomb criterion, and from the energy point of view, a combination of many different paths made of rock fracture surface is also optimal path. At last the physical meaning of the parameters in the formula of angles of strike-displacement is redefined. The study shows that the modified formula is an integral concept based on different expansions of mining-induced crack in overburden, and the direct manifestation of the principle of Steiner Minimum Tree. ©, 2015, Meitan Xuebao/Journal of the China Coal Society. All right reserved.

基于Steiner最小树相似模拟裂纹扩展与能量传播的机理

薛东杰●周宏伟●伟光●栗东平

摘 要

采矿工程中上覆岩层裂纹扩展及其分布规律一直是研究的难点,直接影响井下工作高效开展及安全,对于高瓦斯矿井还涉及到瓦斯抽采效率提高问题。基于Steiner最小树模型建立裂纹拓展与能量传播的关系,指出裂纹的贯通拓展是沿着耗能最小而最快释放能量的路径。并建立相似模型试验中的真实裂隙与数学裂隙模型,将问题定义为约束型的Steiner树问题。覆岩破坏形式遵循基于四点以离层裂隙为主导的模型。进一步开展室内三轴加载试验,表明理论和真实破裂角与赋存深度的关系并不明显。从力学机理上分析,局部岩石的破坏面可以由摩尔库仑准则解释,而从能量角度分析,众多不同岩性破裂面组合而成的路径也是最优路径。最后揭示了岩层移动角公式参数的内在涵义,指出修正公式是煤炭地下开采上覆不同部分岩层裂隙拓展的有机统一,是Steiner最小树原理的直接体现。

引用格式：

Xue DJ, Zhou HW, Ren WG, Li DP. Physical modeling on mining-induced energy release of crack propagation in overlying strata based on steiner minimum tree problem[J]. Journal of China Coal Society, 2015, 40(3): 541–547. 薛东杰, 周宏伟, 任伟光, 栗东平. 基于Steiner最小树相似模拟裂纹扩展与能量传播机理研究[J]. 煤炭学报, 2015, 40(3): 541–547.

EI：20151800797222   DOI：10.13225/j.cnki.jccs.2014.0609

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