弹性基础边界基本顶薄板初次破断的kDL效应

doi:10.13722/j.cnki.jrme.2016.1016

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摘要基本顶的初次破断规律多采用四边固支边界模型分析，但实际的岩层环境难以实现固支。为了研究基本顶实际围岩条件时的破断规律及破断条件，建立弹性基础边界条件弹性薄板力学模型，运用有限差分方法计算弹性基础系数k与基本顶厚度h、弹性模量E、泊松比、跨度L之间的相互关系对基本顶主弯矩及起始破断位置的影响，并根据主弯矩破断准则得出：弹性基础边界时基本顶首先在中部或长边超前煤壁处破断；比值k/E或k/h3或k/(Eh3)不变时基本顶破断位置不变；k/E或k/h3或k/(Eh3)小时基本顶中部先破断、即煤层松软、基本顶厚度及弹性模量大时基本顶中部先破断；k/E或k/h3或k/(Eh3)大时基本顶长边超前煤壁先破断、即煤层坚硬且基本顶厚度及弹性模量小时基本顶长边先破断。弹性基础边界时基本顶的初次破断规律由k，L和基本顶刚度D复合决定，长壁工作面基本顶的破断类型及条件为(k/D)1/4L＞9.6时：长边超前煤壁→中部→短边超前煤壁、或长边超前煤壁→短边超前煤壁→中部，(k/D)1/4L＜9.4时：中部→长边超前煤壁→短边超前煤壁，(k/D)1/4L = (9.5±0.1)时，基本顶中部和长边超前煤壁位置接近同时破断；对于方形工作面，(k/D)1/4L＞10.5时四边超前煤壁区先破断，(k/D)1/4L＜10.1时中部先破断，(k/D)1/4L = (10.3±0.2)时四边超前煤壁区与中部接近同时破断。

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关键词 ：采矿工程, 弹性基础边界, 固支边界, 基本顶, 薄板, 初次破断, 有限差分法

Abstract：The first time fracturing of the main roof is often analyzed with the fixed boundary conditions at four edges which are difficult to achieve in practice. A mechanical model of elastic thin plate with the elastic boundary foundation condition was established. The influences of the elastic foundation coefficient k，the span L，the main roof thickness h，the elastic modulus E，Poisson?s ratio on the principal moments and initial fracture position of the main roof are calculated with the finite difference method. The first time fracturing of the main roof with the elastic foundation boundary calculated based on the fracture criterion of principal moments occurs in the middle or at the long side ahead of the coal wall. When the ratio of k/E or k/h3 or k/(Eh3) is constant，the fracture position of the main roof is not changed. When the ratio of k/E or k/h3 or k/(Eh3) is small，the middle of the main roof fractures firstly，namely，when the coal seam is soft and the thickness and elastic modulus of the main roof are large，the main roof fractures firstly in the middle. When the ratio of k/E or k/h3 or k/(Eh3) is large，the long side edge ahead of the coal wall fractures firstly，namely，when the coal seam is hard，and the thickness and elastic modulus of the main roof are small，the first fracturing position is at the long side edge ahead of the coal wall. The initial fracturing of the main roof with the elastic foundation boundary is determined by k，L and the stiffness D of the main roof.

Key words： mining engineering elastic foundation boundary clamped boundary main roof；thin plate first fracture finite difference method

引用本文:

何富连，陈冬冬，谢生荣. 弹性基础边界基本顶薄板初次破断的kDL效应[J]. 岩石力学与工程学报, 2017, 36(6): 1384-1399.
HE Fulian，CHEN Dongdong，XIE Shengrong. The kDL effect on the first fracture of main roof with elastic foundation boundary. , 2017, 36(6): 1384-1399.

链接本文:

http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2016.1016 或 http://www.rockmech.org/CN/Y2017/V36/I6/1384

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