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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/h~3或k/(Eh~3)不变时基本顶破断位置不变;k/E或k/h~3或k/(Eh~3)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/h~3或k/(Eh~3)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)~(1/4)L>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)~(1/4)L<9.4时:中部→长边超前煤壁→短边超前煤壁,(k/D)~(1/4)L=(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)~(1/4)L>10.5时四边超前煤壁区先破断,(k/D)~(1/4)L<10.1时中部先破断,(k/D)~(1/4)L=(10.3±0.2)时四边超前煤壁区与中部接近同时破断。
The initial breaking principle of the basic roof mostly adopts the four-sided solid boundary model analysis, but the actual rock formation environment is difficult to achieve the solid support. In order to study the rupture law and rupture conditions of the basic top real surrounding rock conditions, a mechanical model of elastic thin plate with elastic foundation boundary conditions is established. The finite difference method is used to calculate the elastic basic coefficient k, the basic top thickness h, elastic modulus E, Poisson’s ratio, Span L on the main roof of the main peak and the initial rupture position, and according to the main bending moment criterion: the elastic foundation of the basic top first in the middle or long edge ahead of the coal wall rupture; ratio k / E or k / h ~ 3 or k / (Eh ~ 3) unchanged; , Ie, the coal seam is soft, the basic roof top thickness and the elastic modulus are large, and the top of the top of the roof is basically broken; when the k / E or k / h ~ 3 or k / (Eh ~ 3) When the coal seam is hard and the basic top thickness and modulus of elasticity are small, the top of the top long edge breaks first. The initial rupture law of the basic roof at the elastic foundation boundary is determined by the combination of k and L and the basic roof stiffness D. The type and conditions of the basic roof at the longwall face are (k / D) ~ (1/4) L> 9.6: Long side leading coal wall → middle → short side leading coal wall or long side leading coal wall → short side leading coal wall → middle, (k / D) ~ (1/4) L <9.4: middle part → long side leading (K / D) ~ (1/4) L = (9.5 ± 0.1), the position of the leading coal wall in the middle part of the top and the long side near to the same time is broken at the same time. For the square face, (k /D)~(1/4)L>10.5, the four sides lead the coal wall area to rupture first, (k / D) ~ (1/4) L <10.1, ) L = (10.3 ± 0.2), the four sides advanced coal wall area and the middle near the same time breaking.