1. School of Resource and Safety Engineering,China University of Mining and Technology(Beijing),Beijing　 100083,China; 2. Mine Construction Branch of Research Institute,China Coal Research Institute,Beijing　 100013,China

建立长边两侧采空（煤柱）与短边两侧弹性基础边界基本顶板结构力学模型,根据薄板主弯矩破断准则并结合偏微分方程有限差分算法计算研究了基本顶破断的影响因素及权重关系。得到:（1） c1与c2煤柱的支撑系数kc1,kc2及宽度Lc1,Lc2不仅显著影响基本顶在两侧煤柱区的主弯矩大小及位置且显著影响短边区及中部区主弯矩大小及位置;（2）基本顶的弹性模量E与厚度h越大,短边实体区及两侧煤柱区的基本顶断裂线深入煤体距离越大; Lc1,Lc2越大,kc1,kc2越小,煤柱区断裂线深入煤柱距离越大;（3） Lc1,kc1,Lc2及kc2较小而E,h较大时,基本顶在c1与c2煤柱区均不断裂,最终断裂形态为非对称“||-X”型;（4） Lc2及kc2较大而h,E,Lc1及kc1较小时,基本顶在c1煤柱区（较弱煤柱）不断裂而在c2煤柱区（较强煤柱）会断裂,最终断裂形态为非对称“C-X”型;（5）两侧煤柱支撑系数及宽度均较大而E,h较小时,断裂形态为非对称横“O-X”型;（6） k,kc1,kc2,E及h均改变而比值k/（Eh3）不变时(其中,比值k/kc1与比值k/kc2也不变),主弯矩大小不变且初次破断位置不变。

The mechanical model of plate structure of main roof with elastic foundation boundary on the two sides of the long side of goaf (coal pillars) and the short side is established in this study. According to the fracture criterion of pri- mary moment of thin plate and combined with finite difference algorithm for partial differential equation,the influence factors and weight relationships of the fracture of main roof are studied and calculated. It is found that ① the support coefficients kc1 ,kc2 and the widths Lc1 ,Lc2 of coal pillars (c1 ,c2 ) can not only obviously affect the values and positions of primary moments on both sides of coal pillar areas,but also obviously affect the values and positions of primary mo- ments of short side region and central region;② the larger the values of elastic modulus E and thickness h of main roof are,the larger the distance from the fracture line of the short-side solid coal area under main roof as well as the coal pillar areas to the surface of solid coal will be;when Lc1 ,Lc2 are larger and kc1 ,kc2 are smaller,the fracture line of coal pillars and the short-side solid coal area is farther away from the surface of coal pillar and closer to the center of coal pillar;③ when the thickness h and elastic modulus E of main roof are larger and the values of Lc1 ,kc1 ,Lc2 and kc2 are smaller,the main roof in zone c1 and zone c2 of coal pillar area will not fracture and the fracture form is the type of asymmetric “ | | -X”;④ when the values of h,E,Lc1 and kc1 are smaller and the values of Lc2 and kc2 are larger,the main roof in zone c1 of coal pillar (weaker) area will not fracture,but the main roof in zone c2 of coal pillar ( stron- ger) area will fracture,so the final fracture form is the type of asymmetric “ C-X”;⑤ when the support coefficients and the width of coal pillars on both sides of goaf are larger as well as the values of E and h are smaller,the fracture form is the type of asymmetric transverse “O-X”;and ⑥ when k,E,h,kc1 and kc2 change,and the ratio k / ( Eh3 ) is unchangeable (the ratio k / kc1 and the ratio k / kc2 are also unchangeable),the values and positions of primary moments and the position of first fracture are invariant.

CHEN Dongdong,XIE Shengrong,HE Fulian,et al. First fracturing of thin plate of main roof with elastic foundation boundary on both sides of the long side of goaf (coal pillars)[J]. Journal of China Coal Society,2018,43(12):3273-3285.