基本顶弹性基础边界薄板模型分析(Ⅱ)——周期破断

摘要

建立弹性基础边界基本顶薄板周期破断力学模型,采用有限差分理论,研究了基本顶厚度h、弹性模量E、边界弹性基础系数k以及k与h,E的比值关系对基本顶主弯矩与周期破断规律的影响,得出,E,h增大时,推进方向长边深入煤壁区及短边深入煤壁区绝对值最大主弯矩Mc与Md、悬顶区后侧的最大主弯矩Mb均增大,Md的增长幅度最大;k增大时,Mc,Mb,Md均减小,Md的减小幅度最大;依据主弯矩破断准则可得:E,h悬顶长度a1较大或k较小时短边深入煤壁区上表面先破断,反之推进方向长边深入煤壁区上表面先破断;比值k/E或k/h3不变时主弯矩M.,Mb,Md不变,起始破断位置不变.弹性基础边界基本顶周期破断类型为:①长边上表面→短边上表面→悬顶区后侧下表面;②短边上表面→长边上表面→悬顶区后侧下表面.%By establishing thin plate mechanical model of main roof with elastic foundation boundary and using the finite difference theory,the paper studied the effect of elastic foundation coefficient k,main roof thickness h,main roof Young modulus E,the hanging roof length a1,the ratio k/E and k/h to the main roof primary bending moment and periodic fracture regularity.It is concluded that with the increase of the E or h,the absolute maximum primary moment Md of short side and Mc of long side,and the maximum primary moment Md of suspended roof's rear boundary all increase;while with the increase of the k,the primary moments Mc,Mb and Md all decrease,and the decrease amplitude of the Md is the biggest.According to the fracture criterion of primary moment,the value of E,h or a1 is big,or the value of k is small,the upper surface of the short side ahead of the coal wall first fractures,whereas the long side ahead of the coal wall first fractures;if the ratio k/E or k/h3 is unchanged,the primary moments Mc,Mb and Md are unchanged and the initial fracture position of main roof is unchanged.The periodical fracture types of main roof with elastic foundation boundary are:① long side upper surface→short side upper surface→lower surface of suspended roof's rear boundary;② short side upper surface→long side upper surface→lower surface of suspended roof's rear boundary.