基本顶弹性基础边界薄板模型分析(Ⅰ)——初次破断

Analysis on thin plate model of basic roof at elastic foundation boundary(Ⅰ) : First breaking

建立基本顶弹性基础边界弹性薄板力学模型,运用偏微分方程有限差分方法,研究了推进步距、弹性基础系数、基本顶厚度与弹性模量对基本顶主弯矩与破断位置的影响,得出:基本顶厚度或弹性模量增大时,中部最大主弯矩M_z增大、长边与短边绝对值最大主弯矩M_c,M_d减小;步距增大时,M_z,M_c,M_d均增大、M_z增长幅度较小;弹性基础系数增大时,M_z减小、M_c,M_d增大;根据主弯矩破断准则得出:推进步距或弹性基础系数小时基本顶中部先破断、反之长边超前煤壁先破断;基本顶厚度或弹性模量小时长边超前煤壁先破断、反之中部先断裂。基本顶厚度或弹性模量越大超前断裂距离越大;弹性基础系数或步距越大超前断裂距离越小。弹性基础边界时,基本顶存在3类破断顺序:1长边—中部—短边;2长边—短边—中部;3中部—长边—短边。

By establishing the basic roof mechanical model of elastic thin plate at elastic foundation boundary and using the finite difference method of partial differential equation,this paper researched the effect of the step length,elastic foundation coefficient,basic roof thickness and elastic modulus on the basic roof main bending moment and fracture positions. It is concluded that with the increase of basic roof thickness or elastic modulus,the maximum main bending moment Mzof the middle roof section increases,and the absolute maximum main bending moment Mc,Mdof roof long side and short side decrease; with the step length increasing,the Mz,Mcand Mdincrease,while the growth rate of the Mzis smaller; and when the elastic foundation coefficient increases,the Mzdecreases,while the Mcand Mdincrease. According to the breaking criterion of the main bending moment,when the step distance or elastic foundation coefficient is small,the middle of basic roof fractures first,whereas the roof long side ahead of the coal wall breaks first; if the basic roof thickness or elastic modulus is small,the long side breaks ahead of the coal wall,whereas the central fractures first. The greater the basic roof thickness or elastic modulus,the farther the pre-breaking distance of main roof; the greater the elastic foundation coefficient or step distance,the smaller pre-breaking distance of main roof.There are three types of basic roof breaking sequence： ① long side-middle-short side; ② long side-short side-middle;③ middle-long side-short side.