采动底板横观各向同性岩体应力解析解

针对采动煤层底板应力计算中将底板层状岩体视为各向同性介质这一问题,通过把横观各向同性弹性理论引入到采动煤层底板应力解析解中,根据开采煤层上覆载荷分布特点,利用半无限横观各向同性弹性体表面受垂直集中力作用的应力分量计算公式,推导出采动横观各向同性底板中的附加应力解析解,并与FLAC^3D数值解进行对比验证。在此基础上,分析了横观各向同性底板与各向同性底板中的附加应力在水平方向上的变化规律。算例显示,在煤层底板同深度下,横观各向同性底板垂直附加应力在采空区的卸载程度要小于各向同性底板,而水平附加应力则与之相反;在工作面两侧的底板中的垂直附加应力与水平附加应力的集中程度横观各向同性底板皆小于各向同性底板;横观各向同性底板的附加剪应力要小于各向同性底板。当底板为横观各向同性岩体,按各向同性岩体计算其应力分布是不合理的,需作必要的修正。

Analytical Solution of Stress in a Transversely Isotropic Floor Rock Mass under Mining

Aiming at the problem in stress calculation of mining seam floor where the layered rock mass is regarded as isotropic medium, the transverse isotropic elastic theory is introduced to the analytic solution of stress in mining coal seam floor. According to the load distribution on overburden of coal seam, using the stress component formula from semi-infinite transversely isotropic body surface under concentrated force, an analytical solution of stress in a transversely isotropic floor rock mass is derived under the condition of mining, and it is verified by comparing the numerical solutions with those by FLAC^3D.On this basis, the change rule of additional stress of the transversely isotropic floor and the isotropic floor is analyzed in the horizontal direction.The results show that: at the same depth of coal seam floor, the degree of unloading of vertical additional stress of the transversely isotropic floor in the goaf is less than that of the isotropic floor. But the horizontal additional stress has the opposite change rule. At the two sides of the working face, the vertical additional stress and horizontal additional stress concentration degree of transversely isotropic floor is smaller than that of the isotropic floor. Additional shear stress in the transversely isotropic floor is less than the isotropic floor. When the floor is a transversely isotropic rock mass, it is not reasonable to calculate the stress distribution by the isotropic rock mass, corrections are necessary.