矩形巷道围岩应力分布的复变函数解
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摘要
为确保煤矿深部开采中矩形巷道的安全,需了解巷道附近围岩的应力分布及其影响因素。采用复变函数的方法,研究双向压力作用下的矩形巷道,得到了围岩中应力的解析解。给出了沿巷道边和水平轴的应力分布,并讨论了矩形巷道的长宽比和面积对应力的影响。结果表明:在矩形巷道的角点处,有应力集中的现象,应力分量都达到了最大值;随矩形巷道长宽比增加,应力最大值增加;长宽比相同时,改变矩形巷道孔口的面积,应力分布不会改变。
To ensure the safety of rectangular roadway in deep mining, the stress distribution of surrounding rock in the vicinity of the roadway and its influencing factors must be understood. The rectangular tunnel under biaxial compression is studied by complex variable method, and the analytical solution of stress in the surrounding rock is obtained. The stress distribution along the edge and horizontal axis of roadway is given, and the influence of the aspect ratio, and the area of the rectangular roadway on the stress is discussed. The results showed that there is the phenomenon of stress concentration in the corner of the rectangular roadway, and the stress components have reached the maximum values. The stress values increase with the aspect ratio of the rectangular roadway. For the same aspect ratio, the stress distribution is not change by changing the area of the aperture of the rectangular roadway.
To ensure the safety of rectangular roadway in deep mining, the stress distribution of surrounding rock in the vicinity of the roadway and its influencing factors must be understood. The rectangular tunnel under biaxial compression is studied by complex variable method, and the analytical solution of stress in the surrounding rock is obtained. The stress distribution along the edge and horizontal axis of roadway is given, and the influence of the aspect ratio, and the area of the rectangular roadway on the stress is discussed. The results showed that there is the phenomenon of stress concentration in the corner of the rectangular roadway, and the stress components have reached the maximum values. The stress values increase with the aspect ratio of the rectangular roadway. For the same aspect ratio, the stress distribution is not change by changing the area of the aperture of the rectangular roadway.
引文
[1]杨巨文,唐治,何峰,等.圆形巷道围岩弹性应力场的复变函数解析[J].安全与环境学报,2015,15(1):148-152.
[2]李铀,袁亮,刘冠学,等.深部开采圆形巷道围岩破损区与支护压力的确定[J].岩土力学,2014,35(1):226-231.
[3]岳高伟,袁军伟,冯帆.梯形断面掘进巷道围岩稳定性数值模拟[J].煤矿安全,2012,43(11):45-47.
[4]杨丽红,何蕴增.无限平面矩形开孔的应力场分析[J].哈尔滨工程大学学报,2002,23(2):106-110.
[5]赵凯,刘长武,张国良.用弹性力学的复变函数法求解矩形硐室周边应力[J].采矿与安全工程学报,2007,24(3):361-365.
[6]郭力,王剑波,李宁.矩形巷道应力集中系数的弹性分析[J].金属矿山,2008(2):45-48.
[7]施高萍,祝江鸿,李保海,等.矩形巷道孔边应力的弹性分析[J].岩土力学,2014,35(9):2587-2593.
[8]何峰,唐治,朱小景,等.矩形巷道围岩应力分布特征[J].数学的实践与认识,2015,45(20):128-134.
[9]陈凯,唐治,崔乃鑫,等.矩形巷道围岩应力解析解[J].安全与环境学报,2015,15(3):124-128.
[10] Zhao G P, Y ang S L. Analytical solutions for rock stress around square tunnels using complex variable theory[J]. International Journal of Rock Mechanics&Mining Sciences,2015, 80:302-307.
[11]耿继原,唐治,朱小景,等.基于矩形巷道应力特征点的空间数据分析[J].安全与环境学报,2016,16(5):158-163.
[12]李明,茅献彪.基于复变函数的矩形巷道围岩应力与变形粘弹性分析[J].力学季刊,2011,32(2):195.
[13]袁林,高召宁,孟祥瑞.基于复变函数法的矩形巷道应力集中系数黏弹性分析[J].煤矿安全,2013,44(2):196-199.
[14]宁德义.基于复变函数法的深部矩形巷道围岩的黏弹性研究[J].煤矿安全,2015,46(5):43-45.
[15] Huo H,Bobet A,Fernández G,et al. Analytical solution for deep rectangular structures subjected to far-field shear stresses[J]. Tunnelling and Underground Space Technology incorporating Trenchless Technology Research, 2006, 21(6):613-625.
[2]李铀,袁亮,刘冠学,等.深部开采圆形巷道围岩破损区与支护压力的确定[J].岩土力学,2014,35(1):226-231.
[3]岳高伟,袁军伟,冯帆.梯形断面掘进巷道围岩稳定性数值模拟[J].煤矿安全,2012,43(11):45-47.
[4]杨丽红,何蕴增.无限平面矩形开孔的应力场分析[J].哈尔滨工程大学学报,2002,23(2):106-110.
[5]赵凯,刘长武,张国良.用弹性力学的复变函数法求解矩形硐室周边应力[J].采矿与安全工程学报,2007,24(3):361-365.
[6]郭力,王剑波,李宁.矩形巷道应力集中系数的弹性分析[J].金属矿山,2008(2):45-48.
[7]施高萍,祝江鸿,李保海,等.矩形巷道孔边应力的弹性分析[J].岩土力学,2014,35(9):2587-2593.
[8]何峰,唐治,朱小景,等.矩形巷道围岩应力分布特征[J].数学的实践与认识,2015,45(20):128-134.
[9]陈凯,唐治,崔乃鑫,等.矩形巷道围岩应力解析解[J].安全与环境学报,2015,15(3):124-128.
[10] Zhao G P, Y ang S L. Analytical solutions for rock stress around square tunnels using complex variable theory[J]. International Journal of Rock Mechanics&Mining Sciences,2015, 80:302-307.
[11]耿继原,唐治,朱小景,等.基于矩形巷道应力特征点的空间数据分析[J].安全与环境学报,2016,16(5):158-163.
[12]李明,茅献彪.基于复变函数的矩形巷道围岩应力与变形粘弹性分析[J].力学季刊,2011,32(2):195.
[13]袁林,高召宁,孟祥瑞.基于复变函数法的矩形巷道应力集中系数黏弹性分析[J].煤矿安全,2013,44(2):196-199.
[14]宁德义.基于复变函数法的深部矩形巷道围岩的黏弹性研究[J].煤矿安全,2015,46(5):43-45.
[15] Huo H,Bobet A,Fernández G,et al. Analytical solution for deep rectangular structures subjected to far-field shear stresses[J]. Tunnelling and Underground Space Technology incorporating Trenchless Technology Research, 2006, 21(6):613-625.