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基于Schwarz-Christoffel变换的圆形隧道围岩应力分布特征研究

崔建斌 姬安召 熊贵明

崔建斌, 姬安召, 熊贵明. 基于Schwarz-Christoffel变换的圆形隧道围岩应力分布特征研究[J]. 应用数学和力学, 2019, 40(10): 1089-1098. doi: 10.21656/1000-0887.390326
引用本文: 崔建斌, 姬安召, 熊贵明. 基于Schwarz-Christoffel变换的圆形隧道围岩应力分布特征研究[J]. 应用数学和力学, 2019, 40(10): 1089-1098. doi: 10.21656/1000-0887.390326
CUI Jianbin, JI Anzhao, XIONG Guiming. Research on Surrounding Rock Stress Distributions for Circular Tunnels Based on the Schwarz-Christoffel Transformation[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1089-1098. doi: 10.21656/1000-0887.390326
Citation: CUI Jianbin, JI Anzhao, XIONG Guiming. Research on Surrounding Rock Stress Distributions for Circular Tunnels Based on the Schwarz-Christoffel Transformation[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1089-1098. doi: 10.21656/1000-0887.390326

基于Schwarz-Christoffel变换的圆形隧道围岩应力分布特征研究

doi: 10.21656/1000-0887.390326
基金项目: 甘肃省自然科学基金(17JR5RM355)
详细信息
    作者简介:

    崔建斌(1972—),男,教授,硕士(通讯作者. E-mail: cuijb0658@163.com).

  • 中图分类号: O241

Research on Surrounding Rock Stress Distributions for Circular Tunnels Based on the Schwarz-Christoffel Transformation

  • 摘要: 隧道围岩应力还原到实际区域的变换方法被越来越多地应用到工程实践中,对复杂形状围岩体内的隧道围岩应力计算方法和隧道围岩稳定性的研究具有重要的实践指导意义.该文建立了不规则岩体中开挖圆形隧道的力学模型,运用复变函数理论,通过映射函数Schwarz-Christoffel变换,得到复平面单位圆到隧道所处多边形岩体的映射函数,在复变函数数域内分析了多边形岩体应力的求解步骤,运用弹性力学理论等推导了不规则岩体中圆形隧道的复变应力函数Φ(ξ)和φ(ξ)的表达式,并得出围岩体任一点应力分量σρ和σθ的解析通式.通过具体算例分析可知,岩体形状对圆形隧道的稳定性有较大的影响,隧道所处4种形状下的围岩体最大应力值分布规律为:顶底板的最大应力值从六边形、五边形、四边形、圆形围岩体依次减小,帮部的最大应力值从圆形、四边形、五边形、六边形围岩体依次减小.
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出版历程
  • 收稿日期:  2018-11-26
  • 修回日期:  2019-03-13
  • 刊出日期:  2019-10-01

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