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浅埋非圆形隧道开挖引起的力学响应解析解

文明

文明. 浅埋非圆形隧道开挖引起的力学响应解析解[J]. 西南交通大学学报, 2023, 58(1): 202-209. doi: 10.3969/j.issn.0258-2724.20210002
引用本文: 文明. 浅埋非圆形隧道开挖引起的力学响应解析解[J]. 西南交通大学学报, 2023, 58(1): 202-209. doi: 10.3969/j.issn.0258-2724.20210002
WEN Ming. Analytical Solution of Mechanical Response inShallow Non-circular Tunnels[J]. Journal of Southwest Jiaotong University, 2023, 58(1): 202-209. doi: 10.3969/j.issn.0258-2724.20210002
Citation: WEN Ming. Analytical Solution of Mechanical Response inShallow Non-circular Tunnels[J]. Journal of Southwest Jiaotong University, 2023, 58(1): 202-209. doi: 10.3969/j.issn.0258-2724.20210002

浅埋非圆形隧道开挖引起的力学响应解析解

doi: 10.3969/j.issn.0258-2724.20210002
基金项目: 国家重点研发计划(2017YFC0805401);国家自然科学基金(51738002);中央级公益性科研院所基本科研业务费(20220502)
详细信息
    作者简介:

    文明(1989—),男,助理研究员,研究方向为交通工程建设安全,E-mail:wenming@bjtu.edu.cn

  • 中图分类号: TU45

Analytical Solution of Mechanical Response inShallow Non-circular Tunnels

Funds: Supported by the National key R&D Program of China(2017YFC0805401);National Natural Science Foundation of China(51738002)
  • 摘要:

    浅埋非圆形隧道的力学分析对城市地铁隧道的施工安全具有重要意义,其求解难点在于如何考虑重力场的影响以及圆环域保角映射函数的确定.为此,在复变函数理论框架下通过重构解析函数的表达,提出了重力条件下浅埋非圆形隧道力学分析的解耦保角映射方法,该方法将解析函数拆分成两组子函数,并采用不同的局部坐标系进行表达,两组子函数可以分别表达地表边界内与隧道边界外的应力与位移场,同时地表边界与隧道边界也可以单独进行保角映射;利用快速Fourier变换将用于确定解析函数的边界条件方程转化为频域方程进行求解;将本文方法应用于浅埋隧道开挖引起的地表沉降分析. 研究结果表明:隧道形状会对地表沉降的大小造成显著影响,其主因素来源于隧道的高跨比;隧道埋深会同时对地表沉降量以及沉降槽宽度产生影响,埋深越小其敏感程度越大;侧压力系数的改变对地表沉降槽的宽度影响较小;与有限元方法相比,本文方法的程序体量极小、计算速度更快且精度更高.

     

  • 图 1  浅埋非圆形隧道力学分析模型

    Figure 1.  Mechanical model of shallow non-circular tunnel

    图 2  常规方法的保角映射

    Figure 2.  Conformal mapping in the conventional method

    图 3  浅埋隧道的解耦保角映射

    Figure 3.  Decoupling conformal mapping for shallow tunnels

    图 4  浅埋非圆形隧道力学分析(单位:m)

    Figure 4.  Mechanical analysis of shallow non-circular tunnel (unit:m)

    图 5  隧道边界环向应力分布对比

    Figure 5.  Comparison of hoop stress distributions attunnel boundary

    图 6  隧道开挖引起地表沉降的影响因素分析(单位:m)

    Figure 6.  Influencing factors analysis of the ground settlement due to tunnel excavation (unit:m)

    图 7  隧道形状对地表沉降的影响

    Figure 7.  Influence of tunnel shape on ground settlement

    图 8  隧道埋深对地表沉降的影响

    Figure 8.  Influence of buried depth on ground settlement

    图 9  侧压力系数对地表沉降的影响

    Figure 9.  Influence of lateral pressure coefficient on ground settlement

    表  1  矩形隧道应力计算结果对比

    Table  1.   Comparison of stress for rectangular tunnel

    有限元法本文方法
    网格尺寸/m应力/MPa项数/项应力/MPa
    0.120.13 301.80
    0.061.80 602.70
    0.032.401202.70
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-01-05
  • 修回日期:  2021-04-16
  • 网络出版日期:  2022-09-23
  • 刊出日期:  2021-04-22

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