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考虑锚杆作用的深埋软岩隧道黏弹塑性力学响应解析

赵南南 邵珠山 郑晓蒙 吴奎 秦溯

赵南南, 邵珠山, 郑晓蒙, 吴奎, 秦溯. 考虑锚杆作用的深埋软岩隧道黏弹塑性力学响应解析. 力学学报, 2022, 54(2): 1-14 doi: 10.6052/0459-1879-21-447
引用本文: 赵南南, 邵珠山, 郑晓蒙, 吴奎, 秦溯. 考虑锚杆作用的深埋软岩隧道黏弹塑性力学响应解析. 力学学报, 2022, 54(2): 1-14 doi: 10.6052/0459-1879-21-447
Zhao Nannan, Shao Zhushan, Zheng Xiaomeng, Wu Kui, Qin Su. Analytical approach to the viscoelasto-plastic mechanical response of deep soft rock tunnel considring the rockbolt reinforcement effect. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(2): 1-14 doi: 10.6052/0459-1879-21-447
Citation: Zhao Nannan, Shao Zhushan, Zheng Xiaomeng, Wu Kui, Qin Su. Analytical approach to the viscoelasto-plastic mechanical response of deep soft rock tunnel considring the rockbolt reinforcement effect. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(2): 1-14 doi: 10.6052/0459-1879-21-447

考虑锚杆作用的深埋软岩隧道黏弹塑性力学响应解析

doi: 10.6052/0459-1879-21-447
基金项目: 国家自然科学基金(11872287) 和陕西省重点研发计划(2019 ZDLGY01-10) 资助项目
详细信息
    作者简介:

    吴奎, 讲师, 主要研究方向: 隧道支护结构设计理论. E-mail: wukuigz@163.com

  • 中图分类号: U45

ANALYTICAL APPROACH TO THE VISCOELASTO-PLASTIC MECHANICAL RESPONSE OF DEEP SOFT ROCK TUNNEL CONSIDRING THE ROCKBOLT REINFORCEMENT EFFECT

  • 摘要: 深埋软岩隧道围岩表现出显著的塑性软化与剪胀特性, 而当下的理论分析很少同时考虑这两点, 导致预测结果与隧道实际变形行为存在一定误差. 为解决该问题, 本文基于Kelvin-Voigt流变模型和Mohr-Coulomb强度准则, 考虑了塑性阶段时围岩软化与剪胀特征, 并引入了掌子面空间约束效应, 建立了深埋软岩隧道黏弹-塑性计算分析模型. 进一步, 为考虑锚杆对隧道围岩的支护作用, 在理论模型中, 利用等效刚度法建立了加固围岩的力学模型. 结合围岩塑性半径与锚杆长度相对关系, 给出了6种工况下考虑锚杆加固作用的隧道黏弹塑性力学响应的时效解答. 此外, 通过数值解与理论结果的对比, 理论模型的正确性和有效性得到了较好的验证. 最后, 为研究锚杆支护对围岩的加固效果, 基于理论解答, 讨论了锚杆安装时间、锚杆刚度及开挖速度对隧道变形的影响. 结果表明: 在不考虑锚杆加固作用下, 开挖速度仅影响围岩前期变形的发展规律, 但对围岩的最终变形量几乎没有影响. 若不考虑塑性变形将大大低估围岩变形, 造成预测结果与实际情况偏差过大. 若隧道开挖速度越快, 锚杆的安装应尽量提前, 才能保证锚杆有效地发挥限制围岩变形的作用. 锚杆刚度与隧道位移存在一种亚线性关系, 且锚杆刚度的增加也能够延长围岩进入塑性变形所需的时间. 本文的研究结果对相关隧道的设计具有一定的指导作用.

     

  • 图  1  流变模型

    Figure  1.  Rheological model

    图  2  岩石应力-应变曲线图

    Figure  2.  Rock stress-strain curve

    图  3  考虑锚杆对围岩加固作用

    Figure  3.  The reinforcement of rockbolt on surrounding rock

    图  4  开挖距离与应力释放系数图

    Figure  4.  Diagram of excavation distance and stress release coefficient

    图  5  锚杆支护结构下围岩计算结构图

    Figure  5.  Calculation structure diagram of surrounding rock under unsupported structure

    图  6  围岩-锚杆力学模型示意图

    Figure  6.  Mechanical model of rockbolt-reinforced surrounding rock

    图  7  数值模型图

    Figure  7.  Numerical model

    图  8  虚拟支护力影响范围

    Figure  8.  Influence scope of virtual supporting force

    图  9  隧道洞壁径向位移解析解及与数值结果比较

    Figure  9.  Comparison of tunnel radial displacement between analytical and numerical results

    图  10  不同开挖速度工况对隧道径向位移的影响

    Figure  10.  Influence of excavation rate on tunnel radial displacement

    图  11  不同锚杆安装时间t1对隧道径向位移的影响

    Figure  11.  Influence of installation time of rockbolt on tunnel radial displacement

    图  12  不同锚杆刚度Eb对隧道径向位移的影响

    Figure  12.  Influence of anchor stiffness Eb on tunnel radial displacement

    表  1  围岩塑性区半径与锚杆加固区半径关系表

    Table  1.   Relationships between the radii of surrounding rock plastic zone and rockbolt-reinforced zone

    Working conditionRadius of plastic softening zoneRadius of plastic residual zoneRadius of bolt reinforcement area
    aR1>R
    bR <RP< R1R1> RP
    cRP≥ R1R<R1RP
    dRP>RsR1Rs< RPR1> R
    eRP> R1RRs< R1Rs <R1RP
    fRsRP< R1RRs< RPR1> RP
    下载: 导出CSV

    表  2  隧道计算参数

    Table  2.   Tunnel calculation parameters

    Mechanical parameters of surrounding rock and rock bolts
    G1/MPaG2/MPaη2/(MPa·d)Eb/MPaμSb/m2SθSZ/m2L/m
    20010010004.50 × 1050.35 × 10−40.04923
    σcpeak
    /MPa
    φpeak/(°)k/MPaσcres/MPahs
    3.18225.64001.74131.5
    Geometric parameters and loadsOther parameters
    R/mP0/MPamRL/mt1/dav/(m·d−1)
    5.63.60.734.68231
    下载: 导出CSV
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  • 收稿日期:  2021-09-15
  • 录用日期:  2021-12-24
  • 网络出版日期:  2021-12-25

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