考虑锚杆作用的深埋软岩隧道黏弹塑性力学响应解析
ANALYTICAL APPROACH TO THE VISCOELASTO-PLASTIC MECHANICAL RESPONSE OF DEEP SOFT ROCK TUNNEL CONSIDRING THE ROCKBOLT REINFORCEMENT EFFECT
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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.Abstract: The surrounding rock of deep soft rock tunnel shows significant plastic softening and dilatancy characteristics. The ignorance of the coupling influences of these two characteristics in current studies leads to the inaccurate prediction results of tunnel deformation. In order to solve the problem, a viscoelasto-plastic calculation model of deep soft rock tunnel is established, based on the Kelvin-Voigt model and Mohr-Coulomb strength criterion. In this model, the plastic softening and dilatancy of surrounding rock are considered and the restriction effect of tunnel face is introduced as well. Furthermore, a mechanical model of rockbolt-reinforced surrounding rock is established by using the equivalent stiffness method, which takes the rockbolt reinforcement into account. Considering the relationship between plastic radius of surrounding rock and bolt length, analytical solutions for tunnel responses under the six conditions are provided. In addition, the reliability and effectiveness of the theoretical derivation are well validated by comparing numerical and analytical results. Finally, the reinforcement effect of rockbolt is discussed based on the analytical solution and a comprehensive parametric investigation is carried out, including the installation time and stiffness of rockbolt and tunnel excavation rate. Results indicate that without considering the rockbolt reinforcement effect, the excavation rate only poses the influence on the development law of early deformation of tunnel, and its influence on the final tunnel displacement can be ignored. The tunnel deformation will be greatly underestimated without considering the plastic deformation of surrounding rock, resulting in a large gap between the predicted and actual results. When the excavation rate is large, the rockbolt should be installed as earlier as possible, to ensure that the rockbolt can play an effective role inmiting surrounding rock deformation. There exists a sub-linear relationship between bolt stiffness and tunnel displacement, and the increase of rockbolt stiffness can prolong the time required for surrounding rock entering plastic deformation. The results of this paper can provide useful guidance for the similar projects.