渗流条件下隧道锚注复合围岩体的解析方法

Analytical method for surrounding rock reinforced by bolts-grouting in tunnel under seepage

锚注法是富水隧道工程中常见的地层加固和止水工法,目前仍缺乏可以同时考虑锚杆−围岩力学相互作用和注浆防水抗渗作用的解析理论。以径向锚注复合围岩体为研究对象,基于达西定律和应力均布法将注浆加固后围岩内的孔隙水压力以及锚杆对围岩的相互作用力代入被加固围岩的应力平衡方程,构建出锚注复合围岩体微分方程,求解出复合围岩体及原岩的渗流场、位移场、有效应力场及锚杆轴向应力场的解析解并进行有限元验证和对比。对比结果表明:解析结果与有限解结果一致;与仅注浆的工况相比,锚注加固可改善围岩的应力状态。然后,基于所得解析解,揭示并讨论了锚注加固参数、支护力、二衬抗渗压力等参数和条件对隧道锚注复合围岩体安全系数的影响规律。规律指出:锚注范围、锚杆密度因子及支护力的增加使安全系数分别以先快后慢、准线性及先慢后快的趋势提高;二衬抗渗压力的增加虽然可减小涌水量,但不利于隧道的稳定。最后,基于所提出的解析解给出了锚杆的参数优化设计方法并给出算例。上述研究成果可为渗流隧道的锚注加固设计提供解析理论参考。

Bolts-grouting is a common reinforcement and waterproofing method in water-rich tunnel engineering.At present,there is still a lack of analytical theories that can simultaneously consider the mechanical interaction between rockbolt and surrounding rock,as well as the waterproof and impermeable effects of grouting.Based on Darcy’s law and"smeared"method,a differential equation of rock bolts-grouting composite surrounding rock was established by substituting the pore water pressure in the surrounding rock after grouting reinforcement and the interaction force between the rockbolt and the surrounding rock into the stress equilibrium equation of the reinforced surrounding rock.By solving the proposed differential equation,the closed-form solutions for pore pressure,displacement,and effective stress on bolts-grouting composite surrounding rock,and stress on the rockbolt are obtained and compared with numerical solutions and the solutions of other scholars.The comparison results show that the analytical results are consistent with the finite element solution;and bolts-grouting reinforcement can improve the stress state of surrounding rock compared with grouting only.Furthermore,based on our closed-form solutions,and the effect of bolts-grouting reinforcement parameters,support pressure,impermeability pressure of lining,and diameter of the tunnel on safety factor is elaborated.These laws indicate that with the increases of bolts-grouting range,rockbolts density factor and supporting pressure,the safety factor increases in the ways of first fast then slow,quasi-linear and first slow then fast,respectively.The increase of impermeability pressure on secondary lining can reduce the water inflow,but it is not conducive to the stability of the tunnel.Finally,based our closed-form solutions,we propose the method of parameter optimization for the bolts-grouting reinforcement in the tunnel as well as case study.