端锚式锚杆–围岩耦合流变模型研究

Coupling rheological model for end-anchored bolt and surrounding rock mass

针对端锚式锚杆–围岩结构体在长时条件下支护作用的演化机制,建立了端锚式锚杆–隧洞围岩耦合作用的结构模型。进行了结构模型的基本假设:①圆形隧洞;②深埋;③各向等压原岩应力;④均质且各向同性黏弹性围岩模型;⑤一维黏弹性锚杆模型;⑥锚杆对围岩作用力整体为面力。基于基本假设建立了端锚式锚杆–围岩耦合流变理论模型。假设围岩和锚杆均为Maxwell模型时,求解了圆形隧洞围岩应力和位移的径向分布随时间变化的解析解,获得了锚杆轴力随时间演变的理论公式。基于锚杆(索)流变模型,进行了FLAC3D数值模拟软件的二次开发;并通过数值模拟与理论计算的对比分析验证了理论模型的合理性,分析了端锚式锚杆–围岩耦合流变规律及其影响因素。该模型对于研究地下隧洞的流变力学行为,分析锚固支护结构的长期稳定性,指导工程支护设计具有重要的基础理论价值。

A structural model for the coupling interaction of end-anchored rock bolt and rock mass is established by analyzing their long-term evolution mechanisms based on the following assumptions： （1） circular cross section; （2） deep tunnel; （3） 2, =1, i.e., axisymmetric problem; （4） homogeneous, isotropic and viscoelastic ground; （5） one-dimensional viscoelastic rock bolt; （6） the bolt forces are treated as two uniformly compressive distributed loads applied at both ends of the bolt. When the Maxwell model is chosen for describing the rheological behaviors of ground and rock bolt, the closed-form solutions are presented for a circular tunnel supported with end-anchored rock bolt. The analytical solutions are compared with the results obtained by the finite difference method through the secondary development of FLAC30. The comparisons show that the analytical solutions provide reasonable results for the end-anchored rock bolt with low to moderate spacings. Under the same rock properties, tunnel geometry and construction and reinforcement characteristics, the analytical and numerical solutions of two tunnels are obtained respectively supported by the rock bolt with different viscosity coefficients. The research shows there is an eigenvalue for the viscosity coefficient of rock bolt with regard to the specific tunnel supported by end-anchored rock bolt. When the viscosity coefficient of rock bolt is larger than the eigenvalue, the axial force of bolt increases with the time, and the rock bolt will play an active part in engineering reinforcement continuously. When the distribution of rock bolts around the tunnel perimeter is linked to the far-field stresses and the material parameters are adapted to the ground, smaller convergence and reduced reinforcement stresses are possible. The proposed rheological model will be useful in predicting the time-dependent closure and the support load and in optimizing support design for tunnels.