隧道围岩中全长粘结式锚杆受力的非线性分析

为分析隧道围岩中全长粘结式锚杆锚固界面剪切作用的非线性特性及其受力特性，建立了锚固界面剪应力与剪切位移的双曲正切函数模型，推导了围岩变形作用下全长粘结式锚杆的荷载传递方程，采用有限差分方法和Newton迭代公式建立了锚杆受力特性计算方法，并采用典型隧道工程锚杆试验实测结果进行了验证。在此基础上，分析了围岩变形作用下全长粘结式锚杆的轴力和界面剪应力分布特征，探讨了锚杆长度、界面剪切强度和初始剪切刚度、围岩位移释放系数等因素对锚杆受力的影响。研究结果表明：①双曲正切函数模型采用单一函数曲线刻画了界面剪应力与剪切位移的非线性关系及锚固界面剪切刚度演变规律，可有效描述隧道围岩中全长粘结式锚杆的受力特性；②锚杆锚固力随着锚固长度的增加而逐渐增大，但其锚固长度存在临界值；超过临界值后，锚杆锚固力基本不变；③随着界面剪切强度和刚度的增加，锚杆锚固力逐渐增大，中性点位置移向临空面一侧，界面剪应力向临空面和锚杆末端聚集；④围岩位移释放系数越小，锚杆支护后所提供的锚固力越大。实际工程中，宜根据围岩稳定状态及所需锚固力大小，合理确定锚杆支护时机和长度。

Nonlinear Analysis on Mechanical Behavior of Fully Grouted Bolt in Tunnels

In order to predict the mechanical behavior of a fully grouted bolt in tunnels,a novel interfacial model with hyperbolic tangent function to describe the relationship of shear stress and interfacial slip has been proposed in this study.Using this model,the load transferring equation of a fully grouted bolt that undergoes the surrounding rock deformation is formulated,and the calculation method for its mechanical behavior is developed by combining the finite difference scheme and Newton iterative formula.The correctness of the proposed interfacial model and calculation method is verified by the testing results of the bolt in a typical tunnel.Then,the distributions of the axial force and shear stress of the bolt induced by the surrounding rock deformation are studied,and the influence from the bolt length,interfacial shear strength and initial shear stiffness as well as the deformation releasing coefficient are illustrated and discussed.The results indicate that the proposed interfacial model with hyperbolic tangent function can effectively characterize the nonlinear relationship between the shear stress and interfacial slip as well as the evolution of the interfacial stiffness,so that it can predict the mechanical behavior of fully grouted bolt in tunnels.Increasing the length of the bolt can increase the anchoring force of the bolt,but there is a critical length for a bolt;Once exceeding this value,the change in the length of a bolt has insignificant influence on its anchoring force.With increases in the interfacial shear strength and initial stiffness,the anchoring force of the bolt gradually increased and the neutral point moves towards the tunnel.Simultaneously,the interfacial shear stress gradually accumulates toward both the tunnel and the far end of the bolt.The smaller the displacement releasing coefficient is,the greater the anchoring effect provided by the bolt is.In the engineering practice,it is advisable to reasonably determine the supporting time and the bolt length according to the stability of the surrounding rock and the required anchoring force.