基于中性点理论,考虑围岩峰后剪胀效应及破坏形式,推导了瞬时稳态下全长锚固锚杆轴向正应力和剪应力表达式,系统性地分析了孔口处锚杆端头轴力和残余黏聚力、剪胀系数和应变软化系数对锚杆杆体轴向正应力、剪应力以及中性点位置的影响。研究结果表明:锚杆轴向正应力沿杆体内端点至外端点呈现出先增大后减小的变化特征,且应力曲线在弹性区与峰后破坏区呈现出明显的差异性;锚杆剪应力沿杆体内端点至外端点呈现先减小后增大的变化特征,且在弹塑性交界处的连续与否与围岩剪胀系数和剪切刚度密切相关;锚杆轴向正应力和剪应力均随着残余黏聚力的增大而减小,随着剪胀系数与应变软化系数的增大而增大;同时,锚杆杆体轴向正应力和外端点侧剪应力均随着孔口处锚杆端头轴力的增大而增大,内端点侧剪应力随着端头轴力的增大而减小。中性点位置随着残余黏聚力的增大呈现出先增大后减小的变化特征,当残余黏聚力大于某一临界值时中性点位于弹性区,反之,位于峰后破坏区;此外,中性点位置也随着剪胀系数、应变软化系数的增大而减小。

Based on the neutral point theory,considering the dilatancy effect and different post-peak failure models of surrounding rock,the formulas of both axial normal stress and shear stress of fully anchored bolts are derived under the condition of stable equilibrium state and the influence of bolt axial force on the end and surrounding rock parameters (residual cohesion,dilatancy coefficient and strain softening coefficient) on axial normal stress,shear stress and neu- tral point is systematically analyzed. Research results prove that the axial normal stress along the bolt shows the varia- ble characteristics of first increase and then decrease from the inner endpoint to outer endpoint,and the stress curves in the elastic zone and the post-peak failure zone show obvious differences;the dilatancy stress along the bolt shows the variable characteristics of first increase and then decrease from inner endpoint to outer endpoint and the change fea- tures of shear stress at the interface between elastic and post-peak failure zone are closely related to the dilatancy coef- ficient and shear stiffness of surrounding rock;the normal stress and dilatancy stress decrease with the increasing residual cohesion and conversely increase with the enlarged dilatancy coefficient and strain softening coefficient;and mean- while with the enlarged bolt axial force on the end,the axial normal stress and the lateral shear stress increase while the inner shear stress decrease;the neutral point shows the variable characteristics of first increase and then decrease with the increasing residual coefficient,and when the residual cohesion is larger than a certain critical value,the neu- tral point is located in the elastic region,otherwise,the neutral point is in the post-peak failure region;in addition,the neutral point decreases as the dilatancy coefficient and strain softening coefficient. The results can provide a theoretical basis for the support design of the fully anchored bolt under the condition of different properties of surrounding rock.

1 全锚锚杆-围岩相互作用力学模型

2 全锚锚杆-围岩相互作用受力分析

   2.1 基本方程

   2.2 围岩应力、变形与峰后破坏区半径的确定

   2.3 全长锚固锚杆受力计算

3 全长锚固锚杆受力影响因素

   3.1 工程条件

   3.2 残余黏聚力对锚杆受力的影响

   3.3 剪胀系数对锚杆受力的影响

   3.4 应变软化系数对锚杆受力的影响

   3.5 稳态下锚杆端头轴力对其受力的影响

4 结论