拉力型锚杆锚固界面剪应力分布偶应力理论分析

锚杆锚固段界面剪应力分布规律是锚杆设计研究的重点，直接影响锚固效果。锚固段界面上的剪应力会引起界面附近的岩土体较大的应变梯度，而用经典弹性理论分析锚固段剪应力时没有考虑应变梯度。偶应力理论引进弯曲曲率，考虑弯曲效应对介质变形特性的影响，基于该理论建立平面应变问题的有限元计算模型，研究拉力型锚杆锚固段界面上的剪应力分布、界面附近的边界层效应和偶应力的尺度效应，并将偶应力理论的计算结果和经典弹性理论的计算结果进行比较。结果表明，在偶应力理论下，拉力型锚杆锚固段界面的剪应力和剪应变有所减小，特别是峰值处的剪应力减少明显；界面处的剪应力不再连续；界面附近的剪应变突变有所改善，出现一个过渡区域。特征长度减小，过渡区域变小，应变梯度增大，第二剪切模量对剪应力分布的影响不明显。

Analysis of shear stress near anchorage interface of tensile-type anchor with couple stress theory

Shear stress distribution in anchorage interface of anchor is the attention points of anchor design. It directly affects anchoring effect. Shear stress in anchorage interface will cause larger strain gradient in rock and soil near anchorage interface. But the strain gradient is not considered in classical elastic theory which is used to analysis shear stress in anchorage interface. Bending curvature is introduced into couple stress theory which considers the effect on the deformation characteristics of the bending. The finite element calculation model for plane strain problem was build up based on couple stress theory. For tensile-type anchor，shear stress in anchorage interface and the boundary layer effect near anchorage interface and scale effect of couple stress were studied. The results of couple stress theory are compared with the results of classical elasticity theory. The results show that the shear stress and shear strain near anchorage interface in couple stress theory are smaller than that in classical theory，especially at the peak of shear stress. The shear stress on interface is not continuous. But shear strain abrupt change on interface has been improved; and a transition region appears near the interface. The characteristic length decreases; transition region becomes smaller; but strain gradient becomes larger. The influence on shear stress distribution in anchorage interface of the second shear modulus is not obvious.