基于双曲线模型的锚杆受力分析与临界锚固长度计算  

Stress Analysis and Critical Anchorage Length Calculation of Anchor Based on Hyperbolic Model

作　　者：朱彦鹏[1,2,3] 娄国庆 黄安平 吴林平 成栋 ZHU Yanpeng;LOU Guoqing;HUANG Anping;WU Linping;CHENG Dong(School of Civil Engineering,Lanzhou University of Technology,Lanzhou 730050,China;Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education,Lanzhou 730050,China;Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province,Lanzhou 730050,China)

机构地区：[1]兰州理工大学土木工程学院,甘肃兰州730050 [2]西部土木工程防灾减灾教育部工程研究中心,甘肃兰州730050 [3]甘肃省土木工程防灾减灾重点实验室,甘肃兰州730050

出　　处：《金属矿山》2024年第12期148-156,共9页Metal Mine

基　　金：国家自然科学基金面上项目(编号:51978321);教育部长江学者和创新团队支持计划项目(编号:IRT_17R51)。

摘　　要：对于锚杆锚固技术,主要是针对岩土体等密闭空间进行施工,对锚杆锚固段的受力情况并不完全清楚,施工质量难以保证。现有的锚杆锚固段应力分布解析解相对繁琐,且现行的锚固长度设计规范和经验法做出的设计长度相对保守。为明确拉力型锚杆锚固段的受力机理并得到拉力型锚杆临界锚固长度计算方法,基于锚杆轴力和锚头位移关系的双曲线模型,通过对锚杆微元体进行受力分析,对锚杆锚固界面非线性剪切—滑移模型进行推导。依据锚杆荷载传递基本方程求解锚固段荷载传递解析解,并通过具体算例探究在锚固范围内轴力和剪应力的变化趋势及分布形式。在荷载作用下锚杆锚固界面表现出明显的弹性黏结阶段、弹塑性变形阶段和加速软化阶段3个过程。剪应力的变化趋势及分布形式与轴力有所不同,随荷载的逐步增大表现为从单调、非线性递减曲线转变为存在峰值且峰值点逐渐向锚固深度方向传递的单峰曲线。假设锚杆锚固界面处于弹性阶段时剪应力沿锚固深度方向呈倒三角形分布的简化模型,得出拉力型锚杆的临界锚固长度计算公式并对计算结果进行验证。通过相关假设求解的荷载传递方程计算简洁、形式简单,能够进一步了解拉力型锚杆锚固界面的分布形式和传递规律,通过相应简化得到的临界锚固长度计算公式为锚固长度设计提供一定的参考价值。For the anchor bolt anchoring technology,it is mainly aimed at the construction of closed space such as rock and soil.The stress of the anchor bolt anchoring section is not completely clear,and the construction quality is difficult to guarantee.The existing analytical solution of the stress distribution in the anchorage section of the bolt is relatively cumbersome,and the design length made by the current anchorage length design specification and the empirical method is relatively conservative.In order to clarify the stress mechanism of the anchorage section of the tensile anchor and obtain the calculation method of the critical anchorage length of the tensile anchor,based on the hyperbolic model of the relationship between the axial force of the bolt and the displacement of the anchor head,the nonlinear shear-slip model of the anchorage interface of the bolt is deduced by analyzing the force of the micro element of the bolt.According to the basic equation of bolt load transfer,the analytical solution of load transfer in anchorage section is solved,and the variation trend and distribution form of axial force and shear stress in anchorage range are explored through specific examples.Under the action of load,the anchorage interface of bolt shows obvious three processes:elastic bonding stage,elastic-plastic deformation stage and accelerated softening stage.The variation trend and distribution form of shear stress are different from those of axial force.With the gradual increase of load,it changes from a monotonic and nonlinear decreasing curve to a unimodal curve with a peak and the peak point gradually transmits to the anchorage depth.Based on the simplified model that the shear stress is inverted triangular distribution along the anchorage depth direction when the anchorage interface of the anchor bolt is in the elastic stage,the calculation formula of the critical an-chorage length of the tensile anchor bolt is obtained and the calculation results are verified.The load transfer equation solved by the relevant ass

关 键 词：双曲线模型 非线性剪切—滑移模型 荷载传递特性 倒三角分布简化模型 临界锚固长度 

分 类 号：TD350[矿业工程—矿井建设]