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考虑倾角影响压力型锚索锚固段应力的近似理论分析
Approximate Theoretical Analysis of Stress in Anchorage Section of Pressure Cable Affected by Anchorage Angle
为了更加精确地研究压力型锚索的锚固机理,考虑平面应力状态的应力分析,基于明德林(Mindlin)理论解推导了压力型锚索锚固段注浆体所受压应力的近似理论解和锚固体与岩土层间剪应力的近似理论解,并进行了算例分析。研究结果表明:锚索倾角与压力型锚索锚固段注浆体应力分布曲线之间存在负相关关系,锚索倾角与锚固段注浆体应力峰值之间存在幂函数关系,且锚索倾角对锚固段注浆体所受压应力和锚固体与岩土层间剪应力的影响较大。所得研究结果进一步丰富了压力型锚索锚固技术的理论研究内容,可为新型锚固技术的开发应用提供一定的参考,也为压力型锚索加固岩土体设计提供理论支撑。
To more accurately investigate the anchorage mechanism of pressure cables,in consideration of plane stress conditions,we derived the approximate theoretical solutions for both the compressive stress of the grouting body of pressure anchor cable and the shear stress between anchor solid and rock-soil layer based on Mindlin’s fundamental solution. Through example analysis,we revealed an inverse relationship between the anchorage angle and the stress distribution curve of the grouting body, as well as a power function relationship between the anchorage angle and the peak stress of the grouting body in the anchoring section. The anchorage angle significantly influences both the compressive stress of the grouting body at the anchoring section and the shear stress at the interface between anchor solid and rock-soil layer. These findings not only enrich the understanding of the pressure cable anchorage mechanism but also provide valuable references for the development and application of new anchoring technologies. Additionally,they offer theoretical support for the design of pressure anchor cables in rock and soil engineering.
压力型锚索 / Mindlin理论 / 应力状态 / 锚固机理 / 锚索倾角
pressure anchor cable / Mindlin’s theoretical solution / stress state / anchorage mechanism / anchorage angle
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为更加精确地研究地震作用下压力型锚索的锚固机理,根据Mindlin基本解,结合单自由度体系的有阻尼强迫振动特点,推导了压力型锚索锚固段注浆体受到的压应力表达式和锚固段较软岩体与注浆体之间剪应力表达式。通过算例分析了简谐荷载的幅值、简谐荷载的圆频率以及低阻尼体系的阻尼比等因素对压力型锚索加固效果的影响。研究结果表明:简谐荷载的幅值和圆频率对压力型锚索加固效果影响较大,低阻尼体系的阻尼比对压力型锚索加固效果影响较小;简谐荷载的幅值与注浆体受到的应力呈线性关系;简谐荷载的圆频率与压力型锚索体系的有阻尼自振圆频率越接近,注浆体受到的应力越大。研究成果可为压力型锚索加固岩土体的抗震设计提供一定的理论参考。
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In the purpose of studying the seismic behavior of pressure-type cable in weak rock and soil under earthquake more accurately, the expressions of prestress and prestress loss under the coupling effect of prestress of anchor rope and creep of rock and soil mass were derived based on the material relaxation of steel strand subjected to long-term load. Furthermore, the expressions of equivalent compressive stress and equivalent shear stress of the anchorage segment of pressure-type anchor cable under circular uniform load were derived using pseudo-static method, Mindlin basic solution and integral simplification method. Case study demonstrated that the loss of prestress was large in the initial stage, stabilized in mid-stage and changed little in later stage, with the loss rate declining consistently. The equivalent stress of mortars in anchorage segment concentrated mainly within 0.5 m from the pressure plate. The maximum equivalent stress was in 0.1 m from the pressure plate rather than on the contact surface between pressure plate and mortars. The research findings enriched the theoretical research in regards to seismic design of pressure-type anchor cables, and offered some references for the reasonable seismic design of slope strengthened with pressure-type cable.
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In order to study the anchoring mechanism of the compression anchors in the loess area, the closed-form solutions for the interfacial shear stress distribution and axial stress distribution along the bond length were derived using the tri-linear model of bond-slip relationship. The related experimental data of the compression anchors were compared to validate the analytical model. The interfacial shear stress distribution by the derived solution is in a good agreement with the experimental results, which demonstrates the validity and reliability of the proposed analytical model. The results indicate that the interfacial stress distribution exhibits an exponential distribution, the interfacial stress is very high near the bearing plate, and reduces with increasing the distance from the bearing plate; the peak shear stress increases with the tensile loads. The research results herein can provide a theoretical basis for the design and calculation of this kind of compression anchors.
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