基于突变理论的单根锚杆脱黏分析

针对工程中单根预应力锚杆的脱黏失效问题，基于突变理论提出一种研究的新思路。在建立简化力学模型的基础上，推导出锚固界面的非线性剪切滑移模型；视预应力锚杆为弹性体，根据弹性理论得出锚杆的总势能；引入突变理论，将锚杆势函数化简为尖点突变模型的标准形式，构建锚杆失效的临界判据，并进行脱黏分析。结果表明：所建非线性剪切滑移模型可以合理考虑锚固界面的软化特性；拉拔荷载作用下，锚杆杆体与周围注浆体的界面剪应力分布逐渐演化为单峰曲线，直至极限状态下整个锚固界面发生软化破坏；推导出的临界松动位移理论公式简单实用，可为研究单根预应力锚杆的脱黏失效提供参考。通过对工程算例进行验算分析，证明所提方法是合理可行的。

Debonding analysis of a single anchor using catastrophe theory

A new method for analyzing the debonding problem of a single prestressed anchor is proposed based on the catastrophe theory. A simplified nonlinear shear slip model of the anchorage interface is proposed. The total potential energy of the anchorage system is obtained using the elastic theory based on the assumption that the anchor is an elastic body. The catastrophe theory is introduced to simplify the energy function of anchor to the normal form of cusp catastrophe model. A failure criterion of anchor is established and the debonding analysis is conducted. The results show that the softening behavior of the anchorage interface can be reasonably described by the established nonlinear shear slip model. The distribution of the shear stress between the rod body and the surrounding grout gradually evolves into a single peak curve with the increasing drawing load, and the whole anchorage interface softens until damages occur at the ultimate state. The proposed theoretical formula for critical loose displacement is simple and practical and may provide theoretical tools for analyzing the debonding of a single prestressed anchor. Finally, the rationality and feasibility of the method proposed is also examined through an engineering project.