地震作用下预应力锚索加固顺层岩坡极限分析

Limit analysis of bedding rock slopes reinforced by prestressed anchor cables under seismic loads

针对地震作用下预应力锚索加固顺层岩坡典型模型,提出了一种地震作用下预应力锚索加固顺层岩坡的极限分析改进方法,该方法考虑了边坡极限状态时锚索的受力变化。基于岩体刚性假设并考虑滑移过程锚索受力变化,结合极限平衡法推导出边坡加固预应力锚索的受力变化公式;地震作用仅考虑地震波传播至滑动面时产生的透射波对边坡稳定性的影响,从功率的角度出发,结合极限分析上限法与强度折减法,考虑预应力锚索受力变化,推导出地震作用下预应力锚索加固顺层岩坡的动安全系数计算理论公式;结合算例,采用考虑与不考虑滑移过程锚索受力变化两种计算方法,分析了在不同入射波波幅、入射角度及滑动面黏聚力、内摩擦角条件下两种方法计算结果的差异。算例结果表明:考虑与不考虑滑移过程锚索受力变化计算方法,计算得出的动安全系数变化规律一致,但考虑滑移过程锚索受力变化的改进计算方法得出的动安全系数动态变化幅度明显更小,反映了锚索的抗震作用效果,可为地震作用下该类型岩坡的预应力锚索加固设计分析提供参考。

An improved limit analysis method was proposed for the bedding rock slope reinforced by pre-stressed anchor cables under seismic loads, according to their typical models. Especially, this improved method considered the force variation of anchor cables when the slope was in a limit equilibrium state. First, based on the assumption of the rigid rock mass and the limit equilibrium method, the formula of the force variation of anchor cables was derived according to the force changes of anchor cables during the sliding process. In this study, the earthquake effect only referred to the influence of the transmitted waves on the stability of the slope when the transmitted waves were generated in the propagation process of the seismic wave into the sliding surface. Second, from the perspective of power, a theoretical formula was derived for calculating the dynamic safety factor of bedding rock slope by combing with the upper bound limit analysis method and the strength reduction method. Finally, in the case study, we analyzed the difference of dynamic safety factors by using two methods with or without considering force variations of anchor cables in the sliding process. Moreover, this study discussed the calculation results by using these two methods under the variations of amplitudes and incident angles of P wave, and the variations of cohesion and friction angles of sliding surface, respectively. The results show that the variation laws of dynamic safety factors obtained by these two methods are consistent. However, the variation degree of dynamic safety factors by the improved method is significantly lower, which indicates that the anti-seismic effect of anchor cables has been fully reflected. This study can provide references for the design and the stability analysis of bedding rock slope reinforced by pre-stressed anchor cables under seismic loads.