基于失稳状态耗能最小原理的预应力锚索加固边坡稳定性上限解析

基于岩土塑性极限分析上限理论的基本原理，考虑预应力锚索的加固效应，分析了单预应力锚索加固措施条件下边坡的稳定性特性，并由此探讨了多预应力锚索共同加固边坡的稳定性能量分析方法。结合强度折减技术，采用内点迭代方法和序列二次规划优化迭代法对锚固边坡安全系数目标函数进行了能量耗散最小化意义上的优化计算。典型算例的分析计算表明：锚索加固效应可以有效地提高边坡的稳定性，预应力锚索设置位置对边坡安全系数、临界滑裂面位置和锚索长度有显著影响。综合考虑锚索设置位置对边坡安全系数和锚索长度的影响，单锚索的最优设置位置应位于边坡中下部区域。采用多排锚索加固既可以保证边坡的安全储备，也可有效避免局部稳定性问题。

Energy analysis method for slopes reinforcing with prestressed anchor cables based on minimum energy principle of instability state

The energy analysis method for stability analysis of slope reinforced by prestressed anchor cables is presented based on geotechnical plastic limit analysis theory, in which the reinforcing effect of prestressed anchor cables is taken into account. The iteration interior point method and sequential quadratic programming method (SQP) are used to calculate the objective function of safety factor incorporating the strength reduction technique and the minimum energy principle of the instability state. Typical example calculation and analysis show that the location of prestressed anchor cable has significant influence on slope safety factor, the location of critical slip surface and the prestressed anchor cable length. Considering the influences of the location of prestressed anchor cable on slope safety factor and length of anchor, the optimal settings of single anchor cable should be located in the lower slope region. Slope reinforced by multi-prestressed-anchor-cables can guarantee the security reserve of slope, and can avoid the local stability problem of slope effectively.