地震作用下锚固土质边坡稳定性解析

Solutions for stability of anchored earth slopes subjected to seismic loading

极限分析上限方法在边坡地震稳定性评价中受到了广泛关注,但已有研究成果均针对某一类具体边坡,获得的解析解往往不具有普遍适用性。以上限定理为基础,基于组合对数螺线的旋转破坏机制,采用拟静力法,推导了具有任意坡面几何特征、任意土层分布和多排锚加固的复杂边坡外功率与内能耗散率平衡方程。在此基础上,结合强度折减技术和最优化方法,提出了地震作用下多排锚加固复杂边坡的稳定性安全系数和屈服加速度系数解析式,并结合Newmark法求解了边坡的永久位移,发展了锚固土质边坡地震稳定性的通用极限分析上限方法。通过典型算例验证与对比分析,表明本文方法具有较高的精度和广泛的适用性,最后将这一方法应用于实际工程。

The limit analysis approach is paid more attention to in the stability analysis of slopes subjected to seismic loading. However, the solutions obtained from the approaches are in general limited to a designated slope or the same kind of slopes. It seems that a wide applicability of the solutions in their present form is rather difficult. Based on the kinematic theorem and the assumption of combined log-spiral rotational failure mechanism, the integral formulation for expressing the rate of external work rate due to soil weight and seismic loading is derived under the framework of pseudo-static method considering the complex geometrical configurations and the multilayer soils in slopes with multi-row anchors. Further, the work-energy balance equation is established, and the analytical expressions for the global factors of safety（FS） and the yield acceleration coefficient of anchored slopes are obtained by using the strength reduction technique combined with the optimization method. Moreover, the permanent displacement with Newmark＇s method is also solved. Several representative examples are employed to validate the analytical solutions, and some comparisons of the FSs and the corresponding critical sliding surfaces obtained by various methods are also made. The results show that the analytical approach can yield the high-accuracy solutions and is widely applicable to the seismic stability analysis of complex slopes with multi-row anchors. Finally, a practical case is analyzed using the proposed approach.