针对评估二级边坡稳定性问题,相较于迭代求解法,边坡稳定性图表提供了一个快速且便捷的方式。基于极限分析上限定理,构建二级边坡整体和局部破坏机构,引入孔隙水压力系数r_u,推导了破坏机构内外功率表达式,求解出二级边坡处于极限平衡状态下c/(γH)和tanφ关系曲线,即极限状态曲线(g-line)。根据g-line图表法,绘制出一系列二级边坡稳定性图表。通过对比验证了稳定性图表的有效性,探讨了边坡孔隙水压力、边坡几何形状及内摩擦角对边坡稳定性及其破坏模式的影响规律。结果表明:孔隙水压力会导致极限状态曲线向外移动,降低边坡稳定性;边坡破坏模式受边坡几何形状影响,凸形边坡及凹形边坡易发生局部破坏,孔隙水压力作用下局部破坏范围扩大;随着土体内摩擦角增大,临界滑动面向坡面移动,整体破坏逐渐转变为局部破坏。利用所建立的边坡稳定性图表可以简单快速得到边坡稳定安全系数及相应的破坏模式,为类似边坡工程稳定性的评估提供一定的参考。

Slope stability charts offer a rapid and efficient alternative to the iterative method for assessing the stability of two-stage soil slopes. Employing the upper bound theorem of limit analysis,the global and local failure mechanisms were constructed for two-stage soil slopes. By incorporating the pore water pressure coefficient r_u,the expressions for internal and external work rates of the failure mechanism were derived,and the relationship curves between c/(γH) and tanφ for two-stage soil slopes in ultimate equilibrium state were obtained,referred to as the limit state curve (g-line). Based on this g-line,a series of two-stage soil slope stability charts were developed. The validity of these charts was confirmed through comparative analysis,and the effects of slope pore water pressure,geometry,and internal friction angle on slope stability and failure modes were systematically investigated. Results reveal that pore water pressure leads to the outward shift of the limit state curve,reducing slope stability. The failure mode of slopes is significantly influenced by their geometric shapes: convex and concave slopes are susceptible to local failures,with the extent of local failure expanding under the influence of pore water pressure. Additionally,as the internal friction angle of soil increases,the critical sliding surface shifts toward the slope surface,transitioning from global to local failure. The developed slope stability charts enable the simple and rapid evaluation of slope’s safety factors and corresponding failure modes,providing a valuable reference for stability assessments in similar slope engineering projects.