中文摘要：

基于极限分析上限法和强度折减技术，根据边坡极限平衡状态下内外能耗相等原理，推导多级台阶式边坡安全系数极限上限表达式。编制序列二次规划法程序，通过搜索边坡最危险滑动面及其对应最小安全系数，探讨土体参数对多级边坡滑动面形态和位置的影响。研究结果表明：多级边坡滑动面形态和位置分布受无量纲参数ηcφ＝c／（γhtanφ）控制。当ηcφ为定值时，黏聚力 c 或内摩擦角φ任一值改变对滑动面位置均无影响，滑动面位置保持不变；当ηcφ增大时，边坡失稳模式由浅层破坏转变为深层破坏，滑动面由近坡面向边坡内部移动。同时，参数 tanφ／Fs 的值随着ηcφ增大而逐渐减小。ηcφ较小时，上陡下缓坡体外形不规则的边坡有可能发生局部失稳，且随着无量纲参数ηcφ的增大，边坡滑动面形态有从局部破坏逐渐变化为整体破坏的趋势。本文研究有助于工程实践中判断多级边坡潜在滑动面位置，快速确定多级边坡安全系数，对高大边坡工程实际的设计施工与防护具有实用价值。

英文摘要：

According to the condition of equating the power of external force to internal dissipation along the ve-locity discontinuities in limit state,the formula of safety factor of multi -stage slope for limit analysis upper bound method can be deduced with the theory of limit analysis upper bound method and the strength reduction technical.The influence of strength parameters on sliding surface of multi -stage slope is discussed by searching for the location of the most dangerous sliding surface and the minimum safety factor through sequential quadratic programming.From the analysis results,the pattern and the location of failure surface is determined by the di-mensionless parameter ηcφ=c/（γhtanφ）.If ηcφremains constant,the location of the critical slip surface is not affected by the cohesion c or internal friction angle φ.With the increase of ηcφ,the failure mode changes from shallow slip to deep slip and the sliding surface moves from the surface near slope to the side slope internal.The value of tanφ/Fs decreases gradually when the ηcφis increasing.The slope which upper gradient is greater than the lower ones is tend to collapse with minor ηcφ.Besides,overall instability is also tend to occur with the in-crease of ηcφ.It turns out to be helpful to judge the location of potential sliding surface and the safety factor of multi -stage slope,which is valuable in the design and construction of high slope engineering.