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中文摘要：
基于有限元计算结果，将边坡稳定性问题转化为图论中寻找最短路问题。通过引入图论中解决最短路问题的Dijkstra算法到搜索边坡最危险滑动面及其安全系数中去，对Dijkstra算法作了一定的改进，建立了一种新的边坡稳定性分析方法——基于Dijkstra算法的极限平衡有限元方法。通过一算例对该法进行验证，计算得的安全系数和危险滑动面位置与推荐答案基本一致，说明该方法应用于边坡工程的可行性。将该方法应用于糯扎渡水电站右岸泄洪洞出口边坡的稳定性分析，与极限平衡法和强度折减法作了比较。研究表明，该方法计算得到的安全系数介于极限平衡法和强度折减法之间；危险滑动面位置与这两种方法计算得到的危险滑动面位置基本一致，该方法应用于复杂岩体边坡的稳定性分析可行。最后，对于逆坡向发展的滑动面，以洛古水电站右岸边坡的稳定性分析为实例，研究了逆坡向发展的滑动面滑动力计算方法：比较分析3DEC和该方法的计算结果，说明该方法适用于逆坡向发展的滑动面的稳定性分析。
英文摘要：
Based on the calculated results of finite element method, the problem of slope stability could be converted into searching for the shortest path in graph theory. A new method of slope stability, limit equilibrium finite element method based on Dijkstra algorithm, was established by applying the improved Dijkstra algorithm which was an algorithm to seek the shortest path in graph theory to search for the minimum safety factor of slopes and the position of most dangerous sliding plane. A classical slope case was specialized to validate this method. The safety factor of slopes and the position of most dangerous sliding plane according to this method were basically consistent with the propositional answer so its feasibility was proved. This method was applied in the stability analysis for the slope of the outlet of the flood discharge tunnel in the fight bank of Nuozhadu Hydropower Station. It was shown that the safety factor of slopes from this method was between that of the limit equilibrium method and that of the strength reduction method, and the position of dangerous sliding plane was basically consistent with that of these two methods. This method could be applied in the stability analysis of complicated rock slopes. Finally, with regard to the sliding surface developing opposite to the slope direction, it was illustrated how to compute the stress of the sliding surface through an example in the stability analysis of the fight bank slope in Luogu Hydropower Station. Comparson between the computed results of 3DEC and those of this method shows that the present method is suitable for the stability analysis of the sliding surface developing opposite to the slope direction.
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