李同录, 邓宏科, 李萍. 2004: 对边坡稳定性分析圆弧条分法的改进. 工程地质学报, 12(S1): 433-438.
    引用本文: 李同录, 邓宏科, 李萍. 2004: 对边坡稳定性分析圆弧条分法的改进. 工程地质学报, 12(S1): 433-438.
    LI Tonglu, DENG Hongke, LI Ping. 2004: REVISION ON THE CIRCLE SLICED METHOD OF SLOPE STABILITY ANALISIS. JOURNAL OF ENGINEERING GEOLOGY, 12(S1): 433-438.
    Citation: LI Tonglu, DENG Hongke, LI Ping. 2004: REVISION ON THE CIRCLE SLICED METHOD OF SLOPE STABILITY ANALISIS. JOURNAL OF ENGINEERING GEOLOGY, 12(S1): 433-438.

    对边坡稳定性分析圆弧条分法的改进

    REVISION ON THE CIRCLE SLICED METHOD OF SLOPE STABILITY ANALISIS

    • 摘要: 边坡稳定性分析中的圆弧条分法在工程实际中被广为应用。但该方法在具体计算时存在两点困难:一是计算过程繁琐,在搜索最危险滑动面时,每给定一个滑动面,都要重新确定分条的边界和高度、宽度和分条数目等参数;二是潜在滑动面的不确定性,针对这一问题已有许多学者提出多种搜索最危险滑动面的方法,这些方法各有优缺点。本文针对这两方面的问题作了一些改进。首先是将边坡的地面线用分段直线方程表示,将滑动面用一圆弧方程表示,这样可以将原公式中的求和部分化为积分式,从而推导出了求解稳定系数的解析式。另一方面是提出了一种搜索最危险滑弧滑动面的简洁方法,该方法先固定圆弧滑动面的后缘点和剪出点,则稳定系数随过这两点圆弧的曲率而变化,通过几何关系将稳定系数的转化为一个距离参数t的一元函数,令该该函数一阶导数为零,求得参数t,并获得稳定系数极小值及其对应的滑动面。若变动后缘点和剪出点,重复以上计算,可最终求得最危险滑动面的位置及相应的稳定系数。

       

      Abstract: The circle sliced method of slope stability analysis is widely employed in engineering practice. But two aspects of difficulties are faced by engineers in using of the method. The first is complex of calculation process, such as for every supposed slip circle, the boundary of slip surface, the width and height of each slice as well as the number of slices have to be defined before computation one by one; The second is uncertainty of potential slip surface, there are some methods of searching the most possible slip surface proposed, each of the them has advantage and shortage. In this paper, the authors make significant revision related to the two aspects. First of all, on the two dimensional section of the slope,the ground surface is regressed as linear equations properly while the slip surface is supposed as circle equation, then the accumulation plus could be substituted by integration in the equation of Fellenus method, the analyzed solution was derived finally. On the other wise, a method for searching the most possible slip surface is suggested. We supposed the coordinates of top point and thrust point of slip surface as known, then the factor of safety varied with curvature of the circle through the two points. We could easily convert the factor of safety to a function of a parameter of length t by aiding of geometric method. Supposed the first derivative of the function equal zero, we could solve the equation to get the value of t . Accordingly the minimum factor of safety and the correspondent radius of slip circle could be defined. As we supposed differential position of top point and thrust point of slip surface, the most minimum factor of safety and the correspondent slip circle could be defined.

       

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