土坡稳定性分析圆弧法的改进及实现

【作者】 邓宏科；

【导师】 李同录；

【作者基本信息】 长安大学 ， 地质工程， 2004， 硕士

【摘要】 圆弧条分法是边坡工程中常用的分析方法之一，计算过程主要分为两步：第一步假定一个滑动面，计算其稳定系数；第二步，变动滑动面位置计算稳定系数，寻找稳定系数最小的滑动面作为最危险滑动面。 本文在将条分转化为积分的基础上，对圆弧条分法作了以下改进： (1)复杂坡形时的处理。通常计算边坡时都将坡面简化为一条直线，实际中边坡坡面形状比较复杂，许多人工边坡还采用了分级放坡的坡形。本文采用直线方程分段描述边坡坡面，建立稳定系数的计算公式，适用于坡面为复杂形状的边坡计算。 当坡形比较复杂时，计算中某些圆弧可能穿过坡面，可以通过缩小过圆弧上端点的切线在x轴上的截距t的变化范围将滑动面限制在坡体以内。先求得过圆弧两个端点和坡面下凸拐点的圆弧中半径最小的一个，根据过该圆弧上端点的切线在x轴上的截距t_o确定t的变化范围(t_o,x_b)，t在此区间内的所有圆弧均在坡体内。 该算法也适合剪出口不在坡脚的情况。 (2)最危险滑动面及其稳定系数的确定。大量计算表明，当t在(t_o,x_b)上连续变化时，k-t，曲线是抛物线的一部分，可以借助数值方法求得极小值；x_b在坡顶连续变化或者x_a在坡脚以前连续变化时，k的值也具有相同的规律，亦可按照数值法计算极小值。依次变动t、x_b、x-a，在极小值中求极小值，最终求得稳定系数的最小值。这样既减少了计算的次数，也使得搜索的过程有系统性，适合编制程序进行计算。 (3)当坡体中的下卧层顶面不透水时，其接触面长期浸水软化，滑动面有可能从接触面的某个点沿接触面剪出，滑动面成为圆弧和直线的组合形状。可以将坡体土分为两部分，分别按照力的平衡和力矩平衡建立稳定系数计算公式，联立即可解得稳定系数。 依次变动t、x_a、x_b进行计算，在极小值中求最小值，最终可以求得潜在滑动面组合及其稳定系数。 针对以上改进，本文编制了计算程序，进行了算例计算，并和前人的计算结果做了比较，表明计算结果是可靠的。更多还原

【Abstract】 In the methods of slope stability analysis, circle slices method is used widely as it is simple and effective. The computation process has two basic steps: at the first, a slip surface is assumed and the factor of slope stability to this slip surface is calculated; second, after calculating a series of factors of assumed slip surfaces, the minimum one is token as the critical slip surface.On the former study, a integral formula has been deduced instead of slices dividing in calculating factor of stability. Some further improvements of the method have been completed in this paper as follow:(1) Computation of factor of slope stability in dip variable landform. Generally the slope surface is simplified to a straight line. Actually the slope surface is dip variable, and also many artificial slopes are step-shaped. So in this paper, the author use straight line to simulate the slope surface in subsections. The formula of factor of slope stability to analyse the slope with dip variable landform is deduced.To some slopes with dip variable landform, some assumed slip surfaces may intersected with slope surface, the situation could not be calculated correctly. So the slip surface is limited within the slope by adjusting the parameter t, t is the x-axis intercept of the tangent which passed through the upper extremity of the circular arc. Passed through the two extremity and the down-protruded inflexion of slope surface, the circular arc is searched which the radius is minimum, t0 correspond to this circular arc. Then the interval of t is confined in (t0,xb), then all circular arcs are within the slope corresponding t in this interval.This method can also be applied to the case that the lower extremity of he circular arc is not at the foot-point of the slope.(2) The determination of the critical slip surface and the corresponding stability factor. When t varied successively in interval (t0,xb), it is indicated that the curve of k-t is a segment of a parabola, so the minimum of k can be calculated by means of numerical method; when xb varied on upper ground of the slope or xa varied in front of the foot of the slope successively, the value of k have the same rule and the minimum can also be obtained by numerical method. So the minimum can be calculated at last if t, xb and xa is changed in turn. Computer program has been designed based on this method, which reduced the quantity of calculating and systematized the process of critical slip surface searching.(3) When there is some underlying aquiclude stratum, the interface is softened because of long-term soaked in water, so the shear failure may occur along the interface. Slip surface is made up of two segments: straight line and circular arc, and the slope can be divided into two segments correspondingly. Formulas of stability factor of the two segments by equilibrium of forces and equilibrium of moment could be set up respectively. The stability factor can be calculated by solving the simultaneous equations.Changing t, xa and xb in turn, the minimum stability factor and corresponding critical slip surface are worked out at last.To above-mentioned improvements, a program is designed and some examples are computed by this program. It is indicated that these results are credible by comparing these results with other results which had been worked out by former scholar.更多还原