土坡滑坡侵蚀稳定性评价的解析方法

滑坡是土坡重力侵蚀最普遍的一种形式，其稳定性分析中的圆弧条分法在工程实际中被广为应用。但该方法的具体计算过程烦琐，而且需要反复试算，存在着不确定性。将土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，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。通过几何关系将稳定系数转化为一个距离参数t的一元函数求得参数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，可最终求得最危险滑动面的位置及相应的稳定系数。

An Analytical Method for Earth Slope Stability Assessment of Landslide

The circle sliced method of analysis of earth slope stability analysis under gravity erosion is widely employed in engineering practice. However, it involves a complex calculation process, and the identification of a potential slip surface is associated with uncertainty. First, on the two dimensional section of slope, the ground surface is regressed as linear equations, while the slip surface is defined by a circle equation; then the accumulation can be substituted by integration with the equation of the Fellenus method. From this the analytical formula was derived. An alternate method for identifying the most likely slip surface is to convert the factor of safety to a function of a parameter of length t, aided by a geometric relation. If it is supposed that the first derivative of the function equals zero, it is possible to solve the equation to get the value of t. Accordingly, the minimum factor of safety and the corresponding radius of the slip circle can be defined. As differential positions for the top point and the thrust point of the slip surface were supposed, the minimum factor of safety and the corresponding slip circle can be defined.