土质边坡空间临界滑动面搜索的优化算法

将二维均质土坡作为平面应变问题,假定滑动面是一个圆弧,将滑弧圆心与半径转变为后缘剪入点、坡脚剪出点和过后缘点滑弧切线与x轴的交点等3个点的横坐标,然后以这3个参数为变量,给定合理的取值区间,应用黄金分割法搜索二维边坡的最小稳定系数及相应的临界滑动面。进一步假定均质土坡的三维空间滑动面为一旋转椭球体,旋转椭球体的竖向中轴面和二维的圆弧面一致,给定椭球体不同的水平轴半径值,采用以上二维滑动面搜索方法可求出不同水平半径所对应的三维最小稳定系数及相应的椭球面。结果表明：边坡的三维稳定系数没有极小值,但有极限值;对于横向延伸长的无限边坡,三维稳定系数逼近二维稳定系数,当旋转椭球长轴与短轴之比大于3时,二者很接近,边坡稳定性可简化为二维来分析;对于受地形、地下水等条件约束的短边坡,三维效应明显,在考虑实际边界条件的情况下按三维来分析。

Optimistic Method for Searching the Spatial Critical Slip Surface of Earth Slopes

Generally,two-dimensional uniform earth slope is considered as a plane strain problem and the slip surface is supposed as a circle arc.Here the coordinates of the center and the radius of the slip circle are presented by three abscissas of top-point,toe-point（at which the slip circle intersects with the surface line） and point of intersection between the x-axis and the line being tangential to the circle at the top-point.The golden block optimization method is applied to search the minimum factor of safety and the corresponding slip circle with the three free variables of the abscissas as given proper domains for them,respectively.Furthermore,three-dimensional slip surface is supposed as a rotational ellipse whose vertical trace is a circle,which is equivalent to the two-dimensional slip circle.After giving series of horizontal radius of the ellipse,the minimum factor of safety and the corresponding ellipse at a series of given horizontal radius are calculated with the method mentioned above in two-dimensional slip surface.The results suggest that three-dimensional factor of safety has a limit other than a minimum.For a slope lengthen laterally enough longer,the factor of safety of three-dimensional approaches that of two-dimensional;as the horizontal radius is more than 3 times of vertical radius for the slip ellipse,the slope stability can be simplified as two-dimensional problem.But for a slope with finite length,such as limited by topography,ground water,etc.,the three-dimensional effect is prominent,three-dimensional analysis should be applied with consideration of boundary conditions.