均质土坡的圆弧滑动分析

Analysis of homogeneous soil slope slipping in circular arc

均质土坡圆弧滑动分析通常需要对圆心坐标和半径的3个参数进行搜索。通过分析圆心水平坐标即圆弧平移对失稳指数的影响,确认危险圆弧或通过坡脚,或圆心水平坐标由半径确定。利用不等式证明垂直边坡的临界滑面通过坡脚,且滑出角度大于内摩擦角。纯黏性边坡倾角大于arctan 2后圆弧滑面通过坡脚;而小于该角度圆心在坡面中垂线上,滑出角度?66.78°的圆弧在半径趋于无限时成为最危险滑面,相应的边坡临界高度为5.520c/γ,保持恒定。具体计算表明,内摩擦系数为0.05,0.1和0.2时,边坡倾角小于40°,34°和22°时最危险滑面不过坡脚,但相应的失稳指数与过坡脚滑面的数值相差不到2%;内摩擦系数大于0.3后最危险滑动圆弧都通过坡脚。就此而言,在评价均质边坡临界高度时直接对过坡脚的圆弧进行搜索即可。本文结果是基于数学分析得到的,可以作为边坡数值计算程序的参考。

The analyses of soil slope in arc slipping need to search three parameters of radius and coordinates of the arc center.By moving the slipping arc horizontally,it is found that the slipping arc must pass through the slope foot or the horizontal coordinate of its center is determined by the radius.It is proved that the slipping arc of vertical slope must pass through the slope foot,where the slipping angle is greater than the internal friction angle.For pure cohesion soil or no friction soil,when the slope angle is greater than arctan √2,the slipping arc passes through the slope foot;otherwise its center on the perpendicular line through the middle point of the slope face and the critical height is 5.520c /γ for the arc with infinite radius and slipping angle - 66.78° at the slope bottom.Based on the numerical calculation,the slipping arcs do not pass through the slope foot when the slope angles are less than 40°,34° and 22° for internal friction coefficient 0.05,0.1 and 0.2 respectively;but their critical heights are only 2 % less than the slipping arcs through slope foot.When internal friction coefficient is greater than 0.3,the slipping arcs pass through the slope foot.So only the arcs passing through slope foot are needed to calculate for the critical height of soil slope.