基于矢量和法的边坡三维极限平衡稳定分析法

Limit equilibrium analysis method based on vector sum method for 3D slope

对于具有复杂几何特征的边坡问题,用二维极限平衡理论难以得到与实际相应的分析结果.基于矢量和法安全系数定义,提出了能满足所有条柱3个力的平衡和滑坡体3个整体力矩平衡的严格通用极限平衡分析法.通过侧向剪力系数和侧向剪力分布函数对条间力进行假定,考虑所有条间剪力对安全系数的影响.利用滑体力的平衡条件和边界条件分别得到条柱各行和各列的安全系数,再利用滑体整体力矩平衡条件确定侧向剪力系数.将条柱底面剪力矢量和的反方向作为潜在滑动方向,通过抗滑力和滑动力在其上的投影之和之比确定整个坡体的矢量和安全系数.典型算例验证了方法的合理性,计算结果表明,完全考虑条间力作用将提高边坡的稳定安全系数.

The 2D limit equilibrium method is not suitable to analyze the stability of slope with complicated geometry. Based on the definition of vector sum factor of safety, a general limit equilibrium method, which satisfies the three force equilibriums for all columns and the three moment equilibriums for total failure mass, was proposed. The lateral shear factors and lateral shear distribution functions were introduced to simplify the interslice force distribution, and all interslice forces were taken into account in calculating the safety factor. The safety factors for each row and column were obtained by force equilibriums and boundary conditions for total failure mass, and the lateral shear factors were determined by solving the torque--equilibrium equations for total failure mass. The vector sum factor was determined according to the vector characteristics of forces against the tendency direction which is the opposite direction of the sum of the shears along the sliding surface. A classical example was adopted to validate the presented method. The numerical results showed that fully consideration of interslice forces improves the safe factor of 3D slope.