基于改进差分进化算法的三维边坡锚固位置优化

Optimization of anchorage location of three dimensional slopes based on improved differential evolution algorithm

基于改进的差分进化算法,在三维锚固力计算基础上考虑锚固力的三维空间分布状态,对三维边坡锚固位置进行合理优化,从而有效节约锚杆数量。利用集中力作用下的半无限弹性空间内一点应力解答,将锚固力等效叠加到边坡滑面正应力和剪应力上,由此推导了关于锚固位置坐标的锚固力函数,并以此作为锚固位置优化的目标函数。对于标准差分进化算法(DE)的改进,将自适应差分进化算法与一般约束乘子算法(PHR)结合,使算法能够解决锚固边坡约束优化问题。算例和工程实例表明,在边坡加固安全系数相同且单根锚杆受力保持不变的情况下,通过本文方法优化锚固位置能节约20%~25%的锚固点数量,该方法可为工程应用提供参考。

Based on the improved differential evolution algorithm,considering the 3D spatial distribution of anchoring force through calculation of the 3D anchoring force,the anchorage position of 3D slope is optimized reasonably to save the number of bolts.By using the stress solution of one point in the semi-infinite elastic space under the action of concentrated force,the anchoring force is superimposed on the normal stress and shear stress of the slope surface.Then the function for anchoring force about the coordinates of the anchorage position is derived,and taken as the objective function of the optimization of the anchorage position.For the improvement of the standard differential evolution algorithm(DE),the adaptive differential evolution algorithm is combined with the general constraint multiplier algorithm(PHR)to solve the problem of constraint optimization of anchoring slopes.Numerical and engineering examples show that with the same safety factor of slope reinforcement and unchanged single anchoring force,through the optimization of anchorage position,the number of anchorage points can be saved by 20%~25%,and the proposed method can provide reference for engineering application.