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

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.