Three-dimensional optimization method for the anchorage direction angle of plane sliding in rock slope

The calculation method of the optimal anchorage direction angle of the common plane sliding in rock slope is studied. The maximum anti-sliding increment that unit length of the free segment of anchor cable can provide is considered as target control variable and the characteristic parameters of slope surface and sliding surface and the anchor cable design parameters treated as the optimization control independent variables.The anchorage force of the anchor cable is decomposed through the system of linear equations obtained by means of coordinate system transformation, and the optimal formula for the length of the free segment of the anchor cable is established from the 3D model of anchor cable supporting. Then a new three-dimensional optimization calculation equation for the anchorage direction angle of the anchor cable is derived. Based on the equation, the fmincon function in MATLAB is used to optimize the anchorage direction angle when the anchor cable reinforcement direction has no restrictions. Finally, through the combination of sensitivity analysis of anchorage direction angle and engineering example analysis, the validity and advancement of the calculation method of the optimal anchorage direction angle recommended in this paper are proved. The new method solves the problem of solving the optimum anchorage direction angle effectively when the strike direction of slope surface and sliding surface are at an angle, which can further improve the profit of the anchoring of the anchor cable and reduce the support cost of the slope.