In this paper

a new method is proposed to calculate the optimal anchorage direction angle for wedge sliding in rock slope. Taking the maximum anti-sliding increment provided by the unit length of the free segment of anchor cable as the target control variable

the characteristic parameters of slope surface and two sliding surfaces and the anchor cable design parameters are adopted as the optimization control independent variables

the pre-tensile force of the anchor cable is decomposed through the linear equations system established through coordinate system transformation. Then a new three-dimensional optimization calculation equation for the anchorage direction angle is obtained. Based on the equation

for case of the anchor cable reinforcement direction is perpendicular to the strike direction of the slope

derivative method is used to optimize the anchorage direction angle. And when the anchor cable reinforcement direction has no restrictions

the fmincon function offered by Matlab is adopted to optimize the anchorage direction angle. Finally

through the comparation of calculation results and engineering measurement

the validity and advancement of the proposed calculation method of the optimal anchorage direction angle are proved. The proposed method can further improve the anchoring effects and reduce the total usage of the anchor cables and the the slope supporting costs.