岩质边坡平面滑动锚固方向角的三维优化方法

以岩质边坡中常见的平面滑动为研究对象，研究其最优锚固方向角的计算方法。将锚索自由段单位长度能提供的最大抗滑增量作为目标控制变量，将坡面和滑动面特征参数与锚索设计参数作为优化控制自变量，通过坐标系转换得到的线性方程组对锚索的预拉力进行分解，并根据锚索支护时的三维模型建立了锚索自由段长度的优化公式，进而推导了用于锚固方向角三维优化的新计算方程。在该方程的基础上借助MATLAB软件中的fmincon函数对锚索加固方向不受限制时的锚固方向角进行了优化。最后通过锚固方向角敏感性分析与工程实例分析相结合，证明了推荐的最优锚固方向角计算方法的有效性与先进性。新方法有效地解决了边坡坡面与滑动面走向存在夹角时最优锚固方向角的求解问题，可进一步提高锚索的锚固效益，降低边坡的支护费用。 

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.