岩质边坡楔形体锚索加固方向角三维优化设计

以岩质边坡中常见的楔形体滑动为研究对象,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,将坡面和两组滑动面的特征参数与锚索设计参数作为优化控制自变量,通过坐标系转换建立线性方程组对锚索的预拉力进行分解,得到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,借助导数法和Matlab软件中的fmincon函数分别对锚索加固方向与坡面走向垂直的二维优化方式和锚索加固方向不受限制时的三维优化方式下的锚固方向角进行了优化。最后通过算例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。新方法可进一步提高锚索的锚固效益,减少锚索的总用量,降低边坡的支护费用。

Three-dimensional optimization design for the direction angle of anchor cable reinforcement in wedge rock slope

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.