基于安全性和经济性多目标优化的岩质边坡锚固计算方法

Rock slope anchoring calculation method based on safety and economy multi-objective optimization

以节理岩质边坡为研究对象,基于塑性力学的极值理论,将滑动面的安全系数和锚固造价共同作为目标函数,将锚固力方向、锚杆长度、结构面的剪力和法向力作为决策变量,结合岩块的平衡方程约束条件、结构面的屈服条件和锚杆的附加约束条件,建立安全性和经济性多目标的岩质边坡锚固非线性数学规划模型,最后采用线性加权和法求解多目标规划模型得到安全系数、锚固造价的最优值以及最优锚固角,该方法具有概念明确、计算精度高等特点。

Taking the jointed rock slope as the research object,the multi-objectives of safety and economy nonlinear mathematical programming model of rock slope anchorage is established based on the extreme value theory of plastic mechanics.This model uses safety coefficient of the sliding surface and the anchor cost as the objective functions,and the direction of the anchoring force,the length of the anchors,the shearing force and normal force of the structural plane as the decision variables.It combines the equilibrium equation constraint of the rock blocks,the yield condition of the structural plane and the additional constraints of the anchors.According to this model,the safety coefficient,optimal anchor cost and optimal anchoring angle are obtained using the linear weighted sum method.This method has the merits of clear concept and high calculation accuracy.