基于严格极限平衡法的边坡安全系数上下限解  

The upper and lower-bound solutions of slope safety factor based on rigorous limit equilibrium method

作　　者：许佳君 朱大勇 姚华彦[1] 段海澎 XU Jiajun;ZHU Dayong;YAO Huayan;DUAN Haipeng(School of Civil Engineering,Hefei University of Technology,230009 Hefei,China;School of Civil Engineering and Architecture,NingboTech University,315100 Ningbo,China;Anhui Transportation Holding Group CO.,LTD.,230088 Hefei,China)

机构地区：[1]合肥工业大学土木与水利工程学院,合肥230009 [2]浙大宁波理工学院土木建筑工程学院,宁波315100 [3]安徽省交通控股集团有限公司,合肥230088

出　　处：《应用力学学报》2023年第3期580-588,共9页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.52079121);浙江大学宁波研究院大湾区环境岩土工程与基础建设新材料研究资助项目(No.20190909HK0202)。

摘　　要：严格极限平衡法满足所有的平衡条件,通常计算精度较高,但不能保证所有条块界面上均不违背摩尔-库仑准则,也不能保证充分发挥其抗剪强度,因此在理论上既不是下限解、也不是上限解,且计算结果一定程度上依赖于条块间作用力关系的假设。将安全系数作为设定值,以滑面正应力为未知变量,将水平地震力影响系数作为目标函数,根据边坡整体的水平力平衡条件,建立目标函数表达式;再根据边坡局部力平衡条件及条块间接触面、滑动面上的破坏准则建立不等式约束条件,根据边坡整体的竖向力与力矩平衡条件建立等式约束。目标函数及约束条件构成标准线性规划数学模型,应用单纯形法可以精确得到设定安全系数下的使边坡达到极限平衡状态的最大与最小水平地震力影响系数。通过迭代求解,得到既定水平地震力影响系数下的基于严格极限平衡的边坡安全系数上下限解答。算例计算结果表明,这种安全系数上下限解范围一般小于5%,且条块间作用力不违背破坏准则且充分发挥抗剪强度,因此计算结果更可靠,且理论上更为严密。The rigorous limit equilibrium method satisfies all of the equilibrium conditions,commonly with high accuracy.However,such a solution may represent neither the lower solution,nor the upper one,as the forces acting upon the interslice surfaces with some assumptions cannot ensure non-violation of failure criterion and full mobilization of those shear strengths,the results of which,to some degree,are dependent upon the assumptions made about the relationships between the interslice forces.In the paper,with the value of the factor of safety initially assumed,the normal stresses acting on the slip surface are taken as the unknowns and the coefficient of horizontal seismic forces as the objective function,the equation of the objective function is established according to the horizontal force equilibrium for the whole body of sliding mass.Then,the inequality constraint conditions are established according to the equilibrium condition of local sliding body and the failure criteria for both interslice surfaces and the slip surfaces,and the equality constraint condition is further established according to the vertical force and moment equilibrium conditions for the whole body of sliding mass.The equation of objective function as well as these constraint conditions thus constitutes a standard linear programming program;the maximum and minimal values of the coefficient of horizontal seismic forces,causing the sliding mass into rigorous limit equilibrium condition,can be precisely determined by using the simplex method.The final upper-and lower bound solutions for values of the factor of safety associated the prescribed coefficient of horizontal seismic force can be obtained by adopting an iterative procedure.The results of example study show that the difference between the upper and lower bounds of the factor of safety is within the range of 5%of the average value.Since the interslice forces on the all the interslice surfaces do not violate the failure criterion and,the shear strength of which is,to the largest extent,mobili

关 键 词：严格极限平衡 安全系数 水平地震力影响系数 上下限解 线性规划 优化 

分 类 号：TU431[建筑科学—岩土工程]