强度折减有限元法中的单元阶次影响分析

Effect of element order on strength reduction finite element method

强度折减有限元法是当前较为有效的边坡稳定性评价方法,且应用越来越广泛。但影响强度折减有限元法的因素有很多,单元阶次是其中比较重要的一个。通过3个经典算例,这些算例分别是二维地基承载力问题、二维边坡和三维边坡问题,分析了单元阶次的选择对强度折减法的影响。计算结果表明:随着单元的增多,线性单元和二次单元都从大于真实解的一侧来逼近真解;相对于二次单元,由于线性单元过"刚",因此,会过高地估计安全系数,对于实际工程会偏于危险,且误差大,二次单元的误差是线性单元误差的1/8左右。在采用系统最大位移收敛与否的评判标准的基础上,利用二次单元来进行强度折减分析,则可以弥补这种线性单元的不足,得到更加合理的安全系数。二次单元比线性单元更适合于强度折减有限元法。

Strength reduction technique by finite element method is an effective method for slope stability evaluation; and it has been used more and more widely. There are many factors influence the result of this method; the order of finite element is an important one of them. The effect of element order on the strength reduction method is analyzed through three classical examples, i.e. 2D foundation problem, 2D slope stability problem and 3D slope stability problem. The results show that both linear element and quadratic element will approach to the exact solution from the upper side as the number of elements increases; but for linear element is too ＇rigid＇; and it will overestimate the safety factor, so it is dangerous for engineering practice. The error with linear element is about eight times larger than that of quadratic element under the same meshes. The shortage of strength reduction method with linear element can be made up by replacing the linear element with quadratic element based on the convergence of the maximum displacement in the system as the stability criteria. Quadratic element is more suitable than linear element for the shear strength reduction finite element method.