Effect of element order on strength reduction finite element method

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.