基于上限有限元原理的双曲线强度折减法

A Strength Reduction Method of Hyperbolic Iteration Based on Upper Bound Finite Element

相对于极限平衡法和有限元法来说,极限分析在边坡的稳定性分析中有着更严谨的理论基础和更明确的物理意义,但传统的极限分析上限法为了避免问题成为非线性规划,均是借助于超载系数来进行分析,而工程边坡用得最多的还是强度储备安全系数。针对这一问题,系统地介绍了极限分析上限有限元原理,并将强度折减技术引入到上限法,针对强度折减系数和超载系数满足双曲线的性质,用一种收敛速度更快的双曲线迭代法进行计算,克服了传统强度折减进行人工试算的不足,具有较高的收敛性。通过算例将所提方法与传统极限平衡法和有限元法进行对比,计算结果吻合度较高,说明了本方法的有效性。

Compared with limit equilibrium method and finite element method,limit analysis has a more rigorous and precise theoretical basis and clearer physical meaning in slope stability analysis.But traditional limit upper bound relies on the overload factor to avoid nonlinear programming whereas most engineering slopes are analyzed by using the factor of strength reduction.In view of this,we introduce the principle of limit upper bound of finite ele-ment analysis and introduce the strength reduction factor into the limit upper bound method.Since the relationship between strength reduction coefficient and overload coefficient is approximately hyperbolic,we present a hyperbolic iteration method to solve the strength reduction factor.This method has a faster convergence speed,and overcomes the shortage of traditional strength reduction method which needs artificial trials.The effectiveness of this method is proved by a numerical example compared with the limit equilibrium method and finite element method.