基于下限原理有限元的强度折减法

Evaluation of strength reduction factor by lower bound limit analysis using finite element method

对于岩土工程中常用的强度折减系数,其规划问题是非线性的,不能直接利用线性规划进行求解。基于四边形单元的下限原理有限元法,根据强度折减系数与超载系数近似符合双曲函数的特点,通过调整强度参数使得超载系数逼近于1[1],可将边坡稳定性分析中常用的强度折减系数的非线性规划求解转化为线性规划求解问题。分析表明,采用拟合双曲线插值法求解强度折减系数的计算效率高于常规的二分法及割线法,且具有较好的收敛性;该方法能够充分利用当前高效的线性规划算法,便于工程应用。

For the strength reduction factor commonly used in geotechnical engineering,its lower limit programming problem is nonlinear and can’t be solved directly by linear programming.Based on the lower limit method and the feature of strength reduction factor and overload factor,the strength reduction factor can be obtained by adjusting the shear strength when the overload factor approach to 1,and thus linear programming algorithm can be fully used.It is shown that the fitted hyperbolic curve method is more efficient and has larger convergence range than conventional methods,such as bisection method and secant method.Suggested method can take full advantage of the efficientcy of linear programming,and is also suitable for application in engineering.