边坡稳定的非线性随机有限元加速收敛算法的研究

Studies on accelerating convergence method in nonlinear stochastic finite element analysis of slope stability

基于滑面应力分析的边坡稳定随机有限元可靠度分析方法,边坡整体可靠指标的求解包含多重循环,如可靠指标的迭代求解循环、非线性随机有限元迭代求解循环、滑面最小可靠指标的搜索循环等。因此,改进非线性随机有限元的迭代计算方法、减少其迭代计算次数对于提高整个程序的运行速度具有重要意义。本文以增量切线刚度法为基础,详细推导了基于修正的Aitken加速法的非线性随机有限元加速迭代公式,并将之应用于边坡稳定的可靠度分析。其中,可靠指标的迭代求解方法是有限步长迭代法。算例表明,本文方法合理可行;采用加速算法可明显减少随机有限元的迭代次数,加速程序的运行效率;若中心点法与有限步长迭代法所求的可靠指标值相差较大,则其对应的滑面位置也相差较大;反之,若中心点法与有限步长迭代法所求的可靠指标值很接近,则其对应的滑面位置也基本一致。

There is much iteration in the stochastic finite element reliability analysis of slope stability which based on the stress analysis of sliding surface, such as the iteration circulation of reliability indices, the iteration circulation of nonlinear stochastic finite element analysis and the searching circulation of the minimum reliability indices of all possible sliding surfaces. Therefore, it is very important to improve the solving method of nonlinear equations and to decrease the number of iteration. The nonlinear stochastic finite element accelerating formula was derived based on the modified Aitken formula and the method of incremental tangent stiffness and was applied to the reliability analysis of a slope. The method of reliability analysis was a limit step length iteration method （LSLIM）. It was demonstrated by a two-layer slope that the proposed accelerating method was feasible. It could reduce the number of iteration and improve the running speed greatly. As to the reliability indices, it was shown that if there existed large differences between the values of reliability indices obtained from the mean first order reliability method （MFORM） and LSLIM, there should be great differences in the locations of these corresponding sliding surfaces, and vise visa.