边坡稳定有限元可靠度分析的有限步长迭代法

LIMIT STEP LENGTH ITERATION METHOD IN FINITE ELEMENT RELIABILITY ANALYSIS OF SLOPE STABILITY

边坡稳定一阶可靠度分析的常用方法是验算点法,该方法在求解可靠指标时需要进行迭代计算。但是,对于边坡稳定的有限元可靠度分析,其功能函数形式常为高度非线性的,采用常规的验算点法可能会出现迭代计算不收敛、无法计算可靠指标的问题。将结构可靠度分析中的有限步长迭代法引入边坡稳定的有限元可靠分析,探讨有限步长迭代法中初始步长及步长调整系数的取值方法。在边坡的可靠指标计算方面,采用以基于滑面应力分析的弹塑性随机有限元理论为基础的方法。其中功能函数的形式是以考虑滑面方向的Mohr-Coulomb屈服准则来建立的;导数的求解采用的是基于增量切线刚度法及Aitken加速算法的偏微分法;边坡整体可靠指标取的是所有可能滑面的可靠指标的最小值。算例分析表明,将有限步长迭代法用于边坡稳定的有限元可靠度分析是可行的,该方法可保证在功能函数为高度非线性时可靠指标的迭代计算也能收敛,而且收敛速度较快,从而大大提高有限元可靠分析的计算速度。

Design point method,in which the iterative calculation is needed to computer the reliability index,is usually used for first-order reliability analysis of slope.However,there exist some cases when the iteration procedure is not covered in the design point method,since the limit state function is often highly nonlinear in the finite element reliability analysis.Therefore,limit step length iteration method（LSLIM）,which is used in the structural reliability analysis,is adopted to perform the reliability analysis of slope stability;and the methods to determine the initial step length and step adjusting coefficient are discussed.As to the calculation of reliability index,the method based on the technique of sliding surface stress analysis and the elastoplastic finite element theory is adopted.The type of the limit state function is set up according to the Mohr-Coulomb yield criterion which can consider the direction of the slip surface;and the derivatives of the stress to the basic stochastic variables of the slope are computed by using partial differential method based on the incremental tangent stiffness method and the accelerating convergence method of Aitken.The overall reliability index is defined as the smallest one of the whole possible sliding surfaces.Analysis results demonstrate that it is feasible to use LSLIM in the finite element reliability analysis of slope stability.LSLIM can assure the convergence of the iteration of reliability index even when the limit state function is highly nonlinear.