基于二维随机场在圆弧曲线上局部平均化的边坡可靠度分析

Slope reliability analysis based on local averaging of two-dimensional random field on an arc curve

土质参数随机场在边坡滑移面上局部平均后的"空间特性"值是控制边坡可靠性的主导因素。以边坡滑移面为圆弧为前提,基于随机场理论进行了公式推导,通过二维随机场在圆弧曲线上的一维局部平均得出了局部平均方差的计算式。以推导出的局部平均方差计算式为基础提出了适用于均质原状边坡的简便可靠度分析方法。方法首先通过少量确定性有限元分析经拟合得出极限状态曲线,然后经过一维局部平均方差计算边坡强度参数的"空间特性"统计指标,最后通过积分计算强度参数分布函数在极限状态曲线危险侧的面积得出边坡失稳概率。经与蒙特-卡罗随机有限元法进行对比表明,提出的基于二维随机场一维局部平均的边坡可靠度分析方法计算结果可靠,可为边坡可靠性分析提供一种新思路。

The local averaging value of the random field of soil strength parameters on the slope slip surface is the main factor that controls the reliability of a slope.Based on the theory of random field,a formula of the local averaging variance is derived by one-dimensional local averaging of two-dimensional random field on the arc curve,and then,a simple reliability analysis method for homogeneous undisturbed slopes is proposed.The method first estimates the limit state curve through a few deterministic finite element analysis,then calculates the statistical index of the slope strength parameters by the one-dimensional local average variance formula,and finally obtains the probability of slope instability by integrating the area of the distribution function of the strength parameters on the dangerous side of the limit state curve.Comparison between the developed method and Monte Carlo stochastic finite element method shows that the proposed method is reliable and can provide a new idea for slope reliability analysis.