KL展开在渗流场随机分析中的初步应用

Application of Karhunen-Loeve Expansion in Stochastic Analysis of Seepage Field

在水力特性参数空间变异性的影响下,渗流场具有一定程度的不确定性。分析了随机场KL展开的特点,阐述KLME渗流随机分析方法的基本原理,发现利用KL展开的均方收敛性和摄动方法的渐进收敛性,并将随机偏微分方程转化为递推的确定性偏微分方程组求解,提高了计算效率;对非饱和渗流场进行随机数值模拟,考虑了非饱和渗透函数的参数场之间不相关、正相关和负相关3种情形,分析表明参数场之间的互相关性对渗流场的统计特征具有较大影响。

There is some degree of uncertainty in seepage field with the influence of spatial variability of hydraulic parameters. The characteristic of KL（Karhunen-Loeve） expansion of random field is analyzed and the principle of KLME method for stochastic analysis of seepage field is presented. It is found that the KLME method has a good computational efficiency because of taking advantage of mean square convergence of KL expansion and asymptotic convergence of perturbation expansion, and transforming the random partial differential equation to a set of recursive deterministic partial differential equations. The stochastic simulation of unsaturated flow is conducted, and the uncorrelated, perfectly positive correlated and negative correlated three cases between parameters of unsaturated hydraulic function are studied. The study result shows that mutual-correlation between hydraulic parameters has large effect on statistics of seepage field.