摘要
将渗透系数作为随机场引入泛函变分表达式中,应用小参数摄动法,推导建立了三维稳定渗流的随机变分原理和相应的随机有限元列式。并由此推导得到了水头、水力坡降的均值和方差表达式。为应用随机有限元方法对随机渗流进行分析提供了理论依据。最后,计算了一个典型堤防的水力坡降均值和标准差,分析了水力坡降标准差与渗透系数变异性之间的关系,结果表明此方法程序实施简便,计算效率较高。
The coefficient of permeability is treated as the random field and introduced into the functional variational formulations. The random variational principle and stochastic finite element formulas are developed using the small parameter perturbation method for the three-dimensional steady seepage. Furthermore, the mean value and standard deviation expressions of the water head and hydraulic gradients are derived. This provides a foundation for the analysis of the stochastic seepage with stochastic finite element method. In the example, the mean value and standard deviation of hydraulic gradient in a typical embankment are calculated. The results also analyzes the relation between the standard deviation of hydraulic gradients and the coefficient of variation of permeability.
出处
《工程力学》
EI
CSCD
北大核心
2006年第6期21-24,共4页
Engineering Mechanics
基金
高等学校博士学科点专项科研基金资助(20040294003)
关键词
工程力学
随机
有限元
渗流
变分原理
engineering mechanics
random
finite element method
seepage
variational principle
