Random variational principle and finite element method in 3-d steady seepage

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.