An effective medium approximation and Monte Carlo simulation in subsurface flow modeling

An effective medium approximation and a refined Monte Carlo simulation procedure for solving the stochastic groundwater flow problem are presented. The effective medium approximation permits one to solve the stochastic groundwater flow problem in a single run to generate the expected pressure head field. The proposed effective hydraulic conductivity expression for the effective medium is of the same form as the local Gardner’s equation and is easy to use.

The refined Monte Carlo simulation procedure uses analytical means to estimate the sample size by controlling the error incurred in using the sample average in place of its population mean at a chosen confidence level. This estimator consistently performs well. Also, a variance reducing estimator which is different from the simple average for pressure head is developed. This estimator takes advantage of the correlation between the saturated conductivity and the pressure head distribution to reduce the output variance and is unbiased. This reduced variance results in a smaller width of uncertainty about the predicted pressure head. Both the effective medium approximation and the Monte Carlo approaches perform well when applied to several problems.