Finite element analysis of transient unsaturated flow: deterministic vs. stochastic approach

Abstract

This study implemented a large scale model for transient flow problems through the vadose zone derived using the stochastic approach to account for spatial variability of soil properties. The heterogeneity of natural soil formations were included in the effective hydraulic conductivity and specific moisture capacity. The set of stochastic differential equations was solved using a finite element formulation. A computer code was developed to implement the stochastic finite element formulation and a mesh generator was also developed to create the finite element mesh. Numerical simulations were performed for different scenarios using real data and the results for pressure head and volumetric water content distribution profiles at different times were compared to analytical and deterministic solutions, and experimental results. The stochastic perturbation approach showed to have the great advantage of being computationally much less expensive than the Monte Carlo method. The stochastic approach predicted significantly slower vertical movement and faster horizontal movement of the wetting front compared to the deterministic approach. The results agreed with field observations. The difference between stochastic and deterministic head pressure and volumetric moisture content profiles was significant and should not be discarded.