Polynomial Chaos expansion for subsurface flows with uncertain soil parameters

The effects of uncertainty in hydrological laws are studied on subsurface flows modeled by Richards' equation. The empirical parameters of the water content and the hydraulic conductivity are considered as uncertain inputs of the model. One-dimensional infiltration problems are treated and the influence of the variability of the input parameters on the position and the spreading of the wetting front is evaluated. A Polynomial Chaos (PC) expansion is used to represent the output quantities and permits to significantly reduce the number of simulations in comparison with a classical Monte-Carlo method. A non-intrusive spectral projection supplies the coefficients of the PC decomposition. Three test cases with different hydrological laws are presented and demonstrate that second order PC expansions are sufficient to represent our quantities of interest owing to smooth dependences for the considered problems. Our results show a correlation between the position and the spreading of the wetting front and an amplification of the input uncertainty for all models. For each test case, five configurations with variable initial saturation state are investigated. The global sensitivity analysis indicates that the relative influence of an input parameter changes according to the output quantity considered and the initial saturation of the soil. The impact of the assumed distributions for the parameters is also briefly illustrated.