Uncertainty analysis and validation of the estimation of effective hydraulic properties at the Darcy scale

The determination of the hydraulic properties of heterogeneous soils or porous media remains challenging. In the present study, we focus on determining the effective properties of heterogeneous porous media at the Darcy scale with an analysis of their uncertainties. Preliminary, experimental measurements of the hydraulic properties of each component of the heterogeneous medium are obtained. The properties of the effective medium, representing an equivalent homogeneous material, are determined numerically by simulating a water flow in a three-dimensional representation of the heterogeneous medium, under steady-state scenarios and using its component properties. One of the major aspects of this study is to take into account the uncertainties of these properties in the computation and evaluation of the effective properties. This is done using a bootstrap method. Numerical evaporation experiments are conducted both on the heterogeneous and on the effective homogeneous materials to evaluate the effectiveness of the proposed approach. First, the impact of the uncertainties of the component properties on the simulated water matric potential is found to be high for the heterogeneous material configuration. Second, it is shown that the strategy developed herein leads to a reduction of this impact. Finally, the adequacy between the mean of the simulations for the two configurations confirms the suitability of the homogenization approach, even in the case of dynamic scenarios. Although it is applied to green roof substrates, a two-component media composed of bark compost and pozzolan used in the construction of buildings, the methodology proposed in this study is generic.