How pore structure non-stationarity compromises flow properties representativity (REV) for soil samples: Pore-scale modelling and stationarity analysis

Classic soil physics relies heavily on the concept of representative elementary volume (REV), which is necessary to perform upscaling from the studied soil samples and parameterize continuum scale hydrological models (e.g., based on Richards or Darcy equations). In this paper, we explore the boundaries of the classic REV concept and conventional representativity studies that claim REV for any given physical property, and that its values converge to a steady value with increasing sample volume. We chose two undisturbed soil samples of standard size from Ah and B horizons, subcropped two subvolumes within each of them and performed pore-scale flow simulations using binarized X-ray microtomography scans as input data. The volume of the simulation domains was 900(3)voxels, with a physical volume within two orders of magnitude of the whole soil core. Based on the 3D pore geometry images and the resulting flow velocity and pressure fields, we performed REV analysis for the saturated hydraulic conductivity and porosity. Although in general subvolumes showed classical REV behaviour (convergence of porosity andsaturated hydraulic conductance (K-sat)to plateau-like behaviour), their flow properties converged to different REV values. We also evaluated the stationarity of pore structures by computing the directional correlation functions to explain the observed non-unique behaviour. We concluded that neither of the studied samples can be considered to be representative due to their structural non-stationarity. We extensively discussed the implications of these results for the upscaling and parameterization of continuum-scale flow models. We argued that the plateau inK(sat)(or any other physical property) is a necessary, but insufficient, condition for the REV, which requires (at least) pore structure stationarity as an additional criterion. REV as a concept is much broader than previously anticipated and the possibility of establishing REVs in structured soils will require an analysis of tensorial flow properties with correct boundary conditions, multiscale soil structure imaging with stationarity analysis, and pore-scale simulations on fused multiscale images. Highlights K(sat)analysis within subvolumes showed classical REV behaviour but resulted in non-unique REVs for the soil samples studied Based on the stationarity analysis we argued that the conventional soil core samples studied were not REVs Plateau-like behaviour in physical properties is a necessary but insufficient condition for REV Soil structure information is necessary to properly establish REV or upscale flow properties