Scale and REV analyses for porosity and pore connectivity measures in undisturbed soil

Abstract

Soil samples with a volume of approximately 100 mL are commonly used for measuring soil properties needed to parameterize continuum models of transport processes in soils. The necessary assumption that the sampled soil volume corresponds to a representative elementary volume (REV) has only been occasionally tested. Furthermore, the few studies so far have focused on bulk properties such as porosity and bulk density and have not investigated the scale-dependence of pore-space connectivity, which is fundamental for transport properties such as the permeability of soil. In this study, we investigated the scale-dependence of morphologic properties of the soil pore-space in 25 undisturbed soil columns sampled from five different depths (8, 23, 33, 53 and 73 cm) from a field site in southern Norway (Skuterud). We conducted the analyses of scale-dependence on regions of interests of 40 × 40 × 40 mm3 from binarized X-ray images with a resolution of 40 µm. We focused our evaluation on imaged porosity and three measures of pore-space connectivity (the connection probability, the Euler-Poincaré number and the critical pore diameter). As pore network connectivity is scale-dependent and because the connectivity of large pores has a very strong impact on the soil permeability, we conducted our analyses considering three contrasting minimum pore diameters, namely 80, 250 and 500 µm.We found that the pore connectivity improved with scale, predominantly due to the presence of pores with diameters of less than 0.25 mm. This stresses the importance of image resolution in scale analyses. We moreover observed that both the mean and the standard deviation of the critical pore diameter increased with scale, which may explain why the mean and standard deviation of the saturated hydraulic conductivity are often found to increase with scale. We detected an REV range for the macroporosity between approximately 15 and 65 mm. This range decreased with an increase in the minimum pore diameter considered. However, we also found evidence contradicting the existence of the detected REV range for the macroporosity due to a lack of statistical homogeneity. No REV range could be found for the three investigated connectivity measures, probably because the evaluated scales were too small. Based on our results we conclude that larger soil samples should be used to measure soil properties and investigate processes that depend on the pore network connectivity, such as permeability or water flow and long-range solute transport. We recommend that future studies should investigate REVs for connectivity measures and investigate which REV criteria are most meaningful in a continuum modelling context. Such studies are needed to evaluate whether REVs for transport properties are common in soils. If not, flow and transport models that explicitly account for heterogeneity are necessary.