Air permeability variations explained by microscopic structure

Macroscopic measurements showed, as expected, that the air permeability increased with air-filled porosity. We also observed positive credible Bayesian ρ between log(ka) measured at various h and microscopic indicators of the porosity, although only log(ka,-70 kPa) was positively correlated to µCT_PO. Given the X-ray µCT image resolution, µCT_PO should be representative of the air-filled PO

Results & Discussions: the field experiment

63

measured at h = -1 kPa although the soil samples were scanned at h = -70 kPa. The choice to scan soil samples at h = -70 kPa was a compromise between the fact that all the potential visible porosity should be air-filled and avoiding cracks due to drying, and this particular correlation suggests that all the potential visible porosity was indeed air-filled. In their study, Katuwal et al. (2015b) and Naveed et al. (2016) both observed a power-law function between, respectively, ka(-2 kPa) or ka(-3 kPa) and µCT_PO. The µCT_PO calculated on their images is equivalent to the Large_PO on our images as previously stated, and we also reported positive correlations between Large_PO and log(ka). Therefore, the difference between µCT_PO and Large_PO might be the part of the PO that should have drained at low negative potential (from the capillary law), but was actually drained at higher negative potential (due to unusable pathways). We refer to Hunt et al. (2013) to name that part of porosity, the inaccessible porosity. This assumption was confirmed by the credible correlations between the inaccessible PO and several microscopic parameters that express a notion of pore network complexity. We previously pointed out that drawback when calculating SWRC from the X-ray µCT data: the connectivity was not taken into account. We here confirmed that the pore network connectivity play a role in the desorption process.

The best regression models calculated on the calibration data (BF) and applied on the validation data reported that the best explaining variable for all measures of log(ka) (RRMSE) was the average pore volume of the smallest pores (Avg_Svol).

That parameter might be seen as a limiting factor, and this suggests that ka was more related to pores size distribution than porosity. Figure 33 displays log(ka, -70kPa) as a function of Avg_Svol and the distribution of the 25 and 75% regression model quantiles are rather narrow. The RRMSE equaled 1.256; or 0.0649 when the two worst predicted validation data points were not taken into account. The RRMSE for log(ka, -30kPa) and log(ka, -10kPa) were around 0.800 with one bad validation data point, and the RRMSE for log(ka, -7kPa) was very high (8.154) with three badly predicted data points out of five. The combination of Avg_Svol and average pore volume of all pores (Avg_Vol) performed slightly better in some cases, and slightly worse in others. Figure 33 shows the predicted log(ka) from Avg_Svol and Avg_Vol versus the observed log(ka) values. Although the RRMSE were acceptable, the regression model distributions (the error bars represent the 75% regression models quantiles) were high which inducing large uncertainty. That combination of two explaining variables was, in all cases, the best regression model of two explaining variables models. Other important explaining variables were the average coordination number (Avg_Z), the proportion of isolated porosity (IPO), the average pore volume of the biggest pores (Avg_Bvol) and the combination of µCT_PO and Large_PO.

Figure 33. Upper graph: logarithmic air permeability measured at a water matric potential of -70kPa (ka) versus the average pore volume of the smallest pores (Avg_Svol). Lower graph:

the predicted logarithmic air permeability (ka) from the average pore volume of the smallest pores (Avg_Svol) and all pores (Avg_Vol) versus the observed logarithmic air permeability.

Error bars represent the 75% regression model quantiles.

Results & Discussions: the field experiment

65 5.3.4. Practical conclusion and discussion

Studying the soil with X-ray µCT is widespread, but studying it with a small voxel size (43³ µm³) is not. First, a pertinent observed link was the positive relationship between the average volume of the biggest pores and that of the smallest ones, suggesting dependence between pores of different volumes.

Then, on one hand, we confirmed previously observed results, such as the better prediction of SWRC near saturation from X-ray µCT derived pore size distribution, although the pore network connectivity was not taken into account. The determination of SWRC through pressure plate measurements are likely more representative of the in-situ soil hydrodynamic, but these are not free of artefacts; for example, air entrapment might result in uncomplete saturation leading to inaccurate estimation of the air-filled macroporosity. We also confirmed that the microscopic global connectivity explained the saturated hydraulic conductivity. On the other hand, we observed unprecedented relationships, such as the degree of anisotropy and fractal dimension also explaining the saturated hydraulic conductivity (with some limitations). It is therefore tempting to combine these three indicators to generate information that could be used across scales and to eventually better estimate Ks.

That value is indeed important when it comes to the prediction of the hydraulic conductivity curve (Vogel and Roth, 1998). We also observed that the average volume of the smallest pores (between 4 x 10⁵ and +/- 8 x 10⁷ µm³) best explained the air permeability; we eventually suggested that parameter works as a limiting factor.

Identifying global parameters that convey the complexity of the pore network is a motivating goal to reach. For example, these parameters could be used for the generation of phenomenological pore network models (e.g. Vogel and Roth, 1998;

Köhne et al., 2011), which in turn could be used for the simulation of fresh equations linking physics and biology to explain water and air fluxes within the soil (Hunt et al., 2013). The accurate characterization of the SWRC is important for the study of life in soil (e.g. microbial development being water content-dependent in Davidson and Janssens, 2006; soil fungal growth in Falconer et al., 2012), as well is the accurate characterization of the soil air permeability (e.g. plant growth in Ben-Noah and Friedman, 2018). Conversely, soil life affects the soil hydrodynamic properties. For example, besides physically modifying the soil structure or the water dynamic by uptake, the root system influences the soil water retention capacities and transport properties by modifying the spatial liquid phase configuration through the physical properties of mucilage (Daly et al., 2017; Pascal et al., 2018). Or as well, microbial biofilms could affect the pores sections and the resulting soil fluid velocities (Kerboas et al., 2018). Soil structure and functions form a single whole, and a comprehensive understanding of the soil water and air dynamic could be achieved when physical and biochemical processes will be coupled and simulated together.

5.4. Research question #2: How do the microscopic parameters