Microscopic parameters

The aggregate porosity (µCT_PO) was larger than any of the other measures although its fractal dimension (FD), total pore network length (L) and number of pores (NP) were smaller (Table 9). This should come from pores larger relatively to its total size (Fig. 36). The comparison of the aggregate porosity indicators to the extrapolated ones (8.99³ µm³) for the same voxel size was not conclusive. It is likely that the hypothesis about the regular and continuous changes in µCT porosity and pore geometries across scales was not valid. As well, the comparison between the sample µCT porosity indicators and the extrapolated ones (21.5³ µm³) was not conclusive. The extrapolated µCT_PO is 150% higher while the number of pores (NP) is overestimated by 400%, the smaller average pore volume counteracts that effects. The hypothesis was that the µCT_PO would increase with resolution, however, the µCT_PO, NP (and therefore L and FD) decreased from the coarsened resolution (43³ µm³) to the original resolution (21.5³ µm³). The pores were likely not

30 mm 5 mm

Results & Discussions: the field experiment

69

distributed in the range made visible by the higher resolution (as shown in Fig. 34).

Peng et al. (2014) and Shah et al. (2016) observed higher porosity and number of pores with higher resolution but also noticed that the resolution effects on X-ray µCT images were certainly dependent on the soil type. In our case, the skeletonization process could have altered the pore decomposition leading to less identified porosity. The comparison of the images from the two resolutions is therefore uncertain. Houston et al. (2013b) also observed that an increase in resolution would increase the amount of noise, and Shah et al. (2016) reported that the partial volume effect artefact increases with resolution. Extra attention should therefore be brought to the image processing. Figure 37 presents the grayscale images with the identified pore space superimposed in white color. The segmentation process with the porosity-based method clearly identified less porosity on the X-ray µCT images at 21.5³ µm³, but we also see that some pores merged as previously (red circle, lower row of Fig. 37).

Table 9. Porosity indicators of the scanned sample (43³ and 21.5³ µm³) and aggregate (8.99³µm³), and from the extrapolation equations.

The degree of anisotropy (DA) increased between resolutions, as FD decreased.

We also observed in our Paper II a negative trend between DA and FD. This is inconsistent with Dal Ferro et al. (2013) who observed higher DA in soil cores than in soil aggregates. The extrapolated FD however increased with resolution due to the larger extrapolated porosity and number of pores. Regarding the sample with a 21.5³ µm³ voxel size, the porosity and number of pores decreased, so did FD. Regarding the aggregate, porosity increased but NP decreased as well as FD. The calculation of FD is dependent on the porosity but also on the number of boxes of the smallest size (Halley et al. 2004).

Figure 37. Upper row: Grayscale X-ray µCT images with the identified pore space in white.

Lower row: Zoom-in of the binary X-ray µCT images. The original resolution (21.5³ µm³) is on the left-hand side and the coarsened resolution (43³ µm³) on the right-hand side.

5.4.2.2. Connectivity indicators

From the coarsened resolution (43³ µm³) to the original one (21.5³ µm³), the proportion of isolated porosity (IPO) and the Euler number (ε) decreased, the number of coordination (Avg_Z) increased as well as the global connectivity (Γ) and the total surface of connections (Con_Surf), see Table 10. This is consistent with our previous observations (Fig. 34) where we hypothesized that medium sizes pore probably merged to form larger pores. The value of Γ reflects that almost all pores were connected to each other. Houston et al. (2013b), comparing soils at 26 and 54³ µm³, did not observe a clear pattern of ε’s evolution. Shah et al. (2016) observed that Avg_Z remained identical for some of their studied rock samples. Again, resolution effects are highly soil-type dependent. The smaller tortuosity with resolution is also consistent with the observed increased pore network connectivity and the fairly

Results & Discussions: the field experiment

71

constant L (Table 9). Regarding the soil aggregate, IPO also decreased, and Avg_Z and Γ also increased with resolution, although not proportionally to the resolution.

Again, inter-aggregate pores were contributors to the high connectivity observed at the sample scale and voxel size of 21.5³ µm³. Con_Surf and ε did not however increase (or decrease for ε) with resolution. This is likely due to the proportionally smaller number of pores (Table 9). The decrease in tortuosity is however consistent.

Table 10. Connectivity indicators of the scanned sample (43³ and 21.5³ µm³) and aggregate (8.99³ µm³).

43³ µm³ 21.5³µm³ 8.99³ µm³

IPO [%] 8.491 4.939 7.609

Avg_Z [-] 3.742 5.607 4.906

SC [voxel^-1] 0.283 0.209 0.172

Con_surf [mm²] 4420 93141 4377

Γ/IJ [-] 0.714 0.998 0.828

ε [-] 7226 6018 7559

τ [-] 1.280 1.253 1.205

5.4.2.3. Hydrodynamic predicators

Using the microscopic values from the X-ray µCT images at the original resolution (21.5³ µm³) to predict log(Ks) and log(ka) led to reasonable results between the 25- 50% quantiles of the regression models, in comparison to the 50-75% for the X-ray µCT images at the coarsened results (43³ µm³), see Table 11. As well, Shah et al. (2016) and Peng et al. (2014) concluded that coarsening the µCT images was sufficient to resolve Lattice-Boltzmann or Kozeny-Carman equations to evaluate sample permeability.

Table 11. Observed and predicted logarithmic values of the saturated hydraulic conductivity (Ks) and air permeability measured at a water matric potential of -70 kPa (ka) for sample #12. Predictions performed from the microscopic parameters extracted from the original resolution X–ray µCT images (21.5³ µm³) and coarsened resolution (43³ µm³) X-ray

µCT images.

log(Ks) [cm/d] log(ka) -70kPa

[µm²]

Laboratory measurements 1.062 1.802

Predicted from Γ [-] DA [-] FD [-] Avg_Svol [mm³]

25% -0.319 0.743 -3.265 1.391

43³ µm³ 50% 0.617 0.986 -0.347 1.8320

75% 1.564 1.224 2.418 2.260

25% 0.201 1.020 -3.585 1.115

21.5³ µm³ 50% 1.329 1.325 -0.782 1.504

75% 2.470 1.622 1.878 1.883

5.4.3. Practical conclusion and discussion

Studying X-ray µCT images at various resolutions leads to various identified pore spaces and various microscopic parameters values. Comparisons between resolutions are highly dependent on the image processing and the pore network decomposition, and the working resolution should ultimately depend on the final research purpose. As also observed by other researchers (for their case studies), it appeared that scanning at the highest possible resolution and then coarsening the X-ray µCT image provide good results for our case study: due to the use of Bayesian statistics, which take into account the uncertainty inherent to the data, the microscopic parameters from the original, or the coarsened, resolution X-ray µCT images were both reasonable predicators of the sample-scale hydrodynamic properties.

Increasing the resolution led to the apparition of yet invisible connections, the soil pore network is indeed a continuum across space. We however observed that the pore distribution of the studied soil is not necessarily better approached with a smaller minimal pore volume. Moreover, the visible minimal volume is limited by the sample size, and finer details about the pore network would therefore come with a loss of information due to the required smaller sample size (Vogel et al., 2010).

After all, we hypothesize that rather than pore volume continuous scale-dependency (as initially proposed); the pore volumes distributions between specified pore sizes could be similar across scales. That statement is similar to theories that postulate about the multifractal behavior of the SWRC (e.g. De Bartolo et al., 2018).

Results & Discussions: the field experiment

73

5.5. Research question #3: How does the air-filled porosity