Hybrid modelling of saturated water flow in percolating and non-percolating macroporous soil media

Bartłomiej Gackiewicz, Krzysztof Lamorski*, Mykola Kochiieru, Cezary Sławiński, Shao Yiu Hsu, Liang Cheng Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The saturated water flow phenomenon is determined by the soil pore transport processes occurring at a micro-scale. In this study, saturated water flow was modeled using two different approaches, depending on the existence of the percolating macropore network. The soil material comprised 26 undisturbed soil cores. Soil samples were scanned using an X-ray micro-CT scanner, and saturated hydraulic conductivity (Ksat), bulk density and particle size distribution were measured. The voxel size for X-ray CT scans of soil cores was 23.6 µm, which allowed soil macropore network discrimination. The macropore network was percolating in 11 samples, while the remaining cores were not. A typical approach based on Navier–Stokes (NS) equations was used for saturated water flow modeling in the case of a percolating samples. In the case of cores with a non-percolating macropore network, the NS modeling approach could not be used. An alternative method of modeling (NS/Darcy) was used in this case, blending: regular NS flow in the well-defined macropores with the Darcy–Forchheimer flow in the remaining part – the soil matrix. Soil matrix is treated by the NS/Darcy model as a pore medium without well-defined pore geometry but with some intrinsic permeability incorporated in the model using the Darcy–Forchheimer equation. Unlike the NS approach, the NS/Darcy model allowed for the simulation of water flow for all soil samples, including those where the macropore network was not percolating. Based on simulations, the Ksat was estimated used for model validation. The analysis of results leads to the proposal of a new hybrid modeling approach, mixing the NS and NS/Darcy modeling approaches. A good estimation of the Ksat was obtained using the proposed model (R2 = 0.61). The NS/Darcy modeling approach was used for the analysis of the macropore flow in the soil media. The simulations show that water permeates through the core, but macropores are a favorable flow path if they exist, even if they are not directly connected to each other. The areas of the soil cores taking part in the preferential, macropore flow were quantified, showing that only a small fraction of the macropores take part in water flow both for percolating and non-percolating cores. But generally, for most of the analyzed flow-related indices, apparent differences in results between percolating and non-percolating samples were observed. Effective flow area (EFA), i.e., the sample area used for water flow with a velocity higher than the threshold velocity (Utr) was analyzed. Considering the macropore flow, only ∼2% of sample volume is responsible for: 82% of the total flux in case of percolated and 34% in case of non-percolated samples. Also, for non-percolated samples, the dependence (R2 = 0.44) between relative flux participation and the effective flow area is observed. The simulation results for the non-percolating samples revealed the relationship between the simulated saturated conductivity of the whole soil sample and the saturated conductivity of the soil matrix and macroporosity. This allowed for developing a simple multiple linear regression model (R2 = 0.98) of the soil core's hydraulic conductivity.

Original languageEnglish
Article number115467
StatePublished - 15 Jan 2022


  • Macropore flow
  • Modelling
  • Percolation
  • Saturated hydraulic conductivity
  • Soil
  • X-ray CT


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