J. Hydrol. Hydromech., Vol. 74, No. 4 - Early view, 2026, p. 1 - 10, doi: .
Scientific Paper, English

Katsutoshi Seki, Martinus Th. van Genuchten, Wolfgang Durner, Luwen Zhuang, Silvia L. B. Bermudez: Trimodal hydraulic models for unsaturated flow: Coupling triple-porosity water retention with general conductivity functions

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• We present trimodal hydraulic models that couple a triple-porosity water retention function (WRF) with a general hydraulic conductivity function (HCF) to predict unsaturated flow from saturation to dry conditions. The WRF is a linear combination of subfunctions representing macro-, meso-, and micro-pores such as, for example, tri-VG (VG+VG+VG), BVV (BC+VG+VG), or VVP (VG+VG+film flow) formulations, where VG and BC present the van Genuchten and Brooks-Corey type functions. The general HCF links K(h) to the measured WRF with only two additional parameters. Applied to soils, construction materials, and a trimodal sandstone, the models reproduce θ(h) and K(h) data across capillary and film-flow regimes and capture the sharp conductivity drop often observed just below saturation without ad hoc interpolation. The tri-VG and BVV models resolve three pore domains and match observed pore-size distributions where trimodality is evident, with VVP offering a compact alternative. The WRF, in practice readily measured over a wide pressure-head range, robustly identifies triple-porosity parameters, while only limited K data can calibrate the HCF. A limitation is that representing the near-saturated K drop requires a corresponding decrease in θ; without accompanying retention data, macropore parameters should not be over-interpreted. Overall, explicit macroporosity within a trimodal WRF plus a parsimonious HCF provides an efficient, unified framework for modeling unsaturated flow.
  
  KEY WORDS: Soil water retention; Unsaturated hydraulic conductivity; Triple-porosity model; Macroporosity; Film flow; General hydraulic conductivity function.
  
  Address:
  - Katsutoshi Seki, Natural Science Laboratory, Toyo University, 5-28-20 Hakusan, Bunkyo-ku, Tokyo 112-8606, Japan. (Corresponding author. Tel.: Fax.: Email: seki_k@toyo.jp)
  - Martinus Th. van Genuchten, Department of Earth Sciences, Utrecht University, Princetonlaan 8a, 3584 CB Utrecht, Netherlands. Department of Nuclear Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.
  - Wolfgang Durner, Soil Science and Soil Physics Division, Institute of Geoecology, Technische Universität Braunschweig, 38092 Braunschweig, Germany.
  - Luwen Zhuang, Center for Water Resources and Environment, and Guangdong Key Laboratory of Marine Civil Engineering, School of Civil Engineering, Sun Yat-sen University, Guangzhou 510275, China.
  - Silvia L. B. Bermudez, Department of Civil Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.