Notes on global permeability – grading curve expressions of granular matter and their grading curve variables

¹ HBM Research Centre, and Environmental Engineering, Óbuda University, Budapest, Hungary
² Doctoral School of Applied Informatics and Applied Mathematics, and Environmental Engineering, Óbuda University, Budapest, Hungary
³ Sándor Rejtő Faculty of Light Industry and Environmental Engineering, Óbuda University, Budapest, Hungary

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 1 December 2025

Abstract

This research aims at the elaboration of a globally valid permeability model. A model-building process is made for this purpose. Starting with a 3-variable model, by adding 10 new variables consecutively (into the product-type model generally used at present), an increasingly better fit was attained on a wider database. The last model, with 13 (partly diameter, partly entropy type) variables, was the best, but it needed a “sharp” inverse problem solver. Earlier, only unimodal samples were used on the same database. Series 1 to 4: artificial mixtures of silt and sand grains, d₁₀ = 0.004 to 0.016 mm, k = 1.67 × 10^ (-5) to 4.76 × 10^ (-3) cm/s. Series 5: sand-gravel d₁₀ = 0.72 to 5.82 mm, k= 0.378 to 50.107 cm/s. Series 9: sand-gravel, k = 7.0^ (-3) to 0.48 cm/s. The fit was not perfect on the training database earlier; the present approach is better on a wider database. The permeability variables were started to be analysed. The meaning of two kinds of harmonic mean diameter and d10 was examined using fractally distributed grading curves, as a function of entropy coordinate A. Results indicated that d₁₀ may vary between the two harmonic mean diameters.