Evaluation of Empirical Hydraulic Conductivity Equations Using Standard and Long-Term Conductivity Measurements

Abstract

Empirical equations for hydraulic conductivity are widely used, but their accuracy is not universal. Gradation-based methods implicitly represent a typical packing state, whereas porosity-dependent methods explicitly account for variations in porosity, which becomes important in density-sensitive materials. This study compares nine empirical methods against three measured conductivity targets: initial measured conductivity ( k _in), standard interpreted conductivity ( k _std), and final late-stage measured conductivity ( k _end), using a laboratory database comprising filter materials, tills, tailings, and one fines-dominated silt. No single equation performed best across all materials and all targets. Most methods agreed most closely with initial measured conductivity ( k _in), but clear exceptions were observed. Chapuis agreed most closely with standard interpreted conductivity ( k _std), whereas Beyer agreed most closely with final late-stage measured conductivity ( k _end). Material domain strongly influenced performance. Filter materials favored porosity-dependent methods, tills favoured Beyer, and tailings favoured Kozeny-Carman. For the till materials represented in this dataset, Beyer was the strongest gradation-based method and aligned most closely with standard interpreted conductivity ( k _std). The main finding is that empirical equations do not represent one single hydraulic conductivity value. Instead, they tend to correspond to different measured conductivity states depending on formulation and material domain. The results, therefore, support domain-based method selection rather than a universal recommendation.