Assessment of empirical formulae for determining the hydraulic conductivity of glass beads

Abstract

Empirical formulae are often used in practice to quickly and cheaply determine the hydraulic conductivity of soil. Numerous relations based on dimensional analysis and experimental measurements have been published for the determination of hydraulic conductivity since the end of 19th century. In this paper, 20 available empirical formulae are listed, converted and re-arranged into SI units. Experimental research was carried out concerning hydraulic conductivity for three glass bead size (diameters 0.2 mm, 0.5 mm and 1.0 mm) and variable porosity. The series of experiments consisted of 177 separate tests conducted in order to obtain relevant statistical sets. The validity of various published porosity functions and empirical formulae was verified with the use of the experimental data obtained from the glass beads. The best fit was provided by the porosity function n3/(1–n)2. In the case of the estimation of the hydraulic conductivity of uniform glass beads, the best fit was exhibited by formulae published by Terzaghi, Kozeny, Carman, Zunker and Chapuis et al.

Empirical formulae are often used in practice to quickly and cheaply determine the hydraulic conductivity of soil. Numerous relations based on dimensional analysis and experimental measurements have been published for the determination of hydraulic conductivity since the end of 19th century. In this paper, 20 available empirical formulae are listed, converted and re-arranged into SI units. Experimental research was carried out concerning hydraulic conductivity for three glass bead size (diameters 0.2 mm, 0.5 mm and 1.0 mm) and variable porosity. The series of experiments consisted of 177 separate tests conducted in order to obtain relevant statistical sets. The validity of various published porosity functions and empirical formulae was verified with the use of the experimental data obtained from the glass beads. The best fit was provided by the porosity function n3/(1–n)2. In the case of the estimation of the hydraulic conductivity of uniform glass beads, the best fit was exhibited by formulae published by Terzaghi, Kozeny, Carman, Zunker and Chapuis et al.