Permeability Test Results With Packed Spheres and Non-Plastic Soils

This paper examines permeability test results with packed spheres and non-plastic soils. Most tests on packed spheres were performed in physics and chemistry, using liquids or gases to measure the intrinsic permeability, K (m²). All K (m²) were converted into saturated hydraulic conductivity k_sat (m/s). Equal spheres and spheres having a unimodal or multimodal grain size distribution curve (GSDC) were tested. We point out interesting differences between the approaches in physics, geotechnique, and hydrogeology, then discuss difficulties with testing methods, before analyzing all test data. We propose a method to fit a GSDC with either a single, or a sum of lognormal equations, which gives a closed-form expression for the specific surface. Then, we assess the performance of predictive methods for k_sat, including the Kozeny–Carman equation. A few methods, which use only a mean particle size, are shown to give excellent predictions for equal spheres and unimodal packings. Other methods, which use the effective size d₁₀ and the void ratio e, are also shown to give excellent predictions for packed spheres and non-plastic soils, in the ranges for which they were initially developed. A new equation is proposed, which successfully predicts k_sat in the range from 1 to 10⁻¹⁰ m/s, when the parameter [d₁₀² e³/(1+e)] varies from 10⁻⁹ to 10² mm², for spheres and non-plastic natural soils.