A Fractal Entropy-Based Effective Particle Model Used to Deduce Hydraulic Conductivity of Granular Soils

Abstract

In this study, a rigorous mathematical approach used to compute an effective diameter based on particle size distribution (PSD) has been presented that can predict the hydraulic conductivity of granular soils with enhanced rigor. The PSD was discretized based on an abstract interval system of fractal entropy, while the effective diameter of soil was computed using the grading entropy theory. The comparisons between current entropy-based effective diameter (DE) and those computed using existing procedures show that the current DE can capture the particle size information of a given soil more accurately than others. Subsequently, the proposed DE was successfully implicated into Kozeny–Carman’s formula to deduce the saturated hydraulic conductivity of soils with enhanced accuracy. The proposed model was tested using current and previously published experimental data from literature. Not surprisingly, the results of the current model and those from previous experimental studies were found to be consistent, which can sufficiently verify the proposed entropy-based effective diameter model.

Keywords

• effective particle diameter
• fractal entropy
• abstract interval
• hydraulic coefficient