A shape factor for particle size distribution caracterization

This paper examines the parameter ν, a shape factor of the particle size distribution (PSD) in granular materials, and its broad applications in geotechnical engineering. Defined as the slope of the PSD in a log-log plot, ν provides a funda-mental measure of distribution shape, capturing the evolution of granular materials under varying conditions. While initially developed to quantify particle break-age, ν has proven to be a versatile tool with applications extending to the modeling of PSD evolution, micromechanical analysis, and the influence of environ-mental factors such as moisture. The paper explores the theoretical foundation of ν, its connections to fractal theory, and its role in describing granular transformations under mechanical and hydraulic influences. Additionally, the relationship between ν and other PSD-based breakage parameters, such as those proposed by Marsal, Hardin, and Einav, is examined, highlighting its advantages as a unifying descriptor of grain size evolution. By synthesizing these perspectives, this study underscores the value of ν as a robust and adaptable parameter for advancing the understanding of granular mechanics and geotechnical engineering.