Title: An Innovative Power-Law Equation of Optimal Grading Curves for Dense Packing

Author(s): Dr Gerard Roquier

Publication: Symposium Paper

Volume: 349

Issue:

Appears on pages(s): 143-160

Keywords: continuous distribution, optimal grading curve, packing density, particle size distribution, Theoretical Packing Density Model (TPDM)

DOI: 10.14359/51732745

Date: 4/22/2021

Abstract:
The search for the optimal grading curve remains an open problem for dense packing in the field of concrete. In France, Caquot considered that the coarsest fraction is the only one that is not submitted to the wall effect. In a grading span and in the case of a fifth root of the diameter as the abscissa parameter, he found a fairly straight broken-line. In some other countries, the Andreasen and Andersen (A&A) cumulative distribution function is a power-law equation with a distribution modulus commonly equal to 0.4 or 0.5. How to unify these two approaches? Validated for ordered and disordered packings and for different particle shapes and textures, the recent Theoretical Packing Density Model (TPDM) clarifies the situation. Firstly, the TPDM highlights curves evolving from A&A’s to Caquot’s as the packing process, characterized by a compaction index K, becomes more and more efficient. Secondly, an innovative power-law equation is proposed to unify the two approaches of A&A and Caquot. The distribution modulus is composed of: K a constantq, the compaction index corresponding to a pouring process K_min and the ratio d/d_maxwhered is the particle diameter and d_max the largest particle size in the distribution.