Rev assessment of granular materials with varied grading based on macro- and micro-mechanical statistical data

Abstract

To assess the mechanical behavior of granular materials in triaxial tests, a mandatory condition is to guarantee a representative elemental volume (REV) sample. This is achieved by limiting the minimum sample size and the coarsest particle in the sample (\(d_\textrm{max}\)). The common geotechnical practice is based on the sample scales H/D and \(\alpha = D/d_\textrm{max}\), where D is the sample diameter and H is its height. While, it is widely accepted that H/D should be between 2 and 2.5, international standards do not agree on the minimum \(\alpha\), and the recommended values vary widely between 5 and 20. Moreover, the impact of particle size distribution on REV is not well understood and is consequently overlooked by most standards. In this paper, we present a study of the effects of \(\alpha\) and grading on the critical shear strength of granular materials. We conducted DEM simulations of triaxial tests on samples with values of \(\alpha\) ranging from 5 to 20 and grading that varied from mono-size particle assemblies to samples, where the ratio between the coarsest and finest particle was \(d_\textrm{max}/d_\textrm{min}\ = 4\). The results show that the minimum \(\alpha\) required to obtain an REV depends on grading. While, for mono-size particle assemblies REV conditions are obtained for \(\alpha \ \ge 12.5\), better graded samples behave as REV once \(\alpha \ \ge \ 8\). A detailed analysis of macro and microscopic parameters reveals that \(\alpha\) is not necessarily the most suitable parameter to assess REV scales. We discover that, in our samples, a unique relationship between critical shear strength and the number of grains carrying interparticle forces (\(N_p^*\)) exists independently of grading. In effect, REV can be systematically defined as long as \(N_p^* \ge 3000\). The physical source of this observation is linked to the evolution of contact arrangement and force transmission mechanisms, which evolve according to the number of particles engaged in load bearing.