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

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 ( \(d_\textrm{max}\) $d_{\text{max}}$ ). The common geotechnical practice is based on the sample scales H/D and \(\alpha = D/d_\textrm{max}\) $\alpha =D/d_{\text{max}}$ , 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 \(\alpha\) $\alpha$ , 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 \(\alpha\) $\alpha$ and grading on the critical shear strength of granular materials. We conducted DEM simulations of triaxial tests on samples with values of \(\alpha\) $\alpha$ 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 \(d_\textrm{max}/d_\textrm{min}\ = 4\) $d_{\text{max}}/d_{\text{min}}=4$ . The results show that the minimum \(\alpha\) $\alpha$ required to obtain an REV depends on grading. While, for mono-size particle assemblies REV conditions are obtained for \(\alpha \ \ge 12.5\) $\alpha \ge 12.5$ , better graded samples behave as REV once \(\alpha \ \ge \ 8\) $\alpha \ge 8$ . A detailed analysis of macro and microscopic parameters reveals that \(\alpha\) $\alpha$ 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 ( \(N_p^*\) $N_p^{\ast }$ ) exists independently of grading. In effect, REV can be systematically defined as long as \(N_p^* \ge 3000\) $N_p^{\ast }\ge 3000$ . 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.