Effect of Uniformity Coefficient on $\mathit{G}/{\mathit{G}}_{\text{max}}$ and Damping Ratio of Uniform to Well-Graded Quartz Sands

The modulus degradation curves, $\mathit{G}\left(\mathit{\gamma }\right)/{\mathit{G}}_{\text{max}}$, and the damping ratio, $\mathit{D}\left(\mathit{\gamma }\right)$, of 27 clean quartz sands with specially mixed grain size distribution curves were measured in approximately 280 resonant column tests. For each material, tests with various pressures and densities were performed. Based on the test data it is demonstrated that the shear modulus degradation is larger for higher values of the uniformity coefficient, ${\mathit{C}}_{\mathit{u}}={\mathit{d}}_{60}\text{/}{\mathit{d}}_{10}$, while it is rather independent of the mean grain size, ${\mathit{d}}_{50}$. The observed ${\mathit{C}}_{\mathit{u}}$ dependence of curves $\mathit{G}\left(\mathit{\gamma }\right)\text{/}{\mathit{G}}_{\text{max}}$ is not adequately described by common empirical equations because these equations were developed based on tests on uniform granular materials. To consider the influence of the uniformity coefficient, the paper proposes correlations of the parameters of the common empirical equations with ${\mathit{C}}_{\mathit{u}}$. Good agreement between the prediction of the extended empirical equations and the experimental data collected from the literature is demonstrated. Furthermore, the test data reveal that the curves of damping ratio, $\mathit{D}\left(\mathit{\gamma }\right)$, and the threshold shear strain amplitude indicating the onset of residual deformation accumulation, ${\mathit{\gamma }}_{\mathit{tv}}$, are rather independent of ${\mathit{d}}_{50}$ and ${\mathit{C}}_{\mathit{u}}$. The threshold shear strain amplitude at the onset of modulus degradation, ${\mathit{\gamma }}_{\mathit{tl}}$, slightly decreases with increasing values of ${\mathit{d}}_{50}$ and ${\mathit{C}}_{\mathit{u}}$.