Simplified Equations for Shear-Modulus Degradation and Damping of Gravels

Two of the most important parameters in any dynamic analysis involving soils are the shear modulus and damping ratio. Based on lab tests on gravels from 18 investigations, simplified equations to define $G/G_{\max }$ and the damping ratio as a function of shear strain, $\gamma$, have been developed. The $G/G_{\max }$ versus $\gamma$ equations rely on two parameters that can be defined in terms of confining pressure and uniformity coefficient. Increasing confining pressure leads to a more linear curve, while increasing the uniformity coefficient leads to a more nonlinear curve shape. $G/G_{\max }$ versus $\gamma$ curves for gravels tend to plot somewhat below curves for sands under similar conditions. Estimates of the standard deviation in $G/G_{\max }$ versus $\gamma$ curves are provided to consider scatter about the mean. The damping ratio versus $\gamma$ equation employs the modified Masing approach with a minimum damping ratio of 1%. In addition, about 67% of the damping data points fall within an error band of $\pm 33\%$ from the computed value. The damping ratio of gravel specimens also decreases as the confining pressure increases, whereas it increases for higher uniformity coefficients. Other direct correlations between damping ratio and factors such as shear strain, uniformity coefficient, and confining pressure did not provide significant improvements in predictive capacity.