Effect of Loading Frequency on Volumetric Strain Accumulation and Stiffness Improvement in Sand under Drained Cyclic Direct Simple Shear Tests

The effect of the loading frequency on the volumetric strain accumulation, stiffness improvement, and damping ratio of silica sand during cyclic shearing of the silica sand was investigated by performing drained cyclic strain-controlled direct simple shear tests. Cyclic shear strain amplitudes (${\gamma }_c$) of 0.5% and 1.0%; vertical effective stresses (${\sigma }_{v0}^{\prime }$) of 100, 200, and 300 kPa; and loading frequencies ($f$) of 0.05, 0.1, 0.5, and 1 Hz were considered. Sand samples were prepared in the loose ($D_r=40\%$) and dense ($D_r=80\%$) states using dry Nakdong River sand. For loose sand tested at ${\sigma }_{v0}^{\prime }=100$ and 200 kPa, the test results showed that the rate of volumetric strain accumulation decreased with increasing $f$, and the decrease was independent of ${\sigma }_{v0}^{\prime }$ and more obvious at the higher ${\gamma }_c$ value. The maximum decrease in the volumetric strain accumulation was 60%, which corresponded to a 20-fold increase in $f$, from 0.05 to 1 Hz. For dense sand tested at ${\sigma }_{v0}^{\prime }=300\mathrm{kPa}$, the accumulated rate of volumetric strain was essentially identical, especially at ${\gamma }_c=1.0\%$. The shear modulus ratio always increased with the increase of $f$ for both loose and dense sand, but the difference between shear modulus ratios at different $f$ was reduced with the increase of ${\sigma }_{\mathit{v}0}^{\prime }$, when the samples were sheared at ${\gamma }_c=1.0\%$. The improvement parameter $t$, which is proposed in this study and which represents the increase in the rate of cyclic stiffness with the number of cycles ($N$), increased linearly with $f$. For loose sand, it increased by approximately 56% and 12% at ${\gamma }_c=0.5\%$ and 1.0%, regardless of ${\sigma }_{v0}^{\prime }$, respectively. The normalized damping ratio (${\lambda }_n$) was independent of $D_r$, ${\sigma }_{v0}^{\prime }$, $f$, and ${\gamma }_c$, and the relationship between ${\lambda }_n$ and $N$ was well expressed by a power function. The effect of the loading frequency on Nakdong River sand inferred from a drained test was similar to that indicated by an undrained test.