## 4 Characteristics and Models of Dynamic Parameters of GRS
### Characteristics of Dynamic Parameters of GRS  
By taking soil that has not undergone any D-W cycle as an example, Figure 12 depicts the dynamic shear modulus \(G_{d}\) and damping ratio \(\lambda\) with the number of load cycles for GRS. It is easy to see that the variation of dynamic parameters with the number of loading cycles has two stages, i.e., the initial loading stage (\(N<20\)) and the late loading stage (\(N\geq 20\)). In the initial loading stage (\(N<20\)), with the increases in the number of loads, the dynamic shear modulus \(G_{d}\) grows rapidly while the damping ratio \(\lambda\) decreases rapidly. It exhibits obvious strain-hardening characteristics [60]. This may be due to the significant compaction effect of soil, and the soil deformation is dominated by plastic deformation. Therefore, the change of dynamic parameters at this stage does not reflect the soil characteristics. In the late loading stage (\(N\geq 20\)), both the increasing rate of dynamic shear modulus and the decreasing rate of damping ratio slows down and afterward reach stabilization (\(N>1000\)). The dynamic shear modulus growth and the damping ratio reduction at this stage are mainly attributable to the particle dislocation and pore compression in the soil, resulting in pore water pressure and further compaction of the soil. The soil enters the elastoplastic deformation stage. When the number of load cycles continues to increase (\(N>1000\)), the soil becomes more dense, and the soil deformation is dominated by elastic deformation. At this stage, dynamic parameters tend to be fixed. Therefore, the change of dynamic parameters at 20-1000 loading cycles is analyzed below. The effect of fines content on the dynamic parameters of GRS is closely related to its water content. When the soil is in the saturated state, the larger the fines contents, the smaller the dynamic shear modulus and the higher the damping ratio [61]. Figure 13 plots the evolution of dynamic parameters with the variation of fines contents of GRS. The dynamic shear modulus shows a trend of decreasing, then increasing, and finally decreasing again with the increase of fines content (see Figure 13a). The damping ratio generally shows an increasing trend with the increase of fines content, and the growth rate slows down as the number of load cycles increases (see Figure 13b). Figure 12: Relationship between the dynamic parameters and the number of loading cycles (T0). Figures 14 and 15 illustrate how the dynamic shear modulus and damping ratio of GRS vary with the number of D-W cycles. The variations of dynamic shear modulus affected by the number of D-W cycles are different for GRS with different fines content (see Figure 14). It is observed that the influence of the number of D-W cycles on the dynamic shear modulus is greater when the fine particle content is low (see Figure 14a-d). Table 6 shows the range of dynamic shear modulus among seven D-W cycles. The range \(G_{d}\) for C0 is nearly three or five times that for C30. Meanwhile, compared with the dynamic shear modulus without D-W cycles, the dynamic shear modulus after several D-W cycles exhibit a decreasing trend (see Table 7, \(G_{d\text{T}}\)\(<\)\(G_{d\text{T}0}\)). Figure 14: Relationship between the dynamic shear modulus and the number of D–W cycles. Figure 13: Relationship between dynamic parameters and fines content (T0). Note: Number of load cycles \({}^{*}\) is the value after logarithmic processing. The relationship between the damping ratio of GRS with D-W cycles is depicted in Figure 15. Compared with the influence of the number of cyclic loading on the damping ratio, the influence of D-W cycles on it is negligible. Table 8. shows the range of damping ratios among seven D-W cycles. It is observed that the differences are very small. It can be concluded that the damping ratio of GRS is less affected by D-W cycles.