## 5 Conclusions  
The dynamic behaviors of GRS in Southern China were experimentally studied. The effects of load cycles, fines content, and D-W cycles were investigated through the dynamic triaxial tests, where four fines contents and seven D-W cycles were considered. The main conclusions are as follows: \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Soil No.** & **D–W Cycles** & \(\mathbf{a_{\lambda}}\) & \(\mathbf{b_{\lambda}}\) & \(\mathbf{R^{2}}\) & **Soil No.** & **D–W Cycles** & \(\mathbf{a_{\lambda}}\) & \(\mathbf{b_{\lambda}}\) & \(\mathbf{R^{2}}\) \\ \hline \multirow{8}{*}{C0} & 0 & \(-0.034\) & \(0.176\) & \(0.9791\) & & 0 & \(-0.043\) & \(0.220\) & \(0.9709\) \\  & 1 & \(-0.032\) & \(0.150\) & \(0.9819\) & & 1 & \(-0.046\) & \(0.175\) & \(0.9957\) \\  & 2 & \(-0.030\) & \(0.124\) & \(0.9960\) & & 2 & \(-0.052\) & \(0.208\) & \(0.9627\) \\  & 3 & \(-0.025\) & \(0.143\) & \(0.9821\) & & 3 & \(-0.031\) & \(0.168\) & \(0.9762\) \\  & 4 & \(-0.025\) & \(0.138\) & \(0.9904\) & & 4 & \(-0.033\) & \(0.190\) & \(0.9628\) \\  & 5 & \(-0.042\) & \(0.210\) & \(0.9604\) & & 5 & \(-0.031\) & \(0.191\) & \(0.9599\) \\  & 6 & \(-0.046\) & \(0.207\) & \(0.9788\) & & 6 & \(-0.038\) & \(0.190\) & \(0.9662\) \\  & 7 & \(-0.052\) & \(0.210\) & \(0.9877\) & & 7 & \(-0.029\) & \(0.174\) & \(0.9401\) \\ \hline \multirow{8}{*}{C10} & 0 & \(-0.039\) & \(0.175\) & \(0.9901\) & & 0 & \(-0.059\) & \(0.256\) & \(0.9557\) \\  & 1 & \(-0.039\) & \(0.196\) & \(0.9825\) & & 1 & \(-0.043\) & \(0.186\) & \(0.9537\) \\  & 2 & \(-0.049\) & \(0.198\) & \(0.9916\) & & 2 & \(-0.043\) & \(0.222\) & \(0.9631\) \\  & 3 & \(-0.031\) & \(0.191\) & \(0.9607\) & & 3 & \(-0.045\) & \(0.187\) & \(0.9648\) \\  & 4 & \(-0.032\) & \(0.189\) & \(0.9769\) & & 4 & \(-0.040\) & \(0.220\) & \(0.9542\) \\  & 5 & \(-0.038\) & \(0.200\) & \(0.9702\) & & 5 & \(-0.038\) & \(0.208\) & \(0.9418\) \\  & 6 & \(-0.029\) & \(0.182\) & \(0.9676\) & & 6 & \(-0.039\) & \(0.214\) & \(0.9491\) \\  & 7 & \(-0.045\) & \(0.211\) & \(0.9894\) & & 7 & \(-0.034\) & \(0.201\) & \(0.9546\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Fitting results (\(\lambda\)). Figure 17: Damping ratio fitting of GRS. (1) The morphology of the hysteresis curve changes with the numbers of load and D-W cycles, as well as the fines content. The hysteresis curve area \(S\), center offset \(d\), and residual strain \(\varepsilon_{sp}\) of GRS vary similarly with the increase of load cycles. They all decrease sharply in the early stage(\(N<20\)), and the reduction rate slows down in the later load stage (\(20\leq N\leq 1000\)) and finally stabilizes in the end(\(N>1000\)). The major axis gradient \(k\) increases with the number of load cycles and approximately changes linearly with \(\log N\). At the same time, as the fines content increases, \(S\), \(d\) and \(\varepsilon_{sp}\) increase and \(k\) decreases. All of these properties fluctuate with the increase of D-W cycles and tend to be stable after about seven D-W cycles. (2) The growth of dynamic shear modulus and the reduction of damping ratio with the number of load cycles can be divided into the rapid change stage(\(N<20\)) and the slow change stage (\(20\leq N\leq 1000\)). Moreover, the dynamic shear modulus and damping ratio show a good linear relationship with the logarithmic number of load cycles and two prediction equations were obtained by the data fitting. With the increase of fines content, the dynamic shear modulus shows a trend of decreasing while the damping ratio shows an increasing trend. The dynamic shear modulus changes with D-W cycles, and it decreases after several D-W cycles. However, the damping ratio is less affected by D-W cycles. (3) The dynamic characteristics of GRS are influenced by the number of load cycles, fines content, as well as the number of D-W cycles. Among them, the number of load cycles has the dominant influence and the number of D-W cycles has the least influence.