## 3 Experiment Results and Analysis of Dynamic Characteristics  
### Analysis of Influence of Reinforced Layer on Dynamic Characteristics of Gravel Soil  
#### 3.1.1 Effect of Number of Reinforced Layers on Axial Cumulative Strain  
Figure 7 compares the relationship between the axial cumulative strain \(c\)d (the peak strain at the end of each cycle) and loading cycle of the samples with different layers of reinforcement loaded under the same frequency (1 Hz). The comparison shows that the deformation of the samples can be divided into three stages: the fast grow stage during the first 100 cycles, the transition stage between 100 and 1000 (or 2000) cycles, and the stabilization stage after 1000 cycles. A similar pattern was observed by [PERSON] [1] on the dynamic characteristics of coarse-grained fillers in roadbeds. During the fast-growing stage, the deformation could double after 100 cycles comparing to that after the first loading cycle, and the rate of increment is the highest in the unreinforced sample and the lowest in the sample with three layers of reinforcement. During the transition stage (100 to 1000-2000 cycles), the deformation increment rate decreases, then stabilizes after that. During the stabilization stage, the deformation almost increases with the number of loading cycles at logarithm scale. The unreinforced sample still has the highest increment rate and the other three samples have almost the same rate of increment with loading cycles.  
Equation (2) is the fitting equation of the axial cumulative strain and the number of loading cycles based on the fitting analysis of the axial cumulative strain and the number of loading cycles under different number of stiffened layers.  
\[\epsilon_{d}=\frac{N}{a+bN+cN^{0.5}} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Series** & **Frequency (Hz)** & **Number of Reinforcement Layers** \\ \hline F0.5-L3 & 0.5 & 3 \\ F1-L0 & 1.0 & 0 \\ F1-L1 & 1.0 & 1 \\ F1-L2 & 1.0 & 2 \\ F1-L3 & 1.0 & 3 \\ F3-L3 & 3.0 & 3 \\ F5-L3 & 5.0 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test loading parameters and working conditions.  
Figure 7: Variation of cumulative axial strain with number of loading cycles under different stiffened layers.  
where \(a\), \(b\), and \(c\) are fitting parameters. The fitted curves using the parameters shown in Table 3 were compared with the test results shown in Figure 7. The comparison suggests that the increment of cumulative axial strain with loading cycles can be fitted with the above equation, regardless of the inclusion of reinforcement. Through comparison, it was found that the values of parameters \(a\), \(b\), and \(c\) vary with the number of stiffened layers. When the number of stiffened layers increases, the value of parameter \(a\) decreases, while the value of parameters \(b\) and \(c\) increase. Due to the limited test conditions, only experiments with the number of stiffened layers of 0-3 were conducted, but it was possible to clarify that there is a corresponding relationship between the number of stiffened layers and the parameters \(a\), \(b\), and \(c\); that is, the parameters \(a\), \(b\), and \(c\) can be used to characterize the influence of the number of stiffened layers on the axial cumulative strain.