# Applicability Study on Modified Argillaceous Slate as Subgrade Filling for High-Speed Railway
## 4 Dynamic Simulation Analysis of Soft-Rock-Modified Soil as Subgrade
### Results of Dynamic Response Analysis  
#### 4.2.1 Dynamic Response Analysis  
To study the dynamic behaviors of subgrade filled with modified WAS, A/B-group subgrade-filling material was substituted by either WAS + 6% quicklime or WAS + ce  
Figure 11: Diagram of dynamic load application. Figure 12: Comparison of dynamic displacement between simulation and test results. ment (3%, 5%, 7%) in the numerical simulation. All other material parameters and work conditions remained consistent. Dynamic responses in different layers are illustrated in Table 12. Variation rules of the dynamic response amplitude and depth on subgrades filled using different materials are depicted in Figure 13.  
Figure 13: Dynamic responses at various depths for different fillings. (**a**) Displacement; (**b**) Velocity; (**c**) Acceleration; (**d**) Stress. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test**} & \multicolumn{4}{c}{**Dynamic Acceleration**} & \multicolumn{4}{c}{**Dynamic Velocity**} & \multicolumn{4}{c}{**Dynamic Displacement**} & \multicolumn{4}{c}{**Dynamic Stress**} \\  & \multicolumn{4}{c}{**(m\(\cdot\)s\({}^{-2}\))**} & \multicolumn{4}{c}{**(mm\(\cdot\)s\({}^{-1}\))**} & \multicolumn{4}{c}{**(\(\times\)10\({}^{-3}\) mm)**} & \multicolumn{4}{c}{**(kPa)**} \\ \cline{2-19}  & **I** & **II** & **III** & **IV** & **V** & **I** & **II** & **III** & **IV** & **V** & **I** & **II** & **III** & **IV** & **V** & **I** & **II** & **III** & **IV** & **V** \\ \hline
1 & 16.5 & 14.5 & 14 & 13.5 & 12 & 9.4 & 7.8 & 5.8 & 5.4 & 5.1 & \(-\)82 & \(-\)63 & \(-\)57 & \(-\)56 & \(-\)53 & 60.5 & 63 & 65 & 68 & 73 \\
2 & 7 & 7.5 & 8.2 & 7.8 & 7 & 7.7 & 5.4 & 4.4 & 4.1 & 3.8 & \(-\)60 & \(-\)52 & \(-\)50 & \(-\)48 & \(-\)48 & 17.5 & 29 & 30 & 32 & 35 \\
3 & 4.8 & 4.8 & 4 & 4.8 & 4.6 & 6.5 & 4 & 3.1 & 2.7 & 2.6 & \(-\)50 & \(-\)40 & \(-\)38 & \(-\)38 & \(-\)36 & 11.8 & 17 & 20 & 22 & 23 \\
4 & 2.3 & 2.2 & 2.2 & 2.2 & 2.1 & 3.3 & 3 & 2.1 & 1.8 & 3.3 & \(-\)25 & \(-\)25 & \(-\)24 & \(-\)25 & \(-\)22 & 4.0 & 6.4 & 6.5 & 7 & 7.3 \\
5 & 2 & 1 & 0.8 & 1 & 0.9 & 1.1 & 1 & 0.9 & 0.8 & 1.1 & \(-\)10 & \(-\)10 & \(-\)10 & \(-\)10 & \(-\)10 & 2.4 & 3.5 & 3.5 & 3.6 & 3.6 \\ \hline \hline \end{tabular} Note: “I” is WAS +6% quickline, “II” is WAS +3% cement, “II” is WAS +5% cement, “IV” is WAS +7% cement. “I” is the surface of bed (depth of \(-\)0.6529 m from rail surface), “2” is the bottom of surface bed (depth of \(-\)0.95259 m from rail surface), “3” is the bottom of bed (depth of \(-\)245259 m from rail surface), “3” and “4” are the subgrade layer (depth of \(-\)7.65259 m and \(-\)16.65259 m from rail surface).  
\end{table} 
Table 12: Dynamic response in different layers. From Figure 13, The vertical displacement, velocity and acceleration on the bed surface were found to increase by 13.8%, 20.5% and 30.1%, respectively, from 5% quicklime + WAS to 3% cement + WAS; and by 3.5%, 3.3% and 10.5%, respectively, from 3% cement + WAS to 5% cement + WAS; and by 3.7%, 7.4% and 1.8%, respectively, from 5% cement + WAS to 7% cement + WAS; and by 12.5%, 5.8% and 5.6%, respectively, from 7% cement + WAS to A/B-group filling. The variation rules of vertical stress are the opposite. The results illustrate that the change rate of dynamic responses was much greater when the subgrade filling changed from quicklime-modified filling to A/B-group filling, than when the subgrade filling changed from cement-modified filling to A/B-group filling. It is inferred that the cement-modified sample is more appropriate as a substitute to A/B-group filling. Additionally, the results indicate that vertical dynamic responses were attenuated rapidly after spreading through the subgrade, particularly on the bed surface. This may be attributed to the damping effect of the subgrade layer. The damping effect caused the train load to spread to deep layers by way of dynamic waves. The greater the stiffness, the faster the dynamic waves diffuse and attenuate.