# 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
#### 4.2.2 Dynamics Strength Analysis  
Dynamic strength was tested using a dynamic triaxial instrument, DTC-306, made in Japan, which was calibrated before testing. The sample was sieved through a 2 mm sieve and then was compacted to a \(\Phi\)35 mm \(\times\) 70 mm cylinder specimen with OMC at a compactness of 0.95. The test was conducted at confining pressures of 0 kPa, 25 kPa, 50 kPa and 100 kPa (stress-controlling) and a sine-wave load with 5 Hz frequency.  
The dynamic strength of the specimen refers to the maximum stress at which the corresponding strain does not exceed a certain allowable value (1% in this study) under the given loading times. The dynamic strength curve, known as the fatigue curve, is usually described by the following power function:  
\[\sigma_{d,f}\ =\ kN^{\theta} \tag{7}\]  
where \(k\) and \(\theta\) are the test parameters, which are influenced by compactness, confining pressure, water content and load frequency; \(\sigma_{d,f}\) is the maximum dynamic stress amplitude when the strain of specimen is 1%.  
\(10^{8}\) is converted from the number of vehicle axles passing through the Wuhan-Guangzhou HSR each year. It is taken as the loading times that a subgrade filling can bear in its service life. Table 13 illustrates the dynamic strength obtained by the fitting equation. Figure 14 shows the relationship between dynamic strength and loading times.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Group** & **Natural Sample** & \multicolumn{3}{c}{**+Quicklime**} & \multicolumn{3}{c}{**+Cement**} \\ \hline \(\chi\)**/\%** & **0** & **5** & **6** & **7** & **3** & **5** & **7** \\ \hline k & 203.97 & 215.62 & 235.62 & 294.62 & 597.82 & 661.03 & 490.04 \\ \(\theta\) & \(-\)0.0498 & \(-\)0.0301 & \(-\)0.0234 & \(-\)0.0381 & \(-\)0.0237 & \(-\)0.02658 & \(-\)0.00475 \\ \(\sigma_{d,f}\)/kPa & 66.17 & 123.84 & 153.10 & 146.03 & 386.30 & 417.00 & 448.99 \\ R & 0.9601 & 0.9623 & 0.9247 & 0.9748 & 0.9573 & 0.9488 & 0.9378 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Dynamic of modified WAS by fitting power function.  
From Figure 13d, it is inferred that the dynamic stress on the bed layer is 73 kPa, and 23 kPa on subgrade layer. According to Formula (1), for the bed layer, \(K_{h}\)= 0.95, \(\sigma_{zl}\)\(\leq\) 73 kPa, \(\sigma_{bcu}\)\(\geq\) 117.8/\(\eta_{g}\). If \(\eta_{g}\)\(=\) 0.95, \(\sigma_{bcu}\)\(\geq\) 194 kPa; if \(\eta_{g}\)\(=\) 0.7, \(\sigma_{bcu}\)\(\geq\) 264.2 kPa. Thus, the dynamic strengths of WAS with 3%, 5% and 7% cement meet the dynamic requirement, while the dynamic strength of WAS with quicklime cannot meet the dynamic requirement.  
For the subgrade layer, \(K_{h}\) = 0.90, \(\sigma_{zl}\)\(\leq\) 23 kPa, based on Formula (1), \(\sigma_{bcu}\)\(\geq\) 52.8/\(\eta_{g}\). If \(\eta_{g}\)\(=\) 0.95, \(\sigma_{bcu}\)\(\geq\) 58.1 kPa; if \(\eta_{g}\)\(=\) 0.7, \(\sigma_{bcu}\)\(\geq\) 78.8 kPa. Thus, the dynamic strengths of WAS with cement and quicklime can both meet the dynamic requirement.