# Applicability Study on Modified Argillaceous Slate as Subgrade Filling for High-Speed Railway
## 4 Dynamic Simulation Analysis of Soft-Rock-Modified Soil as Subgrade
### Dynamic Model Establishment
#### 4.1.2 Model Establishment and Verification  
The calculation length along the line is taken as 63 m; the depth of the subgrade is taken as 5 m. Considering the symmetry of the doublet structure for HSR, only half of the railway line was used in the calculations. The XZ plane is the symmetry plane seen in Figure 10.  
The whole rail-track coupling system was established by finite element software ANSYS and the corresponding APDL language [44; 45]. The subsystems were modeled by different elements, while coupling surfaces of the separate materials were connected to each other without relative displacements. Horizontal fixing was constrained in the symmetrical plane, and the viscoelastic artificial boundary was used in the model at the cutoff of an infinite continuous medium. In addition, Rayleigh damping and a viscoelastic constitutive model were used in this paper. Parameters: Fasteners and a sub-track rubber cushion system were considered as a spring-damp structure with an initial length of 38 m. Adopted total equivalent stiffness was 4.38 \(\times\) 10\({}^{7}\) N/m, and the damp parameter was 4.5 \(\times\) 10\({}^{5}\) N \(\cdot\) s/m, with a CA mortar elastic modulus of 1.25 \(\times\) 10\({}^{9}\) N/m\({}^{3}\) and damping of 8.3 \(\times\) 10\({}^{4}\) N \(\cdot\) s/m\({}^{2}\). Other general calculation parameters are listed in Table 11. The parameters with \({}^{\star}\) marked in the table are estimated from tests mentioned in Section 3. The additional parameters are generic values widely adopted in the literature. Train load: Since the model was used to study the dynamic performance of track and subgrade, the trainload was simplified by a moving wheel-rail force. As shown in Figure 11, At any time \(t\), when vehicle moves in a constant speed the wheel loads are:  
\[f(t)\ =\ p\delta(x-vt) \tag{6}\]  
where \(p\) is wheel load; \(x\) is the wheel position at time \(t\); \(\delta\) is function of \(\delta\), viz., \(\delta(x_{i}=vt_{i})=1\) and \(\delta(x_{i}\
eq vt)=0\), in which \(x_{i}\) is rail ditch position of the track plate, \(x_{i}=x_{0}+\mathrm{i}_{ls}(i=1,2,\,\ldots\), N); \(x_{0}\) is the initial referring point; and \(l_{s}\) is the space between rail ditch. Taking the train (CRH2-300) speed \(v=350\) km/h, two power carriages at the head and tail and six carriages \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \(E\) & \multirow{2}{*}{\(\
u\)} & \(\rho\) & \(\Phi\) & \(\mathbf{C}\) \\  & **(GPa)** & & & (\({}^{\circ}\)) & (kPa) \\ \hline Rail & 210 & 0.3 & 78 & & \\ Track plate & 34.0 & 0.1667 & 30 & - & - \\ Concrete Supporting & 25.5 & 0.20 & 24 & & \\ C15 concrete & 22.0 & 0.25 & 24 & - & - \\ Graded gravel & 1.78 & 0.30 & 24 & 45.8 & 1326 \\ +59 cement & 1.58 & 0.24 & 24 & 39.5 & 160 \\ Graded gravel & 1.58 & 0.26 & 2.35 & 41.8 & 200 \\ A/B-group filling & 0.53 & 0.26 & 1.61 \({}^{\star}\) & 29.0 \({}^{\star}\) & 68.5 \({}^{\star}\) \\ +3\% cement & 0.32 & 0.26 & 1.62 \({}^{\star}\) & 30.6 \({}^{\star}\) & 79.9 \({}^{\star}\) \\ +7\% cement & 0.36 & 0.26 & 1.65 \({}^{\star}\) & 31.8 \({}^{\star}\) & 100.8 \({}^{\star}\) \\ +5\% quicklime & 0.22 & 0.26 & 1.58 \({}^{\star}\) & 28.2 \({}^{\star}\) & 62.1 \({}^{\star}\) \\ +6\% quicklime & 0.24 & 0.26 & 1.59 \({}^{\star}\) & 29.6 \({}^{\star}\) & 76.5 \({}^{\star}\) \\ +7\% quicklime & 0.26 & 0.26 & 1.57 \({}^{\star}\) & 29.2 \({}^{\star}\) & 67.3 \({}^{\star}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Calculation model parameter of tunnel-culvert-culvert transition zone. Figure 10: Numerical Model. in the middle of the train were included. For the power carriage, the coach distance is 11.46 m, the wheelbase is 2.5 m, the vehicle length is 25 m, the axle weight is 14 t and the wheel load is 70 kN. For the trailer, the wheelbase is 2.5 m, vehicle length is 25 m, axle load is 14 t and wheel load is 70 kN. Track and subgrade: The rail was made of No. 60 rail in Japan and the cross-section was an \"I\"-shaped beam; the space between rails was 1435 mm.