## 3 Model Validation  
The ground vibration responses and train-track dynamic interactions obtained from the coupled train-track-soil model with dry soils have been validated in [37]. In order to validate the pore water pressure obtained from LS-DYNA, a numerical model with saturated soils is developed based on the lab-test model, in which the time history curves of the pore water pressure of saturated soils are obtained. The test model consists of a bearing plate, loading steel beam, concrete base, the upper layer of subgrade bed, and the lower layer of subgrade bed. The upper layer of subgrade bed is infiltrated with water to make the soil saturated. A waterproof layer between the two layers of soils is used. A dynamic load with an amplitude of 96 kN and a frequency of 5 Hz, is applied to the bearing plate. The details of this lab-test can be found from [44; 45; 46; 47]. The lab-test model and numerical model are shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{2}{c}{**Density (kg/m\({}^{3}\))**} & \multicolumn{2}{c}{**Gravitational Acceleration (m/s\({}^{2}\))**} & \multicolumn{2}{c}{**Bulk Modulus (GPa)**} \\ \hline \(1000\) & & 9.8 & & 2.2 \\ \hline \end{tabular}
\end{table}
Table 2: Properties of the water.  
Figure 4: \(Cont.\)  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{**Components**} & \multicolumn{1}{c}{**Depth (m)**} & \multicolumn{2}{c}{**Density (kg/m\({}^{3}\))**} & \multicolumn{2}{c}{**Elastic Modulus (MPa)**} & \multicolumn{1}{c}{**Poisson’s Ratio**} \\ \hline \multirow{3}{*}{Subgrade} & Surface layer & 0.4 & 2300 & 200 & 0.25 \\  & Bottom layer & 2.3 & 1950 & 150 & 0.35 \\  & Subgrade body & 2 & 2100 & 110 & 0.3 \\ \hline \multirow{3}{*}{Ground} & First layer & 2.4 & 1900 & 42 & 0.3 \\  & Second layer & 13.1 & 2010 & 83 & 0.36 \\ \hline \multicolumn{2}{c}{Piles} & 15.5 & 2200 & 7000 & 0.2 \\ \hline \end{tabular}
\end{table}
Table 3: Properties of multi-layered soils and piles.  
The time history curves of the pore water pressure at PM-1 and PM-2 are illustrated in Figure 5. The simulated curves exhibit a very good agreement with the shapes of experimental results, but the amplitudes show some differences. The maximum and minimum pore water pressures obtained from experimental and numerical results are shown in Table 4. There was less than an 8% difference between experimental and numerical amplitudes in all cases, indicating the pore water pressure obtained from LS-DYNA was reliable in practice. This agreement of the result is thus considered reasonably acceptable.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{3}{c}{**PM-1**} & \multicolumn{3}{c}{**PM-2**} \\ \cline{2-7}  & **Experimental Value (kPa)** & **Numerical Value (kPa)** & **Difference (\%)** & **Experimental Value (kPa)** & **Numerical Value (kPa)** & **Difference (\%)** \\ \hline Maximum & 18.84 & 17.35 & 7.91 & 17.40 & 16.94 & 2.64 \\ Minimum & 6.00 & 5.64 & 6.00 & 5.96 & 5.72 & 4.03 \\ \hline \end{tabular}
\end{table}
Table 4: Maximum and minimum pore water pressures from experimental and numerical results.  
Figure 4: Lab-test model and numerical model: (**a**) Lab-test model, (**b**) numerical model developed in LS-DYNA, and (**c**) cross section of the numerical model.  
Figure 5: Time history curves of pore water pressure: (**a**) pore-water-pressure measurement (PM)-1 and (**b**) PM-2.