# Idealisations of Dynamic Modelling for Railway Ballast in Flood Conditions
## 4 Discussion on Suitability of Ballast Idealisation
### Past Investigations into Ballast  
The most common dynamic properties of viscoelastic engineering materials are dynamic stiffness and damping. The idealization of ballast has represented the properties of ballast by using spring and dashpot. Such a method has been adopted for multi-body simulations of train-track interaction in rail industry and has been used for condition monitoring tests in the field and/or in the laboratory.  
In the field, [PERSON] and [PERSON] [47] have observed the dynamic characteristics of the ballasted railway track and relevant components. The FRFs [48] were obtained by acquiring the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Types**} & \multirow{2}{*}{**Flooding Level**} & \multicolumn{2}{c}{**Volume of**} & \multirow{2}{*}{**Buoyancy (N)**} & \multirow{2}{*}{**Self-Weight**} \\  & & **Ballast (m\({}^{3}\))** & & & \\ \hline \multirow{6}{*}{\
\begin{tabular}{c} Large-scale \\ ballast bed \\ (natural ballast) \\ (natural ballast) \\ (40 cm \\ \end{tabular} } & 00.00 & 0.00 & 0.00 & 0 \\  & 0.17 & 0.09 & 873.22 & 2438.30 \\ \cline{1-1}  & 20 cm & 0.33 & 0.18 & 1746.44 & 4876.59 \\ \cline{1-1}  & 30 cm & 0.50 & 0.27 & 2619.67 & 7314.89 \\ \cline{1-1}  & 35 cm & 0.58 & 0.31 & 3056.28 & 8534.04 \\ \cline{1-1}  & 40 cm & 0.67 & 0.36 & 3056.28 & 8534.04 \\ \hline \multirow{6}{*}{
\begin{tabular}{c} Small-scale \\ ballast bed \\ (natural ballast) \\ (40 cm \\ \end{tabular} } & 00 cm & 0.00 & 0.00 & 0.00 \\  & 0.03 & 0.02 & 164.69 & 459.87 \\ \cline{1-1}  & 20 cm & 0.06 & 0.03 & 329.39 & 919.74 \\ \cline{1-1}  & 30 cm & 0.09 & 0.05 & 494.08 & 1379.61 \\ \cline{1-1}  & 35 cm & 0.11 & 0.06 & 576.42 & 1609.55 \\ \cline{1-1}  & 40 cm & 0.13 & 0.07 & 576.42 & 1609.55 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The water buoyancy by different materials and containers.  
Figure 25: Typical structure of ballast track [42].  
resonance frequency range of 0 to 1600 Hz, and the 2 degrees-of-freedom models have been established and analysed for modal parameters [49].  
[PERSON] et al. [50] have studied the sleeper-ballast interaction and refered to the use of special pads such as under sleeper pads to reduce ballast settlement and displacement, thereby saving life cycle costs, numerical modelling and a non-destructuve testing (NDT) technique are discussed. The results showed evidence that USP can increase track flexibility and reduce the full track resonant frequency of about 18%, which suggests influence in track dynamic behaviour. The laboratory simulation experiments are generally used together with preloads because the ballasts are consistently under stress during the train passage [51]. [PERSON] et al. [52] applied the static preload to test elastic materials in tracks, and generate the vibration using the instrumental hammer excitation system to obtain ballast's dynamic properties.  
[PERSON] et al. [53] have studied the law of deformation and the degradation behaviour of ballast under static and dynamic loads, applying cyclic loads and specific frequencies to simulate high-speed trains, and to measure the settlement and damage of ballast, indicating that the ballast particle size distribution has a significant influence on ballast degradation, and the settlement of ballast stabilizes within 100,000 load cycles. For the environmentally friendly materials, [PERSON] et al. [54] have focused on the mixing of tire-derived aggregates into polymers in different proportions. Under different types of preload dynamic loads, the FRF method is used to calculate the new materials' significant effect of shock absorption and noise reduction, then propose 10% of tire-derived aggregate is ideal for practical use.