# Model Test of Dynamic Response of Living Poles Slope Under Train Loads
## 2 Model Test of the Living Poles Slope Under the Action of Train Vibration
### Similar Materials  
In model testing, the similarity between the model and the prototype is crucial, and it determines the success or failure of the model simulation prototype. In order to make the model test truly reflect the dynamic characteristics of the prototype, the similarity relationship between the model and the prototype was derived by using the method of dimensional analysis. Since the prototype embankment slope was symmetrical from left to right, one side of the embankment slope was taken for simulation to save labor and material resources. The dimensions of the slope model in this test were about 2.5 m \(\times\) 1.3 m \(\times\) 1.6 m, and the dimensions of the original slope were about 17.5 m \(\times\) 9.1 m \(\times\) 11.2 m, with a dimensional similarity factor of seven. The main similarity constants of the model are shown in Table 1, C = prototype/model.  
The model materials were composed of graded gravel, quartz sand, red clay, and water. The filling materials were selected for the slope model by trial matching method combined with geotechnical tests. The living poles as root analogs of complex geometry in the experiment were made of Acrylonitrile butadiene styrene (ABS) plastic by 3-D printing, which simulated strength (Tr) and stiffness (E) much more realistically than previously used materials (e.g., wood or rubber dowels) [18]. Due to material and technical limitations, simplified simulations of the root system of a living tree stump were required in the tests: (i) The root systems were all circular in cross-section, with the cross-sectional area decreasing linearly from the top to the bottom. (ii) The deformation of the root system in the test occurred within the elastic range. (iii) Only one main root and eight lateral roots were simulated. (The rest of the fine root system had less of an anchoring effect on the soil.) To increase the friction between the living poles and the soil, a layer of quartz sand was evenly glued on the surface of the living poles using epoxy resin as a binder. The completed live stump model was produced as shown in Figure 2a. Track structure simulation was mainly aimed at sleeper and rail components. The rail sleeper should have the necessary elasticity and sturdiness to enable it to fix the rail as well as the ability to resist transverse and longitudinal displacement. The rail must have sufficient bending stiffness, aiming to distribute the train load to more adjacent sleepers to reduce the concentrated load on a single sleeper. After calculating the similarity ratio, moment of inertia and bending stiffness, this test chose to select No. 5 hot-rolled ordinary channel steel (h is 50 mm, b is 37 mm) as the analog track, and fixed the contact position of the track and sleeper by spot welding. The rail model is shown in Figure 2b.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Physical Quantity** & **Similarity Relation** & **Similarity Factor** & **Postscript** \\ \hline Size (L) & \(C_{L}\) & 7 & controlled quantity \\ Density (\(\rho\)) & \(C_{\rho}\) & 1 & controlled quantity \\ elasticity modulus (E) & \(C_{E}\) & 1 & controlled quantity \\ cohesive force (c) & \(C_{c}\)= \(C_{E}\) & 1 & \\ internal friction angle (\(\varphi\)) & \(C_{\varphi}\) & 1 & \\ poisson ratio (\(\mu\)) & \(C_{\varphi}\) & 1 & \\ Load (P) & \(C_{P}\)= \((C_{L})^{2}C_{\rho}\) & 49 & \\ Frequency (f) & \(C_{f}=(C_{L})^{-1}(C_{\rho})^{-1/2}(C_{E})^{1/2}\) & 0.14 & \\ Displacement (u) & \(C_{u}\)= \(C_{L}\) & 7 & \\ Strain (\(\sigma\)) & \(C_{\sigma}\)= \(C_{E}\) & 1 & \\ Time (t) & \(C_{t}=(C_{L})(C_{\rho})^{1/2}(C_{E})^{-1/2}\) & 7 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Similarity constants of model.