## 3 Experimental Programme
### Similarity Rules for Small-Scale Models  
According to API 650: Welded Steel Tanks for Oil Storage [36], the real diameter of the TST prototype can range from 5 m to more than 20 m, depending on the storage requirement of the materials inside. The ratio of the diameter and thickness (\(d/t\)) of the TSTs varied from 600 to 3000. In this study, the scale factor \(\lambda\) was calculated using the ratio of the diameter of the real-world prototype and a small-scale TST (\(d_{p}/d_{m}\)), or the ratio of the height level of the storage liquid in the real-world prototype and small-scale TST (\(hl_{p}/hl_{m}\)), as shown in Equation (13). The selected small-scale models in the paper had a ratio of \(d/t\) around 1400, which is the average value in the API 650 standard. The scale factors of the models were around 1/10 to 1/40, depending on the real-world prototype of the TSTs.  
The pressure measured in a small-scale model should be scaled up to the real-scale. Froude scaling is commonly used in the sloshing model test [37; 38]. A small-scale model test was conducted based on the assumption that a test using Froude scaling can reproduce sloshing impacts that are representative of the real-world prototype. The similarity rules for small-scale TSTs in this study were determined based on Froude number \(F\), as shown in Equation (14). Similarity parameters, including the elastic modulus \(E\) and pressure \(p\), were calculated by using the Cauchy number \(C\) and Euler number \(E_{e}\), respectively (Equations (15)-(18)). These values were determined based on the results of the Froude number regarding the characteristic velocity \(V\)[38].  
\[\lambda=\frac{L_{p}}{L_{m}}=\frac{d_{p}}{d_{m}}=\frac{h_{lp}}{h_{lm}} \tag{13}\]  
\[F=\frac{V}{\left(gL\right)^{1/2}} \tag{14}\]  
\[C=\frac{0.95\rho V^{2}}{E} \tag{15}\]  
\[E_{e}=\frac{p}{\rho V^{2}} \tag{16}\]  
Figure 6: Test setup: connecting the TST with the shaking table machine.  
\[E_{m}=E_{p}\frac{\rho_{m}}{\lambda\rho_{p}} \tag{17}\]  
\[p_{m}=p_{p}\frac{\rho_{m}}{\lambda\rho_{p}} \tag{18}\]  
In Equations (13)-(18), \(L\) is the characteristic length and the subscripts \(p\) and \(m\) denote the prototype and model, respectively. \(V\) is the characteristic velocity, \(E\) is the elastic modulus, \(g\) is the gravitational acceleration, and \(\rho\) is the liquid density.  
It is clear from Equation (18) that using steel balls that have high densities can create a higher pressure for small-scale models compared to a normal liquid. The pressure created from the normal liquid is very small if the same liquid in the model and prototype is used, and the impact of a liquid on small-scale TSTs is trivial. Therefore, the steel balls that replace a normal liquid can be used effectively to evaluate the impact of storage materials in TSTs. Table 6 shows the similarity rules for small-scale models with scale factors of 1/10 and 1/40. The values of the similarity parameters, including the elastic modulus and pressure, were modified by their multiplication with the volume fraction of the steel balls (\(v_{s}\)). This is because there are distances between the steel balls, while there is almost no distance between the liquid particles. It can be seen that the elastic modulus of small-scale models was smaller than this value from the real-world prototype. Therefore, aluminum material in the small-scale models was chosen to replace the steel material in the real-world prototype of the TSTs. The ratio of the elastic modulus of the small-scale model and real prototype was around 0.35.