## 3 Results
### Container Kinematics
#### 3.3.1 Trajectories  
First, the container trajectories are analysed for both OR1 and OR2. Figure 5 illustrates the results for OR1 with Figure 5a showing the trajectory over the test area with the solid grey lines and solid black line representing all the experiments and their mean, respectively, compared with the numerical results represented with a solid red line. Note that the mean experimental values were calculated only up to when data was available for all experimental runs (see Figure 5b). The larger differences between the simulation and the experiments are found during the initial movement, for \(x\leq 3.5\) m, where the simulated container proceeds almost in a straight line in contrast to the real ones which are very often characterised by a transversal motion as shown also by the mean trajectory. However, at a later stage the simulated container also starts a meandering motion reaching a maximum value of \(y=+0.0447\) m at \(x=5.77\) m, slightly further than the experimental one for which the same value occurs at \(x=5.80\) m. This behaviour of the container can be mainly associated with the not perfectly symmetrical distribution of the masses (Section 2.3) as the flow was mainly symmetrical with respect to the \(y\)-coordinate in the experiment (see [PERSON] et al. [20]) as well as in the numerical simulation.  
Figure 5b,c show the evolution of the trajectories components in \(x\) and \(y\), respectively, over time. This helps to additionally identify the point of motion initiation which, although starting slightly before than in the experimental mean due to the slightly higher velocity of the flow, closely matches between simulations and experiments. In Figure 5b it can be noticed that the slope of the \(x\)\((t)\) curve is nearly constant in the simulations, while in the experiments it varies, indicating differences in the velocity as discussed in the next subsection. The performance was measured with the \(nRMSE_{l}\), i.e., Equation (7) for both directions and summarised in Table 3.  
The results for OR2 are shown in Figure 6 and compared with the corresponding experiments, as done for OR1. The numerical trajectory (Figure 6a) follows the mean experimental trajectory but with a divergence from the mean values on the \(y\)-coordinate for \(x>4.5\) m. Additionally, the numerical model is not able to reproduce the experimental container trajectory at the onset of the motion, first towards and then away from the centre of the flume. These differences, which are particularly noticeable in Figure 6c, also affect the \(nRMSE_{l}\) (Table 4) in \(y\)-direction with a higher value than that for OR1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \(x\) & \(y\) \\ \hline \(nRMSE_{l}\) & 0.122 & 0.024 \\ \hline \hline \end{tabular}
\end{table}
Table 3: \(nRMSE_{l}\) values OR1 container trajectory.  
Figure 5: Comparison between experimental and numerical results: (**a**) trajectories and their time evolution in (**b**) \(x\) and (**c**) \(y\) directions for OR1.  
Figure 6: Comparison between experimental and numerical results: (**a**) trajectories and their time evolution in (**b**) \(x\) and (**c**) \(y\) directions for OR2.