## 3 Results  
### Run-Up Height  
Figure 4 shows a comparison between the observed kinematics captured at the maximum run-up using the high-speed camera for each test. As shown in Figure 4, the flow piled up to form a gradual increase in dead zones behind baffles, after which the flow was deflected upwards along the surface of the rigid barrier. In each experiment, the arrival time for the maximum run-up height ranged from 0.50 to 1.46 s (time from entering the baffles to the maximum run-up height at the rigid barrier), and the maximum run-up height was significantly different according to the presence of baffles. In Figure 4a, because of the absence of the interference of baffles, the maximum run-up height was observed, which was much higher than the height of the rigid barrier. In Figure 4b-e, with the baffle arrays, the flow was affected by the first and second rows of baffles, and then the flow dispersed around the baffle arrays. Subsequently, there was a relatively lower run-up height behind the rigid barrier. Figure 5 shows a comparison of the maximum run-up height measured at the rigid barrier. The run-up height for each test was measured at the maximum vertical height for the flow process and was normalized with the flow depth (\(h_{a}\)) before the flow entered the baffles. A horizontal reference line was also plotted for the height of the rigid barrier. The maximum run-up height for the case with no baffles (H0) increased up to 2.65 times that of the rigid barrier height. Meanwhile, the run-up height for cases with baffles (H60 and H120) decreased by an average of 40% compared with the case of no baffles. This can be considered to be the effect of flow impedance caused by the impact with the baffles. Furthermore, taller baffles had a negligible effect on the run-up height, while increasing the number of rows of baffles from one row (R1) to two rows (R2) led to an additional 23% of run-up height reduction. Likewise, the addition of baffle rows exhibited a gradual reduction in the maximum run-up to the height of the rigid barrier (\(h_{r}/h_{a}=6\)). This was because an additional staggered row of baffles decreased the flow discharge, and the energy of the debris flow approaching the rigid barrier decreased thereafter. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Baffle** & **Baffle** & **Number** & **Spacing** & **Transverse** & **Amount** & \\
**Condition** & **Height (H)** & **of Rows** & **Successive** & **Blockage** & **of Soil** & **Designation** \\  & & **(R)** & **Rows (L)** & **Ratio (B)** & **(kg)** & **(kg)** & \\ \hline Without & - & **—** & **—** & **—** & & H0 \\ baffles & & 1 & & & & & H60-R1 \\ With & & 2 & & & & H60-R2 \\ baffles & & 1 & 200 mm * & 40\% & & & H120-R1 \\  & 120 mm & 2 & & & & H120-R2 \\ \hline \hline \end{tabular}
* Spacing from the final row of baffles to the rigid barrier: 200 mm.  
\end{table} 
Table 1: Test conditions. Figure 4: _Cont._  
The analytical approach for run-up height is based on the conservation of mass and momentum. Two methods for the energy principle and momentum-based approach were proposed by [PERSON] et al. (2009) and [PERSON] (2012) [5,25], respectively, to predict the trend line for the run-up height of debris flows. The energy principle proposed by [PERSON] (2012) [5] is given as:  
\[\frac{h_{f}}{h}=1+\frac{v^{2}}{2 gl} \tag{2}\]  
where \(h_{f}\) is the final run-up height (m), \(h\) is the approaching flow height (m), \(v\) is the flow velocity (m/s), and \(g\) is the acceleration of gravity (m/s\({}^{2}\)).