## 3 Results and Discussion
### Model Validation and Analysis  
Comparing the numerical simulation results of the three different interface force models displayed in Table 1, as shown in Figure 8, in the forepart (L = 2-2.2 m) of the dam body, the erosion of the three models to the dam body was observed to be very similar. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Test No.**} & \multicolumn{5}{c}{**Factors**} \\ \cline{2-6}  & **Interfacial Force** & \(\mu\) **(Pa*)** & \(\mu_{0}\) **(Pa)** & \(\mu_{1}\) **(Pa*)** & \(\mu_{2}\) **(Pa*2)** \\ \hline
1 & F\({}_{\mu}\) & & & & \\
2 & F\({}_{\mu}\) + F\({}_{\mathrm{d}}\) & 0.00000101 & 0.00004 & 0.0048 & 0.0197 \\
3 & F\({}_{\mu}\) + F\({}_{\mathrm{d}}\) + F\({}_{\mathrm{vmg}}\) & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental conditions (viscosity values and interfacial force model) adopted for this study. Figure 7: Debris flow free surface for tests 1, 2, 3 (Table 1), (**a**), (**b**) and (**c**) refer to the section upstream the dam body; (**d**), (**e**), and (**f**) refer to the section downstream the dam body. In the middle section (L = 2.2-2.6 m) of the dam body, no. 3 method starts with less sediment if compared with no. 1 and no. 2, and this is more consistent with the experimental results (similarly, in the back half of the dam body, the area between 2.6-3.0 m, due to the consideration of the generalized virtual mass force). The average errors of the three methods against experimental results were 0.022354, 0.03079, and 0.01086, respectively. In order to further study the cause of the difference of dam breach location, the velocity of the particles at the interfacial location was analyzed, as shown in Figure 9.  
By analyzing the characteristics of the velocity distributions (Figure 9), it is possible to notice that the particles in the reservoir area (2.0-2.4 m) have low velocity, and that the particle velocity distribution is concentrated with most particles within the range of 0-0.2 m/s. However after the dam (2.5-3.0 m), because the particles are transforming into free outflow, their gravitational potential energy can be rapidly be converted into kinetic energy. In this region, the average velocity of the particles increases rapidly. Through careful observation, it can also be noticed that the particle velocity in the region of 2.5-3.0 m shows fluctuations, and this result is also consistent with previous research results, that is, SPH particles often propagate kinetic energy by wave conditions. Under the three different models, at t = 0.5 s, the velocity of the three groups did not show significant difference within the range of 2.0-3.0 m, which indicates that at this time, the difference of dam breach degree did not generate any variation in flow velocities; therefore, the difference of dam-break degree is not majorl  
Figure 8: Boundary layer curves under different initiation modes displayed in Table 1.  
Figure 9: Particles velocity distribution within different initiation modes. The force on the boundary particles of the dam was also calculated by pairing particles that had the greatest impact on the dam-break. It was found that in the section of the dam between 2.0-2.5 m, the force direction of the external particles on the dam body is more evenly distributed in the range of \(\{-90^{\circ}+90^{\circ}\}\), which indicates that the particle turbulence in this area may be relatively high. Therefore, it could have a certain randomness for the initiation of particles on the boundary side of the dam. However, as shown in Figure 10, the average velocity of particles at the interface of the front section of the dam body is small and the variation range is small, so according to equation (1), even if the turbulence intensity of the particles in this section is large, it should not be the active area of where the particles starts to move.