# A Mesh-Free Particle Method for Simulation of Mobile-Bed Behavior Induced by Dam Break
## 3 Simulation Results and Discussion
### Simulation of Dam Breaking with Soil Bed  
Newly developed MPS for multiple liquids was applied to simulate the broken dam problem with the soil bed shown in Figure 6. The tank is divided by a gate, which is located 1 m away from the left side of the tank. The left side of the gate is filled with water particles with 0.15 m depth, while the soil bed with various thicknesses is on the right side of the tank. For the soil particle, polyethylene-oxide (PEO) solution was used, which corresponded to the experiment [3]. In the simulation, the thickness of the PEO solution was set to 0.015 m, 0.030 m, 0.058 m, and 0.070 m. The kinematic viscosities of the water particles were \(1.0\times 10^{-6}\) m\({}^{2}\)/s and \(6.0\times 10^{6}\) g/mol, respectively. The densities of water and PEO are 1000 kg/m\({}^{3}\) and 960 kg/m\({}^{3}\), respectively. The gate opened upwards of 1.5 m/s. For this simulation, the total particle usage was 91,640 for 0.015 m of depth of PEO, 100,380 for 0.030 m of depth of PEO, 120,760 for 0.058 m of depth of PEO, and 141,420 for 0.070 m of depth of PEO. The initial particle distance is set to 0.001 m, and the time interval is 0.0001 s. All of the variances that use the initial particle distance and time interval were obtained by the numerical convergence test. The simulation ended at 1 s, and the computational time of each case was 11,720 s, 13,668 s, 19,271 s, and 22,518 s for cases of various thickness, which are 0.015 m, 0.03 m, 0.058 m, and 0.07 m, respectively. Figure 4: Time history of pressure at measuring point. Figure 5: Convergence test for the initial particle distance. Figure 3: Evolution of the collapsed water column. Figure 7 represents comparisons of results with 0.015-m depth of PEO solution between numerical simulation and experiment. By opening the gate, the water column collapsed spontaneously by gravitational force; then, the collided water particle collided with the PEO solution. According to [PERSON] et al., the PEO solution was used to simulate the solid particle [3]. However, its behavior seems to be fluid. This is the reason that the multi-phase MPS method was employed to investigate it. The disturbed PEO solution and the collided water particle form mixed flows and propagated along the tank bed. The PEO solution was thrusted, and then it turned into waves. By recalling the dam break problem without erodible beds, the collapsed water column runs over the bottom of the tank rather than plunging. However, when the collapsed water column collided with the beds, it turned to the plunging waves and mixed, which is shown in both the experiment and the numerical simulation. Moreover, erodible beds were disturbed by an up thrust, which generated waves and propagated fluids. According to comparisons, the overturning wave features and the mixing process were almost the same as the corresponding experiment. There are slight differences between them, but this could be because of small 3D effects from the experiment and the small influence of the roughness of the gate. Since the discrepancy is very small, it can be negligible in any case. Figures 8 and 9 shows the comparisons between the numerical simulations and corresponding experiments with various thicknesses of the PEO solution. The increased amount of PEO solution resisted the propagation of water waves. In this regard, the size of overturning was reduced, and the timing of the generation was delayed. Moreover, in the case of 0.15-m thickness of the PEO solution, the water particle overturned the PEO solution. However, an increased thickness of the PEO solution prevented it. Due to the weight of the soil bed and the collapsed water column, there was more upthrust. These phenomena were observed in both the experiments and the numerical simulation. In the cases of the thick soil layer, which were 0.058 m and 0.07 m, the collapsed water particle ran beneath the PEO solution rather than running over the soil bed.