# Effect of the Rolling Friction on the Heap Formation of Dry and Wet Coarse Discs
## 3 Results and Discussions
### Initial Particles Packing Effect  
The interaction between the particles and the lateral walls has a big influence on the initial packing of the particles. Its effect depends on the rolling friction models but also on the liquid content. In dry conditions, the particles falling phase is similar to a free fall. In that case, the proximity between the particles and the lateral walls is not close enough to create contact forces and moments. Meanwhile, with high liquid volumes with model A, we noticed friction forces that produce a \"wave\" configuration in the granular media, leading to different trajectories of the particles. The attraction between the particles and the sidewalls happens as soon as the liquid content reaches the threshold value of 219% with model A, whereas with model C, it was not noted (Figure 13). At a particular volume of liquid, the capillary attraction force is large enough to bring particles closer to lateral walls. The result is a frictional contact force and a moment that tends to change the trajectory of the particles. To explain the difference of the behavior with models A and C, we isolated the torque produced by the interaction between the particles and the walls. Figure 14 displays the mean value of the torque, by time step, from particle-wall interactions. When  
Model A produces a low torque depending only on the normal force and cannot resist the momentum created by the friction. In contrast, with model C, the combination of the spring and the dashpot torques is high enough to produce rolling resistance. To study the effect of the initial particles' arrangement during the static phase before the walls opening, we have selected and isolated the particles inside the triangle formed by the axis of the bottom wall and the lines passing through (-L/2,0) and (0,60D) on the one hand, and (L/2,0) and (0,60D) on the other hand (see Figure 15). Figure 16 shows the relationship between the fraction of the particles in this triangle and the final height of the wet pile in model A and C cases, respectively. The result shows that in both model A and model C cases, the height of the pile increases when that ratio, i.e., the number of particles in the triangle area decreases, regardless of the volume of liquid in the system. This means that the cohesion force is not significant enough compared to the other forces in the case of coarse discs subjected to a dynamic phase. The height of the pile depends more on the number of particles in the central triangle area than on the volume of liquid. As the  
Figure 14: (**a**) Mean torque between the lateral walls and the particles with models A and C. In (**b**), we highlighted the part of the curves in the dotted blue square corresponding to the initial falling phase. Figure 13: Friction forces between the lateral walls and the particles with models A (**a**) and C (**b**). We notice there is no ”waving” phenomenon with model C.  
number of particles in the triangle increases, this results in an increase in the concentration of the packing, the contact force chain, and the elastic potential energy. The binary cohesion force does not increase. Therefore, after the opening of the lateral walls, the repulsive force between the particles combined with the action of the gravity force decreases the height of the residual pile. The aspect ratio is an important parameter whose study allows a better understanding of the flow dynamics. It is defined as the ratio of the initial height to the initial half-width of the packing. \[A_{a}=\frac{H_{i}}{R_{i}}\]  
The free fall of particles gives us an initial packing of particles that vary slightly according to the amount of liquid and the rolling resistance model. We found out that, for our column aspect ratio \(A_{a}\), the measured final runout radius, \(R_{f}\), is related to the initial radius by \(R_{f}=R_{i}\) (\(1+2.21A_{a}\)) for model A and \(R_{f}=R_{i}\) (\(1+1.87A_{a}\)) for model C.  
Figure 16: Pile height against the fraction of the packing inside the central triangle with model A (**a**) and C (**b**).