# Effect of the Rolling Friction on the Heap Formation of Dry and Wet Coarse Discs
## 3 Results and Discussions
### Model Validation  
We performed experiments in the laboratory using glass beads for the validation of our model. Our study using a macroscopic approach of DEM, we validate our results by comparing the heaps obtained by simulation and experiment. The front and rear walls are totally fixed, and particles can only flow in the lateral direction giving a prismatic heap. To have a concordance of dimensions, we use the projection on the front wall of the result from our experiment, which can be compared with the simulation result [40,41]. This is done by taking our photos from a frontal and perpendicular point of view. For the experiment with 2400 particles, the particles are arranged in 16 \(\times\) 10 \(\times\) 15 inside the confining box. 16 represents the number of particles in the horizontal direction, 10 the number of particles in the vertical direction, and 15 the number of particles in the third dimension. Thus, considering the vertical plane section, we get 16 \(\times\) 10 particles that we will consider for our 2D simulation. In all the experiments, the number of particles in the third dimension does not change. We designed a device made of four vertical glass plates arranged on a horizontal one used as a bottom wall (see Figures 27 and 28). The two lateral plates have central holes allowing a fifth plate to maintain the glass beads before the falling phase. Particles are first put in the upper part of the device before we remove the middle plate and let them fall in the box below and settle under gravity (Figure 27). Finally, we remove the lateral walls. For the numerical simulations, rolling friction is introduced to account for the little groove in the bottom wall of our experimental device. A calibration test was conducted to determine the rolling friction coefficient by a simple angle of repose test. The rolling friction coefficient is found equal to 0.03 after simulations were carried out to match a laboratory calibration test. Model A is used in all our simulations. The glass beads have the characteristics recorded in Table 3.  
Figure 26: Comparative rotational kinetic energy for dry (**a**) and wet (**b**) particles in case B simulations (liquid volume \(5\times 10^{-6}\) m\({}^{3}\)). We determined the value of the restitution coefficient by a simple drop test, and the Young's modulus, Poisson ratio, and viscosity coefficient between glass beads and different materials can be found in the literature. Figures 28-31 show the experiments and simulation results of the heap formation of glass beads with different aspect ratios in dry conditions. Figures 32-35 show the experiments with two different packing conditions and liquid volumes. From the snapshots, we can see that a high aspect ratio generally leads to a low pile height confirming the influence of the initial potential energy on the final height of a soil heap discussed in Section 3.4. Overall, we notice that we have good similarities between the piles obtained in simulations and experiments both in wet and dry conditions. More experiments and simulations were performed with different aspect ratios, and the results are shown in Figure 36. We remark that in both the experiment and simulation, the pile height decreases when the aspect ratio increases. Therefore, the results found with the experiments are in good agreement with the simulation results. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name of Variables** & **Symbol** & **Value** \\ \hline Particle Diameter (mm) & D & 10 \\ Number of particles & - & From 80 to 160 \\ Particle Density (Kg/m3) & \(\rho\) & 2500 \\ Sliding friction coefficient & \(\mu\) & 0.26 \\ Coefficient of restitution & e & 0.73 \\ Coefficient of rolling friction & \(\mu_{r}\) & 0.03 \\ Young’s Modulus (MPa) & E & 11 \\ Poisson Ratio & \(\
u\) & 0.29 \\ Initial packing concentration & c & 0.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Glass beads parameters used in our numerical simulation. Figure 27: Glass beads initial packing in experiment (a) and simulation (b).