# Effect of the Rolling Friction on the Heap Formation of Dry and Wet Coarse Discs
## 3 Results and Discussions
### Rolling Friction Effect on Wet Coarse Soil  
We performed simulations with different liquid volumes to study the system behavior and the effect of the liquid bridge volume's variation on the stability of the particles. We considered two cases:  
In case A, we follow the procedure described before. The particles fall vertically and are subject to rearrangement before opening the sidewalls. This procedure gives us slightly different initial packings depending on the liquid volume and the rolling friction model. In case B, dry conditions with no rolling friction are applied during the falling. Then, the cohesion and capillary forces are applied before the walls' removal, after the particles are settled. In this case, we have the exact initial packings. For monosized discs in the presence of a liquid, we have three states [38]: The pendular condition refers to the low moisture content in a packing in which liquid is retained as discrete lenticular rings at particle contacts. When the moisture content is higher, the rings will merge and form a continuous liquid network, resulting in another state called the funicular state. An increasing rise in moisture content causes the capillary state, in which the pores between particles are totally filled with liquid. In our study, 11 cases with liquid bridge volume varying from 1.4 \(\times\) 10\({}^{-4}\) to 1.4 \(\times\) 10\({}^{-10}\) m\({}^{3}\), covering all of the three states are carried out. These states can be defined according to the liquid content, which is the mass of the liquid over the particle's mass and varies with the initial concentration. The moisture contents corresponding to our liquid volumes vary from 6.14 \(\times\) 10\({}^{-3}\) to 6140%, covering a wide range. Table 2 gives the liquid content corresponding to the three states for a porosity equal to 0.4. In case A, the results show that the wet particles cohesion model effect on coarse discs heap formation is minimal. This effect is mainly noticed in the particle arrangement and the energy variation rather than the heap formation. With very small amounts of liquid corresponding to a pendular state (liquid volume equal to 1.4 \(\times\) 10\({}^{-10}\) m\({}^{3}\) ), the behavior of the particles is similar to the dry condition with the same final heap height for models A and C. The heap only begins to increase when the volume of liquid brings the particles into the funicular states, suggesting an increase in the cohesion and capillary forces enough to influence the bulk behavior. \begin{table}
\begin{tabular}{c c} \hline \hline
**States** & **Liquid Content** \\ \hline Pendular & 0 \(<\) M (\%) \(<\) 9.2 \\ Funicular & 9.2 \(<\) M (\%) \(<\) 26.7 \\ Capillary & M (\%) \(\geq\) 26.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The states of a particles system in presence of a liquid. Figure 9: Simulation phases with 2500 particles: (**a**) the initial phase after the collision of the particles with the bottom wall. In (**b**), particles reach a static equilibrium before the opening of the walls. (**c**) particles enter the dynamic phase. Finally, in (**d**), the particles flow to reach the final static equilibrium state shown in Figure 7c. With the two models, our simulations showed a different behavior on both sides of a threshold liquid content equal to 219% (liquid volume equal to 5 \(\times\) 10\({}^{-6}\) m\({}^{3}\)). With model A, from the threshold value, the pile increase with the liquid volume until the maximum asymptomatic value of 4 cm is reached. For model C, this value gives us a peak of heap equal to 3.8 cm. Then the height decreases with larger liquid volume until an asymptotic value of 3.1 cm. Figure 10 shows the pile height obtained with models A and C with different liquid volumes. The presence of asymptotic behavior for increasingly higher water contents is a common phenomenon reported in various tests with spheres or discs (column collapse, shear strength curves of unconfined radial and axial compression tests, and direct shear tests [18]).