# Effect of the Rolling Friction on the Heap Formation of Dry and Wet Coarse Discs
## 2 Materials and Methods
### Numerical Model  
A 2D DEM simulation is performed using a self-implemented Fortran program to study the dynamic heap formation of wet and dry soil using rolling friction models A, B, and C already described. Particles have a circular shape with a uniform radius. The 2 Dapproach is chosen to simplify the problem. Moreover, it is computationally more efficient. This is very important when simulating a cohesive model because of its computational cost. Other researchers have adopted this approach for real problems and have found satisfactory results. These results are usually applicable to 3D systems [22]. The simulation is done in two parts. First, the particles fall under gravity without initial velocity in a box of 0.62 m width and 1.05 m depth bordered by three walls. This aims to reduce the packing influence on the results and study different cases with different initial dispositions. The drop height H is defined as:  
\[H=2n_{v}d_{v}\]  
where \(n_{v}\) is the number of particles in the vertical direction, and \(d_{v}\) the distance separating two particles in that direction. After several time steps enough to let them settle till they reach a static equilibrium with minimal kinetic energy, we proceed to the second part, which consists of moving the sidewalls outward with a constant velocity \(V_{x\lambda}\) that allows particles to move without any constraint and enter in a dynamic flow phase. The studies indicate that as long as the settling time is not too short, it will not affect the heap formation much [23]. The value of \(V_{x\lambda}\) is chosen so it does not affect the results. It is not too small to avoid contacts between the particles and the walls when they move. It is also not large to prevent the system from being disrupted. Simulations were run as trials, and using the dichotomy method, we chose \(V_{x\lambda}\) equal to 1.8 m/s. The second part of the simulation is run until the particles reach a final static equilibrium state. They reach that state before 4.315 s in all our simulations. The particle system's behavior can then be analyzed, and different parameters of the system can be calculated throughout the flow and after the final static equilibrium. Numerous simulations are run with different dry and wet conditions to study the bulk behavior and the influence of the water content and the rolling friction model. Our simulation test setup is a good way to evaluate the dynamic behavior of liquids and granular materials in transient conditions. They incorporate the 3 critical phases: the triggering phase, the \"fully-developed\" flow, and the final jammed state. Furthermore, the first falling stage of the particles avoids crystal-like ordering of the discs and gives more natural initial packings. The validity of the present model is ensured by experimenting with glass bead dynamic heap formation and its macroscopic comparison with our simulation results. The parameters of the Jumijin sand that we use in our study can be found in the literature [37]. The contact parameters between the particles and the liquid (contact angle and surface tension) are the same as in [17]. The liquid under consideration is water. The parameters used in our simulations are recorded in Table 1: