# Effect of the Rolling Friction on the Heap Formation of Dry and Wet Coarse Discs
## 1 Introduction  
Granular materials are among the most used materials in engineering projects. They are bulk materials composed of powders with particle sizes varying from 0.1 to 100 \(\upmu\)m and granular solids with diameters ranging from 100 to 3000 \(\upmu\)m [1], and after the fluids, they are the second most used material in the industry [2]. Thus, we often have to use numerical methods to study numerous engineering problems related to them: flow through hoppers, slope stability, geotechnical tests, and so on. Models using continuum assumptions were first used to study granular materials. Still, they cannot represent local discontinuities, which play a fundamental role in their behavior [3]. Nowadays, the DEM is widely used in soil mechanics. First introduced by [PERSON] [4] in 1979, DEM considers the material as an assembly of particles free to interact with other particles. It allows us to have a set of data at each time step, including particle positions, interaction forces, torques, etc. This particular approach is essential to the understanding of the relation between the microscopic and macroscopic parameters. A lot of researchers have shown its efficiency to study granular materials and particle flow [5, 6], even though the application of DEM to natural materials still requires further development [7]. The angle of repose is an important macroscopic parameter in characterizing granular materials' behavior, mainly for slope stability issues and the design of retaining structures [8]. Although its definition is not always straightforward and depends on the application and the material's behavior, we distinguish two types of repose angle: static and dynamic [9]. Different methods have been used to determine the angle of repose of materials, but there is no standardization [10]. Among them, we can cite the tilting box method, fixed funnel method, revolving cylinder/drum method, hollow cylinder method, and tilting cylinder method [9; 11]. Column collapse is a good way to study granular materials under different regimes as well as the formation of the final heap. Because of its simplicity, both numerically and experimentally, it has become a preferential way for researchers to study particles. Despite its apparent simplicity, it makes the grains go through all kinetic phases: static before the opening of the sidewalls followed by the triggering phase, dynamic flow after the opening of the walls, and ends up with the jamming state. In DEM, we usually use heap formation experiments to calibrate the numerical simulation models [12; 13; 14]. This method allows researchers to ensure the accuracy of the input parameters and the simulation results. The particle properties are not easy to determine experimentally. Two types of calibration are used. In direct calibration, the simulation is calibrated by empirically measuring the particle properties and then using them as the simulation inputs. In reverse calibration, a bulk property is measured, such as the distribution of particle size, bulk (packing) density, and repose angle. Then, a set of simulation parameters is changed until the measured bulk properties are matched [15]. However, the microscopical and macroscopical behavior of the particles during heap formation simulations involving a dynamic phase are not totally understood. One of the most promising areas of DEM is the numerical study of wet granular materials. Some researches have been carried out in this field and show that it is a reliable tool to investigate wet particle media. [PERSON] et al. [16] studied the attraction between particles of different diameters and the damage ratio using a cohesion contact model, including the Van Der Waals forces. [PERSON] and [PERSON] [17] developed a contact force model which includes the liquid bridge force for wet particle simulation. Despite many assumptions, their study of glass beads' behavior in pan pelletizer shows fair agreements between their simulation and experiment, proving that their model can be used to simulate cohesion forces between particles.