# Optimizing Retention Bunkers in Copper Mines with Numerical Methods and Gradient Descent
## 4 Results
### DEM Model of the Current Bin  
The filling of the bunker was realized through a virtual feeding point that generated the ore flow. This feeding point, located at the top of the retention bunker, simulated the operation of the actual feeding conveyor. It filled the retention bunker with ore at a rate  
Figure 7: Calibration results of the DEM model on a real bin: (**a**) load on the front wheel supports, (**b**) load on the rear wheel supports, (**c**) cumulative load on all wheel supports, and (**d**) filling of the retention bunker during measurement.  
of 7200 Mg/h until a total mass of ore approx. 900 Mg was reached in the bunker. The simulation of emptying the retention bunker and the ore flow through the bin is shown in Figure 8. The simulation of the ore flow in the retention bunker revealed that in the initial phase, there is a core flow of ore, followed by the process of cascading ore from the subsequent layers forming a funnel. When the inclination of the funnel walls reaches an angle equal to the critical angle of respose, the final stage begins, during which the bin is emptied of the remaining ore. Only in this last phase is the ore located in the back part of the bin set in motion. The accumulation of material in the back part of the drawer is clearly visible in Figure 8. During normal operation of the bunkers, to protect the bin, complete emptying of the ore is prevented. Typically, a protective layer about 1 m thick is left above the upper plane of the bin crown. This is to protect the bin components from the falling ore from the feeding conveyor. Therefore, this operational inconvenience is common when using such devices. Calibration studies in real conditions also confirmed the uneven loading of the back part of the drawer. The predominant load concentrates in the front part of the drawer, which is located towards the outlet opening of the bin, as also demonstrated by measurements. The back part of the drawer is not proportionally loaded, causing most of the load to be transferred by the front wheel sets.  
Figure 9 presents the results of the bin operation simulation in the range of emptying the bunker from 900 Mg to 870 Mg (Figure 9b). This range was chosen based on operational experience, as it represents the most common working condition of the bin, and thus the entire analysis and optimization of the bin were conducted in this range. Figure 9a illustrates the changes in the pressure force from the vertical column of material on the bin drawer from the start until the bunker filling point reached 900 Mg. The pressure force on the drawer decreased from about 550 kN to 273 kN, where the load stabilized due to the organized flow of ore. Figure 9c shows how the capacity of the bin changed during the simulation. The average capacity was 588 Mg/h, fitting within the range of real values, which vary between 450 and 750 Mg/h depending on operational conditions. Figure 9d displays how the average particle velocity on the surface of the drawer changed, averaging 0.40 m/s. The fluctuations seen in the time signal are caused by the reciprocating motion of the drawer.  
The differences between the pressures of ore on the receiving bin drawer measured in real working conditions and the values obtained in the simulation result from the simplification of the simulation model, particularly in the context of the digital ore model. Simplification of DEM model parameters can impact real results as this model does not account for all the complex physical and mechanical interactions occurring in the actual  
Figure 8: Ore flow in the current receiving bin in the EDEM environment.  
environment. Nonetheless, the obtained load scale is close to the real values, which allows considering the simulation results as sufficient for further analysis and optimization. These studies aim to determine the direction of load changes, focusing less on their precise value.