# Optimizing Retention Bunkers in Copper Mines with Numerical Methods and Gradient Descent
## 1 Introduction  
The transportation system plays a important role in the entire mining process [1]. Due to the specific method of exploitation using a room-and-pillar system, the transportation system in underground copper ore mines is highly complex [2]. Owing to the widespread use of conveyor belts in material transport [3], there are many strategic points along the route where the ore is transferred from one conveyor to another [4]. This is necessary due to changes in the direction of transport or differences in the elevations of the conveyor belts. Some of the most important elements in the considered transportation system are retention bunkers, which are recognized as a specific, large structure, practically encountered only in this type of mining [5]. Their main task is to maintain the continuity of ore flow, minimize fluctuations associated with changes in material flow, and accumulate the ore [6]. The design of such devices has a significant impact on their operational parameters and should ensure effective, reliable, and safe operation [7]. However, due to the scale and the amount of the material flowing through them [8], they are exposed to various risks. Therefore, a very important aspect is understanding the loads acting on the receiving bin structure located under the retention bunker, which is directly subjected to all static forces from the vertical column of material and dynamic forces from falling rocks [9]. At the loading points of transfer chutes, or retention bunkers, the ore falls onto steel elements and the conveyor belt with a certain force whose value depends on its size and velocity, as well as the geometry of the structure [10]. The geometry of the elements on which the ore impactsand slides affects their durability, and causes the loss of physical properties [11]. Moreover, it can cause blockages and limit the transport capabilities of the entire ore handling system. Due to the specificity of retention bunkers, the number of research studies in this area is very limited, especially when it comes to similar structural solutions, with a primary focus on ore receiving bins. Current research primarily concentrates on the design and structural strength analysis of retention bunkers, considering the loads imposed by the surrounding rock mass [12]. However, these studies are less focused on analyzing structural damage or wear of steel surfaces in retention bunker elements resulting from contact with ore. One of the key challenges in designing such equipment is the gap in knowledge regarding the magnitude and distribution of forces exerted by the ore mass on the structural components of the equipment, along with a shortage of established tools to determine these forces. Additionally, the impact of the design and operational factors of bins on the stress distribution on its structure and the impact on the degradation process have never been clearly formulated. The main factor influencing the process of accelerated abrasive wear is certainly the difference between the hardness of the chute elements and the transported material [13]. Vibrations in structures can significantly impact wear, as induced oscillations can lead to increased friction between moving parts, accelerating their degradation [14]. Additionally, uneven distributions of vibrations can cause uneven loads on structural elements, resulting in locally intensified wear, highlighting the necessity of precise modal analysis in the design and maintenance process [15]. In some optimization works related to conveyor transfer points, the use of numerical methods to simulate the behavior of flowing ore particles or other transported materials is a common practice [16]. Numerical methods are also used to optimize material flow on the conveyor itself or within it [17]. Typically, 3D DEM models are created to examine the wear of conveyor components during material transport, and their usefulness has been unequivocally confirmed [18; 19; 20].