# Deep Learning-Based Estimation of Muckpile Fragmentation Using Simulated 3D Point Cloud Data
## 2 Related Work  
### Estimation for the Particle Size Distribution  
The particle size distribution of blast muckpile has a significant impact on all downstream processes in the mining industry, including loading, hauling, and processing. Figure 2 illustrates the relationship between fragmentation size and unit cost, with the x-axis representing the fragmentation size and the y-axis representing the unit cost. If the fragmentation distribution is skewed towards smaller particles (part A), as shown in Figure 2, useful minerals become excessively fine, resulting in increased costs. Conversely,  
Figure 1: Proposed System Workflow.  
if the particle size distribution is skewed towards larger particles (part C), transportation becomes challenging and additional mechanical crushing is required after blasting, leading to unnecessary costs. To minimize total costs, blasting should be conducted in a manner that achieves an optimal particle size distribution (aiming at part B). However, controlling blasting is complex, as it depends on various factors such as the amount and type of explosives, the number and depth of blasting holes, and the timing of blasting. Consequently, accurate estimation of the particle size distribution of blast nuclepile is essential for optimizing downstream processes, prompting researchers to propose various mathematical models for this purpose, such as the Kuz-Ram mathematical model presented by [PERSON] [8], the Swebrec model proposed by [PERSON] et al. [9], and the Hybrid model introduced by [PERSON] et al. [10].  
\[n=\left(2.2-\frac{14B}{D}\right)\sqrt{\frac{1+SIB}{2}}\left(1-\frac{W}{B} \right)\times\left(abs\left(\frac{BCL-CCL}{L}\right)+0.1\right)^{0.1}\frac{L} {H} \tag{1}\]  
where, \(B\): burden (m), \(S\): spacing (m), \(D\): hole diameter (mm), \(W\): standard deviation of drilling precision (m), \(L\): charge length (m), \(BCL\): bottom charge length (m), \(CCL\): column charge length (m), \(H\): bench height (m).  
The Kuz-Ram mathematical model is a common mathematical model for predicting the size distribution of rock fragments caused by blasting. It is widely used in the mining industry because of the ease of collecting input data and the simplicity of the relationship between blasting design and rock fragmentation results. However, one limitation of this predictive mathematical model is that it tends to underestimate the number of fines produced by the blast, which means it cannot be considered a perfect estimation model. The distinction between 2D and 3D imaging in fragmentation estimation lies in the spatial information captured. 3D imagery, with its depth and volume metrics, provides a comprehensive representation of nuclepile fragments. Our model is specifically designed to leverage this depth of information inherent in 3D data, allowing for a refined fragmentation estimation process. In the diagram illustrating the relationship between fragmentation size and operational costs in mining, depicted in Figure 2, three zones labeled A, B, and C are shown. In zone A, excessive fragmentation leads to increased costs due to the heightened need for drilling and blasting. Conversely, in zone C, while costs for drilling and blasting are diminished, there is a substantial rise in the subsequent transportation and additional crushing expenses. Zone B stands as the optimal middle ground, highlighting the zone of minimum total costs. Here, both the preliminary and subsequent costs converge to provide the most economical mining operation  
Figure 2: Relationship between Fragmentation Size and Operational Costs in Mining.