## 3 Results and Analysis
### Optimization Design of Stope Pillar Parameters  
In underground mining operations, the design of stope pillar parameters is crucial for ensuring the stability and safety of the mining structures and surrounding rock mass. The stope pillars serve as primary support elements that bear the load of the overlying strata and maintain the stability of the openings. The optimization of stope pillar parameters aims at achieving a balance between maximizing the ore recovery and minimizing the risk of ground failure. Based on the onsite experience and relevant requirements of the mine, the maximum span of an open area in Level 650 should not exceed 60 m. When the stope length is greater than 60 m, a pillar needs to be reserved in the middle of the stope, with the interval between pillars not exceeding 60 m. The design thickness of the pillars generally ranges between 12 and 20 m. To enhance the recovery rate, the area where the gangue shown in Figure 2 is situated is proposed to be preserved as a pillar. This study combined theoretical analysis with the onsite experience to carry out the parameter optimization design for the pillar, aiming to determine the optimum thickness of the pillar. In the process of pillar parameter optimization, certain factors are taken into consideration to ensure that the pillar design aligns with the geological conditions, mining  
Figure 10: Comparison of hoop stress distribution curves around the roadway in Stope 101 before and after the excavation of the adjacent roadway. Figure 9: Distribution curve of hoop stress around the roadway in Stope 101 after the excavation of the adjacent roadway. (The red solid line indicates the stress curve, and the black dashed line indicates the opening boundary). requirements safety standards. The optimization process involves evaluating different pillar thicknesses to understand their impact on stope stability, ore recovery overall mining efficiency. The objective is to find a balance between ensuring adequate support and stability in the stope while maximizing the ore recovery rate. Analytical solutions obtained using the complex function theory were employed to arrive at an optimized design for the pillar that meets both safety and operational objectives. Currently, the calculation of pillar strength in underground mines is mainly based on experimental research and case studies. Specifically for underground hard rock mines, [PERSON] and [PERSON] [20] combined the pillar stability analysis with a database of measured pillar strengths and, on the basis of classic rock mass strength calculation methods and empirical methods, proposed the formula for calculating the hard rock pillar strength as follows:  
\[P_{s}=0.44U(0.68+0.52K_{a}) \tag{19}\]  
where \(U\) represents the uniaxial compressive strength of the rock mass, \(P_{s}\) is the pillar strength, and \(K_{a}\) is the pillar friction coefficient. This formula integrates key factors impacting the strength and stability of the pillars in hard rock mining environments. The pillar friction coefficient \(K_{a}\) encapsulates the internal friction and cohesion properties of the rock mass which are crucial for understanding the load-bearing capacity and deformation behavior of the pillars under different mining and geological conditions. This formula provides a more structured and theoretically grounded approach to pillar strength estimation, which can be instrumental in the design and assessment of pillar stability in underground hard rock mines. The formula for calculating the pillar friction coefficient \(K_{a}\) is as follows:  
\[K_{a}=\tan\biggl{[}\cos^{-1}\biggl{(}\frac{1-C_{p}}{1+C_{p}}\biggr{)}\biggr{]} \tag{20}\]  
where \(C_{p}\) is the pillar strength coefficient, which can be obtained by the following:  
\[C_{p}=0.46\biggl{[}\lg(\frac{w}{h}+0.75)\biggr{]}^{\frac{14}{w/h}} \tag{21}\]  
Here, \(w/h\) is the width-to-height ratio of the pillar.