## 4 Numerical Simulation  
### Model Setup  
In this work, PFC3D was employed to simulate the ore draw process of a single draw-bell with different particle size distributions. Prior to drawing, a numerical model must be established. The draw apparatus dimensions are consistent with those of the experimental apparatus; specifically, the internal dimensions are length \(\times\) width \(\times\) height = 700 mm \(\times\) 550 mm \(\times\) 1600 mm. Furthermore, to better characterize the extraction zone features and particle flow behavior under irregular particle conditions, the ore particles in this numerical simulation scheme were also modeled as randomly generated irregular blocks, as shown in Figure 12. This approach successfully circumvents the issue associated with spherical particles: their excessively smooth surfaces prevent the development of sufficient internal locking forces between particles, thereby failing to reasonably characterize the morphology and evolution of the extraction zone. In the experimental tests, ore extraction was achieved by continuously shoveling ore particles out from the outlets at both ends of the drawbell. The depth of shovel penetration into the model outlets was consistently maintained at 2.1 cm. In the numerical simulation, this extraction approach was replicated. However, the key difference lies in the simulation method: a 2.1 cm long wall section was removed from the bottom structure at the ore outlets to create space for particle movement, thereby simulating the ore extraction process. Figure 11: The degree of overlap between adjacent extraction zones under different particle gradations (draw height is 46.2 m). For the construction of irregular blocks, we begin by modeling a three-dimensional ore unit geometry in Rhino and exporting it as an STL file and then utilize the command in PFC3D to construct complex block units. As shown in Figure 13, the ore draw model was generated based on a rigid block model and different particle size ratios within the specified gradations. Figure 13a represents the initial ore draw model under Gradation I conditions. Although discerning particle gradation within the model visually is challenging, careful observation reveals that the number of large blocks in Figure 13a is significantly lower than in the numerical models depicted in Figure 13b,c. The microscopic parameters of the particles significantly influence the numerical simulation outcomes. Therefore, a series of iterative calibration trials need to be conducted prior to the main draw experiments to obtain microscopic parameters capable of characterizing the flow behavior of the fragmented rock during the draw process. The parameter  
Figure 12: The 3D numerical model for isolated draw experiments. Figure 13: The 3D numerical model for draw experiments with different particle gradients. (**a**) Gradient-I. (**b**) Gradient-II. (**c**) Gradient-III. calibration procedure in this numerical simulation comprises two sequential steps: first, assigning particle density parameters based on the actual rock density and then iteratively adjusting the friction coefficient until the extracted zone (EZ) height-versus-mass curve aligns with experimental data to determine the particle friction coefficient (Figure 14). Subsequently, using the calibrated friction coefficient and incorporating the rock's uniaxial compressive strength curve, numerical simulations of rock compression tests are performed while continuously tuning other microscopic parameters until the simulated strength curve converges with the experimental measurements, thereby obtaining the remaining particle strength parameters (Figure 15).