# An Integrated Cellular Automata Model Improves the Accuracy of Secondary Fragmentation Prediction
###### Abstract  
Fine material in caving mining can impact dilution, inrushes, and downstream processing. This work describes the application of a new model to improve the accuracy of the prediction of fine material in block caving mining by coupling a stress model and a fragmentation model, integrating the shear strain effect. This combination seeks to offer a better representation of the secondary fragmentation process than previous models have attained. This approach was implemented through a flow simulator using cellular automata to model the gravitational behavior of broken material during extraction. Physical experiments were then replicated in the flow simulator to couple both models and estimate rock fragmentation under stress. Adding the shear strain effect to the new model showed demonstrable improvements in fine fragmentation estimations, optimizing the results under different confinement conditions. The errors obtained did not exceed 6.8% for 0.8 MPa of confinement, 6.5% for 3 MPa, and 3.8% for 5 MPa, also maintaining a low margin of error for medium and coarser fragments, such as d\({}_{50}\) and d\({}_{80}\). This improvement in predicting the appearance of fine material supports more accurate planning and the implementation of more focused measures to be taken at drawpoints. block caving; secondary fragmentation; cellular automata; shear deformation; fine material 2  
The results of secondary fragmentation can impact caving operations in various ways. First, reducing the size of fragments over time can narrow movement zones, which can affect the design of the extraction level [6]; likewise, the accumulation of fine material in the voids between coarser fragments can generate the formation of cushions. In addition, fine material moves faster than coarse fragments [6,7], which can produce fine invushes [8] and mud rushes in the presence of humidity [9], thus creating operational risks. This fine material is also a source of airborne dust and, in later stages, can negatively influence the efficiency of ore processing [10]. Modeling secondary fragmentation is, therefore, key to mitigating or foreseeing the operational problems that can be triggered by the generation of fine material. Some empirical models have been developed to estimate secondary fragmentation [3,7,10,11,12]. Numerical methods have also been suggested for a more comprehensive representation. For example, Block Cave Fragmentation (BCF) software [13] is a tool that evaluates primary and secondary fragmentation in block caving operations; however, the dynamics of stress are not considered in the estimation of secondary fragmentation [8]. [PERSON] [10] developed the REBOP flow model (today known as Massflow [14]), in which he introduced an empirical approach based on the work of [PERSON] and [PERSON] [15,16] to model secondary fragmentation using compression and shear mechanisms [10,17], but again stresses and the dynamics of gravity flow were not considered in the model. Another approach is FracMan [18,19], which employs a discrete fracture network (DFN) model of secondary fragmentation based on the generation and fragmentation of veinlets. However, although empirical models allow estimates of secondary fragmentation, in general, they do not directly represent the phenomena involved in gravity flow and fragmentation. There are even tools such as PFC that allow a DEM to interact with a DFN for more complex simulations at controlled scales that could be used to include joint effects [20]. On the other hand, numerical methods allow more mechanisms or phenomena to be included; nevertheless, they fail to adequately estimate the generation of fines, especially during gravity flow. To more fully integrate the dynamics involved in fragmentation, [PERSON] et al. [21] proposed a fragmentation model within a gravity flow simulator based on cellular automata to model rock fragmentation during large-scale flow.