Modeling of Minimum Fracture Energy Distribution Through Advanced Characterization and Machine Learning Techniques

This study proposes a data-driven framework to predict the rock mass-specific fracture energy distributions using microstructural descriptors extracted from SEM-EDS automated characterization images. Ore textures were encoded through unsupervised k-means clustering to identify six representative mineralogical patterns. The resulting cluster proportions were then used as input features for supervised machine learning models, which seek to estimate the parameters of the log-normal distribution (median and standard deviation) adjusted to the experimental fracture energy data. Both models (XGBoost and decision tree regressor) were validated through Leave-One-Out cross-validation and showed high accuracy (R2 of 0.80 and 0.91, respectively) and predict over 85% of the energy distributions matched the experimental ones according to Kolmogorov–Smirnov and Cramér–von Mises tests. The proposed method outperforms traditional empirical approaches by incorporating mineralogical variability and predicting the complete distribution of fracture behavior, representing a step toward more efficient, texture-aware comminution practices.