Predicting Rock Fracture Toughness Using a KOA-BP Neural Network: A Case Study from Five Provinces in China

Rock fracture toughness (RFT) is one of the most critical indicators in rock mechanics and is used to determine how fractures propagate in processes such as hydraulic fracturing, rock blasting, tunnel excavation, geothermal energy extraction, and CO₂ sequestration. Determining this fracture toughness on the basis of various rock parameters is an ongoing research area. Previous studies have established simple regression relationships between fracture toughness and individual parameters, achieving varying degrees of success. However, these models are often based on specific rocks and locations, with input parameters selected through intuitive judgment rather than quantitative analysis, leading to a lack of broad acceptance. In this study, a Kepler optimization algorithm (KOA)-optimized BP algorithm was utilized alongside four unoptimized machine learning algorithms and one empirical formula to predict fracture toughness from a set of common geomechanical parameters. Unlike many previous studies, the normalized mutual information (NMI) method was employed in this study to analyze the sensitivity of these parameters to RFT and assess their importance to the model. Quantitative analysis identified 8 parameters—R, B, S, α, T, UCS, Cc, and ν—out of the fifteen potential input parameters as having the highest correlation with fracture toughness, addressing the previous issue of parameter selection on the basis of intuition rather than statistical analysis. This study developed a KOA-BP neural network model as a powerful tool for predicting rock fracture toughness, integrating 3 essential modules. The data processing module normalizes and partitions the dataset to ensure consistency. The KOA optimization module employs the Kepler Optimization Algorithm to iteratively optimize the weights and biases of the BP neural network, addressing challenges such as premature convergence and parameter sensitivity. Lastly, the BP neural network module performs forward propagation and backpropagation to iteratively improve prediction accuracy. The synergy of these modules significantly enhances the model’s predictive performance, demonstrating its superiority over traditional methods in terms of error reduction, goodness of fit, and accuracy. The database for this study was established using granite, mudstone, sandstone, and gypsum, resulting in a KOA-BP model that effectively forecasts the fracture toughness of these 4 rock types. To validate the model’s effectiveness, the dataset was divided into 2 groups: one for training the predictive model and the other for testing its performance. The prediction results were analyzed via 4 metrics—the RMSE, MAPE, R2, and a10. The findings showed that all the machine learning models outperformed the empirical formula. However, the KOA-optimized BP algorithm constructed the best predictive model, demonstrating the strongest performance in predictions. As shown in Table 2, the KOA-BP model achieved an RMSE of 0.100, MAPE of 10.81%, R2 of 0.943, and a10 of 0.525 in the test set. These results provide strong evidence of the model’s superiority in predicting rock fracture toughness.