Intelligent Estimation of Pillar Strength in Pakistan’s Salt Range Rock Salt Mines: Integrating GP-GAN Data Augmentation, Interpretable Machine Learning, and Causal Inference
摘要
Underground rock pillars are critical load-bearing structures in room-and-pillar mining, especially in rock salt mines of Pakistan’s Salt Range where massive high-purity deposits exhibit time-dependent creep deformation. They play an indispensable role in maintaining the integrity of the roof surrounding rock, mitigating roof collapse risks, and ensuring the safety of miners and equipment. Accurate estimation of pillar strength (PS) is, therefore, paramount for optimizing pillar design parameters, enhancing resource extraction efficiency, and avoiding catastrophic accidents. This study proposes a comprehensive intelligent framework for PS estimation in Pakistan’s Salt Range rock salt mines. The framework first adopts a dual-stage data augmentation strategy combining Gaussian perturbation and a generative adversarial network (GP-GAN) to expand the original dataset of 168 pillars and correct distributional biases. It then conducts a comparative analysis of six machine learning (ML) models, including LGBM, RF, XGBoost, CatBoost, DT, and SVR, to identify the optimal predictor. Additionally, Shapley additive explanations (SHAP) were used to quantify feature importance and characterize the relationships between input features and PS. Key feature thresholds were then identified to support engineering interpretation, and the DoWhy framework was applied to estimate directional and quantitative effects of critical factors on PS. Results show that, under the present Salt Range dataset and a fixed train-test split, the GP-GAN strategy improved the representativeness of the training data and enabled the CatBoost model to achieve the best predictive performance among the tested models, with R2 of 0.9888, RMSE of 0.3749, and MAPE of 1.8821%. SHAP analysis was then used to interpret the behavior of the selected predictive model, revealing that pillar height (PH, 35.2%), rock mass rating (RMR, 16.7%), and unconfined compressive strength (UCS, 15.7%) were the most influential predictors and identifying critical thresholds of 3.97 m for PH, 53.35 for RMR, and 21.42 MPa for UCS. These interpretability results describe how the trained model responds to the input variables, but they do not by themselves establish causal relationships. To investigate causality separately, the DoWhy framework was applied under an explicit adjustment set, which estimated average treatment effects (ATEs) of − 2.0199 MPa per 1 m increase in PH, + 0.338 MPa per 1-unit increase in RMR, and + 0.6 MPa per 1 MPa increase in UCS; these estimates were further examined by robustness refutation tests. This study fills key gaps in existing PS research, provides a reliable, interpretable, and practically applicable PS estimation tool for rock salt mining, and offers evidence-based guidelines for pillar design, thereby advancing both academic research on intelligent geomechanical modeling and industrial safety in Pakistan’s Salt Range and similar rock salt mining areas.