GEL-LightGBM: A Gated Empirical-Law Framework for Interpretable Prediction of Rock Uniaxial Compressive Strength

Uniaxial compressive strength (UCS) is a fundamental parameter for rock engineering design and stability assessment, but direct laboratory testing is costly, time-consuming, and often difficult for weak or fractured rocks. To improve predictive accuracy while preserving mechanical interpretability, this study proposes a Gated Empirical-Law LightGBM model (GEL-LightGBM). The framework embeds three representative rock-strength priors, including point-load strength, multi-index strength, and porosity-degradation relationships, as empirical-law experts. A sample-adaptive gating mechanism dynamically assigns its contributions for different rock states, while a controlled residual corrector captures nonlinear deviations between empirical estimates and measured UCS. Using 344 published rock-mechanics samples, porosity, Schmidt rebound hardness, P-wave velocity, and point-load strength index were used as predictors. GEL-LightGBM outperformed LightGBM, XGBoost, random forest, MLP, CNN, SVR, and BPNN, achieving a testing R2 of 0.9790 and an RMSE of 7.5623 MPa. SHAP analysis identified porosity as the dominant factor, contributing 49.0%, followed by rebound hardness (32.2%) and P-wave velocity (17.2%). The strongest interaction occurred between porosity and rebound hardness (2.31 MPa). These findings indicate that GEL-LightGBM provides accurate, stable, and physically interpretable UCS prediction for heterogeneous rock datasets.