Quantification of the GSI Classification System Based on the Rock Mass Waves Velocity Utilizing the Artificial Intelligence Algorithms

The geological strength index (GSI) is a fundamental parameter in rock mechanics and geotechnical engineering that reflects the structural integrity and mechanical behavior of rock masses. Accurate evaluation of this parameter is essential for ensuring the stability, safety, and economic efficiency of underground constructions, mining excavations, and slope stability analyses. However, conventional techniques for determining GSI mainly depend on field observations and qualitative assessments, which are inherently subjective and prone to human bias. These limitations often lead to inconsistencies in classification and may affect the reliability of engineering design decisions. To overcome these shortcomings, the present research employs artificial intelligence (AI) and metaheuristic optimization techniques to establish robust, data-driven predictive models for GSI estimation. A comprehensive dataset was compiled from the Beheshtabad Water Transfer Tunnel in southwestern Iran, comprising paired measurements of compressional (Vp) and shear (Vs) wave velocities, together with field-evaluated GSI values. Because seismic velocities are relatively inexpensive and easy to measure, they serve as practical predictor variables to replace or complement traditional classification systems such as Rock Mass Rating (RMR) and Q-system, which require extensive field and laboratory investigations. Three modeling strategies, i.e., the trust region reflective (TRR) algorithm, the genetic algorithm (GA), and a hybrid TRR–GA approach were explored, to model the nonlinear dependency between GSI and the seismic parameters. Five mathematical formulations, including exponential, logarithmic, power, quadratic polynomial, and linear functions, were systematically tested to determine the most suitable representation of the relationship. Among these, the quadratic polynomial model consistently achieved the highest predictive accuracy across all algorithms. Model performance was evaluated using a suite of statistical metrics, including R2, RMSE, MARE, MAPE, and MSE, along with additional indicators such as Index of Scatter (IOS), Index of Agreement (IOA), and the A20 accuracy index. Comparative analyses revealed that the hybrid TRR–GA model produced the most accurate and stable predictions, outperforming the standalone TRR and GA models. Although both Vp- and Vs-based models yielded satisfactory results, the Vp-based formulations demonstrated slightly superior predictive capability. These findings confirm the advantages of integrating the global optimization strength of GA with the local refinement capability of TRR, resulting in a more robust and efficient predictive model. The study ultimately demonstrates that GSI can be estimated reliably using non-destructive, low-cost seismic measurements, offering a viable alternative to traditional, subjective field-based methods. The proposed hybrid TRR–GA framework provides valuable insights for rock mechanics, tunneling, and geotechnical design, promoting safer and more cost-effective decision-making in engineering practice.