Prediction of Rock Mass Rating Using Seismic Wave Velocities and Metaheuristic Algorithms: A Comparative Study of DE, PS, and Hybrid DE-PS

Accurate determination of rock mass quality plays a critical role in the design and stability assessment of underground structures. Among various classification systems, the Rock Mass Rating (RMR) is widely used in engineering practice; however, its direct determination often requires extensive field investigations and laboratory testing, which can be time-consuming and costly. To address this limitation, the present study investigates the capability of metaheuristic algorithms to estimate RMR using non-destructive geophysical parameters, namely P-wave velocity (Vp) and S-wave velocity (Vs). In this study, three modeling approaches based on Differential Evolution (DE), Pattern Search (PS), and a hybrid DE-PS algorithm were developed to establish quantitative relationships between seismic velocities and RMR values. The models were trained and validated using a dataset obtained from the Beheshtabad water conveyance tunnel, where Vp, Vs, and RMR were measured according to standard field and laboratory procedures. The performance of the proposed models was evaluated using multiple statistical indices, including the coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results indicate that all three models are capable of capturing the underlying relationship between seismic velocities and RMR; however, the hybrid DE-PS model exhibits superior predictive performance compared to the individual DE and PS models. The hybrid approach yields the highest correlation with measured RMR values and the lowest prediction errors, demonstrating improved accuracy and stability. Comparative validation analyses, including cumulative error assessment and residual distribution evaluation, further confirm the robustness of the hybrid model. The findings of this study suggest that the proposed DE-PS-based modeling framework provides a reliable and efficient tool for estimating RMR from seismic velocity data. The developed approach can support preliminary site investigations and decision-making processes in tunneling and rock engineering projects, particularly in situations where direct determination of RMR is limited or impractical.