Improved determination of the S-wave velocity of rocks in dry and saturated conditions: Application of machine-learning algorithms

The determination of S-wave velocity (V_s) is of significant importance in various engineering disciplines, including mining, civil, and geotechnical engineering. It is beneficial to indirectly determine V_s under both dry and saturated conditions and to understand its relationship with influencing input variables: coring depth (H), durability index (DI), water content (W_a), dry density (ρ_d), saturated density (ρ_s), and porosity (n). In this study, we evaluate these relationships using three multiple machine-learning algorithms (MLAs): artificial neural network (ANN), fuzzy inference system (FIS), and gene expression programming (GEP), alongside a linear regression method (LRM) and predict both dry S-wave velocity (V_s-dry) and saturated S-wave velocity (V_s-sat) of rocks. The research involves the analysis of 90 datasets derived from samples of schist, phyllite, and sandstone rocks collected from Azad and Bakhtiari dam sites in Iran. The diversity of these datasets is a key advantage of this study, providing a solid foundation for models training and testing while enhancing the models’ generalizability. Model optimization techniques are employed in the Python, MATLAB, GenXProTools, and SPSS environments to identify the most effective versions of ANN, FIS, GEP, and LRM models, respectively. The prediction performance analysis reveals that all applied models yield acceptable levels of accuracy for predicting V_s-dry and V_s-sat. However, GEP emerges as the best model for predicting both V_s-dry and V_s-sat. The ANN and FIS models also achieve high levels of accuracy, while LRM performs comparatively less well. Additionally, sensitivity analysis conducted using the cosine amplitude method (CAM) highlights the influence of different variables on V_s-dry and V_s-sat. The ρ_d is found to be the most influential parameter on V_s-dry, whereas DI exhibits the least impact. Conversely, the ρ_s significantly affects V_s-sat, while W_a shows the lowest impact. The exceptional performance of these proposed MLAs confirms their applicability in real-world rock engineering and geotechnics projects, offering precise determination of V_s. The diversity of studied rock types and datasets, along with the use of cost-effective and easy measurable inputs, the determination of V_s in both dry and saturated status, and the application of robust MLAs for V_s determination are the main novelties of this study. However, further researches involving additional datasets and more rock types are required to validate these findings.