Application of the metaheuristic algorithms to quantify the GSI based on the RMR classification

Accurate classification of rock masses is an essential task in earth sciences applications. Among various classification systems, the Rock Mass Rating (RMR) and Geological Strength Index (GSI) are the most frequently utilized ones. Unlike the RMR, which is a quantitative classification, GSI is a qualitative system and needs to be converted into a quantitative one as well due to its multiple applicability in both mining and civil engineering projects. With this objective, GSI quantification directly from RMR can be an attractive issue as it remains a complex task still due to the limited accuracy and generalizability of existing empirical models under varying geological conditions. This study addresses this challenge by analyzing data from eleven different rock types and employing three metaheuristic optimization algorithms, namely Particle Swarm Optimization (PSO), Simulated Annealing (SA), and Grey Wolf Optimization (GWO), to develop predictive models for quantifying GSI based on the RMR. Accordingly, five mathematical GSI-RMR equations including linear, power, exponential, polynomial and logarithmic types were first developed using each algorithm. The resulting equations were assessed using six statistical indicators: R², RMSE, MAE, ASE, MAPE, and MARE. According to this evaluation, the best-performing equation from each algorithm was selected as the optimum and further evaluated using both graphical and statistical analyses, including comparisons with conventional empirical relationships. The findings revealed that the derived GSI-RMR equation from the SA algorithm achieved superior performance based on the score analysis and the REC curve. However, complementary evaluation using A20, IOA, and IOS metrics showed that the derived equation GSI-RMR equations from the GWO and PSO algorithms outperformed SA in certain aspects. These results demonstrate the unique strengths of all three proposed GSI-RMR equations and highlight the importance of multi-criteria evaluation. Overall, the proposed models provide a more accurate and generalizable framework for quantifying GSI from RMR, improving upon traditional empirical methods and enhancing the required accuracy compared to the qualitative GSI estimation.