Application of the metaheuristic algorithms to quantify the GSI based on the RMR classification
Abstract 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...
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Nature Portfolio
2025-08-01
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| Online Access: | https://doi.org/10.1038/s41598-025-14332-1 |
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| author | Pouya Koureh Davoodi Farnusch Hajizadeh Mohammad Rezaei |
| author_facet | Pouya Koureh Davoodi Farnusch Hajizadeh Mohammad Rezaei |
| author_sort | Pouya Koureh Davoodi |
| collection | DOAJ |
| description | Abstract 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 fourteen 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. These models were further applied to estimate rock mass strength parameters and to propose suitable support systems for selected rock types, demonstrating their practical applicability in engineering design. |
| format | Article |
| id | doaj-art-8a3f4cab6b60468b88c7d15f66fd6d79 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-8a3f4cab6b60468b88c7d15f66fd6d792025-08-20T04:01:51ZengNature PortfolioScientific Reports2045-23222025-08-0115113010.1038/s41598-025-14332-1Application of the metaheuristic algorithms to quantify the GSI based on the RMR classificationPouya Koureh Davoodi0Farnusch Hajizadeh1Mohammad Rezaei2Department of Mining Engineering, Faculty of Engineering, Urmia UniversityDepartment of Mining Engineering, Faculty of Engineering, Urmia UniversityDepartment of Mining Engineering, Faculty of Engineering, University of KurdistanAbstract 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 fourteen 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. These models were further applied to estimate rock mass strength parameters and to propose suitable support systems for selected rock types, demonstrating their practical applicability in engineering design.https://doi.org/10.1038/s41598-025-14332-1Geological strength indexRock mass ratingParticle swarm optimizationSimulated annealingGrey wolf optimization |
| spellingShingle | Pouya Koureh Davoodi Farnusch Hajizadeh Mohammad Rezaei Application of the metaheuristic algorithms to quantify the GSI based on the RMR classification Scientific Reports Geological strength index Rock mass rating Particle swarm optimization Simulated annealing Grey wolf optimization |
| title | Application of the metaheuristic algorithms to quantify the GSI based on the RMR classification |
| title_full | Application of the metaheuristic algorithms to quantify the GSI based on the RMR classification |
| title_fullStr | Application of the metaheuristic algorithms to quantify the GSI based on the RMR classification |
| title_full_unstemmed | Application of the metaheuristic algorithms to quantify the GSI based on the RMR classification |
| title_short | Application of the metaheuristic algorithms to quantify the GSI based on the RMR classification |
| title_sort | application of the metaheuristic algorithms to quantify the gsi based on the rmr classification |
| topic | Geological strength index Rock mass rating Particle swarm optimization Simulated annealing Grey wolf optimization |
| url | https://doi.org/10.1038/s41598-025-14332-1 |
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