Document Type : Original Research Paper
Authors
1 Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Zijingang, Hangzhou 310058, China
2 Computing Center for Geotechnical Engineering, Zhejiang University, Hangzhou, Zhejiang 310058, China
3 Department of Civil, Construction, Architectural, and Environmental Engineering, University of L'Aquila, L'Aquila 67100, Italy
10.22044/jme.2025.16419.3206
Abstract
Uniaxial compressive strength (UCS) is an essential feature for characterizing and classifying rock masses, forming a critical component of rock failure criteria with extensive applications in mining and geotechnical engineering. This study aims to evaluate the performance of different machine learning (ML) models in forecasting the UCS of sandstone obtained from the Murree and Kamlial formations in the Muzaffarabad area, northwestern Himalayas, Pakistan. The ML models—namely artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), support vector regressor (SVR), random forest (RF), and extreme gradient boosting (XGBoost)—were developed to predict UCS (MPa) based on porosity (η), point load index (Is(50)), Schmidt hammer rebound value (Rn), and aggregate impact value (AIV) as input variables. A dataset containing 80 points was divided using a 70:30 split ratio for training and testing sets. K-fold cross-validation (with 5 to 10 folds) was employed to enhance the models' generalization ability. The performance of the models was evaluated using mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), and coefficient of determination (R²). Results revealed that the XGBoost model outperformed the other models, achieving a high R² value of 0.99 and low error values for MAE (0.789), MSE (1.168), and RMSE (1.080). The overall accuracy of the models can be ranked as follows: XGBoost > RF > ANN > ANFIS > SVR. This study provides a benchmark for predicting the UCS of sandstones and similar rocks where complex geology complicates the collection of intact samples.
Keywords
Main Subjects
[1]. Barzegar, R., Sattarpour, M., Nikudel, M. R., & Moghaddam, A. A. (2016). Comparative evaluation of artificial intelligence models for prediction of uniaxial compressive strength of travertine rocks, case study: Azarshahr area, NW Iran. Modeling Earth Systems and Environment, 2(2), 76.
[2]. Beiki, M., Majdi, A., & Givshad, A. D. (2013). Application of genetic programming to predict the uniaxial compressive strength and elastic modulus of carbonate rocks. International Journal of Rock Mechanics and Mining Sciences, 63, 159-169.
[3]. Ceryan, N., Okkan, U., & Kesimal, A. (2012). Application of generalized regression neural networks in predicting the unconfined compressive strength of carbonate rocks. Rock mechanics and rock engineering, 45(6), 1055-1072.
[4]. Sharma, L. K., Vishal, V., & Singh, T. N. (2017). Developing novel models using neural networks and fuzzy systems for the prediction of strength of rocks from key geomechanical properties. Measurement, 102, 158-169.
[5]. Jalali, S. H., Heidari, M., & Mohseni, H. (2017). Comparison of models for estimating uniaxial compressive strength of some sedimentary rocks from Qom Formation. Environmental Earth Sciences, 76(22), 753.
[6]. Cevik, A., Sezer, E. A., Cabalar, A. F., & Gokceoglu, C. (2011). Modeling of the uniaxial compressive strength of some clay-bearing rocks using neural network. Applied Soft Computing, 11(2), 2587-2594.
[7]. Yesiloglu-Gultekin, N. U. R. G. Ü. L., Gokceoglu, C., & Sezer, E. A. (2013). Prediction of uniaxial compressive strength of granitic rocks by various nonlinear tools and comparison of their performances. International Journal of Rock Mechanics and Mining Sciences, 62, 113-122.
[8]. Cao, J., Gao, J., Nikafshan Rad, H., Mohammed, A. S., Hasanipanah, M., & Zhou, J. (2022). A novel systematic and evolved approach based on XGBoost-firefly algorithm to predict Young’s modulus and unconfined compressive strength of rock. Engineering with computers, 38(Suppl 5), 3829-3845.
[9]. Singh, R., Vishal, V., Singh, T. N., & Ranjith, P. G. (2013). A comparative study of generalized regression neural network approach and adaptive neuro-fuzzy inference systems for prediction of unconfined compressive strength of rocks. Neural Computing and Applications, 23(2), 499-506.
[10]. Suthar, M. (2020). Applying several machine learning approaches for prediction of unconfined compressive strength of stabilized pond ashes. Neural Computing and Applications, 32(13), 9019-9028.
[11]. Torabi, S. R., Ataei, M., & Javanshir, M. (2011). Application of Schmidt rebound number for estimating rock strength under specific geological conditions. Journal of Mining and Environment.
[12]. Moshrefi, S., Shahriar, K., Ramezanzadeh, A., & Goshtasbi, K. (2018). Prediction of ultimate strength of shale using artificial neural network. J Min Environ 9 (1): 91–105.
[13]. Fang, Q., Yazdani Bejarbaneh, B., Vatandoust, M., Jahed Armaghani, D., Ramesh Murlidhar, B., & Tonnizam Mohamad, E. (2021). Strength evaluation of granite block samples with different predictive models. Engineering with computers, 37(2), 891-908.
[14]. Jahed Armaghani, D., Safari, V., Fahimifar, A., Mohd Amin, M. F., Monjezi, M., & Mohammadi, M. A. (2018). Uniaxial compressive strength prediction through a new technique based on gene expression programming. Neural Computing and Applications, 30(11), 3523-3532.
[15]. Singh, V. K., Singh, D., & Singh, T. N. (2001). Prediction of strength properties of some schistose rocks from petrographic properties using artificial neural networks. International Journal of Rock Mechanics and Mining Sciences, 38(2), 269-284.
[16]. Fattahi, H., & Babanouri, N. (2017). Predicting tensile strength of rocks from physical properties based on support vector regression optimized by cultural algorithm. Journal of Mining and Environment, 8(3), 467-474.
[17]. Jalali, S. H., Heidari, M., & Mohseni, H. (2017). Comparison of models for estimating uniaxial compressive strength of some sedimentary rocks from Qom Formation. Environmental Earth Sciences, 76(22), 753.
[18]. Abdi, Y., Garavand, A. T., & Sahamieh, R. Z. (2018). Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis. Arabian Journal of Geosciences, 11(19), 587.
[19]. Fattahi, H. (2020). A new method for forecasting uniaxial compressive strength of weak rocks. Journal of Mining and Environment, 11(2), 505-515.
[20]. Shahani, N. M., Zheng, X., Liu, C., Hassan, F. U., & Li, P. (2021). Developing an XGBoost regression model for predicting young’s modulus of intact sedimentary rocks for the stability of surface and subsurface structures. Frontiers in Earth Science, 9, 761990.
[21]. Jahed Armaghani, D., Tonnizam Mohamad, E., Momeni, E., Narayanasamy, M. S., & Mohd Amin, M. F. (2015). An adaptive neuro-fuzzy inference system for predicting unconfined compressive strength and Young’s modulus: a study on Main Range granite. Bulletin of engineering geology and the environment, 74(4), 1301-1319.
[22]. Armaghani, D. J., Amin, M. F. M., Yagiz, S., Faradonbeh, R. S., & Abdullah, R. A. (2016). Prediction of the uniaxial compressive strength of sandstone using various modeling techniques. International Journal of Rock Mechanics and Mining Sciences, 85, 174-186.
[23]. Zorlu, K., Gokceoglu, C., Ocakoglu, F., Nefeslioglu, H. A., & Acikalin, S. J. E. G. (2008). Prediction of uniaxial compressive strength of sandstones using petrography-based models. Engineering Geology, 96(3-4), 141-158.
[24]. Wan, Z., Xu, Y., & Šavija, B. (2021). On the use of machine learning models for prediction of compressive strength of concrete: influence of dimensionality reduction on the model performance. Materials, 14(4), 713.
[25]. Zhang, J., Ma, G., Huang, Y., Aslani, F., & Nener, B. (2019). Modelling uniaxial compressive strength of lightweight self-compacting concrete using random forest regression. Construction and Building Materials, 210, 713-719.
[26]. Mai, H. V. T., Nguyen, T. A., Ly, H. B., & Tran, V. Q. (2021). Prediction compressive strength of concrete containing GGBFS using random forest model. Advances in Civil Engineering, 2021(1), 6671448.
[27]. Matin, S. S., Farahzadi, L., Makaremi, S., Chelgani, S. C., & Sattari, G. H. (2018). Variable selection and prediction of uniaxial compressive strength and modulus of elasticity by random forest. Applied Soft Computing, 70, 980-987.
[28]. Nguyen-Sy, T., Wakim, J., To, Q. D., Vu, M. N., Nguyen, T. D., & Nguyen, T. T. (2020). Predicting the compressive strength of concrete from its compositions and age using the extreme gradient boosting method. Construction and Building Materials, 260, 119757.
[29]. Negara, A., Ali, S., AlDhamen, A., Kesserwan, H., & Jin, G. (2017, April). Unconfined compressive strength prediction from petrophysical properties and elemental spectroscopy using support-vector regression. In SPE Kingdom of Saudi Arabia Annual Technical Symposium and Exhibition (p. D043S036R002). SPE.
[30]. Sun, J., Zhang, J., Gu, Y., Huang, Y., Sun, Y., & Ma, G. (2019). Prediction of permeability and unconfined compressive strength of pervious concrete using evolved support vector regression. Construction and Building Materials, 207, 440-449.
[31]. Wang, M., Wan, W., & Zhao, Y. (2020). Prediction of the uniaxial compressive strength of rocks from simple index tests using a random forest predictive model. Comptes Rendus. Mécanique, 348(1), 3-32.
[32]. Abdi, Y., Yusefi-Yegane, B., & Jamshidi, A. (2021). Estimation of mechanical properties of sandstones from petrographic characteristics using artificial neural networks (ANNs).
[33]. Koken, E. (2024). Estimating uniaxial compressive strength of pyroclastic rocks using soft computing techniques. Journal of Mining and Environment, 15(3), 977-990.
[34]. Jamshidi, A. (2022). A comparative study of point load index test procedures in predicting the uniaxial compressive strength of sandstones. Rock Mechanics and Rock Engineering, 55(7), 4507-4516.
[35]. Cao, J., Gao, J., Nikafshan Rad, H., Mohammed, A. S., Hasanipanah, M., & Zhou, J. (2022). A novel systematic and evolved approach based on XGBoost-firefly algorithm to predict Young’s modulus and unconfined compressive strength of rock. Engineering with computers, 38(Suppl 5), 3829-3845.
[36]. Shahani, N. M., Zheng, X., Liu, C., Li, P., & Hassan, F. U. (2022). Application of soft computing methods to estimate uniaxial compressive strength and elastic modulus of soft sedimentary rocks. Arabian Journal of Geosciences, 15(5), 384.
[37]. Heidari, M., Mohseni, H., & Jalali, S. H. (2018). Prediction of uniaxial compressive strength of some sedimentary rocks by fuzzy and regression models. Geotechnical and Geological Engineering, 36(1), 401-412.
[38]. Jahed Armaghani, D., Tonnizam Mohamad, E., Hajihassani, M., Yagiz, S., & Motaghedi, H. (2016). Application of several non-linear prediction tools for estimating uniaxial compressive strength of granitic rocks and comparison of their performances. Engineering with Computers, 32(2), 189-206.
[39]. Asadizadeh, M. (2020). Predicting unconfined compressive strength of intact rock using new hybrid intelligent models.
[40]. Kamani, M., Khaleghi Esfahani, M., & Ajalloeian, R. (2020). Prediction of carbonate aggregates properties through physical tests. Geotechnical and Geological Engineering, 38(2), 2169-2186.
[41]. Mustafa, S., Khan, M. A., Khan, M. R., Sousa, L. M., Hameed, F., Mughal, M. S., & Niaz, A. (2016). Building stone evaluation—A case study of the sub-Himalayas, Muzaffarabad region, Azad Kashmir, Pakistan. Engineering Geology, 209, 56-69.
[42]. ASTM. (1985). Standard Test Method for Determination of the Point Load Strength Index of Rock 1. 22(2), 1–9.
[43]. Khademi, F., Jamal, S. M., Deshpande, N., & Londhe, S. (2016). Predicting strength of recycled aggregate concrete using artificial neural network, adaptive neuro-fuzzy inference system and multiple linear regression. International journal of sustainable built environment, 5(2), 355-369.
[44]. Tariq, Z., Abdulraheem, A., Mahmoud, M., Elkatatny, S., Ali, A. Z., Al-Shehri, D., & Belayneh, M. W. (2019). A new look into the prediction of static Young's modulus and unconfined compressive strength of carbonate using artificial intelligence tools. Petroleum Geoscience, 25(4), 389-399.
[45]. Sezer, E. A., Nefeslioglu, H. A., & Gokceoglu, C. (2014). An assessment on producing synthetic samples by fuzzy C-means for limited number of data in prediction models. Applied Soft Computing, 24, 126-134.
[46]. Teymen, A., & Mengüç, E. C. (2020). Comparative evaluation of different statistical tools for the prediction of uniaxial compressive strength of rocks. International Journal of Mining Science and Technology, 30(6), 785-797.
[47]. Farid, M., HosseinAbadi, M. M., Yazdani-Chamzini, A., Yakhchali, S. H., & Basiri, M. H. (2013). Developing a new model based on neuro-fuzzy system for predicting roof fall in coal mines. Neural computing and applications, 23(Suppl 1), 129-137.
[48]. Longjun, D., Xibing, L., Ming, X., & Qiyue, L. (2011). Comparisons of random forest and support vector machine for predicting blasting vibration characteristic parameters. Procedia Engineering, 26, 1772-1781.
[49]. Janitza, S., Tutz, G., & Boulesteix, A. L. (2016). Random forest for ordinal responses: prediction and variable selection. Computational Statistics & Data Analysis, 96, 57-73.
[50]. Friedman, J. H. (2001). Greedy function approximation: a gradient boosting machine. Annals of statistics, 1189-1232.
[51]. Qiu, Y., Zhou, J., Khandelwal, M., Yang, H., Yang, P., & Li, C. (2022). Performance evaluation of hybrid WOA-XGBoost, GWO-XGBoost and BO-XGBoost models to predict blast-induced ground vibration. Engineering with Computers, 38(Suppl 5), 4145-4162.
[52]. Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation coefficients: appropriate use and interpretation. Anesthesia & analgesia, 126(5), 1763-1768.
[53]. Ngo, H. T. T., Pham, T. A., Vu, H. L. T., & Giap, L. V. (2021). Application of artificial intelligence to determined unconfined compressive strength of cement-stabilized soil in Vietnam. Applied Sciences, 11(4), 1949.
[54]. Rodriguez, J. D., Perez, A., & Lozano, J. A. (2009). Sensitivity analysis of k-fold cross validation in prediction error estimation. IEEE transactions on pattern analysis and machine intelligence, 32(3), 569-575.
[55]. Huang, Y., Zhang, J., Ann, F. T., & Ma, G. (2020). Intelligent mixture design of steel fibre reinforced concrete using a support vector regression and firefly algorithm based multi-objective optimization model. Construction and Building Materials, 260, 120457.
)