Abstract
To design and plan effectively, understanding the engineering properties of rocks, such as the Uniaxial Compressive Strength (UCS), is crucial. While direct laboratory testing is a common method for determining UCS, it is often time-consuming, costly, and challenging, especially for soft or highly fractured rocks. Numerous past studies have explored indirect methods using basic rock properties for UCS prediction, and many correlations have been established. This study introduces an innovative indirect approach using machine learning models, including Multiple Linear Regression, Support Vector Regression, Bi-directional Long Short-Term Memory, and two hybrid models’ i.e., artificial neural networks with teaching learning-based optimization (ANN-TLBO) and particle size optimization (ANN-PSO) using Petrographic properties. This study utilized 54 rock samples from three different geological locations in India, with corresponding thin sections prepared and tested in the laboratory. The prediction of UCS was based on unit weight and petrographic analysis, specifically mineral compositions. Statistical analysis showed that the ANN-PSO model outperformed others, achieving R2 and TIC values of 0.9911 and 0.0134 during training, and R2 = 0.9868 and TIC = 0.0154 during testing. We conducted various statistical analyses, including a heatmap matrix, Taylor plot, REC curve and uncertainty analysis to evaluate the model performance. Our results indicate that machine learning models, particularly ANN-PSO, offer a reliable and efficient alternative to traditional methods for predicting UCS. Furthermore, Sensitivity analysis was investigated to check the importance of input parameters to the output parameters. Results identified quartz as the most significant parameter influencing UCS prediction.
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References
Abbaszadeh Shahri A, Maghsoudi Moud F, Mirfallah Lialestani SP (2022) A hybrid computing model to predict rock strength index properties using support vector regression. Eng Comput 38:579–594
Abdul W, Alsulaiman M, Amin SU et al (2021) Intelligent real-time Arabic sign language classification using attention-based inception and BiLSTM. Comput Electr Eng 95:107395
Acharyya A, Ray S, Chaudhuri BK et al (2006) Proterozoic rock suites along South Purulia Shear Zone, Eastern India: evidence for rift-related setting. Geol Soc India 68:1069–1086
Ahmad F, Samui P, Mishra SS (2023) Probabilistic analysis of slope using bishop method of slices with the help of subset simulation subsequently aided with hybrid machine learning paradigm. Indian Geotech J. https://doi.org/10.1007/s40098-023-00796-3
Aladejare AE (2020) Evaluation of empirical estimation of uniaxial compressive strength of rock using measurements from index and physical tests. J Rock Mech Geotech Eng 12:256–268
Aladejare AE, Wang Y (2017) Evaluation of rock property variability. Georisk Assess Manag Risk Eng Syst Geohazards 11:22–41
Aladejare AE, Wang Y (2019) Probabilistic characterization of Hoek-Brown constant mi of rock using Hoek’s guideline chart, regression model and uniaxial compression test. Geotech Geol Eng 37:5045–5060
Armaghani DJ, Tonnizam Mohamad E, Momeni E et al (2016) Prediction of the strength and elasticity modulus of granite through an expert artificial neural network. Arab J Geosci 9:1–16
Asteris PG, Mokos VG (2020) Concrete compressive strength using artificial neural networks. Neural Comput Appl 32:11807–11826
Azadeh A, Ghaderi SF, Sohrabkhani S (2008) A simulated-based neural network algorithm for forecasting electrical energy consumption in Iran. Energy Policy 36:2637–2644
Bardhan A, Manna P, Kumar V et al (2021) Reliability analysis of piled raft foundation using a novel hybrid approach of ANN and equilibrium optimizer. Comput Model Eng Sci 128:1033–1067
Basu A, Aydin A (2006) Predicting uniaxial compressive strength by point load test: significance of cone penetration. Rock Mech Rock Eng 39:483–490
Beiki M, Majdi A, Givshad AD (2013) Application of genetic programming to predict the uniaxial compressive strength and elastic modulus of carbonate rocks. Int J Rock Mech Min Sci 63:159–169
Bieniawski ZT (1974) Estimating the strength of rock materials. J S Afr Inst Min Metall 74:312–320
Bienawski ZT (1976) Rock mass classifications in rock engineering
Bui H-B, Nguyen H, Choi Y et al (2019a) A novel artificial intelligence technique to estimate the gross calorific value of coal based on meta-heuristic and support vector regression algorithms. Appl Sci 9:4868
Bui X-N, Lee CW, Nguyen H et al (2019b) Estimating PM10 concentration from drilling operations in open-pit mines using an assembly of SVR and PSO. Appl Sci 9:2806
Cargill JS, Shakoor A (1990) Evaluation of empirical methods for measuring the uniaxial compressive strength of rock. In: International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts. Elsevier, pp 495–503
Changkakoti A, Gray J, Morton RD, Sarkar SN (1987) The Mosaboni copper deposit, India; a preliminary study on the nature and genesis of the ore-fluids. Econ Geol 82:1619–1625
Çobanoğlu İ, Çelik SB (2008) Estimation of uniaxial compressive strength from point load strength, Schmidt hardness and P-wave velocity. Bull Eng Geol Environ 67:491–498
D’Andrea DV, Fischer RL, Fogelson DE (1965) Prediction of compressive strength from other rock properties. US Department of the Interior, Bureau of Mines
Davoodi S, Mehrad M, Wood DA et al (2023) Predicting uniaxial compressive strength from drilling variables aided by hybrid machine learning. Int J Rock Mech Min Sci 170:105546
Dehghan S, Sattari GH, Chelgani SC, Aliabadi MA (2010) Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks. Min Sci Technol 20:41–46
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the sixth international symposium on micro machine and human science. IEEE, pp 39–43
Fattahi H (2017) Applying soft computing methods to predict the uniaxial compressive strength of rocks from schmidt hammer rebound values. Comput Geosci 21:665–681
Gokceoglu C (2002) A fuzzy triangular chart to predict the uniaxial compressive strength of the Ankara agglomerates from their petrographic composition. Eng Geol 66:39–51
Gokceoglu C, Zorlu K (2004) A fuzzy model to predict the uniaxial compressive strength and the modulus of elasticity of a problematic rock. Eng Appl Artif Intell 17:61–72
Gül E, Ozdemir E, Sarıcı DE (2021) Modeling uniaxial compressive strength of some rocks from turkey using soft computing techniques. Measurement 171:108781
Hawkins AB (2009) Ulusay, R., Hudson, JA (eds.): the complete ISRM suggested methods for rock characterisation, testing and monitoring: (ISRM Turkish National Group). Bull Eng Geol Environ 68:287–288
He J, Serati M, Veidt M, De Alwis A (2024) Determining rock crack stress thresholds using ultrasonic through-transmission measurements. Int J Coal Sci Technol 11:19
Hochreiter S, Schmidhuber J (1997) Long short-term memory. Neural Comput 9:1735–1780
Hoek E, Carranza-Torres C, Corkum B (2002) Hoek-Brown failure criterion-2002 edition. Proc NARMS-Tac 1:267–273
Huang F, **ong H, Chen S et al (2023) Slope stability prediction based on a long short-term memory neural network: comparisons with convolutional neural networks, support vector machines and random forest models. Int J Coal Sci Technol 10:18
Jahed Armaghani D, Tonnizam Mohamad E, Momeni E et al (2015) An adaptive neuro-fuzzy inference system for predicting unconfined compressive strength and Young’s modulus: a study on Main Range granite. Bull Eng Geol Environ 74:1301–1319
Jahed Armaghani D, Tonnizam Mohamad E, Hajihassani M et al (2016) Application of several non-linear prediction tools for estimating uniaxial compressive strength of granitic rocks and comparison of their performances. Eng Comput 32:189–206
Jan MS, Hussain S, e Zahra R et al (2023) Appraisal of different artificial intelligence techniques for the prediction of marble strength. Sustainability 15:8835
Kahraman S (2001) Evaluation of simple methods for assessing the uniaxial compressive strength of rock. Int J Rock Mech Min Sci 38:981–994
Kahraman S (2014) The determination of uniaxial compressive strength from point load strength for pyroclastic rocks. Eng Geol 170:33–42
Kahraman S, Gunaydin O, Fener M (2005) The effect of porosity on the relation between uniaxial compressive strength and point load index. Int J Rock Mech Min Sci 42:584–589
Kahraman S, Fener M, Kozman E (2012) Predicting the compressive and tensile strength of rocks from indentation hardness index. J S Afr Inst Min Metall 112:331–339
Karaman K, Kesimal A (2015) A comparative study of Schmidt hammer test methods for estimating the uniaxial compressive strength of rocks. Bull Eng Geol Environ 74:507–520
Kardani N, Aminpour M, Raja MNA et al (2022) Prediction of the resilient modulus of compacted subgrade soils using ensemble machine learning methods. Transp Geotech 36:100827
Khajevand R (2023) Prediction of the uniaxial compressive strength of rocks by soft computing approaches. Geotech Geol Eng 41:3549–3574
Kumar K, Samui P, Choudhary SS (2023) State parameter based liquefaction probability evaluation. Int J Geosynth Gr Eng 9:76. https://doi.org/10.1007/s40891-023-00495-2
Le LT, Nguyen H, Dou J, Zhou J (2019) A comparative study of PSO-ANN, GA-ANN, ICA-ANN, and ABC-ANN in estimating the heating load of buildings’ energy efficiency for smart city planning. Appl Sci 9:2630
Luo Z, Bui X-N, Nguyen H, Moayedi H (2021) A novel artificial intelligence technique for analyzing slope stability using PSO-CA model. Eng Comput 37:533–544
Matin SS, Farahzadi L, Makaremi S et al (2018) Variable selection and prediction of uniaxial compressive strength and modulus of elasticity by random forest. Appl Soft Comput 70:980–987
Miah MI, Ahmed S, Zendehboudi S, Butt S (2020) Machine learning approach to model rock strength: prediction and variable selection with aid of log data. Rock Mech Rock Eng 53:4691–4715
Mokhtari M, Behnia M (2019) Comparison of LLNF, ANN, and COA-ANN techniques in modeling the uniaxial compressive strength and static Young’s modulus of limestone of the Dalan formation. Nat Resour Res 28:223–239
Monjezi M, Amini Khoshalan H, Razifard M (2012) A neuro-genetic network for predicting uniaxial compressive strength of rocks. Geotech Geol Eng 30:1053–1062
Moradian ZA, Ghazvinian AH, Ahmadi M, Behnia M (2010) Predicting slake durability index of soft sandstone using indirect tests. Int J Rock Mech Min Sci 47:666–671
Nazir R, Momeni E, Armaghani DJ, Amin MFM (2013a) Prediction of unconfined compressive strength of limestone rock samples using L-type Schmidt hammer. Electr J Geotech Eng 18:1767–1775
Nazir R, Momeni E, Armaghani DJ, Amin MFM (2013b) Correlation between unconfined compressive strength and indirect tensile strength of limestone rock samples. Electron J Geotech Eng 18:1737–1746
Nguyen H, Moayedi H, Foong LK et al (2020) Optimizing ANN models with PSO for predicting short building seismic response. Eng Comput 36:823–837
Özdemir E (2022) A new predictive model for uniaxial compressive strength of rock using machine learning method: artificial intelligence-based age-layered population structure genetic programming (ALPS-GP). Arab J Sci Eng 47:629–639
Palmstrøm A (1996) Characterizing rock masses by the RMi for use in practical rock engineering: part 1: the development of the Rock Mass index (RMi). Tunn Undergr Sp Technol 11:175–188
Pradeep T, Samui P (2022) Prediction of rock strain using hybrid approach of ANN and optimization algorithms. Geotech Geol Eng 40:4617–4643
Pradeep T, Bardhan A, Burman A, Samui P (2021) Rock strain prediction using deep neural network and hybrid models of anfis and meta-heuristic optimization algorithms. Infrastructures 6:129
Pradeep T, Bardhan A, Samui P (2022a) Prediction of rock strain using soft computing framework. Innov Infrastruct Solut 7:1–24
Pradeep T, Samui P, Kardani N, Asteris PG (2022b) Ensemble unit and AI techniques for prediction of rock strain. Front Struct Civ Eng 16:858–870. https://doi.org/10.1007/s11709-022-0831-3
Qi Q, Yue X, Duo X et al (2023) Spatial prediction of soil organic carbon in coal mining subsidence areas based on RBF neural network. Int J Coal Sci Technol 10:30
Raja MNA, Shukla SK (2021) Predicting the settlement of geosynthetic-reinforced soil foundations using evolutionary artificial intelligence technique. Geotext Geomembr 49:1280–1293
Raja MNA, Shukla SK (2022) An extreme learning machine model for geosynthetic-reinforced sandy soil foundations. Proc Inst Civ Eng Eng 175:383–403
Raja MNA, Shukla SK, Khan MUA (2022) An intelligent approach for predicting the strength of geosynthetic-reinforced subgrade soil. Int J Pavement Eng 23:3505–3521
Rao RV, Savsani VJ, Vakharia DP (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput Des 43:303–315
Rezaei M, Asadizadeh M (2020) Predicting unconfined compressive strength of intact rock using new hybrid intelligent models. J Min Environ 11:231–246
Sahu A, Sinha S, Banka H (2024) Fuzzy inference system using genetic algorithm and pattern search for predicting roof fall rate in underground coal mines. Int J Coal Sci Technol 11:1–11
Shahani NM, Kamran M, Zheng X et al (2021) Application of gradient boosting machine learning algorithms to predict uniaxial compressive strength of soft sedimentary rocks at Thar Coalfield. Adv Civ Eng 2021:1–19
Sharma PK, Singh TN (2008) A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength. Bull Eng Geol Environ 67:17–22
Singh Rn, Hassani FP, Elkington PAS (1983) The application of strength and deformation index testing to the stability assessment of coal measures excavations. In: ARMA US Rock Mechanics/Geomechanics Symposium. ARMA, p ARMA-83
Singh R, Kainthola A, Singh TN (2012) Estimation of elastic constant of rocks using an ANFIS approach. Appl Soft Comput 12:40–45
Sivamohan S, Sridhar SS (2023) An optimized model for network intrusion detection systems in industry 4.0 using XAI based Bi-LSTM framework. Neural Comput Appl 35:11459–11475
Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14:199–222
Sonmez H, Gokceoglu C, Nefeslioglu HA, Kayabasi A (2006) Estimation of rock modulus: for intact rocks with an artificial neural network and for rock masses with a new empirical equation. Int J Rock Mech Min Sci 43:224–235
Sulukcu S, Ulusay R (2001) Evaluation of the block punch index test with particular reference to the size effect, failure mechanism and its effectiveness in predicting rock strength. Int J Rock Mech Min Sci 38:1091–1111
Sunny MAI, Maswood MMS, Alharbi AG (2020) Deep learning-based stock price prediction using LSTM and bi-directional LSTM model. In: 2020 2nd Novel Intelligent and Leading Emerging Sciences Conference (NILES). IEEE, pp 87–92
Tandon RS, Gupta V (2015) Estimation of strength characteristics of different Himalayan rocks from Schmidt hammer rebound, point load index, and compressional wave velocity. Bull Eng Geol Environ 74:521–533
Topal U, Goodarzimehr V, Bardhan A et al (2022) Maximization of the fundamental frequency of the FG-CNTRC quadrilateral plates using a new hybrid PSOG algorithm. Compos Struct 295:115823
Torabi-Kaveh M, Naseri F, Saneie S, Sarshari B (2015) Application of artificial neural networks and multivariate statistics to predict UCS and E using physical properties of Asmari limestones. Arab J Geosci 8:2889–2897
Ulusay R, Hudson JA (2007) International Society for Rock Mechanics (ISRM), the complete ISRM suggested methods for rock characterization, testing and monitoring, 1974–2006. Ankara
Vapnik V (1999) The nature of statistical learning theory. Springer Science & Business Media
Yagiz S (2011a) Correlation between slake durability and rock properties for some carbonate rocks. Bull Eng Geol Environ 70:377–383
Yagiz S (2011b) P-wave velocity test for assessment of geotechnical properties of some rock materials. Bull Mater Sci 34:947–953
Yagiz S, Sezer EA, Gokceoglu C (2012) Artificial neural networks and nonlinear regression techniques to assess the influence of slake durability cycles on the prediction of uniaxial compressive strength and modulus of elasticity for carbonate rocks. Int J Numer Anal Methods Geomech 36:1636–1650
Yaşar E, Erdoğan Y (2004) Estimation of rock physicomechanical properties using hardness methods. Eng Geol 71:281–288
Yesiloglu-Gultekin N, Gokceoglu C, Sezer EA (2013) Prediction of uniaxial compressive strength of granitic rocks by various nonlinear tools and comparison of their performances. Int J Rock Mech Min Sci 62:113–122
Yilmaz I, Yuksek G (2009) Prediction of the strength and elasticity modulus of gypsum using multiple regression, ANN, and ANFIS models. Int J Rock Mech Min Sci 46:803–810
Yin J, Lei J, Fan K, Wang S (2023) Integrating image processing and deep learning for effective analysis and classification of dust pollution in mining processes. Int J Coal Sci Technol 10:84
Zhang H, Wu S, Zhang Z (2022) Prediction of uniaxial compressive strength of rock via genetic algorithm—selective ensemble learning. Nat Resour Res 31:1721–1737
Zhao E, Sun S, Wang S (2022) New developments in wind energy forecasting with artificial intelligence and big data: a scientometric insight. Data Sci Manag 5:84–95
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MSS: Writing and drafting, Conceptualization, Methodology, Model development. AJ: Supervision, data curation and laboratory testing, writing and drafting. AKV: Supervision, review and editing. TNS: Supervision.
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Sabri, M.S., Jaiswal, A., Verma, A.K. et al. Advanced machine learning approaches for uniaxial compressive strength prediction of Indian rocks using petrographic properties. Multiscale and Multidiscip. Model. Exp. and Des. (2024). https://doi.org/10.1007/s41939-024-00513-4
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DOI: https://doi.org/10.1007/s41939-024-00513-4