Investigating the Relationship between Geochemistry, Leeb Rebound Hardness, and Cerchar Abrasivity Index
Publication: International Journal of Geomechanics
Volume 24, Issue 12
Abstract
Rock hardness and abrasivity are among the most crucial properties that can significantly impact the interaction between rocks and mechanical tools in different parts of geoengineering projects. Accurate estimation of these properties is essential for a better understanding and optimization of geoengineering operations. Hence, the main aim of this study was to develop different machine learning (ML) models based on the geochemical measurements for predicting rock hardness and abrasivity. To do this, 159 rock samples were collected from a gold mine, and portable X-ray fluorescence spectrometry (pXRF), Leeb rebound hardness (LRH), and Cerchar abrasivity index (CAI) tests were performed on the collected rock samples. Three different ML algorithms, including random forest regressor (RFR), support vector regression, and gradient boosting regressor, were applied to develop predictive models for LRH and CAI separately. Considering the fact that the geochemical data are of the compositional type, two scenarios were followed: developing predictive models based on the original data obtained from the pXRF and the centered log-ratio (Clr) transformed data, resulting in the development of six predictive models for LRH and CAI. The performance assessment of the developed predictive models showed that RFR models outperformed the other two ML algorithms in predicting LRH and CAI. In addition, the developed models based on the original data demonstrated a better performance in both cases of LRH and CAI than the trained model based on Clr data. The result indicates that integrated pXRF measurements and RFR technique have strong potential to be used for practical and efficient rock materials characterization during exploration and extraction processes.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors acknowledge the financial support from the Natural Science and Engineering Research Council of Canada (NSERC) under Grant number RGPIN-2020-06196.
References
AFNOR (Association Française de Normalisation). 2000. Determination du pouvoir abrasif d’une roche-Partie 1: Essai de rayure avec une pointe. NF P 94-430-1. Paris: AFNOR.
Aitchison, J. 1986. The statistical analysis of compositional data. London: Chapman and Hall.
Akbay, D., and G. Ekincioğlu. 2022. “Estimating the brittleness values of carbonated rocks with Shore, Schmidt, and Leeb hardness values.” Environ. Earth Sci. 81 (7): 206. https://doi.org/10.1007/s12665-022-10332-w.
Alber, M. 2008. “Stress dependency of the Cerchar abrasivity index (CAI) and its effects on wear of selected rock cutting tools.” Tunnelling Underground Space Technol. 23 (4): 351–359. https://doi.org/10.1016/J.TUST.2007.05.008.
Alin, A. 2010. “Multicollinearity.” Wiley Interdiscip. Rev. Comput. Stat. 2 (3): 370–374. https://doi.org/10.1002/WICS.84.
Aoki, H., and Y. Matsukura. 2007. “A new technique for non-destructive field measurement of rock-surface strength: An application of the Equotip hardness tester to weathering studies.” Earth Surf. Process Landforms 32 (12): 1759–1769. https://doi.org/10.1002/esp.1492.
ASTM. 2010. Standard test method for laboratory determination of abrasiveness of rock using the CERCHAR method. ASTM D7625-10. West Conshohocken, PA: ASTM.
ASTM. 2017. Standard test method for Leeb hardness testing of steel products. ASTM A956. West Conshohocken, PA: ASTM.
Barago, N., E. Pavoni, F. Floreani, M. Crosera, G. Adami, D. Lenaz, F. Larese Filon, and S. Covelli. 2022. “Portable X-ray fluorescence (pXRF) as a tool for environmental characterisation and management of mining wastes: Benefits and limits.” Appl. Sci. 12 (23): 12189. https://doi.org/10.3390/app122312189.
Benavente, D., R. Fort, and M. Gomez-Heras. 2021. “Improving uniaxial compressive strength estimation of carbonate sedimentary rocks by combining minimally invasive and non-destructive techniques.” Int. J. Rock Mech. Min. Sci. 147: 104915. https://doi.org/10.1016/j.ijrmms.2021.104915.
Bergstra, J., and Y. Bengio. 2012. “Random search for hyper-parameter optimization.” J. Mach. Learn. Res. 13: 281–305.
Berhane, T. M., C. R. Lane, Q. Wu, B. C. Autrey, O. A. Anenkhonov, V. V. Chepinoga, and H. Liu. 2018. “Decision-tree, rule-based, and random forest classification of high-resolution multispectral imagery for wetland mapping and inventory.” Remote Sens. (Basel) 10 (4): 580. https://doi.org/10.3390/RS10040580.
Betrò, B. 1991. “Bayesian methods in global optimization.” J. Global Optim. 1 (1): 1–14. https://doi.org/10.1007/BF00120661.
Bhuiyan, M., K. Esmaieli, and J. C. Ordóñez-Calderón. 2019. “Application of data analytics techniques to establish geometallurgical relationships to bond work index at the Paracutu mine, Minas Gerais, Brazil.” Minerals 9 (5): 302–331. https://doi.org/10.3390/MIN9050302.
Bhuiyan, M., K. Esmaeili, and J. C. Ordóñez-Calderón. 2022. “Evaluation of rock characterization tests as geometallurgical predictors of bond work index at the Tasiast mine, Mauritania.” Miner. Eng. 175: 107293. https://doi.org/10.1016/J.MINENG.2021.107293.
Brand, N. W., and C. J. Brand. 2014. “Performance comparison of portable XRF instruments.” Geochem. Explor. Environ. Anal. 14 (2): 125–138. https://doi.org/10.1144/geochem2012-172.
Breiman, L. 2001. “Random forests.” Mach. Learn. 45 (1): 5–32. https://doi.org/10.1023/A:1010933404324.
Brown, G. 2011. “Ensemble learning.” In Encyclopedia of Machine Learning, edited by C. Sammut and G. I. Webb, 312–320. Boston: Springer.
Çelik, S. B., and İ Çobanoğlu. 2019. “Comparative investigation of Shore, Schmidt, and Leeb hardness tests in the characterization of rock materials.” Environ. Earth Sci. 78 (18): 554. https://doi.org/10.1007/s12665-019-8567-7.
Cortes, C., and V. Vapnik. 1995. “Support-vector networks.” Mach. Learn. 20 (3): 273–297. https://doi.org/10.1007/BF00994018.
Crosera, M., E. Baracchini, E. Prenesti, A. Giacomello, B. Callegher, P. Oliveri, and G. Adami. 2019. “Elemental characterization of surface and bulk of copper-based coins from the Byzantine-period by means of spectroscopic techniques.” Microchem. J. 147: 422–428. https://doi.org/10.1016/J.MICROC.2019.03.025.
Davis, D. W. 2002. “U–Pb geochronology of Archean metasedimentary rocks in the Pontiac and Abitibi subprovinces, Quebec, constraints on timing, provenance and regional tectonics.” Precambrian Res. 115 (1–4): 97–117. https://doi.org/10.1016/S0301-9268(02)00007-4.
Deketh, H. 1995. Wear of rock cutting tools: Laboratory experiments on the abrasivity of rock. London: CRC Press.
Demirdag, S., H. Yavuz, and R. Altindag. 2009. “The effect of sample size on Schmidt rebound hardness value of rocks.” Int. J. Rock Mech. Min. Sci. 46 (4): 725–730. https://doi.org/10.1016/j.ijrmms.2008.09.004.
Desarnaud, J., K. Kiriyama, B. Bicer Simsir, K. Wilhelm, and H. Viles. 2019. “A laboratory study of Equotip surface hardness measurements on a range of sandstones: What influences the values and what do they mean?” Earth Surf. Processes Landforms 44 (7): 1419–1429. https://doi.org/10.1002/esp.4584.
Egozcue, J. J., and V. Pawlowsky-Glahn. 2005. “Groups of parts and their balances in compositional data analysis.” Math. Geol. 37 (7): 795–828. https://doi.org/10.1007/S11004-005-7381-9.
EPA. 2007. SW-846 test method 6200: Field portable X-Ray fluorescence spectrometry for the determination of elemental concentrations in soil and sediment. SW-846. Washington, DC: Office of Health and Environmental Assessment, EPA.
Farhadian, A., E. Ghasemi, S. H. Hoseinie, and R. Bagherpour. 2022. “Prediction of rock abrasivity index (RAI) and uniaxial compressive strength (UCS) of granite building stones using nondestructive tests.” Geotech. Geol. Eng. 40 (6): 3343–3356. https://doi.org/10.1007/S10706-022-02095-9/TABLES/5.
Fisher, L., M. F. Gazley, A. Baensch, S. J. Barnes, J. Cleverley, and G. Duclaux. 2014. “Resolution of geochemical and lithostratigraphic complexity: A workflow for application of portable X-ray fluorescence to mineral exploration.” Geochem. Explor. Environ. Anal. 14 (2): 149–159. https://doi.org/10.1144/geochem2012-158.
Friedman, J. H. 2001. “Greedy function approximation: A gradient boosting machine.” Ann. Stat. 29 (5): 1189–1232. https://doi.org/10.1214/AOS/1013203451.
Gaillard, N., A. E. Williams-Jones, J. R. Clark, P. Lypaczewski, S. Salvi, S. Perrouty, N. Piette-Lauzière, C. Guilmette, and R. L. Linnen. 2018. “Mica composition as a vector to gold mineralization: Deciphering hydrothermal and metamorphic effects in the Malartic district, Quebec.” Ore Geol. Rev. 95: 789–820. https://doi.org/10.1016/J.OREGEOREV.2018.02.009.
Garrido, M. E., F. B. Petnga, V. Martínez-Ibáñez, J. B. Serón, C. Hidalgo-Signes, and R. Tomás. 2022. “Predicting the uniaxial compressive strength of a limestone exposed to high temperatures by point load and Leeb rebound hardness testing.” Rock Mech. Rock Eng. 55 (1): 1–17. https://doi.org/10.1007/s00603-021-02647-0.
Ghadernejad, S., and K. Esmaeili. 2024. “The application of small sample theory and confidence interval method to determine the representative mean Leeb rebound hardness value.” Bull. Eng. Geol. Environ. 83 (1): 1–18. https://doi.org/10.1007/S10064-023-03512-W.
Ghorbani, S., S. H. Hoseinie, E. Ghasemi, and T. Sherizadeh. 2022a. “Application of Leeb hardness test in prediction of dynamic elastic constants of sedimentary and igneous rocks.” Geotech. Geol. Eng. 40 (6): 3125–3145. https://doi.org/10.1007/s10706-022-02083-z.
Ghorbani, S., S. H. Hoseinie, E. Ghasemi, T. Sherizadeh, and C. Wanhainen. 2022b. “A new rock hardness classification system based on portable dynamic testing.” Bull. Eng. Geol. Environ. 81 (5): 179. https://doi.org/10.1007/s10064-022-02690-3.
Gomez-Heras, M., D. Benavente, C. Pla, J. Martinez-Martinez, R. Fort, and V. Brotons. 2020. “Ultrasonic pulse velocity as a way of improving uniaxial compressive strength estimations from Leeb hardness measurements.” Constr. Build. Mater. 261: 119996. https://doi.org/10.1016/j.conbuildmat.2020.119996.
Haffez, G. S. A. 2012. “Correlation between work index and mechanical properties of some Saudi Ores.” Mater. Test. 54 (2): 108–112. https://doi.org/10.3139/120.110302.
Hall, G. E. M., G. F. Bonham-Carter, and A. Buchar. 2014. “Evaluation of portable X-ray fluorescence (pXRF) in exploration and mining: Phase 1, control reference materials.” Geochem. Explor. Environ. Anal. 14 (2): 99–123. https://doi.org/10.1144/geochem2013-241.
Helt, K. M., A. E. Williams-Jones, J. R. Clark, B. A. Wing, and R. P. Wares. 2014. “Constraints on the genesis of the Archean oxidized, intrusion-related Canadian Malartic gold deposit, Quebec, Canada.” Econ. Geol. 109 (3): 713–735. https://doi.org/10.2113/econgeo.109.3.713.
Hoseinie, S. H., M. Ataei, and R. Mikaiel. 2012. “Comparison of some rock hardness scales applied in drillability studies.” Arab. J. Sci. Eng. 37 (5): 1451–1458. https://doi.org/10.1007/S13369-012-0247-9.
Houshmand, N., K. Esmaeili, S. Goodfellow, and J. Carlos Ordóñez-Calderón. 2023. “Predicting rock hardness using Gaussian weighted moving average filter on borehole data and machine learning.” Miner. Eng. 204: 108448. https://doi.org/10.1016/J.MINENG.2023.108448.
Houshmand, N., S. GoodFellow, K. Esmaeili, and J. C. Ordóñez Calderón. 2022. “Rock type classification based on petrophysical, geochemical, and core imaging data using machine and deep learning techniques.” Appl. Comput. Geosci. 16: 100104. https://doi.org/10.1016/J.ACAGS.2022.100104.
Hui, S. 2018. “Collaboration to reduce wear and corrosion cost for the mining industry.” In Proc., Int. Symp. on Wear Resistant Alloys for the Mining and Processing Industry CBMM, 2018. Pittsburgh, PA: The Minerals, Metals, & Materials Society
İnce, I., and A. Bozdağ. 2021. “An investigation on sample size in Leeb hardness test and prediction of some index properties of magmatic rocks.” Arabian J. Geosci. 14 (3): 182. https://doi.org/10.1007/s12517-021-06478-9.
ISRM. 2013. “ISRM suggested method for determining the abrasivity of rock by the CERCHAR Abrasivity test.” Rock Mech. Rock Eng. 47 (1): 261–266. https://doi.org/10.1007/s00603-013-0518-0.
Jamal, A., R. Kumar, R. P. Singh, N. P. Singh, and A. Kumar Digarse. 2016. “Determination of longevity of teeth in buckets of loading equipment in coal mines—A case study.” Int. J. Sci. Technol. Res. 5 (2): 25–35.
Jones, D. R. 2001. “A taxonomy of global optimization methods based on response surfaces.” J. Global Optim. 21 (4): 345–383. https://doi.org/10.1023/A:1012771025575.
Kadachi, A. N., and M. A. Al-Eshaikh. 2012. “Limits of detection in XRF spectroscopy.” X-Ray Spectrom. 41 (5): 350–354. https://doi.org/10.1002/XRS.2412.
Karrari, S. S., M. Heidari, J. K. Hamidi, and E. S. Teshnizi. 2023. “Predicting geomechanical, abrasivity, and drillability properties in some igneous rocks using fabric features and petrographic indexes.” Bull. Eng. Geol. Environ. 82 (4): 1–22. https://doi.org/10.1007/S10064-023-03144-0.
Komorowski, M., D. C. Marshall, J. D. Salciccioli, and Y. Crutain. 2016. “Exploratory data analysis.” In Secondary analysis of electronic health records, 185–203. Cham, Switzerland, Springer.
Kynčlová, P., P. Filzmoser, and K. Hron. 2016. “Compositional biplots including external non-compositional variables.” Statistics 50 (5): 1132–1148. https://doi.org/10.1080/02331888.2015.1135155.
Lang, H., R. Botha, K. Hume, S. Sandler, and M. Haest. 2022. “Minesense technology empowering bucket resolution mine to mill reconciliation.” In Proc., Int. Mining Geology Conf. Brisbane, Australia: AusIMM.
Leeb, D. 1979. “Dynamic hardness testing of metallic materials.” NDT Int. 12 (6): 274–278. https://doi.org/10.1016/0308-9126(79)90087-7.
Li, Q., J. Li, L. Duan, and S. Tan. 2021. “Prediction of rock abrasivity and hardness from mineral composition.” Int. J. Rock Mech. Min. Sci. 140: 104658. https://doi.org/10.1016/J.IJRMMS.2021.104658.
Lundberg, S. M., and S. I. Lee. 2017. “A unified approach to interpreting model predictions.” Adv. Neural Inf. Process. Syst. 2017: 4766–4775. https://doi.org/10.48550/arXiv.1705.07874.
Lypaczewski, P., B. Rivard, N. Gaillard, S. Perrouty, N. Piette-Lauzière, C. L. Bérubé, and R. L. Linnen. 2019. “Using hyperspectral imaging to vector towards mineralization at the Canadian Malartic gold deposit, Québec, Canada.” Ore Geol. Rev. 111: 102945. https://doi.org/10.1016/J.OREGEOREV.2019.102945.
Majeed, Y., M. Z. Abu Bakar, and I. A. Butt. 2020. “Abrasivity evaluation for wear prediction of button drill bits using geotechnical rock properties.” Bull. Eng. Geol. Environ. 79 (2): 767–787. https://doi.org/10.1007/S10064-019-01587-Y.
Pavoni, E., M. Crosera, E. Petranich, G. Adami, J. Faganeli, and S. Covelli. 2020. “Partitioning and mixing behaviour of trace elements at the Isonzo/Soča River mouth (Gulf of Trieste, northern Adriatic Sea).” Mar. Chem. 223: 103800. https://doi.org/10.1016/J.MARCHEM.2020.103800.
Plinninger, R., H. Kasling, and K. Thuro. 2004. “Wear prediction in hardrock excavation using the CERCHAR abrasiveness index (CAI).” In Proc., Eurock 2004 and 53rd Geomechanics Colloquium, 599–604. Salzburg, Austria: ISRM.
Proceq, S. A. 2007. Equotip 3 portable hardness tester, operating instructions. Schwerzenbach, Switzerland: Proceq SA.
Raskevicius, T., G. Beaudoin, K. Kyser, S. Perrouty, and N. Gaillard. 2020. “Whole-rock δ2H and δ18O footprint of the Canadian Malartic gold deposit, Pontiac Subprovince, Québec, Canada.” Miner. Deposita 55 (5): 991–1008. https://doi.org/10.1007/S00126-019-00919-Y.
Robert, F. 2011. “Internal structure of the Cadillac tectonic zone southeast of Val d’Or, Abitibi greenstone belt, Quebec.” Can. J. Earth Sci. 26 (12): 2661–2675. https://doi.org/10.1139/e89-226.
Robert, F., K. H. Poulsen, K. F. Cassidy, and C. J. Hodgson. 2005. “Gold metallogeny of the superior and Yilgarn cratons.” In Economic Geology and the Bulletin of the Society of Economic Geologists, 100th Anniversary Volume, edited by J. W. Hedenquist, J. F. H. Thompson, R. J. Goldfarb, and J. P. Richards, 1001–1033. Littleton, CO: Society of Economic Geologists
Rostami, J., A. Ghasemi, E. Alavi Gharahbagh, C. Dogruoz, and F. Dahl. 2014. “Study of dominant factors affecting Cerchar abrasivity index.” Rock Mech. Rock Eng. 47 (5): 1905–1919. https://doi.org/10.1007/S00603-013-0487-3.
Sibilia, M., et al. 2021. “A multidisciplinary study unveils the nature of a Roman ink of the I century AD.” Sci. Rep. 11 (1): 1–12. https://doi.org/10.1038/s41598-021-86288-x.
Teymen, A. 2020. “The usability of Cerchar abrasivity index for the estimation of mechanical rock properties.” Int. J. Rock Mech. Min. Sci. 128: 104258. https://doi.org/10.1016/J.IJRMMS.2020.104258.
Turner, R., D. Eriksson, M. Mccourt, J. Kiili, V. Z. Xu, H. J. Escalante, and K. Hofmann. 2021. “Bayesian optimization is superior to random search for machine learning hyperparameter tuning: Analysis of the black-box optimization challenge 2020.” Proc. Mach. Learn. Res. 133: 3–26. https://doi.org/10.48550/arXiv.2104.10201.
Wu, J., X. Y. Chen, H. Zhang, L. D. Xiong, H. Lei, and S. H. Deng. 2019. “Hyperparameter optimization for machine learning models based on Bayesian optimization.” J. Electron. Sci. Technol. 17 (1): 26–40. https://doi.org/10.11989/JEST.1674-862X.80904120.
Wu, Y., X.-Z. Li, L.-C. Deng, J.-F. Liu, C.-J. Zou, and C. Zhang. 2024. “Rock abrasiveness prediction based on multi-source physical, mechanical and mineralogical properties.” Preprint (Version 1), submitted February 5, 2024. https://doi.org/10.21203/RS.3.RS-3908916/V1.
Yarali, O., E. Yaşar, G. Bacak, and P. G. Ranjith. 2008. “A study of rock abrasivity and tool wear in coal measures rocks.” Int. J. Coal Geol. 74 (1): 53–66. https://doi.org/10.1016/J.COAL.2007.09.007.
Zhang, W., Z. Wang, Z. Shi, P. Xu, and Z. Chang. 2022. “Influence mechanism of high temperature on drilling rate and hardness of sandstone.” Nat. Resour. Res. 31: 2589–2601. https://doi.org/10.1007/s11053-022-10076-1.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 12 • December 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Oct 16, 2023
Accepted: Jun 12, 2024
Published online: Sep 26, 2024
Published in print: Dec 1, 2024
Discussion open until: Feb 26, 2025
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.