Abstract
In recent years, several soft computing models have been proposed to estimate the elastic modulus of magmatic rocks. However, there are lacks in models that consider the different weathering degrees in determining the elastic modulus of rocks. In the literature, mechanical properties are widely used as inputs in predictive models for weathered rocks; however, there are only a few models that use index properties representing the effect of weathering on magmatic rocks. In this study, support vector regression (SVR) Gaussian process regression (GPR), and artificial neural network (ANN) models were developed to predict the elastic modulus of magmatic rocks with different degrees of weathering. The inputs selected by the best subset regression approach were porosity, P-wave velocity, and slake durability index. Key performance indicators (KPIs) were computed to validate the accuracy of the developed models. In addition to KPIs, Taylor diagrams and regression error characteristic (REC) curves were used to assess the performance of the developed prediction models. In this study, considering the difficulties of expressing the error using only RMSE and MAE, a new performance index (PI), PIMAE, was proposed using normalized MAE instead of normalized RMSE. It was also indicated that PIRMSE and PIMAE should be used together in performance analysis. When considering the Taylor diagram, PIRMSE, and PIMAE, the GPR models performed best, and the SVR model performed the worst in both the training and test periods. Similarly, according to the REC curve in both periods, the performance of the SVR was the worst, while the performance of the ANN model was the best. The PIRMSE and PIMAE values of the GPR model for the test data were 1.3779 and 1.4142, respectively, and they were 1.2567 and 1.4139, respectively, for the ANN model. According to the computed response surfaces, an increase in the P-wave velocity, and a decrease in the porosity increased the elastic modulus. However, changes in slake durability index only had a minor effect on the elastic modulus.
This is a preview of subscription content, log in via an institution to check access.
reproduced from Taylor 2001)
Similar content being viewed by others
Availability of data and material
The manuscript has included data and is given as electronic supplementary data.
Code availability
Not applicable.
References
Aboutaleb S, Behnia M, Bagherpour R, Bluekian B (2018) Using non-destructive tests for estimating uniaxial compressive strength and static Young’s modulus of carbonate rocks via some modeling techniques. Bull Eng Geol Environ 77:1717–1728. https://doi.org/10.1007/s10064-017-1043-2
Acar MC, Kaya B (2020) Models to estimate the elastic modulus of weak rocks based on least square support vector machine. Arab J Geosci 13:1–12. https://doi.org/10.1007/s12517-020-05566-6
Agatonovic-Kustrin S, Beresford R (2000) Basic concepts of artificial neural network (ANN) modeling and its application in pharmaceutical research. J Pharm Biomed Anal 22:717–727. https://doi.org/10.1016/S0731-7085(99)00272-1
Ahmadi H, Rodehutscord M (2017) Application of artificial neural network and support vector machines in predicting metabolizable energy in compound feeds for pigs. Front Nutr 4:27. https://doi.org/10.3389/fnut.2017.00027
Ajalloeian R, Mansouri H, Baradaran E (2017) Some carbonate rock texture effects on mechanical behavior, based on Koohrang tunnel data. Iran Bull Eng Geol Environ 76:295–307. https://doi.org/10.1007/s10064-016-0861-y
Alemdag S, Gurocak Z, Cevik A, Cabalar AF, Gokceoglu C (2016) Modeling deformation modulus of a stratified sedimentary rock mass using neural network, fuzzy inference and genetic programming. Eng Geol 203:70–82. https://doi.org/10.1016/j.enggeo.2015.12.002
Alikarami R, Torabi A, Kolyukhin D, Skurtveit E (2013) Geostatistical relationships between mechanical and petrophysical properties of deformed sandstone. Int J Rock Mech Min Sci 63:27–38. https://doi.org/10.1016/j.ijrmms.2013.06.002
Armaghani DJ, Tonnizam Mohamad E, Momeni E, Narayanasamy MS, Amin MFM (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. https://doi.org/10.1007/s10064-014-0687-4
Armaghani DA, Mohamad TE, Momeni E, Monjezi M, Narayanasamy MS (2016) Prediction of the strength and elasticity modulus of granite through an expert artificial neural network. Arab J Geosci 9:48. https://doi.org/10.1007/s12517-015-2057-3
Armaghani DJ, Momeni E, Asteris P (2020) Application of group method of data handling technique in assessing deformation of rock mass. Metaheuristic Comput Appl 1:1–18. https://doi.org/10.12989/mca.2020.1.1.001
Atici U (2016) Modelling of the elasticity modulus for rock using genetic expression programming. Adv Mater Sci Eng 8:45. https://doi.org/10.1155/2016/2063987
Aufmuth RE (1974) A systematic determination of engineering criteria for rock (No. CERL-TR-M-799 Final Rept)
Barton N (2007) Fracture-induced seismic anisotropy when sharing is induced in production from fractured reservoirs. J Seism Explor 16:115
Behnia D, Behn M, Shahriar K, Goshtasbi K (2017) A New predictive model for rock strength parameters utilizing GEP method. Proc Eng 191:591–599. https://doi.org/10.1016/j.proeng.2017.05.222
Behzadafshar K, Sarafraz ME, Hasanipanah M, Mojtahedi Tahir MM (2019) Proposing a new model to approximate the elasticity modulus of granite rock samples based on laboratory tests results. Bull Eng Geol Environ 78:527–1536. https://doi.org/10.1007/s10064-017-1210-5
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. https://doi.org/10.1016/j.ijrmms.2013.08.004
Bejarbaneh BY, Bejarbaneh EY, Amin MFMl, (2018) Intelligent modelling of sandstone deformation behaviour using fuzzy logic and neural network systems. Bull Eng Geol Environ 77:345–361. https://doi.org/10.1007/s10064-016-0983-2
Bektas O, Jones JA, Sankararaman S, Roychoudhury I, Goebel K (2019a) A neural network framework for similarity-based prognostics. MethodsX 6:383–390. https://doi.org/10.1016/j.mex.2019.02.015
Bektas O, Jones JA, Sankararaman S, Roychoudhury I, Goebel K (2019b) A neural network filtering approach for similarity-based remaining. Int J Adv Manuf Technol 101:87–103. https://doi.org/10.1007/s00170-018-2874-0
Bi J, Bennett KP (2003) Regression error characteristic curves. In: Proceedings of the 20th international conference on machine learning (ICML-03), pp 43–50
Bidgoli MN, Zhao Z, Jing L (2013) Numerical evaluation of strength and deformability of fractured rocks. J Rock Mech Geotech Eng 5(2013):419–430. https://doi.org/10.1016/j.jrmge.2013.09.002
Bijl H, Schön TB, van Wingerden J-W, Michel Verhaegen M (2017) System identification through online sparse Gaussian process regression with input noise. IFAC J Syst Control 2:1–11. https://doi.org/10.1016/j.ifacsc.2017.09.001
Brotons V, Tomás R, Ivorra S, Grediaga A, Martínez-Martínez J, Benavente D, Gómez-Heras M (2016) Improved correlation between the static and dynamic elastic modulus of different types of rocks. Mater Struct Constr. https://doi.org/10.1617/s11527-015-0702-7
Cargill JS, Shakoor A (1990) Evaluation of empirical methods for measuring the uniaxial compressive strength of rock. Int J Rock Mech Min Sci 27:495–503. https://doi.org/10.1016/0148-9062(90)91001-N
Ceryan N (2014) Application of support vector machines and relevance vector machines in predicting uniaxial compressive strength of volcanic rocks. J African Earth Sci. https://doi.org/10.1016/j.jafrearsci.2014.08.006
Ceryan S (2015) New weathering indices for evaluating durability and weathering characterization of crystalline rock material: a case study from NE Turkey. J Afr Earth Sci 103:54–64. https://doi.org/10.1016/j.jafrearsci.2014.12.005
Ceryan N (2016) A review of soft computing methods application in rock mechanic engineering. Handbook of research on advanced computational techniques for simulation-based engineering. IGI Global, pp 1–70
Ceryan S (2018) Weathering indices used in evaluation of the weathering state of rock material. In: Ceryan N (ed) Handbook of research on trends and digital advances in engineering geology, Chap 4. IGI Global United States of America, pp 132–186
Ceryan S, Tudes S, Ceryan N (2008a) A new quantitative weathering classification for igneous rocks. Environ Geol 55:1319. https://doi.org/10.1007/s00254-007-1080-4
Ceryan S, Tudes S, Ceryan N (2008b) Influence of weathering on the engineering properties of Harsit granitic rocks (NE Turkey). Bull Eng Geol Environ 67:97–104. https://doi.org/10.1007/s10064-007-0115-0
Chai T, Draxler TT (2014) Root mean square error (RMSE) or mean absolute error (MAE)?—arguments against avoiding RMSE in the literature. Geosci Model Dev 7:1247–1250. https://doi.org/10.5194/gmd-7-1247-2014
de Vilder SJ, Brain MJ, Rosser NJ (2019) Controls on the geotechnical response of sedimentary rocks to weathering. Earth Surf Process Landf 44:1910–1929. https://doi.org/10.1002/esp.4619
Deere DU, Miller RP (1966) Engineering classification and index properties for intact rock. Illinois Univ At Urbana Dept Of Civil Engineering
Dehghan S, Sattari G, Chehreh CS, Aliabadi MA (2010) Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks. Min Sci Technol. https://doi.org/10.1016/S1674-5264(09)60158-7
Desai KM, Survase SA, Saudagar PS et al (2008) Comparison of artificial neural network (ANN) and response surface methodology (RSM) in fermentation media optimization: case study of fermentative production of scleroglucan. Biochem Eng J 41:266–273. https://doi.org/10.1016/j.bej.2008.05.009
Desboulets LDD (2018) A review on variable selection in regression analysis. Econometrics 6:45. https://doi.org/10.3390/econometrics6040045
Diamantis K, Gartzos E, Migiros G (2014) Influence of petrographic characteristics on physico-mechanical properties of ultrabasic rocks from central Greece. Bull Eng Geol Environ 73:1273–1292. https://doi.org/10.1007/s10064-014-0584-x
Dinçer I, Acar A, Çobanoğlu I, Uras Y (2004) Correlation between Schmidt hardness, uniaxial compressive strength and Young’s modulus for andesites, basalts and tuffs. Bull Eng Geol Environ 63:141–148. https://doi.org/10.1007/s10064-004-0230-0
Erguler ZA, Ulusay R (2009) Water-induced variations in mechanical properties of clay-bearing rocks. Int J Rock Mech Min Sci 46:355–370. https://doi.org/10.1016/j.ijrmms.2008.07.002
Fener M, Kahraman S, Bilgil A, Gunaydin O (2005) A comparative evaluation of indirect methods to estimate the compressive strength of rocks. Rock Mech Rock Eng 38:329–343. https://doi.org/10.1007/s00603-005-0061-8
Ghasemi E, Kalhori H, Bagherpour R, Yagiz S (2018) Model tree approach for predicting uniaxial compressive strength and Young’s modulus of carbonate rocks. Bull Eng Geol Environ 77:331–343. https://doi.org/10.1007/s10064-016-0931-1
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. https://doi.org/10.1016/j.engappai.2003.11.006
Gokceoglu C, Ulusay R, Sonmez H (2000) Factors affecting the durability of selected weak and clay-bearing rocks from Turkey, with particular emphasis on the influence of the number of drying and wetting cycles. Eng Geol 57:215–237. https://doi.org/10.1016/S0013-7952(00)00031-4
Guven IH (1993) Geological and metallogenic map of the eastern black sea region; 1: 250000 Map. Publications of Mineral Research and Exploration General Directorate of Turkey
Ham FM, Kostanic I (2000) Principles of neurocomputing for science and engineering. McGraw-Hill Higher Education, p 672 (ISBN:978-0-07-025966-9)
Haque MM, Rahman A, Hagare D, Chowdhury RK (2018) A comparative assessment of variable selection methods in urban water demand forecasting. Water 10:419. https://doi.org/10.3390/w10040419
Heap MJ, Lavallée Y, Petrakova L et al (2014) Microstructural controls on the physical and mechanical properties of edifice-forming andesites at Volcán de Colima, Mexico. J Geophys Res Solid Earth 119:2925–2963. https://doi.org/10.1002/2013JB010521
Heidari M, Khanlari GR, Momeni AA (2010) Prediction of elastic modulus of intact rocks using artificial neural networks and non-linear regression methods. J Appl Sci Res 4:5869–5879
Hippolyte JC, Müller C, Sangu E, Kaymakci N (2017) Stratigraphic comparisons along the Pontides (Turkey) based on new nannoplankton age determinations in the Eastern Pontides: geodynamic implications. Geol Soc Spec Publ 428:323–358. https://doi.org/10.1144/SP428.9
Hoek E, Diederichs MS (2006) Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci 36:203–215. https://doi.org/10.1016/j.ijrmms.2005.06.005
Hong X, Gao J, Jiang X, Harris CJ (2014) Estimation of Gaussian process regression model using probability distance measures. Syst Sci Control Eng 1:655–663. https://doi.org/10.1080/21642583.2014.970731
Huang Y, Lan Y, Thomson SJ, Fang A, Hoffmann WC, Lacey RE (2010) Development of soft computing and applications in agricultural and biological engineering. Comput Electron Agric 71(2):107–127. https://doi.org/10.1016/j.compag.2010.01.001
Huang XB, Zhang Q, Zhu HH, Zhang LY (2017) An estimated method of intact rock strength using gaussian process regression. In: 51st US rock mechanics/geomechanics symposium. American Rock Mechanics Association
International Society for Rock Mechanics (2007) The complete ISRM suggested methods for rock characterization, testing and monitoring: 1974–2006. In: Ulusay H (ed) Suggested methods prepared by the commission on testing methods. International Society for Rock Mechanics, p 628
Kahraman S, Gunaydin O, Alber M, Fener M (2009) Evaluating the strength and deformability properties of Misis fault breccia using artificial neural networks. Expert Syst Appl 36:6874–6878. https://doi.org/10.1016/j.eswa.2008.08.002
Karakus M, Kumral M, Kilic O (2005) Predicting elastic properties of intact rocks from index tests using multiple regression modelling. Int J Rock Mech Min Sci 42:323–330. https://doi.org/10.1016/j.ijrmms.2004.08.005
Kayabasi A, Gokceoglu C, Ercanoglu M (2003) Estimating the deformation modulus of rock masses: a comparative study. Int J Rock Mech Min Sci 40:55–63. https://doi.org/10.1016/S1365-1609(02)00112-0
Khandelwal M, Singh TN (2009) Correlating static properties of coal measures rocks with P-wave velocity. Int J Coal Geol 79:55–60. https://doi.org/10.1016/j.coal.2009.01.004
Khandelwal M, Singh TN (2011) Predicting elastic properties of schistose rocks from unconfined strength using intelligent approach. Arab J Geosci 4:435–442. https://doi.org/10.1007/s12517-009-0093-6
Kim E, Stine MA, de Oliveira DBM, Changani H (2017) Correlations between the physical and mechanical properties of sandstones with changes of water content and loading rates. Int J Rock Mech Min Sci 100:255–262. https://doi.org/10.1016/j.ijrmms.2017.11.005
Ko J, Jeong S, Lee JK (2016) Large deformation FE analysis of driven steel pipe piles with soil plugging. Comput Geotech 71:82–97. https://doi.org/10.1016/j.compgeo.2015.08.005
Kumar M, Samui P, Naithani AK (2013) Determination of uniaxial compressive strength and modulus of elasticity of travertine using machine learning techniques. Int J Adv Soft Comput Appl 54:1–13
Kumar M, Bhatt MR, Samui P (2014) Modeling of elastic modulus of jointed rock mass: Gaussian process regression approach. Int J Geomech 14:06014001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000318
Kurtuluş C, Irmak TS, Sertçelik I (2010) Physical and mechanical properties of Gokceada: Imbros (NE Aegean Sea) island andesites. Bull Eng Geol Environ 69:321–324. https://doi.org/10.1007/s10064-010-0270-6
Lee SG, De Freitas MH (1989) A revision of the description and classification of weathered granite and its application to granites in Korea. Q J Eng Geol 22:31–48. https://doi.org/10.1144/gsl.qjeg.1989.022.01.03
Liu Z, Shao J, Xu W, Shi C (2013) Estimation of elasticity of porous rock based on mineral composition and microstructure. Adv Mater Sci Eng. https://doi.org/10.1155/2013/512727
Liu Z, Shao J, Xu W et al (2014) Prediction of elastic compressibility of rock material with soft computing techniques. Appl Soft Comput J 22:118–125. https://doi.org/10.1016/j.asoc.2014.05.009
Madhubabu N, Singh PK, Kainthola A et al (2016) Prediction of compressive strength and elastic modulus of carbonate rocks. Measurement 88:202–213. https://doi.org/10.1016/j.measurement.2016.03.050
Mahdiabadi N, Khanlari G (2019) Prediction of uniaxial compressive strength and modulus of elasticity in calcareous mudstones using neural networks, fuzzy systems, and regression analysis. Period Polytech Civ Eng 63:104–114. https://doi.org/10.3311/PPci.13035
Mallows CL, Sloane NJA (1973) An upper bound for self-dual codes. Inf Control 22:188–200. https://doi.org/10.1016/S0019-9958(73)90273-8
Manouchehrian A, Sharifzadeh M, Hamidzadeh Moghadam R, Nouri T (2013) Selection of regression models for predicting strength and deformability properties of rocks using GA. Int J Min Sci Technol 23:495–501. https://doi.org/10.1016/j.ijmst.2013.07.006
Marques EAG, Barroso EV, Filho APM, do Vargas EA (2010) Weathering zones on metamorphic rocks from Rio de Janeiro-Physical, mineralogical and geomechanical characterization. Eng Geol 111:1–18. https://doi.org/10.1016/j.enggeo.2009.11.001
Mashayekhi M, Kaliakin VN, Meehan CL et al (2020) Simulation of aggregate behavior in low confinement geotechnical applications. Comput Geotech 125:103678
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 J 70:980–987. https://doi.org/10.1016/j.asoc.2017.06.030
Mielke PW Jr, Berry KJ (2001) Permutation methods: a distance function approach. Springer, New York (ISBN 978-1-4757-3449-2)
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. https://doi.org/10.1007/s11053-018-9383-6
Momeni A, Hashemi SS, Khanlari GR, Heidari M (2017) The effect of weathering on durability and deformability properties of granitoid rocks. Bull Eng Geol Environ 76:1037–1049. https://doi.org/10.1007/s10064-016-0999-7
Momeni E, Dowlatshahi MB, Omidinasab F, Maizir H, Armaghani DJ (2020) Gaussian process regression technique to estimate the pile bearing capacity. Arab J Sci Eng 45:8255–8267. https://doi.org/10.1007/s13369-020-04683-4
Nefeslioglu HA (2013) Evaluation of geo-mechanical properties of very weak and weak rock materials by using non-destructive techniques: ultrasonic pulse velocity measurements and reflectance spectroscopy. Eng Geol 160:8–20. https://doi.org/10.1016/j.enggeo.2013.03.023
Ocak I, Seker SE (2012) Estimation of elastic modulus of intact rocks by artificial neural network. Rock Mech Rock Eng 45:1047–1054. https://doi.org/10.1007/s00603-012-0236-z
Omoruyi F, Obubu M, Ifunanya O et al (2019) Comparison of some variable selection techniques in regression analysis. Am J Biomed Sci Res 6:281–293. https://doi.org/10.34297/AJBSR.2019.06.001044
Ozkat EC, Franciosa P, Ceglarek D (2017a) A framework for physics-driven in-process monitoring of penetration and interface width in laser overlap welding. Proc CIRP 60:44–49. https://doi.org/10.1016/j.procir.2017.01.043
Ozkat EC, Franciosa P, Ceglarek D (2017b) Laser dimpling process parameters selection and optimization using surrogate-driven process capability space. Opt Laser Technol 93:149–164. https://doi.org/10.1016/j.optlastec.2017.02.012
Ozkat EC, Franciosa P, Ceglarek D (2017c) Development of decoupled multi-physics simulation for laser lap welding considering part-to-part gap. J Laser Appl 29:022423. https://doi.org/10.2351/1.4983234
Pan J, Meng Z, Hou Q et al (2013) Coal strength and Young’s modulus related to coal rank, compressional velocity and maceral composition. J Struct Geol 54:129–135. https://doi.org/10.1016/j.jsg.2013.07.008
Park YW, Klabjan D (2020) Subset selection for multiple linear regression via optimization. J Glob Optim 1:1–32. https://doi.org/10.1007/s10898-020-00876-1
Ranjbar-Karami R, Kadkhodaie-Ilkhchi A, Shiri M (2014) A modified fuzzy inference system for estimation of the static rock elastic properties: a case study from the Kangan and Dalan gas reservoirs, South Pars gas field, the Persian Gulf. J Nat Gas Sci Eng 21:962–976. https://doi.org/10.1016/j.jngse.2014.10.034
Rasmussen CE (2004) Gaussian processes in machine learning. Lect Notes Comput Sci. https://doi.org/10.1007/978-3-540-28650-9_4
Rezaei M (2018) Indirect measurement of the elastic modulus of intact rocks using the Mamdani fuzzy inference system. Measurement 129:319–331. https://doi.org/10.1016/j.measurement.2018.07.047
Rezaei M (2020) Feasibility of novel techniques to predict the elastic modulus of rocks based on the laboratory data. Int J Geotech Eng 14:25–34. https://doi.org/10.1080/19386362.2017.1397873
Rezaei M, Majdi A, Monjezi M (2014) An intelligent approach to predict unconfined compressive strength of rock surrounding access tunnels in longwall coal mining. Neural Comput Appl 24:233–241. https://doi.org/10.1007/s00521-012-1221-x
Roy GD, Singh TN (2018) Regression and soft computing models to estimate young’s modulus of CO2 saturated coals. Measurement 129:91–101. https://doi.org/10.1016/j.measurement.2018.07.016
Roy GD, Singh TN (2020) Predicting deformational properties of Indian coal: soft computing and regression analysis approach. Measurement 149:106975. https://doi.org/10.1016/j.measurement.2019.106975
Saedi B, Mohammadi SD, Shahbazi H (2018) Prediction of uniaxial compressive strength and elastic modulus of migmatites using various modeling techniques. Arab J Geosci 11:574. https://doi.org/10.1007/s12517-018-3912-9
Saedi B, Mohammadi SD, Shahbazi H (2019) Application of fuzzy inference system to predict uniaxial compressive strength and elastic modulus of migmatites. Environ Earth Sci 78:208. https://doi.org/10.1007/s12665-019-8219-y
Samui P, Kim D, Jagan J, Roy SS (2019) Determination of uplift capacity of suction caisson using gaussian process regression, minimax probability machine regression and extreme learning machine. Iran J Sci Technol Trans Civ Eng 43:651–657. https://doi.org/10.1007/s40996-018-0155-7
Shakoor A, Bonelli RE (1991) Relationship between petrographic characteristics, engineering index properties, and mechanical properties of selected sandstones. Environ Eng Geosci 28:55–71. https://doi.org/10.2113/gseegeosci.xxviii.1.55
Sharma VS, Sharma SK, Sharma AK (2008) Cutting tool wear estimation for turning. J Intell Manuf 19:99–108. https://doi.org/10.1007/s10845-007-0048-2
Singh TN, Verma AK (2012) Comparative analysis of intelligent algorithms to correlate strength and petrographic properties of some schistose rocks. Eng Comput 28:1–12. https://doi.org/10.1007/s00366-011-0210-5
Singh R, Kainthola A, Singh TN (2012) Estimation of elastic constant of rocks using an ANFIS approach. Appl Soft Comput J 12:40–45. https://doi.org/10.1016/j.asoc.2011.09.010
Singh R, Umrao RK, Ahmad M et al (2017) Prediction of geomechanical parameters using soft computing and multiple regression approach. Measurement 99:108–119. https://doi.org/10.1016/j.measurement.2016.12.023
Sonmez H, Tuncay E, Gokceoglu C (2004) Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara Agglomerate. Int J Rock Mech Min Sci 41:717–729. https://doi.org/10.1016/j.ijrmms.2004.01.011
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. https://doi.org/10.1016/j.ijrmms.2005.06.007
Suykens JAK, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9:293–300. https://doi.org/10.1023/A:1018628609742
Taylor KE (2001) Summarizing multiple aspects of model performance in a single diagram. J Geophys Res Atmos 106:7183–7192. https://doi.org/10.1029/2000JD900719
Tian H, Shu J, Han L (2019) The effect of ICA and PSO on ANN results in approximating elasticity modulus of rock material. Eng Comput 35:305–314. https://doi.org/10.1007/s00366-018-0600-z
Tiryaki B (2008) Predicting intact rock strength for mechanical excavation using multivariate statistics, artificial neural networks, and regression trees. Eng Geol 99:51–60. https://doi.org/10.1016/j.enggeo.2008.02.003
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. https://doi.org/10.1007/s12517-014-1331-0
Tugrul A (2004) The effect of weathering on pore geometry and compressive strength of selected rock types from Turkey. Eng Geol 75:215–227. https://doi.org/10.1016/j.enggeo.2004.05.008
Umrao RK, Sharma LK, Singh R, Singh TN (2018) Determination of strength and modulus of elasticity of heterogenous sedimentary rocks: an ANFIS predictive technique. Measurement 126:194–201. https://doi.org/10.1016/j.measurement.2018.05.064
Undul O, Florian A (2015) Influence of micro-texture on the geo-engineering properties of low porosity volcanic rocks. Eng Geol Soc Territ 6:69–72. https://doi.org/10.1007/978-3-319-09060-3_12
Vapnik VN (1995) The nature of statistical learning theory. Springer, New York, p 187 (ISBN 0-387-94559-8)
Wang HY, Ding WX, Yang JJ (2014) Study on the engineering properties of saturated red sandstone. Appl Mech Mater 638:589–593
Willmott C, Matsuura K (2005) Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Clim Res 30:79–82
Willmott CJ, Matsuura K, Robeson SM (2009) Ambiguities inherent in sums of squares based error statistics. Atmos Environ 43:749–752. https://doi.org/10.1016/j.atmosenv.2008.10.005
Wyering LD, Villeneuve MC, Wallis IC et al (2014) Mechanical and physical properties of hydrothermally altered rocks, Taupo Volcanic Zone, New Zealand. J Volcanol Geotherm Res 288:76–93. https://doi.org/10.1016/j.jvolgeores.2014.10.008
Xia M, Zhao C, Hobbs BE (2014) Particle simulation of thermally-induced rock damage with consideration of temperature-dependent elastic modulus and strength. Comput Geotech 55:461–473. https://doi.org/10.1016/j.compgeo.2013.09.004
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. https://doi.org/10.1002/nag.1066
Yasar E, Erdogan Y (2004) Correlating sound velocity with the density, compressive strength and Young’s modulus of carbonate rocks. Int J Rock Mech Min Sci 41:871–875. https://doi.org/10.1016/j.ijrmms.2004.01.012
Yilmaz I (2009) A new testing method for indirect determination of the unconfined compressive strength of rocks. Int J Rock Mech Min Sci 46:1349–1357. https://doi.org/10.1016/j.ijrmms.2009.04.009
Yilmaz I, Yuksek AG (2008) An example of artificial neural network (ANN) application for indirect estimation of rock parameters. Rock Mech Rock Eng 41:781–795. https://doi.org/10.1007/s00603-007-0138-7
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. https://doi.org/10.1016/j.ijrmms.2008.09.002
Zhang L (2017) Evaluation of rock mass deformability using empirical methods—a review. Undergr Space 2:1–15. https://doi.org/10.1016/j.undsp.2017.03.003
Acknowledgements
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this manuscript. The manuscript has included data and is given as electronic supplementary data.
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
Not applicable.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this manuscript.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ceryan, N., Ozkat, E.C., Korkmaz Can, N. et al. Machine learning models to estimate the elastic modulus of weathered magmatic rocks. Environ Earth Sci 80, 448 (2021). https://doi.org/10.1007/s12665-021-09738-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12665-021-09738-9