Elastic modulus of steel fiber-reinforced concrete: application of optimized algorithms

Xi  Chen

doi:10.6180/jase.202605_29(5).0020

Elastic modulus of steel fiber-reinforced concrete: application of optimized algorithms

Xi ChenThis email address is being protected from spambots. You need JavaScript enabled to view it.

School of Civil Engineering, Sifang College of Shijiazhuang Railway University, Shijiazhuang City, Hebei Province, China

Received: April 12, 2025
Accepted: July 13, 2025
Publication Date: October 18, 2025

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202605_29(5).0020

Incorporating steel fibers into plain concrete has been shown to effectively improve the load-bearing capacity of structural elements. As of now, the impact of fibers on the fundamental mechanical characteristics of Steel Fiber Reinforced Concrete (SFRC) and the associated uncertainties remain inadequately characterized, and precise models for predicting their mechanical properties are lacking. This significantly restricts the applicability in actual buildings. The study investigates various factors affecting settlement, including the water-tocement ratio, sand-to-cement mass ratio, coarse aggregate-to-cement mass proportion, fiber reinforcement coefficient, fiber morphology parameter, coarse aggregate size, superplasticizer-to-cement mass ratio, and fiber tensile yield strength. This research evaluates three approaches for forecasting E_cy, emphasizing the use of a hybrid optimization approach, the Electric Eel Foraging (EEF), with Gradient Boosting regression (GB) and Random Forests regression (RF) methods. Based on the available data, it is likely that RF-EEF and GB-EEF will be able to accurately compute the E_cy. The GB-EEF approach exhibited a high level of functional dependability throughout the training and evaluation phases, as shown by the R² values of 0.9764 and 0.9822. Findings of 0.9892 and 0.9965 , achieved utilizing the RF-EEF technique, were relatively close. Feature importance depicted the highest impact of coarse aggregates to cement ratio and fiber kinds on the target by 0.9961 and 0.995.

Keywords: Reinforced concrete; Steel fiber; Machine learning; Electric eel foraging optimizer; Parameter significanc

[1] B. Bennett, P. Visintin, and T. Xie, (2022) “Global warming potential of recycled aggregate concrete with supplementary cementitious materials" Journal of Building Engineering 52: 104394. DOI: https://doi.org/10. 1016/j.jobe.2022.104394.
[2] R. S. Benemaran, M. Esmaeili-Falak, and M. S. Kord lar, (2024) “Improvement of recycled aggregate concrete using glass fiber and silica fume" Multiscale and Multidisciplinary Modeling, Experiments and Design 7: 1895–1914. DOI: https://doi.org/10.1007/s41939 023-00313-2.
[3] B. D. G. Sepulveda, P. Visintin, and D. J. Oehlers, (2022) “Fatigue bond-slip properties of steel reinforcing bars embedded in UHPFRC: Extraction and development of an accumulated damage law" Case Studies in Construction Materials 17: e01370. DOI: https: //doi.org/10.1016/j.cscm.2022.e01370.
[4] Y. Yu, X.-Y. Zhao, J.-J. Xu, S.-C. Wang, and T.-Y. Xie, (2022) “Evaluation of shear capacity of steel fiber rein forced concrete beams without stirrups using artificial intelligence models" Materials 15: 2407. DOI: https: //doi.org/10.3390/ma15072407.
[5] Y. Yu, X.-Y. Zhao, J.-J. Xu, S.-C. Wang, and T.-Y. Xie, (2022) “Evaluation of shear capacity of steel fiber rein forced concrete beams without stirrups using artificial intelligence models" Materials 15: 2407. DOI: https: //doi.org/10.3390/ma15072407.
[6] X.-Q. Qu, R. Wang, J.-M. Zhang, and B. He, (2023) “Influence of soil plug on the seismic response of bucket foundations in liquefiable seabed" Journal of Marine Science and Engineering 11: 598. DOI: https: //doi.org/10.3390/jmse11030598.
[7] X. Wu, F. Ding, P. Xiang, Y. Wang, Z. Yu, and C. Liu, (2022) “Multiaxial damage ratio strength criteria for fiber reinforced concrete" Journal of Engineering Mechanics 148: 04022029. DOI: https: //doi.org/10.1061/(ASCE)EM.1943-7889.0002109.
[8] M. Esmaeili-Falak and R. S. Benemaran, (2024) “Ap plication of optimization-based regression analysis for evaluation of frost durability of recycled aggregate concrete" Structural Concrete 25: 716–737. DOI: https: //doi.org/10.1002/suco.202300566.
[9] S. Kim, M. Usman, C. Park, and A. Hanif, (2021) “Durability of slag waste incorporated steel fiber-reinforced concrete in marine environment" Journal of Building Engineering 33: 101641. DOI: https: //doi.org/10.1016/j.jobe.2020.101641.
[10] C. Frazão, A. Camões, J. Barros, and D. Gonçalves, (2015) “Durability of steel fiber reinforced self-compacting concrete" Construction and Building Materials 80: 155–166. DOI: https: //doi.org/10.1016/j.conbuildmat.2015.01.061.
[11] A. Parvez and S. J. Foster, (2015) “Fatigue behavior of steel-fiber-reinforced concrete beams" Journal of Structural Engineering 141: 04014117. DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0001074.
[12] L. Jin, R. Zhang, G. Dou, and X. Du, (2018) “Fire resistance of steel fiber reinforced concrete beams after low velocity impact loading" Fire Safety Journal 98: 24–37. DOI: https: //doi.org/10.1016/j.firesaf.2018.04.003.
[13] X. H. Wang, S. Jacobsen, J. Y. He, Z. L. Zhang, S. F. Lee, and H. L. Lein, (2009) “Application of nanoindentation testing to study of the interfacial transition zone in steel fiber reinforced mortar" Cement and Concrete Research 39: 701–715. DOI: https: //doi.org/10.1016/j.cemconres.2009.05.002.
[14] R. Mu, Y. F. Ma, H. Li, X. W. Wang, and P. Zhang, (2015) “Analysis of the distribution of steel fiber in aligned steel fiber reinforced concrete using digital X-ray CT scanning" Journal of Chinese Electron Microscopy Society: 487–491.
[15] W. Abbass, M. I. Khan, and S. Mourad, (2018) “Evaluation of mechanical properties of steel fiber reinforced concrete with different strengths of concrete" Construction and building materials 168: 556–569. DOI: https: //doi.org/10.1016/j.conbuildmat.2018.02.164.
[16] Y. H. Luo, J. L. Liang, D. S. Yang, B. W. Zhou, B. Hu, and L. Yang, (2018) “Configuration and operation optimization of electricity-gas-heat energy hub considering reliability" Automation of Electric Power Systems 42: 47–54.
[17] M.H.JamshidiandM.Arefi,(2024)“Elasticanalysisof functionally graded porous cylinders under uniform internal pressure by using shear deformation theory" Mechanics of Advanced Materials and Structures 31: 11393 11412. DOI: https: //doi.org/10.1080/15376494.2024.2304154.
[18] L.Wu,Z.Xiang,H.Jiang,M.Liu,X.Ju,andW.Zhang, (2022) “A review of durability issues of reinforced concrete structures due to coastal soda residue soil in China" Journal of Marine Science and Engineering 10: 1740. DOI: https: //doi.org/10.3390/jmse10111740.
[19] T.Y.Zhu,(2011) “The mechanical properties of steel fiber reinforced concrete at low fiber content" Zhengzhou: Zhengzhou University:
[20] M. Açikgenç, M. Ula¸s, and K. E. Alyamaç, (2015) “Using an artificial neural network to predict mix compositions of steel fiber-reinforced concrete" Arabian Journal for Science and Engineering 40: 407–419. DOI: https: //doi.org/10.1007/s13369-014-1549-x.
[21] M. Esmaeili-Falak and R. S. Benemaran, (2024) “Ensemble extreme gradient boosting based models to predict the bearing capacity of micropile group" Applied Ocean Research 151: 104149. DOI: https: //doi.org/10.1016/j.apor.2024.104149.
[22] Y. Zhu, L. Huang, Z. Zhang, and B. Bayrami, (2022) “Estimation of splitting tensile strength of modified recycled aggregate concrete using hybrid algorithms" Steel and Composite Structures: 389–406. DOI: https: //doi.org/10.12989/scs.2022.44.3.389.
[23] B. M. Yaychi and M. Esmaeili-Falak, (2024) “Estimating axial bearing capacity of driven piles using tuned random forest frameworks" Geotechnical and Geological Engineering 42: 7813–7834. DOI: https: //doi.org/10.1007/s10706-024-02952-9.
[24] Y. Dawei, Z. Bing, G. Bingbing, G. Xibo, and B. Razza ghzadeh, (2023) “Predicting the CPT-based pile set-up parameters using HHO-RF and PSO-RF hybrid mod els" Structural Engineering and Mechanics, An Int’l Journal 86: 673–686. DOI: http: //dx.doi.org/10.12989/sem.2023.86.5.673.
[25] R. Liang and B. Bayrami, (2022) “Estimation of frost durability of recycled aggregate concrete by hybridized Random Forests algorithms" Steel and Composite Structures: 91–107. DOI: https: //doi.org/10.12989/scs.2023.49.1.091.
[26] M. Esmaeili-Falak, H. Katebi, M. Vadiati, and J. Adamowski, (2019) “Predicting triaxial compressive strength and Young’s modulus of frozen sand using artificial intelligence methods" Journal of Cold Regions Engineering 33: 04019007. DOI: https: //doi.org/10.1061/(ASCE)CR.1943-5495.0000188.
[27] K. Zhang, Y. Zhang, and B. Razzaghzadeh, (2024) “Application of the optimal fuzzy-based system on bearing capacity of concrete pile" Steel and Composite Structures 51: 25–41. DOI: https: //doi.org/10.12989/scs.2024.51.1.025.
[28] M. Açikgenç, M. Ula¸s, and K. E. Alyamaç, (2015) “Using an artificial neural network to predict mix compositions of steel fiber-reinforced concrete" Arabian Journal for Science and Engineering 40: 407–419. DOI: https: //doi.org/10.1007/s13369-014-1549-x.
[29] T. F. Awolusi, O. L. Oke, O. O. Akinkurolere, A. O. Sojobi, and O. G. Aluko, (2019) “Performance comparison of neural network training algorithms in the modeling properties of steel fiber reinforced concrete" Heliyon 5: DOI: https: //doi.org/10.1016/j.heliyon.2018.e01115.
[30] O. Karahan, H. Tanyildizi, and C. D. Atis, (2008) “An artificial neural network approach for prediction of long term strength properties of steel fiber reinforced concrete containing fly ash" Journal of Zhejiang University SCIENCEA9:1514–1523. DOI: https: //doi.org/10.1631/jzus.A0720136.
[31] Y. ¸Sahin and F. Köksal, (2011) “The influences of matrix and steel fibretensile strengths on the fracture energy of high-strength concrete" Construction and Building Materials 25: 1801–1806. DOI: https: //doi.org/10.1016/j.conbuildmat.2010.11.084.
[32] J. G. Yue, Y. F. Xia, and H. Fang, (2021) “Experimental study on fracture mechanism and tension damage constitutive relationship of steel fiber reinforced concrete" China Civ. Eng. J 54: 93–106.
[33] I. S. Ibrahim and M. B. C. Bakar, (2011) “Effects on mechanical properties of industrialised steel fibres addition to normal weight concrete" Procedia engineering 14: 2616–2626. DOI: https://doi.org/10.1016/j.proeng.2011.07.329.
[34] N. Buratti, C. Mazzotti, and M. Savoia, (2011) “Post cracking behaviour of steel and macro-synthetic fibre reinforced concretes" Construction and building materials 25: 2713–2722. DOI: https: //doi.org/10.1016/j.conbuildmat.2010.12.022.
[35] B. R. Rajeshwari and M. V. N. Sivakumar, (2020) “In fluence of coarse aggregate properties on specific fracture energy of steel fiber reinforced self compacting concrete" Advances in concrete construction: 173–181. DOI: https: //doi.org/10.12989/acc.2020.9.2.173.
[36] Q. Li, Y. Fang, Y. Chen, Q. Wu, G. Lin, and Z. Pang, (2020) “Experimental study on mechanical properties of concrete with adding steel fiber at early age" Concrete 6: 102–105.
[37] L. L. Niu, S. P. Zhang, and Y. X. Wei, (2019) “Effect of fiber dosage on the mechanical property of SFRC" China Concr. Cem. Prod 3:
[38] M. Gul, A. Bashir, and J. A. Naqash, (2014) “Study of modulus of elasticity of steel fiber reinforced concrete" Int. J. Eng. Adv. Technol 3: 304–309.
[39] F. Minelli, A. Conforti, E. Cuenca, and G. Plizzari, (2014) “Are steel fibres able to mitigate or eliminate size effect in shear?" Materials and structures 47: 459–473. DOI: https: //doi.org/10.1617/s11527-013-0072-y.
[40] G. Tiberti, F. Minelli, and G. Plizzari, (2015) “Cracking behavior in reinforced concrete members with steel fibers: A comprehensive experimental study" Cement and concrete research 68: 24–34. DOI: https: //doi.org/10.1016/j.cemconres.2014.10.011.
[41] T.Y.Zhu,(2011) “The mechanical properties of steel fiber reinforced concrete at low fiber content" Zhengzhou: Zhengzhou University:
[42] W.Zhao,L. Wang, Z. Zhang, H. Fan, J. Zhang, S. Mir jalili, N. Khodadadi, and Q. Cao, (2024) “Electric eel foraging optimization: A new bio-inspired optimizer for engineering applications" Expert systems with applications 238: 122200. DOI: https: //doi.org/10.1016/j.eswa.2023.122200.
[43] S. Zhao, T. Zhang, S. Ma, and M. Wang, (2023) “Sea horse optimizer: a novel nature-inspired meta-heuristic for global optimization problems" Applied Intelligence 53: 11833–11860. DOI: https: //doi.org/10.1007/s10489-022-03994-3.
[44] G. K. F. Tso and K. K. W. Yau, (2007) “Predicting electricity energy consumption: A comparison of regression analysis, decision tree and neural networks" Energy 32: 1761–1768. DOI: https: //doi.org/10.1016/j.energy.2006.11.010.
[45] S. Araki, M. Shima, and K. Yamamoto, (2018) “Spatiotemporal land use random forest model for estimating metropolitan NO2 exposure in Japan" Science of The Total Environment 634: 1269–1277. DOI: https: //doi.org/10.1016/j.scitotenv.2018.03.324.
[46] H. Hong, H. R. Pourghasemi, and Z. S. Pourtaghi, (2016) “Landslide susceptibility assessment in Lianhua County (China): a comparison between a random forest data mining technique and bivariate and multivariate statistical models" Geomorphology 259: 105–118. DOI: https: //doi.org/10.1016/j.geomorph.2016.02.012.
[47] O. Rahmati, H. R. Pourghasemi, and A. M. Melesse, (2016) “Application of GIS-based data driven random forest and maximum entropy models for groundwater potential mapping: a case study at Mehran Region, Iran" Catena 137: 360–372. DOI: https: //doi.org/10.1016/j.catena.2015.10.010.
[48] J. H. Jeong, J. P. Resop, N. D. Mueller, D. H. Fleisher, K. Yun, E. E. Butler, D. J. Timlin, K.-M. Shim, J. S. Gerber, and V. R. Reddy, (2016) “Random forests for global and regional crop yield predictions" PloS one 11: e0156571. DOI: https: //doi.org/10.1371/journal.pone.0156571.
[49] H. Rao, X. Shi, A. K. Rodrigue, J. Feng, Y. Xia, M. Elhoseny, X. Yuan, and L. Gu, (2019) “Feature selection based on artificial bee colony and gradient boosting decision tree" Applied Soft Computing 74: 634–642. DOI: https: //doi.org/10.1016/j.asoc.2018.10.036.