The fracture energy of the concrete is an important parameter which can be used to identify the fracture process of concrete members, especially when subjected to tension and flexural loading. Practices to measure this property in experiments can be expensive and time-consuming. In this study, a statistical model using Linear Genetic Programming is introduced to predict concretes' fracture energy with three readily measured input parameters, namely, compressive strength, maximum aggregate size, and water to cemented ratio. The model was developed and trained based on a dataset of 64 measured experimental values taken from published research. The performance of the model was evaluated using statistical indices such as the coefficient of determination, root mean squared error, and mean absolute error, and compared with previously proposed empirical models. The experimental results show that the proposed LGP- based model is superior to old regression-based equations in accuracy and generalization. This model can be a useful methodology for engineers in design and analysis, minimizing the need for large amount of laboratory testing.
Nematzadeh, M., Nazari, A., Tayebi, M. Post-Fire Impact Behavior and Durability of Steel Fiber-Reinforced Concrete Containing Blended Cement–Zeolite and Recycled Nylon Granules as Partial Aggregate Replacement. Archives of Civil and Mechanical Engineering, 2022; 22 (1). doi:10.1007/s43452-021-00324-1.
Tayebi, M., Nematzadeh, M. Post-Fire Flexural Performance and Microstructure of Steel Fiber-Reinforced Concrete with Recycled Nylon Granules and Zeolite Substitution. Structures, 2021; 33: 2301–2316. doi:10.1016/j.istruc.2021.05.080.
Ziamiavaghi, B., Toufigh, V. Fracture Toughness Evaluation of Ground Granulated Blast Furnace Slag Concrete Using Experimental Study and Machine Learning Techniques. Engineering Fracture Mechanics, 2023; 291: 109577. doi:10.1016/j.engfracmech.2023.109577.
Jafarzadeh, H., Nematzadeh, M. Evaluation of Post-Heating Flexural Behavior of Steel Fiber-Reinforced High-Strength Concrete Beams Reinforced with FRP Bars: Experimental and Analytical Results. Engineering Structures, 2020; 225: 111292. doi:10.1016/j.engstruct.2020.111292.
Juki, M. I., Awang, M., Annas, M. M. K., Boon, K. H., Othman, N., Kadir, A. A., Roslan, M. A., Khalid, F. S. Relationship between Compressive, Splitting Tensile and Flexural Strength of Concrete Containing Granulated Waste Polyethylene Terephthalate (PET) Bottles as Fine Aggregate. Advanced Materials Research, 2013; 795: 356–359. doi:10.4028/www.scientific.net/AMR.795.356.
Mohammed, A. A. Flexural Behavior and Analysis of Reinforced Concrete Beams Made of Recycled PET Waste Concrete. Construction and Building Materials, 2017; 155: 593–604. doi:10.1016/j.conbuildmat.2017.08.096.
Bažant, Z. P., Becq-Giraudon, E. Statistical Prediction of Fracture Parameters of Concrete and Implications for Choice of Testing Standard. Cement and Concrete Research, 2002; 32 (4): 529–556. doi:10.1016/S0008-8846(01)00723-2.
Comité Euro-International du Béton (CEB), Fédération Internationale de la Précontrainte (FIP). CEB-FIP model code 1990: design code. Lausanne (CH): Comité Euro-International du Béton (CEB); 1993.
Uomoto, T., Ishibashi, T., Nobuta, Y., Satoh, T., Kawano, H., Takewaka, K., et al. Standard specifications for concrete structures—2007. Tokyo (JP): Japan Society of Civil Engineers; 2008.
Paul, S., Das, P., Kashem, A., Islam, N. Sustainable of Rice Husk Ash Concrete Compressive Strength Prediction Utilizing Artificial Intelligence Techniques. Asian Journal of Civil Engineering, 2024; 25 (2): 1349–1364. doi:10.1007/s42107-023-00847-3.
Nematzadeh, M., Mousavimehr, M., Shayanfar, J., Omidalizadeh, M. Eccentric Compressive Behavior of Steel Fiber-Reinforced RC Columns Strengthened with CFRP Wraps: Experimental Investigation and Analytical Modeling. Engineering Structures, 2021; 226: 111389. doi:10.1016/j.engstruct.2020.111389.
Shirvani, M. A., Khodaparast, A., Herozi, M. R., Mousavi, R., Fallah-Valukolaee, S., Ghorbanzadeh, A., Nematzadeh, M. Pre- and Post-Heating Mechanical Properties of Concrete Containing Recycled Fine Aggregate as Partial Replacement of Natural Sand and Nano-Silica as Partial Replacement of Cement: Experiments and Predictions. Archives of Civil and Mechanical Engineering, 2023; 23 (4). doi:10.1007/s43452-023-00760-1.
Parsa-Sharif, M., Nematzadeh, M., Bahrami, A. Post-Fire Load-Reversed Push-out Performance of Normal and Lightweight Concrete-Filled Steel Tube Columns: Experiments and Predictions. Structures, 2023; 51: 1414–1437. doi:10.1016/j.istruc.2023.03.091.
Nemati, M., Nematzadeh, M., Rahimi, S. Effect of Fresh Concrete Compression Technique on Pre- and Post-Heating Compressive Behavior of Steel Fiber-Reinforced Concrete: Experiments and RSM-Based Optimization. Construction and Building Materials, 2023; 400: 132786. doi:10.1016/j.conbuildmat.2023.132786.
Hammoudi, A., Moussaceb, K., Belebchouche, C., Dahmoune, F. Comparison of Artificial Neural Network (ANN) and Response Surface Methodology (RSM) Prediction in Compressive Strength of Recycled Concrete Aggregates. Construction and Building Materials, 2019; 209: 425–436. doi:10.1016/j.conbuildmat.2019.03.119.
Hu, T., Zhang, H., Zhou, J. Machine Learning-Based Model for Recognizing the Failure Modes of FRP-Strengthened RC Beams in Flexure. Case Studies in Construction Materials, 2023; 18: 2076. doi:10.1016/j.cscm.2023.e02076.
Nematzadeh, M., Shahmansouri, A. A., Fakoor, M. Post-Fire Compressive Strength of Recycled PET Aggregate Concrete Reinforced with Steel Fibers: Optimization and Prediction via RSM and GEP. Construction and Building Materials, 2020; 252: 119057. doi:10.1016/j.conbuildmat.2020.119057.
Tajeri, S., Sadrossadat, E., Bazaz, J. B. Indirect Estimation of the Ultimate Bearing Capacity of Shallow Foundations Resting on Rock Masses. International Journal of Rock Mechanics and Mining Sciences, 2015; 80: 107–117. doi:10.1016/j.ijrmms.2015.09.015.
Rostami, M. F., Sadrossadat, E., Ghorbani, B., Kazemi, S. M. New Empirical Formulations for Indirect Estimation of Peak-Confined Compressive Strength and Strain of Circular RC Columns Using LGP Method. Engineering with Computers, 2018; 34 (4): 865–880. doi:10.1007/s00366-018-0577-7.
Alavi, A. H., Aminian, P., Gandomi, A. H., Esmaeili, M. A. Genetic-Based Modeling of Uplift Capacity of Suction Caissons. Expert Systems with Applications, 2011; 38 (10): 12608–12618. doi:10.1016/j.eswa.2011.04.049.
Ashrafian, A., Shahmansouri, A. A., Akbarzadeh Bengar, H., Behnood, A. Post-Fire Behavior Evaluation of Concrete Mixtures Containing Natural Zeolite Using a Novel Metaheuristic-Based Machine Learning Method. Archives of Civil and Mechanical Engineering, 2022; 22 (2). doi:10.1007/s43452-022-00415-7.
Li, Z., Gao, Y., Zhu, Z., Tian, W. Data-Guided for Discovering High-Strength, Cost-Effective, and Low-Carbon Rice Husk Ash Concrete. Journal of CO2 Utilization, 2024; 83: 102786. doi:10.1016/j.jcou.2024.102786.
Hrstka, O., Kučerová, A., Lepš, M., Zeman, J. A Competitive Comparison of Different Types of Evolutionary Algorithms. Computers and Structures, 2003; 81 (18–19): 1979–1990. doi:10.1016/S0045-7949(03)00217-7.
Koza, J. R., Poli, R. Chapter 5, Genetic programming. In: Ghosh A, Tsutsui S, editors. Advances in evolutionary computing. Berlin: Springer; 2003.
Gandomi, A. H., Alavi, A. H., Sahab, M. G., Arjmandi, P. Formulation of Elastic Modulus of Concrete Using Linear Genetic Programming. Journal of Mechanical Science and Technology, 2010; 24 (6): 1273–1278. doi:10.1007/s12206-010-0330-7.
Chen, L., Wang, Z., Khan, A. A., Khan, M., Javed, M. F., Alaskar, A., Eldin, S. M. Development of Predictive Models for Sustainable Concrete via Genetic Programming-Based Algorithms. Journal of Materials Research and Technology, 2023; 24: 6391–6410. doi:10.1016/j.jmrt.2023.04.180.
Alaskar, A., Alfalah, G., Althoey, F., Abuhussain, M. A., Javed, M. F., Deifalla, A. F., Ghamry, N. A. Comparative Study of Genetic Programming-Based Algorithms for Predicting the Compressive Strength of Concrete at Elevated Temperature. Case Studies in Construction Materials, 2023; 18: 2199. doi:10.1016/j.cscm.2023.e02199.
Gandomi, A. H., Mohammadzadeh S., D., Pérez-Ordóñez, J. L., Alavi, A. H. Linear Genetic Programming for Shear Strength Prediction of Reinforced Concrete Beams without Stirrups. Applied Soft Computing Journal, 2014; 19: 112–120. doi:10.1016/j.asoc.2014.02.007.
Nikbin, I., Rahimi R., S., Allahyari, H. A New Empirical Formula for Prediction of Fracture Energy of Concrete Based on the Artificial Neural Network. Engineering Fracture Mechanics, 2017; 186: 466–482. doi:10.1016/j.engfracmech.2017.11.010.
Smith, G. N. Probability and statistics in civil engineering. Glasgow (UK): Collins Professional and Technical Books; 1986.
Francone, F. Discipulus Lite™ owner’s manual. Version 4.0. Bozeman (MT): Register Machine Learning Technologies; 2004.
Nazari, A. , & Lale Arefi, S. (2025). Data-Driven Modeling of Concrete Fracture Energy Using Linear Genetic Programming. Civil Engineering and Applied Solutions, 1(1), 89-98. doi: 10.22080/ceas.2025.29159.1008
MLA
Ali Nazari; Shahin Lale Arefi. "Data-Driven Modeling of Concrete Fracture Energy Using Linear Genetic Programming", Civil Engineering and Applied Solutions, 1, 1, 2025, 89-98. doi: 10.22080/ceas.2025.29159.1008
HARVARD
Nazari, A., Lale Arefi, S. (2025). 'Data-Driven Modeling of Concrete Fracture Energy Using Linear Genetic Programming', Civil Engineering and Applied Solutions, 1(1), pp. 89-98. doi: 10.22080/ceas.2025.29159.1008
CHICAGO
A. Nazari and S. Lale Arefi, "Data-Driven Modeling of Concrete Fracture Energy Using Linear Genetic Programming," Civil Engineering and Applied Solutions, 1 1 (2025): 89-98, doi: 10.22080/ceas.2025.29159.1008
VANCOUVER
Nazari, A., Lale Arefi, S. Data-Driven Modeling of Concrete Fracture Energy Using Linear Genetic Programming. Civil Engineering and Applied Solutions, 2025; 1(1): 89-98. doi: 10.22080/ceas.2025.29159.1008