Abstract
Fracture properties are crucial for the design and application of concrete materials. The fracture energy which represents the fracture performance of concrete always suffers the influence of various factors, making it difficult to accurately predict the fracture energy of concrete with traditional methods. Thus, the artificial intelligence (AI) approaches are employed to establish the predictive models for the concrete fracture energy. Additionally, the firefly meta-heuristic algorithm (FA) is used to search for the optimum model hyper-parameters. The FA algorithm is proved to be efficient in tuning the hyper-parameters of the three models, and optimum values are obtained within ten iterations. Compared with the single classification and regression tree algorithm (CART), the ensemble algorithm appears to be more accurate and generalizable. Moreover, through the importance evaluation of different features in the optimum predictive model, the aggregate characteristics (aggregate size distribution and maximal aggregate size) and specimen size have been proven to be dominant factors for the predictive models, which should be carefully considered in predictive work regarding concrete fracture properties.
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Afrazi M, Lin Q, Fakhimi A (2022) Physical and numerical evaluation of Mode II fracture of quasi-brittle materials. International Journal of Civil Engineering 20:993–1007, DOI: https://doi.org/10.1007/s40999-022-00718-z
Akcaoglu T, Tokyay M, Celik T (2005) Assessing the ITZ microcracking via scanning electron microscope and its effect on the failure behavior of concrete. Cement and Concrete Research 35(2):358–363, DOI: https://doi.org/10.1016/j.cemconres.2004.05.042
An S, Liu W, Venkatesh S (2007) Fast cross-validation algorithms for least squares support vector machine and kernel ridge regression. Pattern Recognit 40(8):2154–2162, DOI: https://doi.org/10.1016/j.patcog.2006.12.015
Asteris PG, Lourenço PB, Roussis PC, Adami CE, Armaghani DJ, Cavaleri L, Chalioris CE, Hajihassani M, Lemonis ME, Mohammed AS, Pilakoutas K (2022) Revealing the nature of metakaolin-based concrete materials using artificial intelligence techniques. Construction and Building Materials 322:126500, DOI: https://doi.org/10.1016/j.conbuildmat.2022.126500
Asteris PG, Skentou AD, Bardhan A, Samui P, Pilakoutas K (2021) Predicting concrete compressive strength using hybrid ensembling of surrogate machine learning models. Cement and Concrete Research 145:106449, DOI: https://doi.org/10.1016/j.cemconres.2021.106449
Barkhordari MS, Massone LM (2022) Failure mode detection of reinforced concrete shear walls using ensemble deep neural networks. International Journal of Concrete Structures and Materials 16:33, DOI: https://doi.org/10.1186/s40069-022-00522-y
Bazant ZP, Becq-Giraudon E (2002) Statistical prediction of fracture parameters of concrete and implications for choice of testing standard. Cement and Concrete Research 32(4):529–556, DOI: https://doi.org/10.1016/s0008-8846(01)00723-2
Bazant ZP, Mohammad TK (1991) Size dependence of concrete fracture energy determined by RILEM work-of-fracture method. International Journal of Fracture 51(2):121–138, DOI: https://doi.org/10.1007/978-94-011-3638-9_9
Breiman L (2001) Random forests. Machine Learning 45(1):5–32, DOI: https://doi.org/10.1023/A:1010933404324
Breiman L, Friedman J, Olshen RA, Stone CJ (1984) Classification and regression trees. Routledge, NY, USA, 1–368
Bui DT, Pradhan B, Lofman O, Revhaug I (2012) Landslide susceptibility assessment in vietnam using support vector machines, decision tree, and naive bayes models. Mathematical Problems in Engineering 2012:1–26, DOI: https://doi.org/10.1155/2012/974638
Carpinteri A, Chiaia B (1995) Multifractal nature of concrete fracture surfaces and size effects on nominal fracture energy. Materials and Structures 28(8):435–443, DOI: https://doi.org/10.1007/bf02473162
Cavaleri L, Barkhordari MS, Repapis CC, Armaghani DJ, Ulrikh DV, Asteris PG (2022) Convolution-based ensemble learning algorithms to estimate the bond strength of the corroded reinforced concrete. Construction and Building Materials 359:129504, DOI: https://doi.org/10.1016/j.conbuildmat.2022.129504
Chan JCW, Paelinckx D (2008) Evaluation of random forest and Adaboost tree-based ensemble classification and spectral band selection for ecotope mapping using airborne hyperspectral imagery. Remote Sensing of Environment 112(6):2999–3011, DOI: https://doi.org/10.1016/j.rse.2008.02.011
Chang CS, Wang TK, Sluys LJ, van Mier JGM (2002) Fracture modeling using a micro-structural mechanics approach - I. Theory and formulation. Engineering Fracture Mechanics 69(17):1941–1958, DOI: https://doi.org/10.1016/s0013-7944(02)00070-x
Chen B, Liu JY (2004) Effect of aggregate on the fracture behavior of high strength concrete. Construction and Building Materials 18(8): 585–590, DOI: https://doi.org/10.1016/j.conbuildmat.2004.04.013
De Ona R, Eboli L, Mazzulla G (2014) Key factors affecting rail service quality in the northern Italy: A decision tree approach. Transport 29(1):75–83, DOI: https://doi.org/10.3846/16484142.2014.898216
Dietterich TG (2000) Ensemble methods in machine learning 1st International workshop on multiple classifier systems (MCS2000), June 21–23, Cagliari, Italy
Dorigo M, Stützle T (2003) The ant colony optimization metaheuristic: Algorithms, applications, and advances. Handbook of metaheuristics. Springer, Boston, MA, USA 250–285
Duan K, Hu X, Wittmann FH (2007) Size effect on specific fracture energy of concrete. Engineering Fracture Mechanics 74(1–2):87–96, DOI: https://doi.org/10.1016/j.engfracmech.2006.01.031
Einsfeld RA, Velasco MSL (2006) Fracture parameters for high-performance concrete. Cement and Concrete Research 36(3):576–583, DOI: https://doi.org/10.1016/j.cemconres.2005.09.004
Elices M, Guinea GV, Planas J (1997) On the measurement of concrete fracture energy using three-point bend tests. Materials and Structures 30(6):375–376, DOI: https://doi.org/10.1007/bf02480689
Elices M, Rocco CG (2008) Effect of aggregate size on the fracture and mechanical properties of a simple concrete. Engineering Fracture Mechanics 75(13):3839–3851, DOI: https://doi.org/10.1016/j.engfracmech.2008.02.011
Eyo EU, Abbey SJ, Lawrence TT, Tetteh FK (2022) Improved prediction of clay soil expansion using machine learning algorithms and meta-heuristic dichotomous ensemble classifiers. Geoscience Frontiers 13(1):101296, DOI: https://doi.org/10.1016/j.gsf.2021.101296
Fakhri D, Khodayari A, Mahmoodzadeh A, Hosseini M, Ibrahim HH, Mohammed AH (2022) Prediction of Mixed-mode I and II effective fracture toughness of several types of concrete using the extreme gradient boosting method and metaheuristic optimization algorithms. Engineering Fracture Mechanics 276, Part B:108916, DOI: https://doi.org/10.1016/j.engfracmech.2022.108916
Fanelli G, Dantone M, Gall J, Fossati A, Van Gool L (2013) Random forests for real time 3D face analysis. International Journal of Computer Vision 101(3):437–458, DOI: https://doi.org/10.1007/s11263-012-0549-0
Freund Y, Schapire RE (1999) A short introduction to boosting. Journal of Japanese Society for Artificial Intelligence 14(5):771–780, DOI: https://doi.org/10.11517/jjsai.14.5_771 (in Japanese)
Giaccio Q Zerbino R (1998) Failure mechanism of concrete - Combined effects of coarse aggregates and strength level. Advanced Cement Based Materials 7(2):41–48, DOI: https://doi.org/10.1016/s1065-7355(97)00014-x
Han X, Chen Y, Xiao Q, Cui K, Chen Q, Li C, Qiu Z (2021a) Determination of concrete strength and toughness from notched 3 PB specimens of same depth but various span-depth ratios. Engineering Fracture Mechanics 245:107589, DOI: https://doi.org/10.1016/j.engfracmech.2021.107589
Han X, Cui K, Xiao Q, Zhao W, Li C (2022) Determining the fracture properties of pervious concrete specimens with various microstructures and geometries. Theoretical and Applied Fracture Mechanics 117:103151, DOI: https://doi.org/10.1016/j.tafmec.2021.103151
Han X, Xiao Q, Cui K, Hu X, Chen Q, Li C, Qiu Z (2021b) Predicting the fracture behavior of concrete using artificial intelligence approaches and closed-form solution. Theoretical and Applied Fracture Mechanics 112:102892, DOI: https://doi.org/10.1016/j.tafmec.2020.102892
Hu X, Duan K (2004) Influence of fracture process zone height on fracture energy of concrete. Cement and Concrete Research 34(8): 1321–1330, DOI: https://doi.org/10.1016/j.cemconres.2003.12.027
Hu X, Wittmann FH (1992) Fracture energy and fracture process zone. Materials and Structures 25(6):319–326, DOI: https://doi.org/10.1007/bf02472590
Karihaloo BL, Abdalla HM, Imjai T (2003) A simple method for determining the true specific fracture energy of concrete. Magazine of Concrete Research 55(5):471–481, DOI: https://doi.org/10.1680/macr.55.5.471.37590
Kim H, Wagoner MP, Buttlar WG (2008) Simulation of fracture behavior in asphalt concrete using a heterogeneous cohesive zone discrete element model. Journal of Materials in Civil Engineering 20(8):552–563, DOI: https://doi.org/10.1061/(asce)0899-1561(2008)20:8(552)
Kim SK (1996) The constant fracture angle model for cementitious materials. PhD Thesis, New Jersey Institiute of Technology, Newark, NJ, USA
Liao J, Asteris PG, Cavaleri L, Mohammed AS, Lemonis ME, Tsoukalas MZ, Skentou AD, Maraveas C, Koopialipoor M, Armaghani DJ (2021) Novel fuzzy-based optimization approaches for the prediction of ultimate axial load of circular concrete-filled steel tubes. Buildings 11(12):629, DOI: https://doi.org/10.3390/buildings11120629
Lin W, Wu Z, Lin L, Wen A, Li J (2017) An ensemble random forest algorithm for insurance big data analysis. Ieee Access 5:16568–16575, DOI: https://doi.org/10.1109/access.2017.2738069
Lu P, Chen S, Zheng Y (2012) Artificial intelligence in civil engineering. Mathematical Problems in Engineering 2012:1–22, DOI: https://doi.org/10.1155/2012/145974
Mahmoodzadeh A, Mohammadi M, Abdulhamid SN, Ibrahim HH, Ali HFH, Salim SG (2021) Dynamic reduction of time and cost uncertainties in tunneling projects. Tunnelling and Underground Space Technology 109:103774, DOI: https://doi.org/10.1016/j.tust.2020.103774
Mahmoodzadeh A, Mohammadi M, Salim SG, Ali HFH, Ibrahim HH, Abdulhamid SN, Nejati HR, Rashidi S (2022a) Machine learning techniques to predict rock strength parameters. Rock Mechanics and Rock Engineering 55:1721–1741, DOI: https://doi.org/10.1007/s00603-021-02747-x
Mahmoodzadeh A, Nejati HR, Mohammadi M, Ibrahim HH, Khishe M, Rashidi S, Ali HFH (2022c) Prediction of Mode-I rock fracture toughness using support vector regression with metaheuristic optimization algorithms. Engineering Fracture Mechanics 264:108334, DOI: https://doi.org/10.1016/j.engfracmech.2022.108334
Mahmoodzadeh A, Nejati HR, Mohammadi M, Ibrahim HH, Khishe M, Rashidi S, Mohammed AH (2022d) Developing six hybrid machine learning models based on gaussian process regression and metaheuristic optimization algorithms for prediction of duration and cost of road tunnels construction. Tunnelling and Underground Space Technology 130:104759, DOI: https://doi.org/10.1016/j.tust.2022.104759
Mahmoodzadeh A, Nejati HR, Mohammadi M, Mohammed AS, Ibrahim HH, Rashidi S (2022b) Numerical and Machine learning modeling of hard rock failure induced by structural planes around deep tunnels. Engineering Fracture Mechanics 271:108648, DOI: https://doi.org/10.1016/j.engfracmech.2022.108648
Maity Q Roy SK, Verdegay JL (2020) Analyzing multimodal transportation problem and its application to artificial intelligence. Neural Computing & Applications 32(7):2243–2256, DOI: https://doi.org/10.1007/s00521-019-04393-5
Michalski RS, Carbonell JG, Mitchell TM (1983) Machine Learning: An Artificial Intelligence Approach. Springer-Verlag, Heidelberg, Berlin, Germany 1–572
Mohammad SB, Danial JA, Ahmed SM, Ulrikh DV (2022) Data-driven compressive strength prediction of fly ash concrete using ensemble learner algorithms. Buildings 12(2):132, DOI: https://doi.org/10.3390/buildings12020132
Nallathambi P, Karihaloo BL (1986) Determination of specimen-size independent fracture toughness of plain concrete. Magazine of Concrete Research 38(135):67–76, DOI: https://doi.org/10.1680/macr.1986.38.135.67
Oh BH, Jang SY, Byun HK (1999) Prediction of fracture energy of concrete. KCI Concrete Journal 11(3):211–221, https://www.koreascience.or.kr/article/JAKO199911921262412.page
Patil D, Raj R, Shingade P, Kulkarni B, Jayaraman VK (2009) Feature selection and classification employing hybrid ant colony optimization/random forest methodology. Combinatorial Chemistry & High Throughput Screening 12(5):507–513, DOI: https://doi.org/10.2174/138620709788488993
Petersson PE (1980) Fracture energy of concrete: Practical performance and experimental results. Cement and Concrete Research 10(1):91–101, DOI: https://doi.org/10.1016/0008-8846(80)90055-1
Pour AE, Afrazi M, Golshani A (2022) Experimental study of the effect of length and angle of cross-cracks on tensile strength of rock-like material. Iranian Journal of Science and Technology, Transactions of Civil Engineering 46:4543–4556, DOI: https://doi.org/10.1007/s40996-022-00891-0
Raphael JM (1984) Tensile strength of concrete. Journal Proceedings, Journal of the American Concrete Institute 81(2):158–165
Ren J, Zhao H, Zhang L, Zhao Z, Xu Y, Cheng Y, Wang M, Chen J, Wang J (2022) Design optimization of cement grouting material based on adaptive boosting algorithm and simplicial homology global optimization. Journal of Building Engineering 49:104049, DOI: https://doi.org/10.1016/j.jobe.2022.104049
RILEM Draft Recommendation (1985) Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams. Materials and Constructions 18(106):287–290, DOI: https://doi.org/10.1007/bf02472918
Roesler J, Paulino G, Gaedicke C, Bordelon A, Park K (2007a) Fracture behavior of functionally graded concrete materials for rigid pavements. Transportation Research Record (2037):40–49, DOI: https://doi.org/10.3141/2037-04
Roesler J, Paulino GH, Park K, Gaedicke C (2007b) Concrete fracture prediction using bilinear softening. Cement & Concrete Composites 29(4):300–312, DOI: https://doi.org/10.1016/j.cemconcomp.2006.12.002
Rossello C, Elices M, Guinea GV (2006) Fracture of model concrete: 2. Fracture energy and characteristic length. Cement and Concrete Research 36(7):1345–1353, DOI: https://doi.org/10.1016/j.cemconres.2005.04.016
Safavian SR, Landgrebe D (1991) A survey of decision tree classifier methodology. Ieee Transactions on Systems Man and Cybernetics 21(3):660–674, DOI: https://doi.org/10.1109/21.97458
Saouma VE, Broz JJ, Brühwiler E, Boggs HL (1991) Effect of aggregate and specimen size on fracture properties of dam concrete. Journal of Materials in Civil Engineering 3(3):204–218, DOI: https://doi.org/10.1061/(asce)0899-1561(1991)3:3(204)
Shah SP, Swartz SE, Ouyang CS (1995) Fracutre mechanics of concrete: Application of fracture mechanics of concrete, rock and other quasibrittle materials. John Wiley & Sons, Hoboken, NJ, USA 1–588
Shingala NR, Sata AV, Delvadiya PV (2018) A novel analysis of artificial intelligence in mechanical engineering application. Journal of Artificial Intelligence Research & Advances 5(3):35–38, DOI: https://doi.org/10.37591/joaira.v5i3.1857
Siregar APN (2016) The effect of aggregate size distribution on fracture energy of concrete. PhD Thesis, University of Surrey, Guildford, Surrey, UK
Van Mier JGM, Van Vliet MRA (2003) Influence of microstructure of concrete on size/scale effects in tensile fracture. Engineering Fracture Mechanics 70(16):2281–2306, DOI: https://doi.org/10.1016/s0013-7944(02)00222-9
Wittmann FH, Roelfstra PE, Mihashi H, Huang YY, Zhang XH, Nomura N (1987) Influence of age of loading, water-cement ratio and rate of loading on fracture energy of concrete. Materials and Structures 20(2):103–110, DOI: https://doi.org/10.1007/BF02472745
Yang XS (2008) Firefly algorithm. Nature-inspired metaheuristic algorithms. Luniver Press, Frome, BA11 6TT, UK 79–90
Yang XS (2010a) Firefly algorithm, stochastic test functions and design optimisation. International Journal of Bio-Inspired Computation 2(2):78–84, DOI: https://doi.org/10.1504/ijbic.2010.032124
Yang XS (2010b) Nature-inspired metaheuristic algorithms. Luniver press, Frome, BA11 6TT, UK, 1–124
Zhang P (1993) Model selection via multifold cross-validation. The Annals of Statistics 21(1):299–313, DOI: https://doi.org/10.1214/aos/1176349027
Zhang G, Hu MY, Patuwo BE, Indro DC (1999) Artificial neural networks in bankruptcy prediction: General framework and cross-validation analysis. European Journal of Operational Research 116(1):16–32, DOI: https://doi.org/10.1016/S0377-2217(98)00051-4
Zhang J, Zulkernine M, Haque A (2008) Random-forests-based network intrusion detection systems. Ieee Transactions on Systems Man and Cybernetics Part C-Applications and Reviews 38(5):649–659, DOI: https://doi.org/10.1109/tsmcc.2008.923876
Zhao Y, Li Z, Xu S (2005) Brittle behaviour of high strength concrete. 11th international Conference on Fracture, March 20–26, Turin, Italy
Zhao Y, Liu Y, Xu B (2021) Effect of coarse aggregate size distribution on fracture toughness of concrete based on boundary effect model. Theoretical and Applied Fracture Mechanics 113:102970, DOI: https://doi.org/10.1016/j.tafhiec.2021.102970
Zhou FP, Barr BIG, Lydon FD (1995) Fracture properties of high-strength concrete with varying silica fume content and aggregates. Cement and Concrete Research 25(3):543–552, DOI: https://doi.org/10.1016/0008-8846(95)00043-c
Zhou Z, Wang C, Han X (2022) Safety evaluation of cracked concrete structures with crack length index. Theoretical and Applied Fracture Mechanics 122:103662, DOI: https://doi.org/10.1016/j.tafmec.2022.103662
Zhu Y, Zhang Z, Yang Y, Yao Y (2014) Measurement and correlation of ductility and compressive strength for engineered cementitious composites (ECC) produced by binary and ternary systems of binder materials: Fly ash, slag, silica fume and cement. Construction and Building Materials 68:192–198, DOI: https://doi.org/10.1016/j.conbuildmat.2014.06.080
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Zhang, Q., Zhou, X. Predicting the Fracture Characteristics of Concrete Using Ensemble and Meta-heuristic Algorithms. KSCE J Civ Eng 27, 2940–2951 (2023). https://doi.org/10.1007/s12205-023-0965-4
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DOI: https://doi.org/10.1007/s12205-023-0965-4