Abstract
An equivalent relationship between stationary dynamic load and moving vehicular load is of necessity and importance for the fact that pavement responses from nondestructive testing devices with high speeds are usually validated with responses from falling weight deflectometer (FWD), which applies stationary dynamic loads to pavements. Also, two-dimensional (2D) axisymmetric finite element (FE) models with statinary dynamic loads are still popular to represent pavements in service conditions for their less storage space and computational time compared with three-dimensional (3D) FE models. This study aims to provide a methodology using the FE model updating implemented with artificial intelligence algorithms to obtain equivalent stationary dynamic loads applied in 2D axisymmetric FE pavement models for moving vehicular loads applied in 3D FE pavement models. The 2D axisymmetric FE models can eventually provide similar results as 3D FE models but with higher efficiency. Besides, obtained equivalent relationship is independent of structural and material properties such as layer thickness and moduli. This finding significantly extends the application of this equivalent relationship. Furthermore, techniques applied in this study can be used as references for problems in pavement materials and structures such as the model updating, model equivalency, and model optimization.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig7_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig8_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig9_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig10_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig11_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig12_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig13_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00366-021-01306-w/MediaObjects/366_2021_1306_Fig14_HTML.png)
Similar content being viewed by others
References
Elbagalati O, Elseifi M, Gaspard K, Zhang Z (2018) Development of the pavement structural health index based on falling weight deflectometer testing. Int J Pavement Eng 19(1):1–8
Lytton RL (1989) Backcalculation of pavement layer properties. In Nondestructive testing of pavements and backcalculation of moduli, ASTM International
Deng Y, Luo X, Zhang Y, Lytton RL (2020) Determination of complex modulus gradients of flexible pavements using falling weight deflectometer and artificial intelligence. Mater Struct 53(4):1–17
Terzi S, Saltan M, Küçüksille EU, Karaşahin M (2013) Backcalculation of pavement layer thickness using data mining. Neural Comput Appl 23(5):1369–1379
Sangghaleh A, Pan E, Green R, Wang R, Liu X, Cai Y (2014) Backcalculation of pavement layer elastic modulus and thickness with measurement errors. Int J Pavement Eng 15(6):521–531
Saltan M, Terzi S, Küçüksille EU (2011) Backcalculation of pavement layer moduli and Poisson’s ratio using data mining. Expert Syst Appl 38(3):2600–2608
Li M, Wang H (2019) Development of ANN-GA program for backcalculation of pavement moduli under FWD testing with viscoelastic and nonlinear parameters. Int J Pavement Eng 20(4):490–498
Wang H, Al-Qadi IL (2009) Combined effect of moving wheel loading and three-dimensional contact stresses on perpetual pavement responses. Transp Res Rec 2095(1):53–61
Deng Y, Luo X, Gu F, Zhang Y, Lytton RL (2019) 3D simulation of deflection basin of pavements under high-speed moving loads. Constr Build Mater 226:868–878
Steele DA, Vavrik WR (2004) Rolling wheel deflectometer (RWD) demonstration and comparison to other devices in Texas. ARA Project, 15874
Carlson P, Storey B, Poorsartep M, Stevens C, Ettelman B, Lindheimer TE, Dastgiri M, Khodakarami A, Miles J, Song D, Lytton RL (2017) Advancing innovative high-speed remote-sensing highway infrastructure assessment using emerging technologies: technical report (No. FHWA/TX-16/0–6869–1). Texas A&M Transportation Institute.
Elseifi MA, Gaspard K, Wilke PW, Zhang Z, Hegab A (2015) Evaluation and validation of a model for predicting pavement structural number with rolling wheel deflectometer data. Transp Res Rec 2525(1):13–19
Elbagalati O, Elseifi MA, Gaspard K, Zhang Z (2017) Implementation of the structural condition index into the Louisiana pavement management system based on rolling wheel deflectometer testing. Transp Res Rec 2641(1):39–47
Maser K, Schmalzer P, Shaw W, Carmichael A (2017) Integration of traffic speed deflectometer and ground-penetrating radar for network-level roadway structure evaluation. Transp Res Rec 2639(1):55–63
Flintsch GW, Ferne B, Diefenderfer B, Katicha S, Bryce J, Nell S (2012) Evaluation of traffic-speed deflectometers. Transp Res Rec 2304(1):37–46
Muller WB, Roberts J (2013) Revised approach to assessing traffic speed deflectometer data and field validation of deflection bowl predictions. Int J Pavement Eng 14(4):388–402
Zofka A, Sudyka J, Maliszewski M, Harasim P, Sybilski D (2014) Alternative approach for interpreting traffic speed deflectometer results. Transp Res Rec 2457(1):12–18
Nasimifar M, Thyagarajan S, Siddharthan RV, Sivaneswaran N (2016) Robust deflection indices from traffic-speed deflectometer measurements to predict critical pavement responses for network-level pavement management system application. J Transp Eng 142(3):04016004
Elseifi MA, Abdel-Khalek AM, Gaspard K, Zhang Z, Ismail S (2011) Evaluation of continuous deflection testing using the rolling wheel deflectometer in Louisiana. J Transp Eng 138(4):414–422
Madsen SS, Pedersen NL (2019) Backcalculation of Raptor (RWD) Measurements and Forward Prediction of FWD Deflections Compared with FWD Measurements. In International airfield and highway pavements conference 2019 (pp 382–391). American Society of Civil Engineers.
Gedafa D, Hossain M, Miller R, Steele D (2012) Surface deflections of perpetual pavement sections. Current trends, advances, and challenges, In Pavement Performance (ASTM International)
Katicha SW, Flintsch GW, Ferne B, Bryce J (2014) Limits of agreement method for comparing TSD and FWD measurements. Int J Pavement Eng 15(6):532–541
Levenberg E, Pettinari M, Baltzer S, Christensen BML (2018) Comparing traffic speed deflectometer and falling weight deflectometer data. Transp Res Rec 2672(40):22–31
Loulizi A, Al-Qadi IL, Lahouar S, Freeman TE (2002) Measurement of vertical compressive stress pulse in flexible pavements: representation for dynamic loading tests. Transp Res Rec 1816(1):125–136
Qin J (2010) Predicting flexible pavement structural response using falling weight deflectometer deflections. Master thesis, Ohio University, Athens, OH
Leiva-Villacorta F, Timm D (2013) Falling weight deflectometer loading pulse duration and its effect on predicted pavement responses. In: Transportation Research Board 92nd Annual Meeting, Washington DC, United States.
Wang H, Al-Qadi IL (2012) Importance of nonlinear anisotropic modeling of granular base for predicting maximum viscoelastic pavement responses under moving vehicular loading. J Eng Mech 139(1):29–38
Kim M (2007) Three-dimensional finite-element analysis of flexible pavements considering nonlinear pavement foundation behavior. PhD dissertation. University of Illinois, Urbana-Champaign, Urbana, IL
Li M, Wang H, Xu G, Xie P (2017) Finite-element modeling and parametric analysis of viscoelastic and nonlinear pavement responses under dynamic FWD loading. Constr Build Mater 141:23–35
Wang H, Li M (2016) Comparative study of asphalt pavement responses under FWD and moving vehicular loading. J Transp Eng 142(12):04016069
Al-Qadi IL, Xie W, Elseifi MA (2008) Frequency determination from vehicular loading time pulse to predict appropriate complex modulus in MEPDG. Asphalt Paving Technol Proc 77:739
Ulloa A, Hajj EY, Siddharthan RV, Sebaaly PE (2012) Equivalent loading frequencies for dynamic analysis of asphalt pavements. J Mater Civ Eng 25(9):1162–1170
Manual AUS (2012) Abaqus Version 6.12 Documentation. Dassault systemes SIMULIA corporation, Providence, RI, USA
Herr WJ, Hall JW, White TD, Johnson W (1995) Continuous deflection basin measurement and backcalculation under a rolling wheel load using scanning laser technology. In: Proceedings of ASCE 1995 Transportation Congress, Vol. 1 and 2, San Diego, pp 600–611
Friswell M, Mottershead JE (2013) Finite-element model updating in structural dynamics (vol 38). Springer, Berlin
Qin S, Zhang Y, Zhou YL, Kang J (2018) Dynamic model updating for bridge structures using the kriging model and PSO algorithm ensemble with higher vibration modes. Sensors 18(6):1879
Eberhart R, Kennedy J (1995) Particle swarm optimization. Proc IEEE Int Conf Neural Netw 4:1942–1948
Shabbir F, Omenzetter P (2015) Particle swarm optimization with sequential niche technique for dynamic finite-element model updating. Comput Aided Civ Infrastruct Eng 30(5):359–375
Lu P, Chen S, Zheng Y (2012) Artificial intelligence in civil engineering. In: Mathematical Problems in Engineering, vol 2012
Gandomi AH, Yang XS, Talatahari S, Alavi AH (2013) Metaheuristic applications in structures and infrastructures. Newnes, London
Bergh FVD (2001) An analysis of particle swarm optimizers. Doctoral dissertation, University of Pretoria, Pretoria, South Africa
Sun J, Feng B, Xu W (2004) Particle swarm optimization with particles having quantum behavior. In: Proceedings of the 2004 congress on evolutionary computation (IEEE Cat. No. 04TH8753) (Vol 1, pp 325–331) IEEE
Sun J, Xu W, Feng B (2004) A global search strategy of quantum-behaved particle swarm optimization. In: IEEE conference on cybernetics and intelligent systems, Vol 1, pp 111–116, IEEE
Yang ZL, Wu A, Min HQ (2015) An improved quantum-behaved particle swarm optimization algorithm with elitist breeding for unconstrained optimization. Comput Intell Neurosci 41
Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT Press, Cambridge
Serrano NMB, Nieto PJG, Sánchez AS, Lasheras FS, Fernández PR (2018) A Hybrid Algorithm for the Assessment of the Influence of Risk Factors in the Development of Upper Limb Musculoskeletal Disorders. International Conference on Hybrid Artificial Intelligence Systems. Springer, Cham, pp 634–646
Hao H, Xia Y (2002) Vibration-based damage detection of structures by genetic algorithm. J Comput Civ Eng 16(3):222–229
Caicedo JM, Yun G (2011) A novel evolutionary algorithm for identifying multiple alternative solutions in model updating. Struct Health Monit 10(5):491–501
Syswerda G (1991) A study of reproduction in generational and steady-state genetic algorithms. In: Foundations of genetic algorithms, Vol 1, pp 94–101. Elsevier
Brill ED, Flach JM, Hopkins LD, Ranjithan SMGA (1990) MGA: a decision support system for complex, incompletely defined problems. IEEE Trans Syst Man Cybern 20(4):745–757
Baugh JW Jr, Caldwell SC, Brill ED Jr (1997) A mathematical programming approach for generating alternatives in discrete structural optimization. Eng Optim 28(1–2):1–31
Loughlin DH, Ranjithan SR, Brill ED Jr, Baugh JW Jr (2001) Genetic algorithm approaches for addressing unmodeled objectives in optimization problems. Eng Optim 33(5):549–569
Omkar SN, Khandelwal R, Ananth TVS, Naik GN, Gopalakrishnan S (2009) Quantum behaved Particle Swarm Optimization (QPSO) for multi-objective design optimization of composite structures. Expert Syst Appl 36(8):11312–11322
Gu F, Luo X, Luo R, Lytton RL, Hajj EY, Siddharthan RV (2016) Numerical modeling of geogrid-reinforced flexible pavement and corresponding validation using large-scale tank test. Constr Build Mater 122:214–230
Zhang Y, Gu F, Luo X, Birgisson B, Lytton RL (2018) Modeling Stress-dependent anisotropic elastoplastic unbound granular base in flexible pavements. Transp Res Rec 2672(52):46–56
Zhang Y, Birgisson B, Lytton RL (2015) Weak form equation–based finite-element modeling of viscoelastic asphalt mixtures. J Mater Civ Eng 28(2):04015115
De Beer M, Fisher C, Jooste FJ (2002) Evaluation of non-uniform tyre contact stresses on thin asphalt pavements. Ninth international conference on asphalt pavements 5:19–22
Wang H, Al-Qadi IL, Stanciulescu I (2012) Simulation of tyre–pavement interaction for predicting contact stresses at static and various rolling conditions. Int J Pavement Eng 13(4):310–321
Ling M, Luo X, Hu S, Gu F, Lytton RL (2017) Numerical modeling and artificial neural network for predicting J-integral of top-down cracking in asphalt pavement. Transp Res Rec 2631(1):83–95
Funding
The authors received no specific funding for this work.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Deng, Y., Zhang, Y., Luo, X. et al. Development of equivalent stationary dynamic loads for moving vehicular loads using artificial intelligence-based finite element model updating. Engineering with Computers 38, 2955–2974 (2022). https://doi.org/10.1007/s00366-021-01306-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-021-01306-w