An analytical probability distribution model for extreme bridge traffic load effects based on WIM data and extreme value theory

Abstract

Accurate prediction of extreme bridge traffic load effects is essential for ensuring structural safety under increasing heavy-vehicle traffic. This study develops an analytical probability distribution model that directly links traffic condition parameters, bridge configuration parameters, and vehicle weight statistics to the parameters of the Type III Extreme Value Distribution (EVD). Using WIM data and MCS, short-term measurements were extended to long-term traffic, and bridge load effects were obtained through influence-line analysis. By correlating the EVD parameters with site-specific characteristics, semi-empirical analytical equations were derived that generalize Bailey’s model from European bridges to bridges in China. Results show that upper bound parameters remain consistent with theoretical limits, while the shape and position parameters require regional calibration due to heavier truck distributions. Validation using measured and simulated data confirms the model’s accuracy and applicability. The proposed analytical model provides a novel, efficient framework for region-specific prediction of extreme traffic load effects and supports reliability-based bridge design and assessment.

Keywords

Bridge safety assessment / Weigh-in-motion (WIM) data / Traffic loads / Monte Carlo simulation / Extreme value distribution / Site-specific models

References

[1] Ang, A. H. S., & Tang, W. H. (1990). Probability Concepts in Engineering Planning and Design: Vol. II-Decision, Risk and Reliability. The Statistician, 2(3), 574.

[2] Bailey, S. F., & Hirt, M. A. (1996). Site specific models of traffic action effects for bridge evaluation. Recent Advances in Bridge Engineering: Evaluation, Management and Repair.

[3] Bailey, S. F. (1996). Basic principles and load models for the structural safety evaluation of existing road bridges.

[4] Bishai D, Quresh A, James P, Ghaffar A. National road casualties and economic development. Health Econ, 2006.

[5] Caprani, C. C. (2005). ARROW@TU Dublin ARROW@TU Dublin Other resources School of Civil and Structural Engineering Probalistic analysis of highway bridge traffic loading Probalistic analysis of highway bridge traffic loading. https://arrow.tudublin.ie/engschcivoth

[6] Cheng Z, Zhang N, Gao C, Du X, Zhou S. Amplification factor analysis of a simply supported beam under moving loads. Adv Mech Eng, 2022.

[7] China. (2013). Chinese suggestions on Sub-categories of commercial vehicles. 06(February), 5–7.

[8] Enright B, O’Brien EJ. Monte Carlo simulation of extreme traffic loading on short and medium span bridges. Struct Infrastruct Eng, 2013, 9(12): 1267-1282.

[9] Fu, Z., Ji, B., Cheng, M., & Maeno, H. (2013). Statistical Analysis of Cause of Bridge Collapse in China.

[10] M He P Liang xian J Liu F Yang X Zhao 2024 A new model to simulate the site-specific traffic load with consideration of precise axle load and microscopic behavior Struct Infrastruct Eng 20 6 928 943https://doi.org/10.1080/15732479.2022.2131848

[11] Huang, H., Zhou, J., Zhang, J., Xu, W., Chen, Z., & Li, N. (2019). Effects of Revised Toll-by-Weight Policy on Truck Overloading Behavior and Bridge Infrastructure Damage Using Weigh-in-Motion Data: A Comparative Study in China. Advances in Civil Engineering, 2019. https://doi.org/10.1155/2019/5910463

[12] Kalin J, Žnidarič A, Anžlin A, Kreslin M. Measurements of bridge dynamic amplification factor using bridge weigh-in-motion data. Struct Infrastruct Eng, 2022, 18(8): 1164-1176.

[13] Kim J, Song J. A comprehensive probabilistic model of traffic loads based on weigh-in-motion data for applications to bridge structures. KSCE J Civ Eng, 2019, 23(8): 3628-3643.

[14] Li M, Huang TL, Liao JJ, Zhong J, Zhong JW. WIM-based vehicle load models for urban highway bridge. Lat Am J Solids Struct, 2020, 17(5): 1-20.

[15] Lydon M, Taylor SE, Robinson D, Mufti A, Brien EJO. Recent developments in bridge weigh in motion (B-WIM). J Civ Struct Health Monit, 2016, 6(1): 69-81.

[16] Morales-Nápoles O, Steenbergen RDJM. Analysis of axle and vehicle load properties through Bayesian networks based on weigh-in-motion data. Reliab Eng Syst Saf, 2014, 125: 153-164.

[17] O’Connor A, Enevoldsen I. Probability-based assessment of highway bridges according to the new Danish guideline. Struct Infrastruct Eng, 2009, 5(2): 157-168.

[18] Rizqiansyah A, Caprani CC. Hierarchical Bayesian modeling of highway bridge network extreme traffic loading. Struct Saf, 2024.

[19] Shi Y, Li Y, Cai Q, Zhang H, Wu D. How does heterogeneity affect freeway safety? A simulation-based exploration considering sustainable intelligent connected vehicles. Sustainability, 2020.

[20] Wang X, Ruan X, Casas JR, Zhang M. Probabilistic model of traffic scenarios for extreme load effects in long-span bridges. Struct Saf, 2024.

[21] Xie, H.-B., Wang, Y.-F., Wu, H.-L., & Li, Z. (2014). Condition Assessment of Existing RC Highway Bridges in China Based on SIE2011. Journal of Bridge Engineering, 19(12). https://doi.org/10.1061/(asce)be.1943-5592.0000633

[22] Zhou J, Li T, Ye X, Shi X. Safety assessment of widened bridges considering uneven multilane traffic-load modeling: case study in China. J Bridge Eng, 2020.

[23] Zhou J, Zheng Y, Tan Z, Wei B, Zhou X, Ruan X. Feasibility study of bridge load testing using ongoing traffic through rapid estimation of traffic load effects for network-level highway bridges assisted by site-specific ETC data. J Civ Struct Health Monit, 2025.

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