Relationship between the extreme value distribution of bending moments and traffic characteristics for simply supported bridges based on WIM data

Abstract

Extreme traffic loads significantly challenge the safety and cost-effectiveness of highway bridges, especially under site-specific traffic conditions. Conventional assessments often rely on overly conservative load models, leading to excessive structural design. In this study, a framework for the prediction of maximum bending moments in simply supported bridges is developed by integrating weigh-in-motion (WIM) data, traffic microsimulation, and generalized extreme value (GEV) regression modeling to establish relationships between the GEV parameters (μ, σ, ξ) and traffic factors—heavy vehicle proportion, bridge span length, vehicle speed, headway, and traffic volume. Using one-year WIM data from 7.4 million vehicles, the developed models for μ and σ exhibit high predictive accuracy (R²>0.95) and are validated through leave-one-out cross-validation. The prediction of ξ is less accurate (R² ≈ 0.6), requiring further improvement. Applying these models to a 1 000-year return level yields a reliable, data-driven extrapolation, supporting optimized bridge design and safety assessment under varying traffic conditions.

Keywords

site-specific factors / extreme value / traffic load / weigh-in-motion (WIM) / generalized extreme value (GEV) parameters / Monte Carlo simulation

References

[1] ZHOU J Y, CAPRANI C C, ZHANG L W. On the structural safety of long-span bridges under traffic loadings caused by maintenance works[J]. Engineering Structures, 2021, 240: 112407.

[2] KAWAKATSU T, AIHARA K, TAKASU A, et al. Data-driven bridge weigh-in-motion[J]. IEEE Sensors Journal, 2023, 23(15): 17064-17077.

[3] OBRIEN E, HAJIALIZADEH D, ENRIGHT B, et al. Factors affecting the accuracy of characteristic maximum load effects[M]//Bridge Traffic Loading. London: CRC Press, 2021: 143-184.

[4] ZHOU J Y, WU W R, CAPRANI C C, et al. A hybrid virtual-real traffic simulation approach to reproducing the spatiotemporal distribution of bridge loads[J]. Computer-Aided Civil and Infrastructure Engineering, 2024, 39(11): 1699-1723.

[5] LYDON M, TAYLOR S E, ROBINSON D, et al. Recent developments in bridge weigh in motion (B-WIM)[J]. Journal of Civil Structural Health Monitoring, 2016, 6(1): 69-81.

[6] GAO X, DUAN G X, LAN C G, et al. Bayesian updates for an extreme value distribution model of bridge traffic load effect based on SHM data[J]. Sustainability, 2021, 13(15): 8631.

[7] LU N W, WANG H H, WANG K, et al. Maximum probabilistic and dynamic traffic load effects on short-to-medium span bridges[J]. Computer Modeling in Engineering & Sciences, 2021, 127(1): 345-360.

[8] WANG X J, RUAN X, CASAS J R, et al. Probabilistic model of traffic scenarios for extreme load effects in long-span bridges[J]. Structural Safety, 2024, 106: 102382.

[9] LI M, HUANG T L, LIAO J J, et al. WIM-based vehicle load models for urban highway bridge[J]. Latin American Journal of Solids and Structures, 2020, 17(5): e290.

[10] RIZQIANSYAH A, CAPRANI C C. Hierarchical Bayesian modeling of highway bridge network extreme traffic loading[J]. Structural Safety, 2024, 111: 102503.

[11] HUI Y X, WANG W W, LIU X N. Comfort evaluation of prefabricated and assembled pedestrian cable-stayed bridges[J]. Journal of Southeast University (English Edition), 2023, 39(1): 26-32.

[12] YUAN Z J, WANG H, MAO J X, et al. Influence study of main cable displacement-controlled device type of long-span suspension bridges on structural mechanical properties[J]. Journal of Southeast University (English Edition), 2025, 41(1): 27-36.

[13] XING C X, SHU Y W, ZHU X J, et al. Multistage seismic damage constitutive model and parameter calibration of reinforced concrete columns[J]. Journal of Southeast University (English Edition), 2024, 40(4): 386-395.

[14] LING T Y, DENG L, HE W, et al. Determination of dynamic amplification factors for small- and medium-span highway bridges considering the effect of automated truck platooning loads[J]. Mechanical Systems and Signal Processing, 2023, 204: 110812.

[15] PRADEEP A. Dynamic amplification effect on bridges under traffic loads: Parametric study and novel design integration approach[D]. Montreal, Québec, Canada: Concordia University. 2025.

[16] KALIN J, ŽNIDARIČ A, ANŽLIN A, et al. Measurements of bridge dynamic amplification factor using bridge weigh-in-motion data[J]. Structure and Infrastructure Engineering, 2022, 18(8): 1164-1176.

[17] XIE W, BAO Y Y, TIE N, et al. Sensitivity analysis of parameters influencing ED and self-centering capacity in self-centering bridge bents with ED beams using validated numerical model[J]. Journal of Southeast University (English Edition), 2025, 41(3): 338-347.

[18] DAI B R, WU D J, LI Q. Investigation of multiple-presence factor for traffic loads on road-rail bridges based on a novel extreme value analysis approach[J]. Structural Safety, 2022, 96: 102199.

[19] DAI B R, XIA Y, LI Q. An extreme value prediction method based on clustering algorithm[J]. Reliability Engineering & System Safety, 2022, 222: 108442.

[20] XIA H W, NI Y Q, WONG K Y, et al. Reliability-based condition assessment of in-service bridges using mixture distribution models[J]. Computers & Structures, 2012, 106: 204-213.

[21] HASSAN R, HEKMATI ATHAR S P, TAHERI M, et al. Regression model for structural health monitoring of a lab scaled bridge[C/OL]// Proc SPIE 11594, NDE 4.0 and Smart Structures for Industry, Smart Cities, Communication, and Energy. 2021. https://doi.org/10.1117/12.2592037.

[22] SVECHNIKOV E, SNIJDER H H, MALJAARS J, et al. Probabilistic design life selection procedure for a steel bridge[J]. ce/papers, 2023, 6(3/4): 477-482.

[23] LIU Y Y, ZHOU J Y, SU J X, et al. Residual capacity assessment of in-service concrete box-girder bridges considering traffic growth and structural deterioration[J]. Structural Engineering and Mechanics, 2023, 85(4): 531-543.

[24] SAHA P, ROY R. A descriptive study of vehicle class-wise headways using mixed traffic data[J]. Journal of the Institution of Engineers (India): Series A, 2022, 103(4): 1287-1298.

[25] KHAKIFIROOZ M, FATHI M, DU L L. Reliability assessment of vehicle-to-vehicle communication networks through headway distribution and information propagation delay[J]. Transportation Research Interdisciplinary Perspectives, 2024, 24: 101053.

Funding

National Natural Science Foundation of China(52278149)

Natural Science Foundation of Jiangsu Province(BZ2024015)

Opening Project of State Key Laboratory for Track Technology of High-Speed Railway(2023YJ375)

Opening Project of Zhejiang Engineering Centre of Road and Bridge Intelligent Operation and Maintenance Technology(202402G)