Vol. 1 No. 1 (2026)
Statistical Calibration of Partial Safety Factors for Bridge Design Codes Using FORM
Abstract
Partial safety factors — the load and resistance factors embedded in limit state design codes — are the primary mechanism through which structural design codes translate probabilistic reliability targets into deterministic design practice. Their calibration against explicit reliability targets using the First-Order Reliability Method (FORM) is a mathematically rigorous process that remains poorly documented and rarely applied in the context of bridge design codes in developing regions. This paper presents a comprehensive statistical calibration framework for partial safety factors applicable to bridge design codes, grounded in the Hasofer-Lind-Rackwitz-Fiessler (HL-RF) FORM algorithm. The framework is applied to six bridge structure types — reinforced concrete slab, pre-stressed concrete box girder, steel composite, reinforced concrete arch, steel truss, and cable-stayed — with material statistical parameters characterised from African and international laboratory databases. For each bridge type, the resistance model uncertainty, dead load bias, and live load statistics are quantified and used to compute the target reliability index beta under the ultimate limit state (ULS). Calibrated partial factors gamma_G (dead load) and gamma_Q (live load) are derived that achieve a target reliability index of beta = 4.3 for a 50-year reference period, consistent with the EN 1990 Annex B recommendation for consequence class CC2 bridges. Results reveal that the EN 1990 default factors overestimate required safety for steel composite and truss bridges — suggesting material efficiency gains of 5 to 9% — and underestimate required safety for reinforced concrete arch bridges in tropical climates, which require gamma_G = 1.38 and gamma_Q = 1.60 to achieve the target beta. The sensitivity
Read the Full Article
The HTML galley is loaded below for inline reading and better discovery.
How to Cite
Keywords
Research Snapshot
Desktop reading viewReferences
- AASHTO. (2020). AASHTO LRFD Bridge Design Specifications (9th ed.). American Association of State Highway and Transportation Officials, Washington, D.C.
- ACI Committee 214. (2011). Guide to Evaluation of Strength Test Results of Concrete (ACI 214R-11). American Concrete Institute.
- Ang, A. H.-S., & Tang, W. H. (2007). Probability Concepts in Engineering: Emphasis on Applications in Civil and Environmental Engineering (2nd ed.). Wiley.
- Bjerager, P. (1988). Probability integration by directional simulation. Journal of Engineering Mechanics, 114(8), 1285–1302.
- Breitung, K. (1984). Asymptotic approximations for multinormal integrals. Journal of Engineering Mechanics, 110(3), 357–366.
- CEN. (2002). EN 1990: Eurocode — Basis of Structural Design. European Committee for Standardization, Brussels.
- CEN. (2004). EN 1992-1-1: Eurocode 2 — Design of Concrete Structures — Part 1-1. European Committee for Standardization.
- Ditlevsen, O., & Madsen, H. O. (1996). Structural Reliability Methods. Wiley, Chichester.
- Ellingwood, B. R., Galambos, T. V., MacGregor, J. G., & Cornell, C. A. (1980). Development of a probability-based load criterion for American National Standard A58. NBS Special Publication 577, National Bureau of Standards.
- Frangopol, D. M., & Liu, M. (2007). Maintenance and management of civil infrastructure based on condition, safety, optimisation, and life-cycle cost. Structure and Infrastructure Engineering, 3(1), 29–41.
- Gulvanessian, H., & Holicky, M. (2005). Eurocodes: using reliability analysis to combine action effects. Proceedings of the Institution of Civil Engineers — Structures and Buildings, 158(4), 243–252.
- Hasofer, A. M., & Lind, N. C. (1974). Exact and invariant second-moment code format. Journal of the Engineering Mechanics Division, ASCE, 100(1), 111–121.
- JCSS. (2001). Probabilistic Model Code. Joint Committee on Structural Safety. https://www.jcss-lc.org.
- Madsen, H. O., Krenk, S., & Lind, N. C. (1986). Methods of Structural Safety. Prentice-Hall, Englewood Cliffs.
- Melchers, R. E. (1999). Structural Reliability: Analysis and Prediction (2nd ed.). Wiley, Chichester.
- Mureithi, E. W., Mwangi, S. M., & Gariy, Z. C. A. (2019). Axle load spectrum for pavement design: weigh-in-motion data from the Northern Corridor, Kenya. Journal of the South African Institution of Civil Engineering, 61(4), 30–40.
- Nowak, A. S. (1999). Calibration of LRFD Bridge Design Code. NCHRP Report 368. Transportation Research Board.
- Nowak, A. S., & Collins, K. R. (2000). Reliability of Structures. McGraw-Hill, Boston.
- Rackwitz, R., & Fiessler, B. (1978). Structural reliability under combined random load sequences. Computers and Structures, 9(5), 489–494.
- Sorensen, J. D. (2004). Notes in Structural Reliability Theory and Risk Analysis. Aalborg University.
- Thoft-Christensen, P., & Baker, M. J. (1982). Structural Reliability Theory and Its Applications. Springer, Berlin.
- Vrouwenvelder, A. C. W. M. (1997). The JCSS probabilistic model code. Structural Safety, 19(3), 245–251.
- Zhang, H., Chandrangsu, T., & Rasmussen, K. J. R. (2010). Probabilistic study of the strength of steel scaffold systems. Structural Safety, 32(6), 393–408.
- Zhao, Z., & Haldar, A. (1996). Bridge fatigue damage evaluation and updating using non-destructive inspections. Engineering Fracture Mechanics, 53(5), 775–788.
- Zhu, M., McKenna, F., & Scott, M. H. (2018). OpenSeesPy: Python library for the OpenSees finite element framework. SoftwareX, 7, 6–11.
- Copyright © 2024 Aduot Madit Anhiem. Open access under CC BY 4.0 International License.
- | DOI: https://doi.org/10.XXXXX/ajmses.XXXX.XXXX