Earthquake Engineering and Engineering Vibration

, Volume 11, Issue 3, pp 293–301 | Cite as

Towards multiple hazard resilient bridges: a methodology for modeling frequent and infrequent time-varying loads Part I, Comprehensive reliability and partial failure probabilities

  • Zach Liang
  • George C. Lee


The current AASHTO load and resistance factor design (LRFD) guidelines are formulated based on bridge reliability, which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability. This is a major advancement in bridge design specifications. However, LRFD is only calibrated for dead and live loads. In cases when extreme loads are significant, they need to be individually assessed. Combining regular loads with extreme loads has been a major challenge, mainly because the extreme loads are time variables and cannot be directly combined with time invariant loads to formulate the probability of structural failure. To overcome these difficulties, this paper suggests a methodology of comprehensive reliability, by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated as time invariant. Based on these conditions, the extreme loads (also referred to as multiple hazard or MH loads) can be broken down into single effects. In Part II of this paper, a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example. There are three major steps in establishing load factors from MH load distributions: (1) formulate the failure probabilities; (2) normalize various load distributions; and (3) establish design limit state equations. This paper describes the formulation of the failure probabilities of single and combined loads.


multiple hazards bridge probability-based design comprehensive reliability partial failure probability 


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Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity at BuffaloBuffaloUSA
  2. 2.Department of Civil, Structural and Environmental EngineeringUniversity at BuffaloBuffaloUSA

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