China
Africa
Explore chapters and articles related to this topic
Probabilistic risk analysis in geomechanics and water engineering
Published in R. N. Chowdhury, Geomechanics and Water Engineering in Environmental Management, 2017
It is obvious from the above that, if either the probability distribution or the first two statistical moments of the performance function (the safety factor) are known, the probability of failure can be calculated. Accurate determination of the probability distribution of FS, based on direct integration, from the probability distributions of the contributing random variables is usually impractical. Several methods have been proposed to deal with the determination of the first two statistical moments instead. Among these are the First-Order Second-Moment method (FOSM), the Mean-value First-Order Second-Moment method (MFOSM) and the Second Order Method (SOM). For a discussion of these methods the reader may refer to Ang and Tang (1984), Madsen et al. (1986) and Yen (1989). Most of these methods are based on approximation of a Taylor series expansion of the performance function. In the first order methods the series is truncated by ignoring all the higher order terms. In the second order method second order terms are retained in addition to the first order terms and, therefore, the method gets very involved. The first order methods have ben used widely but suffer from the disadvantage that partial derivatives of the function have to be evaluated and, in some cases, this has not be possible so far. However, recently, Chowdhury and Xu (1990) have successfully used the rational polynomial technique (Zhou, 1982) to calculate the partial derivatives arising in a FOSM slope reliability analysis on the basis of rigorous limit equilibrium methods.
Fatigue of steel bridge infrastructure
Published in Hyun-Moo Koh, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Health Monitoring and Informatics, 2008
Hyun-Moo Koh, Dan M. Frangopol
The importance of the Life Cycle Cost (LCC) analysis for construction projects of bridge has been recognized over the last decades. Accordingly, theoretical models, guidelines, and supporting software have been developed for the LCC analysis of bridges. However, it is difficult to predict LCC precisely since the costs occurring throughout the service life of the bridge depend on various parameters such as design, construction, maintenance, and environmental conditions. This paper presents a methodology for the optimal design of bridge structure. Total LCC for the service life is calculated as the sum of initial cost, damage cost, maintenance cost, repair and rehabilitation cost, and user cost. The optimization method is applied to design a bridge structure with minimal cost, in which the objective function is set to LCC and constraints are formulated on the basis of Korean Bridge Design Code. Initial cost is calculated based on standard costs of the Korea Construction Price Index and damage cost on damage probabilities to consider the uncertainty of load and resistance. An advanced first-order second moment method is used as a practical tool for reliability analysis using damage probability. Maintenance cost and cycle are determined by a stochastic method and user cost includes traffic operation costs and time delay costs. Optimal design is performed for various bridge types such as steel-box girder bridge, plate girder bridge, PSC-I girder bridge including the substructure and the effects of various parameters are investigated. This study performed optimal LCC design of a 4@40m bridge with width of 15.6m according to the type of superstructure and supporting piers. The types of superstructure were concrete slab, steel box girder and PSC-I girder, and those of the piers were single-column or double-column piers.
Benefit-cost ratio analysis of retrofit strategies for bridges considering the resilience effect
Published in Hiroshi Yokota, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Life-Cycle Sustainability and Innovations, 2021
MCS (Zheng, 2015) and the moment method (Zhao and Lu, 2016) are used in this work to calculate the system reliability of a bridge structure. The moment method includes 2nd moment method (2M), 3rd moment method - 3P-lognormal distribution moment method (3M) and simplified 4th moment method (4M). Second moment method is the simplest method when compared with third moment and forth moment method. However, in higher complexity, second moment method may lose its accuracy. Therefore, third moment method and forth moment method are derived. Thus, 3P-lognormal distribution method simplified fourth moment reliability index method proposed by the literature (Zhao and Lu, 2016). Are used. Furthermore, for a complicated and implicit function, it is more convenient to adopt a point estimate method for calculating the moment values instead of a direct estimation method. In this work, seven-point estimation method (Zhao and Lu, 2016) and Nataf transformation method (Li and Yuan, 2011) are combined to calculate the first four moment values of a limit state function, including mean value (μ), standard deviation (σ), third moment (α3σ3) and fourth moment (α4σ4)
Seismic resilience analysis of a retrofit-required bridge considering moment-based system reliability
Published in Structure and Infrastructure Engineering, 2021
Chiu ChienKuo, Yamaguchi Eiki, Daniel Santoso
The second moment method is simpler method than the third moment and fourth moment methods because it uses only the first two moments (mean and standard deviation) to evaluate the system reliability. Equations (14) and (15) yield and using only the first two moments (mean and standard deviation):