A review of probabilistic methods of assessment of load effects in bridges

Abstract

This paper reviews a range of statistical approaches to illustrate the influence of data quality and quantity on the probabilistic modelling of traffic load effects. It also aims to demonstrate the importance of long-run simulations in calculating characteristic traffic load effects. The popular methods of Peaks Over Threshold and Generalized Extreme Value are considered but also other methods including the Box-Cox approach, fitting to a Normal distribution and the Rice formula. For these five methods, curves are fitted to the tails of the daily maximum data.Bayesian Updating and Predictive Likelihood are also assessed, which require the entire data for fittings. The accuracy of each method in calculating 75-year characteristic values and probability of failure, using different quantities of data, is assessed. The nature of the problem is first introduced by a simple numerical example with a known theoretical answer. It is then extended to more realistic problems, where long-run simulations are used to provide benchmark results, against which each method is compared. Increasing the number of data in the sample results in higher accuracy of approximations but it is not able to completely eliminate the uncertainty associated with the extrapolation. Results also show that the accuracy of estimations of characteristic value and probabilities of failure are more a function of data quality than extrapolation technique. This highlights the importance of long-run simulations as a means of reducing the errors associated with the extrapolation process.

Threshold selection for extreme value estimation of vehicle load effect on bridges

“…The condition of j \ 1 is defined to guarantee the existence of the expectation. Equation (1) shows that the expectation of excesses is linear in u with gradient j/(1 -j) and intercept s u /(1 -j). For a set of samples (X 1 , X 2 ,..., X n ), the empirical estimate of the mean of excesses can be obtained as follows…”

“…A large volume of research work has been conducted on the assessment of load-carrying capacity of bridges and it is possible to evaluate the load-carrying capacity reasonably. 1,2 Vehicle load effect of bridges, one of the great sources of uncertainty, is mainly studied in this article. Vehicle load effect mainly refers to stress/strain, internal force (such as bending moments, shear force), and deformation induced by vehicles passing through bridges.…”

Vehicle Loads for Assessing the Required Load Capacity Considering the Traffic Environment

“…Gu et al [4] presented a Bayesian distribution model of overloaded vehicles. O'Brien et al developed traffic load models with various probabilistic methods [5][6][7][8]. They also considered the dynamic effects in addition to static effects [9].…”

Simplified probabilistic model for maximum traffic load from weigh-in-motion data

“…One important application is projecting the data to estimate the maximum traffic actions that bridges may be subjected to within a reference period. Several methods have been proposed to this end (Treacy et al 2014, O´Brien et al 2015. However, most of these are based on complicated and cumbersome simulation processes that require excessive computational effort and specialized expertise making them difficult to implement in everyday engineering practice when evaluating the safety of specific bridges.…”