Skip to Main content Skip to Navigation

Statistical analysis of traffic loads and traffic load effects on bridges

Abstract : Most of the bridges are less than 50 m (85%) in France. For this type of bridges, the traffic load may govern the design and assessment. Road freight transportation has increased by 36.2% between 1995 and 2010 in Europe, and the volume of freight transport is projected to increase by 1.7% per year between 2005 and 2030. It is thus vital important to insure European highway structures to cater for this increasing demand in transport capacity. Traffic load model in standard or specification for bridge design should guarantee all newly designed bridges to have sufficient security margin for future traffic. For existing bridges, the task is to assess their safety under actual and future traffic, and a prioritization of the measures necessary to ensure their structural integrity and safety. In addition, to address this growth without compromising the competitiveness of Europe, some countries are contemplating the introduction of longer and heavier trucks for reducing the number of heavier vehicles for a given volume or mass of freight, reducing labour, fuel and other costs. Many different methods have been used to model extreme traffic load effects on bridges for predicting characteristic value for short or long return period. They include the fitting a Normal or Gumbel distribution to upper tail, the use of Rice formula for average level crossing rate, the block maxima method and the peaks over threshold method. A review of the fundament and the use of these methods for modelling maximum distribution of bridge is presented. In addition, a quantitative comparison work is carried out to investigate the differences between methods. The work involves two studies, one is based on numerical sample, and the other is based on traffic load effects. The accuracy of the methods is evaluated through the typical statistics of bias and root mean squared error on characteristic value and probability of failure. In general, the methods are less accurate on inferring the failure probability than on characteristic values, perhaps not surprising given such a small failure probability was being considered (〖10〗^(-6) in a year). Although none of methods provides predictand as accurately as expected with 1000 days of data, the tail fitting methods, especially the peaks over threshold method, are better than the others. A study on peaks over threshold method is thus carried out in this thesis. In the POT method, the distribution of exceedances over a high enough threshold will be a member of generalized Pareto distribution (GPD) family. The peaks over threshold method is extensively used in the domains such as hydrology and finance, while seldom application can be found in bridge loading problem. There are numerous factors, which affect the application of peaks over threshold on modelling extreme value, such as the length and accuracy of data available, the criteria used to identify independent peaks, parameter estimation and the choice of threshold. In order to provide some guidance on selecting parameter estimation when applying POT to bridge traffic loading, we focus on the effect that method used to estimate the parameters of the GPD has on the accuracy of the estimated characteristic values. Many parameter estimators have been proposed in the statistical literature, and the performance of various estimators can vary greatly in terms of their bias, variance and sensitivity to threshold choice and consequently affect the accuracy of the estimated characteristic values. The conditions, assumptions, merits and demerits of each parameter estimation method are introduced; especially their applicability for traffic loading is discussed. Through this qualitative discussion on the methods, several available methods for traffic loading are selected. It includes the method of moments (MM), the probability weighted moments (PWM), the maximum likelihood (ML), the penalized maximum likelihood (PML), the minimum density power divergence (MDPD), the empirical percentile method (EPM), the maximum goodness-of-fit statistic and the likelihood moment (LM). To illustrate the behaviour and accuracy of these parameter estimators, three studies are conducted. Numerical simulation data, Monte Carlo simulation traffic load effects and in-field traffic load effect measurements are analyzed and presented. The comparative studies investigate the accuracy of the estimates in terms of bias and RMSE of parameters and quantile. As expected, the estimators have different performance, and the same method has different performance in these three sets of data. From the numerical simulation study, the MM and PWM methods are recommended for negative shape parameter case, especially for small size sample (less than 200), while the ML is recommended for positive shape parameter case. From the simulated traffic load effect study, the ML and PML provide more accuracy estimates of 1000-year return level when the number of exceedances over 100, while the MM and PWM are better than others when sample size is less than 100. Moreover, application on monitored traffic load effects indicates that the outliers have significant influence on the parameter estimators as all investigated methods encounter feasibility problem. As been stated in statistical literature, a frequent cause of outlier is a mixture of two distributions, which may be two distinct sub-populations. In the case of bridge loading, this can be a potential reason to result in the feasible problem of parameter estimator. Literature points out that the traffic load effect is induced by loading event that involves different number of vehicles, and the distribution of the load effects from different loading events are not identically distributed, which violates the assumption of classic extreme value theory that the underlying distribution should be identically independent distributed. With respect to non-identical distribution in bridge traffic load effects, non-identical distribution needs to be addressed in extreme modelling to account for the impacts in inference. Methods using mixture distribution (exponential or generalized extreme value) has been proposed in the literature to model the extreme traffic load effect by loading event. However, it should be noticed that the generalized extreme value distribution is fitted to block maxima, which implies the possibility of losing some extremes, and the use of exponential distribution is objective. We intend to explicitly model the non-identically distributed behaviour of extremes for a stationary extreme time series within a mixture peaks over threshold (MPOT) model to avoid the loss of information and predetermination of distribution type. For bridges with length greater than 50 m, the governing traffic scenario is congested traffic, which is out of the scope of this study. Moreover, the traffic loading may not govern the design for long span bridge. However, the traffic loading may be also importance if the bridge encounter traffic induced fatigue problem, components like orthotropic steel deck is governed by traffic induced fatigue load effects. We intend to explore the influence of traffic load on the fatigue behaviour of orthotropic steel deck, especially the influence of the loading position in terms of transverse location of vehicle. Measurements of transverse location of vehicle collected from by weigh-in-motion (WIM) systems in 2010 and 2011 four French highways showed a completely different distribution model of transverse location of vehicle to that recommended in EC1. Stress spectrum analysis and fatigue damage calculation was performed on the stresses induced traffic on orthotropic steel deck of Millau cable-stayed bridge. By comparing the stresses and damages induced by different traffic patterns (through distributions of transverse location of vehicle), it was found that the histogram of stress spectrum and cumulative fatigue damage were significantly affected by the distribution of transverse location of vehicle. Therefore, numerical analysis that integrates finite element modelling and traffic data with distributions of transverse location of vehicles can help to make an accurate predetermination of which welded connections should be sampled to represent the health of the deck. Bridge, traffic effects, traffic, extrapolation, extreme effects
Mots-clés : PONT
Complete list of metadata

Cited literature [167 references]  Display  Hide  Download
Contributor : Ifsttar Cadic Connect in order to contact the contributor
Submitted on : Thursday, February 20, 2014 - 1:44:15 PM
Last modification on : Thursday, September 1, 2022 - 11:06:52 AM
Long-term archiving on: : Tuesday, May 20, 2014 - 3:20:26 PM


Files produced by the author(s)


  • HAL Id : tel-00949929, version 1



Xiao Yi Zhou. Statistical analysis of traffic loads and traffic load effects on bridges. Structural mechanics [physics.class-ph]. UNIVERSITE PARIS-EST, 2013. English. ⟨tel-00949929⟩



Record views


Files downloads