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.

The accurate estimation of site-specific lifetime extreme traffic load effects is an important element in the cost-effective assessment of bridges. A common approach is to use statistical distributions derived from weigh-in-motion (WIM) measurements as the basis for Monte Carlo simulation of traffic loading over a number of years, and to estimate lifetime bridge load effects by extrapolation from the results of this simulation. However, results are sensitive to the assumptions made, not just with regard to vehicle weights but also to number of axles, inter-axle spacings and gaps between vehicles. This paper carries out a critical review of the assumptions involved in the process. It presents a comprehensive model for Monte Carlo simulation of bridge loading for free-flowing traffic that can be applied to different sites, and shows how the model matches results obtained from extensive sets of WIM measurements for highway sites in five European countries. The model allows for the simulation of vehicles which are heavier and have more axles than those recorded in the WIM data, and uses techniques for modeling axle configuration that can be applied to any type of vehicle. The model presented in this paper has been optimized to allow the simulation of 1000 or more years of traffic and this greatly reduces the variance in the process of calculating estimates for lifetime loading from the simulation model. Using this approach, it is possible to analyze the type of loading scenarios that cause the maximum lifetime load effects. Conclusions can be drawn about the type of vehicles likely to be involved in maximum lifetime loading scenarios, and the results highlight the importance of special vehicles in bridge loading. The approach described here does not remove the uncertainty inherent in estimating lifetime maximum loading from data collected over time periods which are much shorter than the bridge lifetime.

Publication informationStructural Safety, 33 (4-5): 296-304Publisher Elsevier This is a form of smoothed bootstrap in which kernel functions are used to add randomness to measured traffic scenarios. It is shown that it gives a better fit to the measured data than models which assume no correlation. Results are presented from long-run simulations of traffic using the different models and these show that correlation may account for an increase of up to 8% in lifetime maximum loading.

Publication informationEngineering Structures, 32 (12) AbstractMore accurate assessment of safety can prevent unnecessary repair or replacement of existing bridges which in turn can result in great cost savings at network level. The allowance for dynamics is a significant component of traffic loading in many bridges and is often unnecessarily conservative. Critical traffic loading scenarios are considered in this paper with a model that allows for vehicle-bridge interaction and takes into account the road surface condition. Characteristic dynamic allowance values are presented for the assessment of midspan bending moment in a wide range of short to medium span bridges for bi-directional traffic.

To predict characteristic extreme traffic load effects, simulations are sometimes performed of bridge loading events. To generalize the truck weight data, statistical distributions are fitted to histograms of weight measurements. This paper is based on extensive WIM measurements from two European sites and shows the sensitivity of the characteristic traffic load effects to the fitting process. A semi-parametric fitting procedure is proposed: direct use of the measured histogram where there are sufficient data for this to be reliable and parametric fitting to a statistical distribution in the tail region where there are less data. Calculated characteristic load effects are shown to be highly sensitive to the fit in the tail region of the histogram.