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Traffic modelling and simulation

The research presented herein is heavily reliant on the software tools developed as part of this work. The efficacy and power of the software has implications for the manner in which bridge load research is carried out: for example, larger sample sizes generally result in more accurate load effect prediction. Accordingly, in this work, the object-orientated approach to programming is used. An explanation of this method, and the programs based upon it, is given in Chapter 4. As a result of these developments, it is now possible to simulate 5 years of traffic for a typical heavily trafficked European trunk motorway on a typical high-specification desktop personal computer. This traffic may be used to assess load effects from any form of influence line or slices of an influence surface. The statistical analysis outlined later may then be applied to the complex of results gathered.

Headway modelling

Intuitively, the gap between successive trucks has important implications for the quantity of load that may be applied to a bridge: this work describes, in quantitative terms, the implications for various lengths and load effects. It is found that existing headway (gap plus the lead truck length) models do not focus on the small headways that are critical for bridge loading events. A new method of modelling headway for this critical range is presented: it exhibits less variability in load effect estimation; conforms to the physical requirements of traffic; and preserves measured headway distributions. This method is described in Chapter 5, along with comparisons to existing methods.

Composite distribution statistics

The load effect output from the process of measurement, modelling, and traffic simulation, requires a statistical analysis to permit estimations of future load effect values. Extreme value analysis assumes that the data to be analysed is independent (or, at most, has minor dependence) and identically distributed. When daily maxima (for example) are considered as the basis for further statistical analysis, it is shown here that although this data is independent, it is not identically distributed. Physically, this is manifest as the difference in load effect between 2- and 3-truck crossing events, for example. Intuitively, such events are not identically distributed, and as such, should not be mixed as a single distribution in an extreme value statistical analysis. A method termed composite distribution statistics is presented which accounts for the different distributions of load effect caused by different event types. Exact equations are derived, as well as asymptotic expressions which facilitate the application of the method. The method is checked against results derived from the exact distribution, and compares favourably. Also, the method is applied to the output from the simulation process and compared with the traditional approach. It is shown that the composite distribution statistics method can give significantly different results.

Prediction of extreme load effects

The raison d’être of the bridge loading model, and subsequent statistical analysis, is the prediction of extreme, or maximum lifetime, load effects. Basic prediction techniques are outlined in Chapter 3, but more advanced methods are required to reflect the complexity of the underlying process and its model, such as the method of composite distribution statistics developed as part of this work. Such extrapolation methods, are subject to substantial variability: different samples give different estimates of lifetime load effect. To allow for this variability, the method of predictive likelihood is used in this work. This is a relatively new area of Frequentist statistics and is not yet adopted in many practical fields of research. Predictive likelihood yields many benefits for the bridge loading problem. Most importantly, the variability of the predicted extreme can be calculated. Further, sources of uncertainty, such as the random variation of the data and of the parameter fits to the data, can be taken into account. Therefore the result of a predictive likelihood analysis gives a measure of the uncertainty inherent in the bridge loading problem, and enables this uncertainty to be taken into account.

Multivariate extreme value analysis

The full spectrum of bridge traffic load modelling must account for the effect of dynamic interaction between the traffic and the bridge during crossing events. The modelling and simulation described in this work are strictly static analyses. To allow for the effects of dynamics at the return period of bridge loading, 10 years of traffic were simulated for a bridge which has been tested and modelled extensively by other authors. These results are used as a basis for dynamic models of crossing events. Both of these data sets form the basis of a multivariate extreme value analysis which allows for the correlation between the static and dynamic aspects of a crossing event. Using re-sampling techniques, estimates for a site dynamic allowance factor are made. It is shown that, while dynamic amplification may be large (around 30%) for some individual events, the allowance that should be made for dynamics to obtain an appropriate overall lifetime load effect value is much less (around 5%).