Probalistic analysis of highway bridge traffic loading

Many bridges of the world’s highway networks have been in service for decades and are subject to escalating volumes of traffic. Consequently, there is a growing need for the rehabilitation or replacement of bridges due to deterioration and increased loading. The assessment of the strength of the existing bridge is relatively well understood, whereas the traffic loading it is subject to, is not as well understood. Accurate assessment of the loading to which bridges may be subject, can result in significant savings for the highway maintenance budgets internationally. In recent years, a general approach has emerged in the research literature: the characteristics of the traffic at a site are measured and used to investigate the load effects to which the bridge may be subject in its remaining lifetime. This research has the broad objective of developing better methods of statistical analysis of highway bridge traffic loading. The work focuses on short- to medium-length (approximately 15 to 50 m), single- or two-span bridges with two opposing lanes of traffic. Dynamic interaction of the trucks on the bridge is generally not included. Intuitively, it can be accepted that the gap between successive trucks has important implications for the amount of load that may be applied to any given bridge length. This work describes, in quantitative terms, the implications for various bridge lengths and load effects. A new method of modelling headway for this critical time-frame is presented. When daily maximum load effects (for example) are considered as the basis for an extreme value statistical analysis of the simulation results, it is shown 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. 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. Due to sampling variability, the estimate of lifetime load effect varies for each sample of load effect taken. In this work, the method of predictive likelihood is used to calculate the variability of the predicted extreme for a given sample. In this manner, sources of uncertainty can be taken into account and the resulting lifetime load effect is shown to be calculated with reasonable assurance. To calculate the total lifetime load effect static load effect plus that due to dynamic interaction), the results of dynamic simulations based on 10-years of static results are used in a multivariate extreme value analysis. This form of analysis allows for the inherent correlation between the total and static load effect that results from loading events. A distribution of dynamic amplification factor and estimates for a site dynamic allowance factor are made using parametric bootstrapping techniques. It is shown that the influence of dynamic interaction decreases with increasing static load effect

Towards an Improved Teaching of Structural Behaviour

The interpretation of mathematical models and how they relate to the physical world is a key skill of the practice of structural engineering. At undergraduate level, there has been a noted reduction in students’ physical intuition in recent years. The teaching of structural engineering must therefore adapt itself to these new realities to maintain public confidence in the safety of society’s infrastructure. The work carried out for this Fellowship project tacked the identified deficits at two ends of the spectrum of physical intuition. Third year students were introduced to basic structural models, whilst final year students were exposed to the inner workings of structural engineering software so that they may better link their hand calculations and typical commercial software. Pre-and post-testing using multiple choice questions were used to ascertain the effectiveness of the interventions. The results are generally inconclusive as evidence was found that the multiple choice questions may not be the best form of assessing interventions in physical reasoning. It is clear that more work remains to be done in this area

A New Congested Traffic Load Model for Highway Bridges

Long span highway bridges are critical components of any nation’s infrastructure. Therefore accurate assessment of highway bridge loading is essential, and it is well known that congested traffic governs load effect for such bridges. Current congestion models use conservative assumptions about traffic and inter-vehicle gaps. This research investigates congested traffic flow through the use of traffic microsimulation which has the ability to reproduce complex traffic phenomena based on driver interactions. A time series model has been developed to produce a speed time-series similar to the results of the microsimulation. The speed time-series from the new model, combined with the established speed-gap relationship from the microsimulation, form the basis of a more computationally efficient congested traffic model. It is shown that the new model replicates aspects of microsimulation traffic well. However, the resulting load effects do not match as well as expected, and so further development of the model is required

Lane Changing Control to Reduce Traffic Load Effect on Long-Span Bridges

Long span bridges are critical parts of a nation’s infrastructure network and congested traffic loading is the governing form of traffic loading. Groups of trucks travelling in conveys are created when fast-er moving vehicles, such as cars, change lane. In this research the authors investigate how the control of these lane-changing events can help reduce the traffic load effects on long span bridges. Real traffic data is used to simulate a traffic stream on a virtual road and bridge using a microsimulation model. Various lane-changing restrictions are examined and compared to the typical case of free lane changing. It is shown that restriction of lane changing is an effective means of reducing long-span bridge traffic load effect. This result may assist bridge owners in implementing measures to prolong the life of existing infrastructure

Bayesian Generative Modelling of Student Results in Course Networks

We present an innovative modelling technique that simultaneously constrains student performance, course difficulty, and the sensitivity with which a course can differentiate between students by means of grades. Grade lists are the only necessary ingredient. Networks of courses will be constructed where the edges are populations of students that took both connected course nodes. Using idealized experiments and two real-world data sets, we show that the model, even though simple in its set-up, can constrain the properties of courses very well, as long as some basic requirements in the data set are met: (1) significant overlap in student populations, and thus information exchange through the network; (2) non-zero variance in the grades for a given course; and (3) some correlation between grades for different courses. The model can then be used to evaluate a curriculum, a course, or even subsets of students for a very wide variety of applications, ranging from program accreditation to exam fraud detection. We publicly release the code with examples that fully recreate the results presented here

Experiences of aiding autobiographical memory using the sensecam

Human memory is a dynamic system that makes accessible certain memories of events based on a hierarchy of information, arguably driven by personal significance. Not all events are remembered, but those that are tend to be more psychologically relevant. In contrast, lifelogging is the process of automatically recording aspects of one's life in digital form without loss of information. In this article we share our experiences in designing computer-based solutions to assist people review their visual lifelogs and address this contrast. The technical basis for our work is automatically segmenting visual lifelogs into events, allowing event similarity and event importance to be computed, ideas that are motivated by cognitive science considerations of how human memory works and can be assisted. Our work has been based on visual lifelogs gathered by dozens of people, some of them with collections spanning multiple years. In this review article we summarize a series of studies that have led to the development of a browser that is based on human memory systems and discuss the inherent tension in storing large amounts of data but making the most relevant material the most accessible

The Effect of Lane Changing on Long-Span Highway Bridge Traffic Loading

Maximum loading on long-span bridges typically occurs in congested traffic conditions. As traffic becomes congested car drivers may change lane, increasing the tendency for trucks to travel in platoons. For long-span bridges this phenomenon may increase the regularity and severity of bridge repair programs, with potential significant associated costs. This research investigates the effect of lane changing by car drivers on bridge loading. A Monte Carlo simulation model in which individual car drivers probabilistically decide, based on a lane-changing bias probability, whether or not to change lane has been developed. The sensitivity of bridge loading to this factor is investigated for different bridge lengths and traffic compositions. This research concludes that the lane-changing behavior of car drivers has an effect on bridge loading for long-span bridges, and the magnitude of this effect is quite sensitive to the percentage of trucks in the traffic

Finding the Distribution of Bridge Lifetime Load Effect by Predictive Likelihood

To assess the safety of an existing bridge, the loads to which it may be subject in its lifetime are required. Statistical analysis is used to extrapolate a sample of load effect values from the simulation period to the required design period. Complex statistical methods are often used and the end result is usually a single value of characteristic load effect. Such a deterministic result is at odds with the underlying stochastic nature of the problem. In this paper, predictive likelihood is shown to be a method by which the distribution of the lifetime extreme load effect may be determined. A basic application to the prediction of lifetime Gross vehicle Weight (GVW) is given. Results are also presented for some cases of bridge loading, compared to a return period approach and important differences are identified. The implications for the assessment of existing bridges are discussed

Characteristic Vertical Response of a Footbridge Due to Crowd Loading

The characteristic vertical vibration of a flexible footbridge subject to crowd loading is examined in this paper. Typically, bridge vibrations produced from a crowd of pedestrians are estimated by using an enhancement factor applied to the effect caused by a single pedestrian. In this paper, a single pedestrian model, represented by a spring mass damper, which incorporates variables such as pedestrian mass and body stiffness, is used to calibrate a computationally efficient moving force model. This calibrated moving force model is further used in Monte Carlo simulations of non-homogenous crowds to estimate characteristic vertical vibration levels. Enhancement factors, which could be applied to simple single pedestrian moving force models in estimating the response due to a crowd are thus derived. Such enhancement factors are then compared to previously published values. It is found that the greatest difference between the spring mass damper and moving force models respectively occurs when the bridge frequency is at the mean crowd pacing frequency. For bridges with frequencies even slightly removed from this mean, moving force models appear adequate

Study of Same-lane and Inter-lane GVW Correlation

Extensive work has been done over the last two decades on the simulation of traffic loading on bridges. The methodology used is to generate a number of years of simulated traffic and to use extreme value statistics to predict more accurately the characteristic loading for a given bridge. The parameters and probability distributions used in the Monte Carlo simulation must be based on observed sample traffic data. Some previous studies have made unsubstantiated assumptions regarding correlation between the Gross Vehicle Weights (GVW) of trucks in the same lane, or between trucks in adjacent, same direction lanes. For this paper, an extensive database of Dutch Weigh-in-Motion data is analysed. Data are collected from two same-direction lanes and are time-stamped to the nearest 0.01 seconds. The statistical characteristics of this set of data are presentd, and various techniques are used to establish the nature and extend of GVW correlation