1 Faculty of Built Environment, University of New South Wales, Sydney, 2052, Australia 2 Faculty of Engineering, University of New South Wales, Sydney, 2052, Australia
Email: [email protected]
Abstract: Transport infrastructure represents a major investment for any economy. There are
not only the direct capital and maintenance costs, but significant indirect costs when such infrastructure fails. Given the increasing propensity for severe and more frequent extreme weather events, especially flooding and significant storm damage, bridges have become a critical point of focus. Design standards struggle to keep pace with the rapid changes in bridge design across the various materials, quality, applied loadings, levels of fatigue, and significance to transport networks each bridge represents. Capital and maintenance expenditure needs to reflect the particular level of resilience required for each individual bridge construction. Conventional cost management techniques recognise that the resilience of a bridge can be expressed as a function of the probability that one or more bridge components will fail given a particular weather event and the period or cost of recovery should such a failure occur. However, current formulations fail to provide a methodology that is sufficiently simple and robust for use by infrastructure planners, operators and regulators to evaluate a multitude of bridges on a regular basis. This study presents a new approach to modelling the resilience of transport infrastructure based on linear and non-linear multiple regression equations. The model predicts the resilience of individual bridges and can be expanded to include the broader cost and other implications of proactive versus reactive flood risk management for transport infrastructure. The equations adopt a design methods framework and reference the probability and known impact of previous weather events along with the probability and aggregated costs of bridge repair work to estimate an optimum resource expenditure balance between risk mitigation, preparedness, response and recovery. The methodology has broad application across any multi-criteria decision-making problem.
Keywords: Additive Models, Cost Management, Flood Risk Resilience, Risk Management,
Transport Infrastructure
1.
INTRODUCTIONThe frequency of extreme flood events in Australia has increased dramatically over recent years, and consequently the economic loss associated with flood events has ballooned (Guha- Sapir et al., 2011). Like many countries globally, Australia is now highly susceptible to flood damage. For example, recently in 2017, Cyclone Debbie created major floods in Queensland with devastating impact. The storm killed at least twelve people, primarily as a result of extreme flooding, and transport infrastructure was inundated across the state (ABC News, Retrieved 8 April 2017). Flooding was also the cause of damage to 15,000 kilometres of road and rail network and approximately 100 significant bridges and culverts in 2011 (Setunge et al., 2014).
Research into the risk management of extreme weather events has tended to focus on the cost consequences of impact and response rather than factors such as resilience (Blong, 2004, and Mojtahedi et al. 2017). Certainly, no research has been found that examines the factors that might influence the resilience of transport infrastructure more specifically, or the particular impact of flooding on transport infrastructure in Australia (Pritchard, 2013). Transport
infrastructure is of special significance because it also serves a critical role before, during and after flood events to reduce the vulnerability of the community more generally. The problem is complex, however, because the vulnerability of individual transport infrastructure will vary by context, depending on factors such as population, elevation, network criticality, maintenance and age (Meyer, 2008).
In any transport network, bridges are often the most vulnerable elements because of their susceptibility to catastrophic collapse (Meyer, 2008, IPCC, 2012). Most bridges in Australia are constructed over rivers, and the most common form of flooding in Australia is river flooding (AGO, 2006). It is essential for effective flood risk management to identify bridges that may be vulnerable to flood events and to mitigate those associated risks.Risk mitigation is aimed at increasing the resilience of transport infrastructure, and the costs of mitigation must be weighed against the benefits offered by increased resilience to the cost consequences of flood damage. A recent analysis of current design standards for bridges concludes that standards have struggled to keep pace with the rapid changes in bridge design across the various materials, quality, applied loadings, levels of fatigue, and significance to transport networks each bridge represents (Mohseni and Setunge, 2016). At the same time, other studies have shown that the more these factors are considered, the greater the complexity of the design models that tend to result and the less practical the guidelines and standards become (Aflatooni et al., 2013). This has had particular impact on the budgeting of capital and maintenance expenditure, because each individual bridge warrants a unique cost management response.
The genuine complexities associated with analysing the flood risk of individual bridges has resulted in a relative neglect of mathematical evaluation of bridge designs is neglected in previous research. In this study, we review the factors associated with the design of bridges and present a novel mathematical approach to evaluate the relationship between the potential cost impact of bridge damage due to flood risk factors and the cost of mitigation.The equations adopt a design methods framework and reference the probability and known impact of previous weather events along with the probability and aggregated costs of bridge repair work to estimate an optimum resource expenditure balance between risk mitigation, preparedness, response and recovery. The methodology has broad application across any multi-criteria cost optimisation problem.
2. CRITICAL FACTORS FOR RESILIENT BRIDGE DESIGN
When seeking to analyse a complex problem comprising a range of variables the common approach is to apply a parametric regression method. Parametric regression defines a function in which the terms comprise a finite number of unknown parameters derived from numerical data on each of the variables of interest. In the context of transport resilience and risk management, which is highly dependent on the vagaries of individual situations, the variables of interest can vary significantly between situations. In such circumstances, regression is better defined in nonparametric terms across a set of functions. Originally proposed by Friedman and Stuetzle (1981), the additive model method offers a robust and simple to interpret approach to the effect analysis of multiple variables. The additive model takes the form of a familiar regression model, but builds each model from a restricted class of nonparametric regression models. Each nonparametric model uses a one-dimensional smoother to generate linear combinations of the predictor variables in an iterative fashion.
The additive modelling approach provides distinct advantages over alternative nonparametric approaches and is entirely more general than standard stepwise regression procedures (Friedman and Stuetzle, 1981). The additive model approach results in a regression model, but the relationship between each variable and the response is allowed to be flexible and/or linear in nature, as indicated by the following formula:
∑ 𝑓𝑗 𝑛 𝑗=1 (𝑥𝑗) = ∑ 𝛽𝑗 𝑛 𝑗=1 × 𝑥𝑗𝑛 (1)
Where, f(x) represents linear or non-linear relationships between phenomena.
Based on Equation (1), we develop an additive statistical equation for analysing transport infrastructure flood specific to bridge risk-based resilience as follows:
𝑟 = 𝛼 + ∑ 𝑓𝑗 𝑝
𝑗=1
(𝑥𝑗) + 𝜖 (2)
Where, r is the resilience of a bridge to a flood event, α is the intercept, f(x) is a linear or non- linear function between the response and the relevant indicator, and ϵ is the overall error of the model.
Additive models have the strong properties of linear or nonlinear models in so far as they are in a familiar regression form and easy to interpret, but are superior in that they relax the assumption of a linear (or known nonlinear) relationship in the data. Thus, the additive model approach is not a purely nonparametric method (which is one of the potential limitations of the proposed framework), but does represent an effective compromise between flexibility and simplicity.
To begin to build an additive model the first challenge is to identify the principal components. Choice of the principal component is dependent on the range of candidate components and the availability of data. Nonparametric regression does require larger sample sizes than parametric models because the data must support the development of a model structure as well as supply the model estimates. For the purposes of this study, a representative set of eight principal components is used. However, the same framework and approach can be applied to an unlimited number of principal components where relevant data is available. Based on a broad review of the literature, the following eight principal components are used in this study of bridge resilience in the context of flood risks: