Bridges have a fundamental role in transportation infrastructure and the overall world economy; as such, their targeted performance must be met. Complying with the requirements for modern bridge design requires accurate modelling and a careful analysis of the vulnerability to natural hazards. Local scour and other hydraulic-related processes (e.g., channel migration, flood-associated loads, and wood debris accumulation) have been proven to be the main reasons for bridge collapse [1
], thus affecting the functionality of the transport system. Evidence of such a pivotal danger is the scientific literature, which has reported several failures of infrastructures triggered by flooding events in the USA, the United Kingdom, and Europe [2
]. In this last decade, scientists and practitioners have put considerable effort into focusing on the vulnerability of riverine bridges to natural hazards, particularly flooding and local scouring events [7
The structural integrity of bridges that cross rivers can be compromised by hydrodynamic forces as well as by the loading effect caused by the accumulation of floating wood debris at the piers. Most commonly, the type of debris that endangers bridge safety consists of waterborne debris (e.g., tree trunks and limbs) that are transported by the water current during flooding events [8
]. The presence of debris jams at the piers of bridges may cause an increase in the upstream water levels (afflux
) and a backwater effect, thus posing an additional flood hazard for the nearby areas [9
]. Wood debris, once stranded at the piers, can also lead to an increase in the hydrodynamic actions and trigger an exacerbation of the local scour [10
]. Local scour is an equally threatening process that can lead to uncovering the piers’ foundations and reducing their lateral stiffness and load-bearing capacity [11
]. Local scour at bridges results from the removal of sediment from around the base of the pier caused by the onset of horseshoe vortices [12
]. The action exerted by local scour has been responsible for 60% of bridge failures in the United States, according to [13
]. Despite a variety of failure modes associated with local scour, vertical and lateral modes were most frequently observed [14
]. Therefore, it is evident that flood-induced hydrodynamic and debris impact can undermine the structural safety of bridges and lead to severe structural damage and consequent economic losses [15
In order to assess the vulnerability of bridges to floods and develop resilient countermeasure strategies, the implementation of fragility curves represents a reliable and consolidated methodology [16
]. Unlike deterministic approaches, vulnerability analysis consists of computing the conditional probability of exceedance of a defined damage state for a considered hazard or a combination of them. While the vulnerability of bridges to seismic performance has been widely investigated [17
], little is known about how flooding events and related processes can simultaneously affect the structural vulnerability of a bridge. Moreover, although the flood-related risk was included in seismic vulnerability analysis, its contributions were not considered the main cause of bridge failure [22
]. Nevertheless, due to the incumbency of changes in global climate, recent studies have started to implement a more accurate vulnerability analysis of bridges against floods. For instance, the authors of [24
] carried out a flood vulnerability analysis by taking into account the simultaneous contribution of bridge scour, structural deterioration of the steel reinforcements and piles, and the increased water pressure due to debris accumulation around bridge piers. Another approach was presented by [25
], who included the geotechnical uncertainties provided by the foundation design in the vulnerability analysis. Additionally, the authors of [26
] presented a holistic approach where the fragility curves were implemented examining different combinations of scouring conditions and earthquake loadings for a reinforced concrete bridge with shallow foundations. Another efficient framework has been introduced by [27
], who identified the possible modes to bridge failure caused by scour-related processes. An interesting perspective is also offered by [28
], who provides a performance-based engineering framework on a flood fragility analysis of a bridge subjected to various loading scenarios and local scour. Fragility curves were also employed to illustrate the exceedance probability of the limit states of a masonry bridge exposed to scour-induced support rotation [29
]. In spite of the lack of a classic fragility analysis approach, the authors of [30
] offer a comprehensive and innovative analysis of local scour. Using artificial intelligence techniques, the authors implement a probabilistic methodology that can predict scour depths created by regular waves on groups of piles. It is also discussed that probabilistic approaches should be able to incorporate uncertainties for the most critical parameters that influence local scour depths (e.g., pile diameter, average flow velocity) [31
Driven by these emerging research perspectives, the presented framework refers to a vulnerability analysis methodology that aims at using a probabilistic approach to grasp some of the uncertain variables that affect bridge resilience to floods. Particular focus is placed on the procedure for modelling wood debris accumulation on the bridge piers. The vulnerability analysis of this study is implemented for both the serviceability and ultimate limit state to provide an overall view of the structure’s performance. The variability of material and geotechnical properties, hydrodynamic loading, wood debris size accumulation, and scour magnitude is taken into account to illustrate different scenarios through the analytical implementation of vulnerability surfaces and two failure modes. The process of a random sampling of the variables is performed with a very efficient stratified sampling approach (i.e., Latin Hypercube Sampling (LHS)), thus abandoning the typical Monte Carlo simulation.
The strength and stiffness of the construction materials (e.g., concrete and reinforcing steel) are some of the major sources of uncertainties in civil engineering structures. Their assigned values are critical determinants of the behavior of a structure [32
]. Thorough studies have been undertaken to assess the statistical parameters and models of materials properties [33
], thus providing solid support when considering such uncertainties in vulnerability analysis. Similarly, the natural variability of soil properties and especially the influence of soil spatial variability on structural performance have also been widely investigated [35
]. The same cannot be said when considering the uncertainties provided by the actions of flood and wood debris loading and local scouring. The gap in information and criteria to incorporate flood-related processes into the vulnerability analysis of bridges, as opposed to earthquakes, may be due to the difficulties related to monitoring such processes. The complexity of hydraulic data, the high cost of monitoring techniques, and the stochasticity inherent in flood-related processes may discourage researchers and practitioners from exploring such crucial conditions for bridge vulnerability evaluation [37
This work aims to implement the aforementioned methodology and create a reliability analysis framework to investigate flood vulnerability through a real-bridge case study. The originality of this paper stands in offering an analysis framework that considers the addition of both hydraulics and geotechnical model uncertainties to the ones that are commonly established in the vulnerability analysis of bridges (e.g., material uncertainties). The novelty of this paper also relies upon the way the vulnerability analysis is addressed. The largest part of the existing studies on bridge vulnerability analysis has often modelled the hydrodynamic and wood debris loads by referring to government guidelines or bridge design specifications (e.g., AASHTO LRFD Bridge Design Specification [25
]). However, such references are rather simplistic and differ widely due to a lack of consistency in cross-countries methodology comparisons [13
]. Furthermore, the use of regulations and standard specifications can lead to an inherent conservatism that is not beneficial for vulnerability analysis since it overestimates the probability of reaching the considered damage limit state analysis. For this reason, the goal of this study is to utilize the latest research outputs to provide a different perspective and a source of comparison to the most relevant existing guidelines.
In this paper, a flood vulnerability analysis of a real-case roadway bridge is performed. The vulnerability of the bridge is examined by considering the concurrent action of gravity loads, hydrodynamic loads, wood debris accumulation and local scour. The interaction between local scour and the accumulation of debris is also considered, and its implementation is based on an equivalent-pier-width approach. Due to the lack of stationary hydraulic conditions at the site, the vulnerability analysis is performed with consideration of both flow velocity and water height as input parameters. This leads to the representation of the vulnerability analysis results as a surface in a three-dimensional domain.
The main purpose of this paper is to examine the results of three different scenarios. One examines the condition with no debris, while the second and third evaluate two different debris modelling approaches. The first approach relies on the recommendations drawn from the AS5100.2-2004 standard, whereas the second approach refers to the model proposed by Panici and Almeida [48
], which, compared to the standards-based methodology, involves a more elaborate and refined analytical procedure. The research of the second approach is motivated by the absence of accurate guidelines for modelling processes of wood debris accumulation at bridge piers.
Based on the results, it is clear that the bridge is more likely to exceed its serviceability and ultimate limit states in presence of wood debris compared to the condition with no debris. The accumulation of debris at the bridge pier is shown to be responsible for the increase in local scour depths. As the debris and scour action interact, the SLS and ULS of the bridge occur for smaller flooding events compared to the scenario with no debris. Nevertheless, the bridge is more likely to fail for values of
located in the upper prediction interval of the
relationship. This finding is not dependent on the modelling approach considered. Overall, the results of this study indicate that the use of Panici and Almeida’s model [48
] offers less conservative estimates of the bridge response to severe floodings. This may be due to the fact that the novel modelling approach is able to provide a more analytical definition of the size and shape of the debris accumulation. The triangular shape, in fact, yields less severe scouring depths compared to the use of the rectangular shape suggested in the AS5100.2-2004 standard [53
A sensitivity analysis is also performed and is used to examine the variation of the scour depths, bridge’s utilization ratios and governing failure mechanisms for the three scenarios and different water heights. From this analysis, it is shown that the AS5100.2-2004 standard produces the most unfavorable results. For instance, the exceedance of the ultimate limit states due to scour only occurs when implementing the recommendations provided in the Australian Standard. A similar outcome occurs when examining the values of utilization ratios of the structure. It is clear that for most of the values of
, the AS5100.2-2004 Standard is the only scenario that leads to the exceedance of the ULS for the highest values of the utilization ratio (95% percentile). It also emerges that local scour plays a crucial role in most of the hydraulic conditions considered, and its influence is more significant for the second scenario than the third. This confirms what was found in the literature [64
] and makes it clear that computing the magnitude of the local scour is essential when examining bridge vulnerability to flood and bridge failure modes. For water height reaching the deck, the performance of the bridge is mainly threatened by the failure of the pier bearing instead. However, in this case, the difference between the two debris models becomes less evident.
In spite of the effectiveness of the presented vulnerability approach, there are limitations that need to be taken into account. For instance, the poor quality and amount of hydraulic data and a lack of an appropriate numerical modelling approach do not allow a reasonable estimation of the hydrodynamic-related loads. Hydraulic data input are essential in flood vulnerability analysis. Hence, more appropriate and consistent monitoring of the hydraulic variables is encouraged as it can be extremely beneficial in the vulnerability assessment of riverine bridges. Similarly, the knowledge gap related to the mechanisms governing the accumulation of debris jams at bridge piers, as well as the lack of monitoring data on wood debris recruitment and transportation represents a limitation for the reliability of the results of the analysis. Another aspect to consider is the simplified finite-element modelling employed in this study, which, due to a complicated interaction between the structure, soil, hydrodynamic loads and local scour, owns further examinations. A similar evaluation applies to the coefficient of variations of the materials, geotechnical characteristics, hydrodynamic forces, local scour depth and size of wood debris accumulation. The values assigned to the coefficient of variations are, in fact, based on isolated recommendations found in the literature. Moreover, important processes such as afflux, river bed-load transport and the degradation of the bridge’s materials are not included in the analysis as the present study does not account for the time-dependent assessment of the bridge’s vulnerability. Due to the complex interplay between debris loads, scour, and hydraulic forces, the research examination assessing bridge flood vulnerability should be carefully addressed. Despite the acknowledged limitations, the presented framework bridges some of the gaps existing in the standards-based approach providing a more up-to-date and faithful methodology for bridge vulnerability analysis. Therefore, more effort should be devoted to improving and updating the existing standards and guidelines concerning the modelling of hydrodynamic-related processes. Particularly, the interplay between debris accumulation and local scour would need further examination as it is shown to substantially affect the bridge’s vulnerability.
It is hoped that this study will inspire future research into improving and upgrading the vulnerability analysis framework. For instance, the implementation of faithful hydraulic numerical modelling techniques, along with local scour monitoring solutions, can help to validate the proposed modelling approach and assess the performance of the asset throughout its lifespan. At the same time, the developed approach represents a valuable tool for supporting targeted visual inspection and Structural Health Monitoring campaigns. Vulnerability surfaces can provide useful insight into the selection of the key parameters that should be verified and monitored at different stages of a bridge’s life-cycle to determine its level of performance [65
]. Furthermore, considering a life-cycle perspective, bridge vulnerability assessment is also beneficial for quantitatively determining the risk severity of hazards on bridges and helping to evaluate the effectiveness of potential resilient countermeasures for risk mitigation. This study can provide policymakers, engineering consultants, bridge engineers and stakeholders with a valid and reliable method of estimating the anticipated economic and functional losses associated with flooding hazards, implementing effective decision-making processes, and selecting sustainable and resilient strategies.