Flood events are the most frequent cause of damage to infrastructure compared to any other natural hazard, and global changes (climate, socioeconomic, technological) are likely to increase this damage. Transportation infrastructure systems are responsible for moving people, goods and services, and ensuring connection within and among urban areas. A failed link in these systems can impact the community by threatening evacuation capability, recovery operations and the overall economy. Bridges are critical links in the wider urban system since they are associated with little redundancy and a high (re)construction cost. Riverine bridges are particularly prone to failure during flood events; in fact, the risks to bridges from high river flows and erosion have been recognized as crucial at global level. The interaction of flow, structure and network is complex, and not fully understood. This study aims to establish a rigorous, multiphysics modeling approach for the assessment of the hydrodynamic forces impacting inundated bridges, and the subsequent structural response, while understanding the consequences of such impact on the surrounding network. The objectives of this study are to model hydrodynamic forces as demand on the bridge structure, to advance a performance evaluation of the structure under the modeled loading, and to assess the overall impact at systemic level. The flood-prone city of Carlisle (UK) is used as a case study and a proof of concept. Implications of the hydrodynamic impact on the performance and functionality of the surrounding transport network are discussed. This research will help to fill the gap between current guidance for design and assessment of bridges within the overall transport system.
Bridges are crucial elements of the transport network given their high construction costs and the lack of alternatives routes. Anthropogenic and natural events are a threat to bridge safety and network serviceability (Yang and Frangopol, 2020). Bridges act as bottlenecks for surrounding roads, and thus any service disruption can knock out communities' access and connections, impair emergency planning and evacuation routes and impact economies and businesses.
Some disruptive events are growing in frequency and severity. In particular, the impacts of flooding have been exacerbated in recent years by urbanization (e.g., increase of impermeable surfaces), inappropriate land use in flood-prone areas and climate change. Rainfall events that lead to flooding are becoming more frequent and intense (Solomon et al., 2007), triggering bridge incidents and failures all over the world (Cumbria, UK, 2009; Drake, Colorado, 2013; Texas, 2018; Greece, 2020). As recent examples, Grinton Bridge in North Yorkshire (UK) and Keritis Bridge in Crete (Greece) were both washed away by floodwaters in 2019.
Riverine bridges are intrinsically vulnerable to flooding, as they are located in the area of the riverbed. In fact, flood and scour represent one of the most frequent causes of bridge failures (Hunt, 2009; Wardhana and Hadipriono, 2003; Khan, 2015; Ahamed et al., 2020). Although, scour is recognized as the biggest threat for bridges over water (and available scour-related literature is much more robust), hydrodynamic forces could be as critical for bridge piers on bedrock (where scour is unlikely) and for the decks of all flooded bridges (Kim et al., 2017; Oudenbroek et al., 2018). In terms of consequences, natural hazards can damage bridges structurally (thus causing direct physical damage), but these events can also result in functional failures that cause travel time delays and rerouting that lead to indirect losses (Alabbad et al., 2021). Any bridge failure, whether structural or functional, has the potential to impose heavy consequences to owners or responsible authorities, as well as dire expenses. Therefore, understanding the potential impact of flooding to bridges is a compelling need of communities in areas of flood risk.
Currently, a limited number of studies investigated the consequences of extreme flooding to bridges and the surrounding network (Yang and Frangopol, 2020). Practical application and case studies of real bridges tend to be focused on other natural hazards (e.g., earthquakes: Kilanitis and Sextos, 2019; Ertugay et al., 2016; Zhou et al., 2010). This study aims to establish a rigorous, multiphysics modeling approach for assessing hydrodynamic forces on inundated bridges, subsequent structural response and consequences of such impact on the surrounding network. The objectives of this study are to model hydrodynamic forces as demand on the bridge structure, to advance a performance evaluation of the structure under the modeled loading and to assess the overall impact at systemic level. Implications of the hydrodynamic impact on the performance and functionality of the surrounding transport network are discussed. This research will help to fill the gap between current guidance for design and assessment of bridges within the overall transport system.
Transport networks are formed by multiple links (i.e., roads) and their performance relies on a number of parameters, such as availability of alternative routes (redundancy), road capacity or traffic demand, among others. A bridge failure often means a critical link is taken out of service. Bridges are usually costly assets to repair, have little redundancy and are likely to be crossed by a high number of users, especially if they belong to strategic road networks (e.g., highways). Therefore, bridge closure or failure can impact the overall performance of the road network and the failure consequences have to be investigated from a system perspective (Yang and Frangopol, 2020). The assessment of the systemic impact is a complex and multi-disciplinary problem, at the interface of hydrology, fluid dynamics, structural analysis and transport modeling.
Scour damage is a significant concern for many bridge structures and has been extensively studied (e.g., Pregnolato et al., 2021a; Wang et al., 2017; Hung and Yau, 2017; AASHTO, 2002); the more common methods include using the HEC-18 (Arneson et al., 2012; Vardanega et al., 2021) or CIRIA scour equations (Kirby et al., 2015; HE, 2012). However, assessing scour damages is not the main focus of this paper.
On the contrary, literature about modeling the hydrodynamic forces of the fluid on bridges due to riverine floods is limited, especially concerning fragility models or reliability analysis (Pregnolato, 2019; Gidaris et al., 2017). Existing research investigated tsunami impact to bridges (e.g., Motley et al., 2016; Lomonaco et al., 2018; Qin et al., 2018; Winter et al., 2017), where computational fluid dynamics (CFD) techniques are used to compute hydrodynamic forces on bridges and components. Li et al. (2021) advanced a CFD-based numerical study on the tsunami-induced scour around bridge piers. Kerenyi et al. (2009) applied CFD to compute hydrodynamic forces on inundated bridge decks, however the analysis was limited to the evaluation of drag and lift forces, without investigating impact and consequences. Bento et al. (2021) suggested CFD as a more sophisticated technique for modeling flow depth and velocities at sites. Multi-hazard studies have investigated the interaction and implication of multiple hazards acting on a single structure (Gidaris et al., 2017; Carey et al., 2019), especially between earthquake and tsunami. Other studies (Mondoro and Frangopol, 2018; Liu et al., 2018; Yilmaz et al., 2016) that tackled flood impact on bridges generally expressed the hazard through flood hazard curves, generated via flood-frequency analysis; however, a detailed hydraulic analysis was beyond the scope of their work. While tsunami loading of bridges will often result in much higher forces than riverine flows, the prevalence of riverine flooding relative to tsunami events necessitates further study and could have a far-reaching effect.
To the authors' knowledge, no study has comprehensively investigated the impact of high-river flows on bridges accounting for the complexity of the hydrodynamic forces to which the bridge is subjected and the associated structural and functional response. Moreover, the impact of the reduced service on a bridge on the surrounding network is rarely addressed in the literature. Given this limited availability of models, this paper aims at establishing a multilevel modeling framework to address these issues in one combined approach. This aim is achieved by developing an integrated framework to assess the flooding impact on riverine bridges from the structural to the network level (Pregnolato et al., 2021b) and applying it to a real case study in the UK. This research tackles varying flow conditions (velocity and depth) to understand the structural response across given simulated flooding conditions. This work is novel since it represents a first attempt to couple CFD analysis with both finite element (FE) and network analysis for bridges subjected to flooding, in an effort to capture both the cause and effect of flooding. It is expected that this approach will be useful for understanding structural damage and functional loss for a range of bridges, and ultimately for assessing risk for any coastal or riverine structure where large-scale water inundation is expected.
This paper adopts a risk-based framework to assess the impact of high river flows on bridges and surrounding roads (Fig. 1). The framework proposes a comprehensive method that encompasses the traditional four risk modules (hazard, exposure, vulnerability and consequences; Grossi and Kunreuther, 2005) and includes hydrodynamic force modeling, bridge susceptibility to the hazard, performance evaluation and network-level impact assessment. This study adopts specific models/software, but the precise chosen sub-models are not critical. In fact, all models/software are interchangeable, and it is reasonable to expect that the presented approach would be appropriate for software packages that ensure similar configuration.
The first step is to determine the intensity measures of flooding in terms
of flow depth and velocity (see Sect. 2.1). For modeling fluvial
flooding, most 2D hydrodynamic models can simulate flood depths and flow
velocity, e.g., LISFLOOD-FP (
The second step consists of modeling the interaction between the water and
the bridge, as well as the subsequent flood-induced loads. A simplified
vulnerability and criticality assessment (Johnson and Whittington, 2011)
includes the evaluation of the local flow conditions and corresponding
hydrodynamic forces that represent the load on the bridge structure using
CFD techniques. Here, the C
The proposed risk-based methodological flowchart to integrate modeling of hydrodynamic forces, performance and network-level analysis. Abbreviations: CFD – computational fluid dynamics; FEM – finite element model.
The third step is to determine the response of the bridge subjected to flood
through an advanced structural analysis approach such as FE
analysis. There are many available FE models, such as Abaqus FEA
(
Bridge failure states investigated due to flood loading.
The general limit-states philosophy considers that specifications should satisfy “specified limit states to achieve the objectives of constructability, safety and serviceability” (AASHTO, 2017). In this work, the failure of a bridge is seen as twofold: (i) structural (also strength limit state), when the bridge deck, piers or foundation reach the ultimate limit state or permanent deformations; (ii) functional (also service limit state), when the bridge cannot perform its service as usual. A structural failure directly leads to a functional failure, e.g., the bridge collapses; preventive closure could also take place when bridge conditions are considered unsafe. Nevertheless, a bridge could be unserviceable but still structurally sound, e.g., when floodwater or debris cover the deck. Hydraulic pressures (drag, lift and overturning moment) are assessed for potentially dislodging the deck from piers, when submerged or partially submerged, and overtopping of the deck is evaluated qualitatively from the CFD model. Though these limit states have significantly different long-term consequences, both result in potential functional failure. The importance of long-term effects should be defined based on local transportation needs.
The last step is to assess consequences, by including the impact of the
bridge failure within the wider transport network. Transport models such as
Ideally, boundary conditions should be provided by gauging stations;
however, no river gauges are present near the bridge of interest, as is
often the case in practical scenarios. This study adopted the 2D
hydrodynamic model
As input data,
Three-dimensional (3D) CFD software is capable of resolving fine details of
flood flow around bridges on a local scale such as splashes, eddies or flow
separation, which cannot be captured by depth-averaged methods (such as
For this study, the 3D CFD code
A structural analysis approach is functional for: (i) simulating relevant structural response mechanisms, which differ based on bridge type, and (ii) characterizing loading derived from the associated CFD model. FE analysis is commonly employed in structural engineering to simulate the response of bridges to natural hazards for the purpose of design and performance evaluation. Modern reinforced concrete and steel bridge structures are commonly formed of girders, cap beams and pier walls or columns which can be modeled as assemblages of line and spring elements; this approach is common in practice and can be implemented in a wide variety of structural analysis programs. To model nonlinear response, which is especially important when considering extreme loads associated with natural hazards, line elements may employ concentrated or distributed plasticity formulations that make use of nonlinear hinges or fiber sections. Rotational, shear and/or axial spring elements can be used to simulate the response of discrete components such as connections and bearings. Alternatively, continuum finite-element analysis can be employed for members if complex local response of components (e.g., local buckling and/or deformation) is of interest; however, this approach is significantly more computationally expensive. Other approaches, such as the discrete-element method, may be well suited for masonry bridges.
In this work, modeling with line and spring elements is performed, so this
approach will be discussed in greater detail. The considered bridge consists
of a girder superstructure supported on reinforced concrete piers.
Component response and demands based on the structural analysis can be used to assign a damage state for the bridge. Here, the structural damage is evaluated as slight, moderate, extensive, or complete damage based on the Federal Emergency Management Agency (FEMA) Hazus manual (FEMA, 2003). Each of these damage states is associated with level of functionality and repair effort. The qualitative description of damage states and average repair cost per square meter (square foot) is available in literature for hurricanes (Padgett et al., 2008) and earthquakes (Hazus manual – FEMA, 2003); Gehl and D'Ayala (2018) offered a qualitative damage scale of potential damage state and failure modes for the bridge components, which could be associated with functionality losses and remedial actions. Table 1 adapts such literature to riverine flooding using additional works and expert opinion: it lists four identified damage states (from slight to complete), and associated average repair cost and days of closure due to remedial works (Porter et al., 2011; Gardoni, 2018; Lam and Adey, 2016).
Bridge damage states (Gehl and D'Ayala, 2018) associated with average repair cost per square meter (Padgett et al., 2008; FEMA, 2003) and average days of closure due to repair (Porter et al., 2011; Gardoni, 2018; Lam and Adey, 2016).
The relationship between the CFD and structural analysis is critical to the
implementation of the proposed framework as outlined in the vulnerability
analysis block in Fig. 1. Both analyses must adequately represent the
bridge geometry, and the CFD output and structural analysis input loading
must be compatible. Here, the coupling approach between
the bridge superstructure (deck and girders) is modeled as a rigid, 2D cross
section with a unit length out of plane and subjected to steady-state flow
at different water depths and velocities in the steady-state reactions (output from the gravity loads and the steady-state reactions from
It is noted that the bridge superstructure is rigid in the computational fluid dynamics model (an important simplification to facilitate the analysis) but not in the finite-element model.
The impact of a bridge failure in terms of consequences (
Table 1 (Sect. 2.3) was functional to compute
The city of Carlisle is a flood-prone city (area: 1040 km
The case study is the city of Carlisle, UK:
As a proof of concept, the M6 highway bridge over the River Eden was considered. The bridge is comprised of a girder superstructure supported by hammerhead piers. A schematic model of this bridge is shown in Fig. 4 with approximate pier column (reinforced concrete), girder (concrete-encased steel) and bearing pad dimensions.
Approximate geometry of M6 bridge as modeled in
The pier columns are elliptically shaped and oriented to reduce hydraulic drag. The columns taper to a width of 4134 mm and depth of 1676 mm at the base. The girders are supported on fixed, laminated elastomeric bearing pads with dowels at the southern end of each span and free spherical bearings at the northern end. Salient bridge and flow input data are summarized in Table 2.
Input data of this study for the exemplary CFD analysis of the M6 bridge (Carlisle, UK).
The CFD simulation was initiated at given inundation heights and flow
velocity, as modeled by the
To reduce computation time and provide conservative results, a unit width
segment of the bridge superstructure located above the deepest point of the
Eden River beneath the M6 Bridge was analyzed in
Figure 6 shows converged
The horizontal forces presented in Fig. 6a show significant peaks at the bridge deck edges for components 1 and 20, due to the asymmetric pressure distributions that these components experienced when comparing their upstream and downstream faces than the interior components (which were shielded from higher velocity flows by the exterior components). Additionally, the exterior components included the traffic barriers, which significantly increased their surface area on which fluid pressure acted compared to the interior components.
At the upstream edge of the deck, component 1 absorbed the primary impact of the incoming flood flow at its peak velocity since it was on the upstream side of the deck, resulting in it carrying the largest positive horizontal forces. At the downstream edge of the deck, component 20 was initially subjected to positive horizontal forces due to the flow impacting its bottom flange and the lower portion of its web, but for flow heights greater than 14.0 m, its horizontal force decreased until it became negative by a flow height of 16.0 m. The gradual decrease in component 20's horizontal force may be attributed to differences in the vertical surface areas of and the flow velocities near its upstream and downstream sides that resulted in larger fluid pressures acting on the downstream faces than the upstream faces. The total vertical surface area of the downstream faces was larger than that of the upstream faces by an amount equivalent to the deck section, which provided additional area on which fluid pressure acted in the upstream direction. Complex flow characteristics that contributed to the velocity differences include: (1) the recirculatory flow patterns between the girders of components 19 and 20 and in the corner between the deck top and traffic barrier that led to reduced pressures on upstream faces of component 20; (2) the turbulent eddies that were shed off of the leading edge of component 20's girder bottom flange that redirected the flow toward the downstream faces of component 20; and (3) the flow over the top of the bridge deck rejoining the flow beneath the bridge at the downstream edge of the deck, which contributed to the formation of turbulent eddies in the bridge deck wake. Also, if any air was trapped between girders, a lesser water level between the girders would further decrease component 20's horizontal force.
The vertical forces shown in Fig. 6b are of similar magnitude to the horizontal force values in Fig. 6a. When the flow height was small prior to the flood overtopping the bridge (i.e., 12.5 to 13.0 m), the vertical forces on both halves of the bridge were roughly uniform except for the components nearest to the upstream edge of the bridge. In these cases, the vertical forces on components 1–3 decreased due to fluid pressure acting downward on the top of the girder bottom flanges. For flow heights of 13.5 to 16.0 m, the vertical forces on the upstream half of the bridge initially increased due to buoyancy forces increasing (due to increasing flow depth), but it started to decrease at a flow height of 14.0 m as the flood began to overtop the bridge. By a flow height of 17.0 m, the bridge was submerged enough that buoyancy caused the vertical forces on the upstream half of the bridge to increase again.
For the downstream half of the bridge, uplift due to buoyancy increased until a flow height of 15.0 m. At this point, the flow overtopped the superstructure crest at the midpoint of the bridge. This change in flow behavior caused the vertical forces on the downstream half of the bridge to decrease until the bridge was sufficiently submerged at a flow height of 18.0 m.
Overturning moment results acting about the
Converged simulated component loads for flow velocity
equals 3 m s
The
To analyze the bridge, gravity loads were first applied based on the
self-weight of the structural components; no live loads were considered. The
lateral forces, vertical forces, and roll moments determined from
Under the range of investigated loading, yielding or cracking was not
detected in the girders or columns, and the simulated hydraulic forces were
not large enough to overcome the self-weight of the structure, which would
result in uplift of the superstructure. However, the elastomeric bearing
pads sustained large shear demands near the design limits specified by
Sect. 14.7.5 of the AASHTO loss of frictional resistance between the bearing and girder based on the
ratio of shear and normal forces on the bearings, excessive shear deformation, and excessive shear strain due to combined axial load, rotation and shear
deformation.
The solid lines in Fig. 7 compare maximum shear forces, deformations, and
strains in any of the elastomeric bearings for each of the loading scenarios
investigated; Fig. 7a, c and e show these engineering demand
parameters versus flow velocity and Fig. 7b, d and f show
corresponding values with respect to flow height. The data suggest that peak
steady-state demands on any of the elastomeric bearings in the bridge occur
around a flow height 15 m, at which point the bridge has just reached full
inundation. In addition, below a flow height of 15 m, demands consistently
increase with velocity; such an increase in demand after full inundation is
not consistently observed, which suggests that the loading is primarily
associated with hydrodynamic effects that are a function of the effective
area of the cross section, and may also be affected by the fact that the
flow around the superstructure is less turbulent. To expand the data set,
linear extrapolation to flow velocities of up to 6 m s
The Commentary to the AASHTO
Figure 7c and d show peak shear strains due to loading perpendicular to
the short edge of the bearing pad (see Fig. 4b) due to combined axial load
(
In Eqs. (4)–(6) equations,
The shear deformation demand on the bearing
Maximum simulated demand on elastomeric bearings in M6 bridge,
including
The results of the loosely coupled CFD and structural analyses described in
Sect. 3.2 suggest a potential for either girder unseating due to loss of
frictional resistance or excessive shear deformation, which may lead to
debonding and delamination for this particular bridge. In addition, damage
associated with these limit states is most expected at a flow height of 15 m
and flow velocity of at least 5 m s
Routes for crossing the river Eden along the highway in baseline and disrupted conditions; private and heavy vehicles are rerouted on different journeys when the M6 bridge is disrupted.
The cost of the impact due to the M6 bridge disruption is computed in terms of direct and indirect consequences using Eq. (1); output and input values are specified in Table 5.
Output and input data for the impact cost calculation considering disruption due to an extreme flood event on the M6 bridge in Carlisle. Abbreviations: VTT – value of travel time; HGV – heavy good vehicle; VOC – vehicle operating cost; ADT – average daily traffic.
The values of Value of Travel Time (VTT) of HGVs (Heavy Good Vehicles,
working condition) and average private cars (unspecified conditions) can be
found in the UK Department for Transport (DfT) appraisal methods,
illustrated in the Cost Benefit Analysis (COBA) manual (DfT, 2009). Data
regarding the additional travel time for rerouting has been computing via
transport modeling (Sect. 2.5) and verified with Google Maps
(Fig. 8); for the UK, topological road network
links are freely available nationwide. Data regarding Average Daily Traffic
(ADT) flow are freely available (
The repair cost (
For the case study undertaken (Carlisle, UK; 1-in-a-500-years event), the total cost of the flood impact to the bridge is GBP 566 663.81, considering 7 d of bridge closure. The largest proportion (93.5 %) of this cost is due to the indirect cost of rerouting traffic (GBP 75 697.12 per day of closure, i.e., GBP 529 879.81); the 6.5 % of the total cost is due to direct damages only (GBP 36 784.00).
This study developed an integrated method that uses a multiphysics,
multilevel approach for assessing the effect of flooding hazards on a local
transportation network. For the city of Carlisle (UK), a 1-in-500-years
flooding event was simulated and the resulting hydrodynamic forces on the
highway bridge (M6) modeled. While simulated hydrodynamic forces and finite
element (FE) analysis did not show uplift failure, overtopping of the bridge
is shown to occur at inundation heights of 14 m and above. Given the
potential for flood-related disruption of traffic, overtopping should be
considered temporary network failure in its own right. The elastomeric
bearings supporting the bridge girders approached shear deformations near
design limits at a flow height of 15 m, and a potential loss of frictional
resistance between the elastomer and concrete is also observed. While these
limit states were not exceeded for flow velocities up to 3 m s
The produced outputs are conceptual results and thus approximate and indicative for multiple reasons. First, there is a dearth of UK-specific data regarding bridge repairs, duration time of repair, etc.; research or survey to solicit post-flood data are highly recommended to improve impact estimates. For example, a bridge could be partially closed during repairs (according to its damage state) and allow traffic in one direction. Second, the modeling approach presented herein used several intentional simplifications for demonstration purposes, including reducing the CFD domain, neglecting soil-foundation effects and scour modeling, and assumed rigidity of the structural system among others. In scenarios where these issues (or others) may be of more concern for a particular bridge, the fidelity of the modeling approach could be improved. Additionally, the failure states presented here may not translate broadly to the general bridge inventory, but additional or alternative structural/functional failure states could be applied. Third, the impact analysis was limited to private cars and HGVs for demonstration purposed; however, advanced transport appraisal could better capture users' choices and the engineering response of lifelines by including a wider range of vehicles categories and traffic scenarios. In terms of impact, the presence of floodwater on the roads is not simulated for limiting the focus of this work on riverine flooding and the bridge impact consequences; for properly analyzing the flooding impact to road networks, simulation of surface water flooding should be undertaken; this analysis would be a study on its own, and currently out of the scope of this piece of research. Flood impact on other parts of the network would limit the capacity of the alternative routes, causing additional delays to the traffic; thus, obtained results represent an underestimation of the overall systemic cost. Nevertheless, the proposed approach of impact analysis can give modelers and analysts a comprehensive method for assessing susceptibility to flooding and relative consequences at systemic level and the case study presented here represents an archetype for this approach.
Thus, the importance of this study consists in the proof of concept of a new holistic methodology which uses a multilevel approach to improve the fidelity of network failure predictions, taking advantage of seemingly disparate physical models. The computed hydrodynamic forces were applied directly into a traditional FE model to predict the global structural response to identify critical structural components and damage states. Notably, the hydrodynamic forces induced large demands on bearings that are often not considered in design. Because of the critical nature of bridges to a transportation network, the impact analysis revealed that indirect cost cover almost all the total cost due to flooding; this consideration is fundamental for infrastructure owners and managers when managing assets and budgets.
Next steps of this study will analyze the impact of the closure for a second bridge (e.g., the masonry arch Eden Bridge – data permitting), in isolation first and then in combination with the M6 bridge. Future work should investigate the impacts of other limit states which could result in total or partial bridge closure; a wider range of bridge types should be investigated too. Such analyses would benefit from 3D CFD and FE models to help refining demands on the structure and reducing uncertainty in the predicted bridge performance. Ultimately, this approach can be applied to any coastal or riverine structure where large-scale water inundation is expected.
This paper focused on riverine bridges prone to failures during flood events. This study established rigorous practices of Computational Fluid Dynamics (CFD) for modeling hydrodynamic forces on inundated bridges, and understanding the consequences of such impact on the surrounding network. The hydrodynamic forces were modeled as demand on the bridge structure and inputted into a vulnerability analysis of the structure; the performance evaluation showed a moderate damage state of the bridge which was used to approximate the overall direct and indirect consequences. For the city of Carlisle (UK) and a 1-in-500-years flooding, results showed that the flood impact to the M6 bridge (highway bridge) caused more than GBP 500 000 of damages of which 93.5 % indirect damages (rerouting and delays). The relevance of this work resides in the integrated method that couple practices of CFD with performance and network analysis, which allows to estimate the cost due to flooding impact to a bridge considering the surrounding transport system. Infrastructure owners and managers, as well as modelers and researchers, should build on this work to better predict local fluid pressures that may lead to bridge structural failure and related network-wide consequences.
Bridge data were shared from Highways England (now National Highways) via a data transfer agreement. Publicly available data sources used for this study include: OpenStreetMap (
MP and MRM conceived the research work; PB developed the flood hazard; AOW and DM developed the CFD analysis; ADS developed the structural; MP developed the network analysis; MRM supervised the work. All authors contributed to the writing and review of the paper.
The contact author has declared that neither they nor their co-authors have any competing interests.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors also gratefully acknowledge the following people for their support: Mark Pooley at Highways England; John L. Kelsall at Phoenix Architecture & Planning; and Mohammad Fereshtehpour at Ferdowsi University of Mashhad.
Maria Pregnolato has been supported by the Engineering and Physical Sciences Research Council (ESPRC) LWEC (Living With Environmental Change) Fellowship (grant nos. EP/R00742X/1 and 2). Paul Bates has been supported by a Royal Society Wolfson Research Merit award.
This paper was edited by Kai Schröter and reviewed by four anonymous referees.