Assessing flooding impact to riverine bridges: an integrated analysis

. 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, multi-physics 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 be-tween current guidance for design and assessment of bridges within the overall transport system


Introduction 24
Bridges are crucial elements of the transport network given their high construction costs and the lack of alternatives routes. 25 Man-made and natural events are a threat to bridge safety and network serviceability (Yang and Frangopol, 2020). Bridges 26 act as bottlenecks for surrounding roads, and thus any service disruption can knock-out communities' access and 27 connections, impair emergency planning and evacuation routes, as well as impact economies and businesses. 28 Some disruptive events are growing in frequency and severity. In particular, the impacts of flooding have been exacerbated 29 in recent years by urbanisation (e.g. increase of impermeable surfaces), inappropriate land use in flood-prone areas and 30 climate change. Rainfall events that lead to flooding are becoming more frequent and intense (Solomon et al., 2007), 31 triggering bridge incidents and failures all over the world (Cumbria, UK, 2009; Drake, Colorado, 2013; Texas, 2018; Greece, 32 Objectives of this study are to model hydrodynamic forces as demand on the bridge structure, to advance a reliability 48 analysis of the structure under the modelled loading and to assess the overall impact at systemic level. Implications of the 49 hydrodynamic impact on the performance and functionality of the surrounding transport network are discussed. This 50 research will help to fill the gap between current guidance for design and assessment of bridges within the overall transport 51 system. 52

Background 53
Transport networks are formed by multiple links (i.e. roads), and their performance relies on parameters, such as availability 54

129
The general limit-states philosophy considers that specifications should satisfy "specified limit states to achieve the 130 objectives of constructability, safety and serviceability" (AASHTO, 2017). In this work, the failure of a bridge is seen as 131 twofold: (i) structural (also strength limit state): when the bridge deck, piers or foundation reach the ultimate limit state or 132 permanent deformations; (ii) functional (also service limit state): when the bridge cannot perform its service as usual. A 133 structural failure directly leads to a functional failure, e.g. the bridge collapses; preventive closure could also take place 134 when bridge conditions are considered unsafe. Nevertheless, a bridge could be unserviceable but still structurally sound, e.g. 135 when floodwater or debris cover the deck. Hydraulic pressures (drag, lift and overturning moment) are assessed for 136 https://doi.org/10.5194/nhess-2020-375 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License. potentially dislodging the deck from piers, when submerged or partially sub-merged, and overtopping of the deck is 137 evaluated qualitatively from the CFD model. Though these limit states have significantly different long-term consequences, 138 both result in potential functional failure. The importance of long-term effects should be defined based on local 139 transportation needs. 140 The last step is to assess consequences, by including the impact of the bridge failure on the wider transport network. 141 Transport models such as ESRI™ ArcGIS Network Analyst (https://bit.ly/2GPMknl), SUMO (http://sumo.sourceforge.net/) or 142 MatSIM (https://www.matsim.org/) are suitable for computing routing and delays associated with a disrupted network link 143 (such as a closed bridge). Road network data are publicly available from sources such as Digimap® 144 (https://digimap.edina.ac.uk/), which provides Ordnance Survey road maps. These contain topographic information of roads 145 including name, location, length, capacity and type. After configuring the transportation network model with the collected 146 data, routing and accessibility can be investigated using network-based spatial analysis and transport appraisal techniques 147 (Arrighi et al., 2020;Pregnolato et al., 2016). This impact analysis links the structural damage of a bridge due to flooding 148 with the reduced performance of the local road network the bridge serves for, approximating the wider consequences. 149

Fluvial flooding simulation 150
Ideally, boundary conditions should be provided by gauging stations; however, no river gauges are present near the bridge of 151 interest. This study adopted the 2D hydrodynamic model LISFLOOD-FP, which allows to simulate flood depths and flow 152 velocity to set up CFD boundary conditions for a flood scenario and from available gauge data. As input data, LISFLOOD-FP requires a DEM (Digital Elevation Model) of the area, channel and boundary condition 160 information (e.g. channel friction, width and depth, hydrograph) and evaporation). Flow depth and velocity (for each cell) 161 are the output considered, since they represent the intensity measures of the hazard adopted by this study. The impact of 162 bridges on flow is not explicitly represented in this particular application. 163

Computational fluid dynamics (CFD) 164
3D computational fluid dynamics (CFD) software is capable of resolving fine details of flood flow around bridges on a local 165 scale such as splashes, eddies, or flow separation, which cannot be captured by depth-averaged methods (such as 166 LISFLOOD-LP). Also, bridges present a problem for depth-averaged tools since the computational mesh is two-dimensional 167 and cannot be discretized vertically, which does not allow for a gap underneath a bridge superstructure. To accurately model 168 such behaviors is crucial when estimating flow-induced force demands, which requires the use of a fine, three-dimensional 169 mesh. Additionally, using higher fidelity, three-dimensional models allow for localized loads to be measured on individual 170 faces of a structure, which may be used to determine whether or not individual components fail versus entire structures 171 . 172 For this study, the three-dimensional CFD code OpenFOAM was selected. Flood flows were modelled using the interFoam 173 solver, which is a two-phase solver that relies upon Volume of Fluid (VoF) method (Tryggvason et al., 2011) to track the 174 interface between water and air phases. The underlying governing equations that are implemented in interFoam are the method. More specifically, pressure-velocity coupling was achieved using the PIMPLE algorithm, which is a combination of 178 the Pressure-Implicit Split-Operator (PISO) and Semi-Implicit Method For Pressure-Linked Equations (SIMPLE). Since the 179 RANS system of equations does not constitute a well-posed system due to the so-called Reynolds stress tensor that arises 180 from the Reynolds-averaging process, a suitable turbulence model that introduces additional equations must be chosen to 181 close the system. For this study, the k-ω Shear Stress Transport (SST) model was used due to its ability to handle severely-182 separated flows near sharp corners better than other similar models such as the Standard, Renormalization Group (RNG), or 183 realizable k-ε models. OpenSees is seldom used to model structural response to fluids because of the complexity of the fluid loading and the 190 required coupling mechanism between fluid and solid solvers; thus, the present work is among the first of its kind using 191 OpenSees. Other recent research has sought to implement coupling between these multi-physics models. Stephens et al. 192 (2017) demonstrated how OpenSees can be "loosely coupled" (i.e. with no interaction between CFD and FE models) with 193 OpenFOAM to characterize structural response due to sequential earthquake and tsunami loading. Since the fluid load is applied to the structure at steady-state conditions, there are no transient effects on the structure and the 202 above limit states can be evaluated using standard practice. In this work, girders and columns are modeled as nonlinear fiber-203 based line elements capable of simulating concrete cracking and steel yielding. In addition, elastomeric bearing pads are 204 modeled as six-degree-of-freedom elastic springs with shear strain limit states evaluated based on design limits in the 205

American Association of State Highway and Transportation Officials (AASHTO) Load and Resistance Factor Design 206
(LRFD) Bridge Design Specifications (2017) and as recommended by Stanton et al. (2008). To predict girder unseating, the 207 ratio of shear and normal forces on the bearing pads is computed to evaluate frictional demand on the girder-bearing pad 208 interface; similarly, uplift is predicted directly from the normal force developed in the bearing. 209 According to the level of damage, the structural deficiency is evaluated as slight, moderate, extensive, or complete damage 210 (FEMA, 2003). These four damage states are assigned to discriminate damages which lead to similar loss of functionality 211 and equivalent repair efforts. The qualitative description of these states are adapted for flooding, after the previous work of 212

Impact assessment 217
The impact of a bridge failure in terms of consequences (C) includes direct consequences (Cdir) and indirect consequences 218 (Cind), which relate the surrounding transport network (Argyroudis et al., 2019). The total costs C is computed as (Eq. 3): 219 where Crepair is the cost associated with repair or replacement of the bridge, Cclean is the cost associated with the debris 220 removal (due to flooding), Cdetour is the additional vehicle operating due to the detour and Cdelay is the cost associated with trip 221 delays of normal traffic. Indirect costs may also include a fee for closing the bridge that the bridge owner has to pay to 222 transport operators/agencies (e.g. for railways, highways). 223 Table 1 lists four identified damage states (from slight to complete), and associated average repair cost and days of closure 224 due to remedial works; the table was developed on existing works and expert opinion. Gehl

256
All input data are summarized in Table 2. 257

316
Scour is also a concern for many riverine bridges, and an example evaluation based on the M6 bridge is shown here using 317 the HEC-18 (FHWA) and CIRIA scour equations. Figure 6 shows estimated scour depths at the bridge piers for worst-case 318 assumptions for soil (i.e. highly mobile soil). For both methods, there is little or no variation with flow depth due to the tall, 319 narrow geometry of the piers. Although the CIRIA scour equation is independent of flow velocity, when the flow velocity 320 exceeds the soil threshold velocity (case shown in Figure 6), its scour depth estimates resulted similar to the FHWA equation 321 for flow velocity between 2 and 3 m/s. Scour depths in this range (i.e. between 1 and 2 m) would likely result in significantly 322 altered foundational restraint and therefore require more sophisticated fluid-soil-structure interaction modelling. Explicit 323 scour modelling was out of the scope of this work, and it is noted that the M6 bridge foundation is cut into sandstone, so 324 significant scour would not be expected in this case study. 325 https://doi.org/10.5194/nhess-2020-375 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License.

327
Oveall, the damage state is estimated as moderate (refer to Table 1) because: (i) the bearings approach but do not exceed 328 limit states under the analysed velocities; (ii) scour is not significant; (iii) water level overtop the bridge deck. 329

Network impact and consequence assessment 330
A moderate damage state implies the bridge closure for 5-12 days (see Table 1). In the case of the M6 bridge, it closure 331 causes disruptions to all southbound and northbound users that are travelling along the M6 (Figure 7). Compared to the 332 baseline journey, results show that private cars are delayed by 12 minutes and have additional ca. 9 km due to rerouting. 333 HGVs cannot travel via the historic Eden Bridge (city centre) and are subjected to a longer rerouting, which leads to 19 334 minutes and ca. 20 km of delay and additional travelling respectively. 335

338
The cost of the impact due to the M6 bridge disruption is computed in terms of direct and indirect consequences using Eq. 3, 339 4; output and input values are specified in Table 3. 340 https://doi.org/10.5194/nhess-2020-375 Preprint. Discussion started: 23 December 2020 c Author(s) 2020. CC BY 4.0 License.  The repair cost (Crepair) was computed using Table 1  flooding is an extreme and rare event. The additional vehicle operating due to the detour per day (Cdetour) was calculated 355 using Eq. 4; the cost associated with trip delays (Cdelay) was calculated using Eq. 5. 356 For the case study undertaken (Carlisle, UK; 1-in-a-500-ys event), the total cost of the flood impact to the bridge is 357 £566,663.81, considering seven days of bridge closure. The largest proportion (93.5%) of this cost is due to the indirect cost 358 of rerouting traffic (£75,697.12 per day of closure, i.e. £529,879.81); the 6.5% of the total cost is due to direct damages only 359 (£36,784.00). Given the potential for flood-water disruption of traffic, this should be considered temporary network failure in its own right. 366 For this particular location, the elastomeric bearings supporting the bridge girders approached shear strains near design limits 367 for compression loading. While this limit was not exceeded for flow velocities up to 3 m/s, extrapolation to faster flow rates 368 suggests potential bearing delamination. This notwithstanding, the bridge would functionally fail at a flow height of between 369 13.5 and 14.0 m (i.e. was not fit for purpose) due to inundation of the deck even if the structure sustains no damage. The 370 impact analysis showed that indirect damages covered the 93.5% of the total cost of damages to the bridge, proving that 371 limiting the assessment to repairs and debris cleaning would greatly underestimate the impact of flooding to bridges. 372 The produced outputs are conceptual results, thus approximate and indicative, for a number of reasons. First, the UK is poor 373 of data regarding bridge repairs, duration time of repair, etc.; research or survey to solicit post-flood data are highly 374 recommended to improve impact estimates. For example, a bridge could be partially closed during repairs (according to its 375 damage state) and allow traffic in one direction. Second, the impact analysis was limited to private cars and HGVs for 376 demonstration purposed; however, advanced transport appraisal could better capture users' choices and the engineering 377 response of lifelines by including a wider range of vehicles categories and traffic scenarios. In terms of impact, the presence 378 of floodwater on the roads is not simulated for limiting the focus of this work on the bridge impact consequences. Flooded 379 roads are likely to cause additional delays to the traffic, so obtained results may underestimated the overall systemic cost. 380 Nevertheless, the proposed approach of impact analysis can give community leaders a robust method for assessing 381 susceptibility to flooding and relative consequences at systemic level. 382 The importance of this study consists in the proof of concept of a new holistic methodology using a combined CFD-FE 383 approach to improve the fidelity of network failure predictions. The adopted high-fidelity 3D analysis approach allowed to 384 include 3D effects (e.g. variations in the vertical dimension that include the clearances under a bridge) of the flow in the 385 vicinity of the bridge; this is relevant to planners and designers to better predict local fluid pressures that may lead to 386 structural failure. The computed hydrodynamic forces were applied directly into a traditional FE model to predict the global 387 structural response to identify critical structural components and damage states. Notably, the hydrodynamic forces induce 388 large demands on bearings that are not considered in design. Because of the critical nature of bridges to a transportation 389 network, the impact analysis revealed that indirect cost cover almost all the total cost due to flooding; this consideration is 390 fundamental for infrastructure owners and managers when managing assets and budgets. 391 Next steps of this study will analyze the impact of the closure for a portfolio of bridges, in isolation and any combination of 392 them. Future work should investigate the impacts of other limit states which could result in total or partial bridge closure; a 393 wider range of bridge types should be investigated too. Such analyses would benefit from 3D CFD and FE models to help 394 refining demands on the structure and reducing uncertainty in the predicted bridge reliability. Ultimately, this approach can 395 be applied to any coastal or riverine structure where large-scale water inundation is expected. 396

CONCLUSION 397
This study focused on riverine bridges prone to failures during flood events. This study established rigorous practices of 398 Computational Fluid Dynamics (CFD) for modelling hydrodynamic forces on inundated bridges, and understanding the 399 consequences of such impact on the surrounding network. The hydrodynamic forces were modelled as demand on the bridge 400 structure and inputted into a reliability analysis of the structure; the reliability analysis showed a moderate damage state of 401 the bridge which was used to approximate the overall direct and indirect consequences. For the City of Carlisle (UK) and a method that couple practices of CFD with reliability and network analysis, which allows to estimate the cost due to flooding 405 impact to a bridge considering the surrounding transport system. Infrastructure owners and managers, as well as modelers 406 and researchers, should build on this work to better predict local fluid pressures that may lead to bridge structural failure and 407 related network economic consequences. 408

DATA AVAILABILITY STATEMENT 409
All relevant and publicly available data will be shared via the DataBris repository of the University of Bristol if the paper 410 will be accepted for publication; data sources are clearly specified throughout the paper. 411