In the UK and many other countries, bridges are designed, inspected and maintained so as to withstand damage during events that are “reasonably foreseeable” over their intended service life (TSO, 2009). As with many infrastructure assets, there is a balance to be struck between the costs of reducing the risk of scour, likely damage and expectations of public safety. Design guides, monitoring, inspections and detailed modelling all help to establish the level of resources needed to achieve an appropriate balance, noting that the question of what is appropriate is ultimately a matter of judgement and policy.

Risk-based asset management concepts are widely applied to help to inform these judgements. A risk assessment involves considering the outcomes that could result from a combination of drivers, such as extreme weather events, and the performance of assets when subjected to those events (Johnson et al., 2015). Kirby et al. (2015) and Arneson et al. (2012) give comprehensive guidance for scour risk management, including references to numerous industry and government agency scour management protocols, including the UK Design Manual for Roads and Bridges (Highways England, 2016), US National Bridge Inspection Standards (FHWA, 2016), and US Forest Service scour assessment process (Kattell and Eriksson, 1998).

Scour risk management guidance typically deals with uncertainty through a combination of quantitative and qualitative analysis within a tiered structure, where relatively inexpensive, rapid high-level screening is used to prioritise further investment of resources for more detailed assessments at bridges where scour may be more likely to occur or where its consequences may be worst. Multiple factors are typically considered at each level within a tiered assessment, including physical characteristics of the bridge structures, the watercourses that they cross, their wider flow and sediment regimes and historical observations or recent changes relating to scour.

Most guidance involves some probabilistic analysis, which is usually introduced through the estimation of potential scour depth for an assumed “design flood”, specified in terms of an annual exceedance probability (AEP or equivalently a return period, which when expressed in units of years is numerically equal to 1/AEP). The design flood scour estimate can be compared with an estimated or known foundation depth to calculate a risk score. Recommended design flood conditions for UK railway and road bridge scour assessments are 1/200 AEP. In the USA the design condition is typically 1/100 AEP, but with a margin of safety that the structure should not fail in a 1/500 AEP event (Kirby et al., 2015). The probabilistic analysis is one part of the broader scour risk assessment protocols set out in industry guidance.

In this study the objective is to focus on uncertainties and their role in the probabilistic analysis of scour. In contrast to a design event analysis, we seek to explore how uncertainty about scour risk could be captured through a generic fragility model for bridge failure probability, reflecting a range of loading conditions, and including possible increases in vulnerability following exposure to flooding.

We ask explicitly how a general probabilistic failure model of this type could be formulated. The underlying motivation is an interest in generalising from a detailed understanding of scour at specific bridges in order to consider the risks aggregated over a network or portfolio of assets to support analysis either for a “generic bridge” or in a distributed, network-scale model of risk. The former case represents situations in which there may be inadequate information to carry out a detailed risk assessment. The latter is important in the context of strategic decisions about future planning, investment and operations for various infrastructure systems (e.g. Hall et al., 2016). This type of generalisation may not be appropriate for application to engineering decisions at individual assets, but is relevant as part of the higher-level risk screening that forms one tier in scour management approaches applied in practice.

In the first stage of the elicitation, and following some discussion of issues and available information, the experts in the group were asked to complete a series of paired comparisons structured around the following question: what are the most important factors that should be considered when assessing scour risk to bridges?. In each case the probabilistic inversion technique was used to calculate a group score and associated uncertainty.

The factors to be ranked were proposed by the project team and amended following an initial group discussion at the workshop (Table 2). The initial discussion raised concerns that the risk assessment priorities for piers and abutments may differ. The analysis was therefore carried out twice, treating scour at bridge piers and scour at abutments as separate issues. Results are shown in Table 3 for each of the potential assessment factors and in Fig. 2, from which the scores for scour risk to abutments and piers can be compared.

In the expert group's view, the most important factors when assessing vulnerability to scour (though with only weak discrimination between the factors) were as follows:

scour history, i.e. whether or not scour has been a problem in the past;

In the quantitative elicitation, the expert group was asked to estimate bridge failure probabilities, associated with scour caused by flooding under a range of conditions. In each case, the experts were asked for lower, central and upper values, corresponding to their judgements about the 5th, 50th and 95th percentiles of the range within which the true failure probability lies. The individual responses were pooled, with and without weighting, using the classical model (Cooke, 1991).

The failure probabilities were requested under various different conditions relating to flood return period, type of watercourse, type of bridge foundations, type of monitoring/inspection and maintenance policy in force. The definitions of generic types of watercourse, foundation and maintenance regime generated lengthy debate, primarily reflecting geographical differences in emphasis between the UK and North American experts. The following definitions were eventually adopted as a working compromise with the general assent of the group. The group agreed to have in mind physiographic and climatic conditions typical of the UK context, i.e. predominantly a humid temperate climate and a mixture of upland and lowland rivers, and to exclude more extreme (by UK standards) environments such as large continental-scale rivers, alpine rivers or rivers flowing in arid regions.

Two generic types of watercourse were specified: (1) unmanaged watercourse – no channel or upstream measures specifically designed to reduce scour risk (such as active vegetation management to reduce risk of debris or promote sediment stability) and (2) managed watercourse – actively managed to control or reduce scour risk (or for other primary purposes also serving to reduce scour risk).

Two generic foundation types were specified: (1) shallow foundations – a class including some historical masonry structures in the UK, particularly in lowland rivers, where foundations may be shallow pads or piles; (2) deep/bedrock – a class that would include modern deep piles and also historical structures build directly onto solid bedrock, for example some UK bridges over upland rivers.

Three potential asset management regimes were specified, one of which relates to current practice: (1) none – a counterfactual assumption (at least for UK, North America and regions with rigorous engineering codes) of no investment of resources in monitoring, inspection or maintenance of scour protection maintenance works; (2) routine – an investment of resources roughly similar to present-day good practice in the UK, USA, Canada or New Zealand; (3) premium – a counterfactual and significantly enhanced level of investment in inspection, monitoring and maintenance, featuring proactive, highly precautionary investments in maintenance and scour protection.

After much discussion, the workshop group settled on a definition of failure as damage caused by the flood event to the structure, foundations or approaches, probably due to scour that is sufficient to cause a threat to safety, disrupt service and require repair action, cause collapse or would cause collapse if left unattended. Note that this is a less restrictive definition of failure than one in which only a catastrophic collapse of the structure would be considered.

The findings of the workshop were well aligned with current industry guidance on scour assessment, highlighting the importance of foundation depth, scour depth (either measured or predicted from modelling), river typology (i.e. whether a steep channel or lowland watercourse) and foundation material (e.g. clay, rock or unknown type), which are all taken into consideration.

Additionally, the expert group identified other factors that are potentially important when assessing scour risk and that might be given greater emphasis in risk assessment guidance. These factors highlight the potential influence of changes to a watercourse at and around a bridge: dredging or sand/gravel extraction, removal of weirs near the bridge and influence of flood defences.

The group also highlighted the importance of inspection and assessment regimes (i.e. the level of resources committed to scour monitoring and assessment or changes in that commitment) in controlling the risk posed by bridge scour.

Risk factors relating to hydraulic conditions during flood events (flood flow magnitude, duration and flow velocities around the structure) and morphological regime (dredging) were consistently ranked by the group as important for determining scour vulnerability, although there was considerable ambiguity about the relative importance of many other factors, supporting the application of multi-factorial approaches to risk assessment.

In addition to variables expressed on physical scales, the return period (or exceedance probability) of a flood event was identified as a possible approach to define a generic loading condition for the development of bridge scour fragility functions. Fragility functions are not incorporated into routine scour management guidance. The data presented here could be used to give some context to functions of this type should there be future work to develop reliability analysis models based on fragility concepts.

Experts' estimates of failure probability appear to increase systematically as the assumed loading increases, i.e. with increasing flood event severity. Their failure probability estimates also differ, as might be expected, with respect to assumed differences in vulnerability relating to bridge foundation type, watercourse characteristics and the number of resources committed to inspection and maintenance.

Expert judgements about fragility for any given bridge during a relatively modest flood event of 25-year return period indicated failure probabilities of around 1 % or smaller, with uncertainties ranging from around 0.01% up to a few percent.

For an extreme flood with a 500-year return period, experts' central estimates suggest that a well-maintained bridge in a morphologically stable channel with modern or bedrock foundations has less than a 20 % chance of failing due to scour, rising to nearer 50 % for a poorly maintained bridge, or a bridge in an unstable channel on weak foundations; however uncertainty about these estimates is very wide, with experts judging that the true chance of failure could conceivably be less than 1 % or nearly 95 %.

Different assumptions about the foundations and watercourse type led to large variations in estimates of the uncertainty about failure probabilities under assumptions of no maintenance or routine (i.e. business-as-usual) maintenance, particularly for the more extreme flood events (100-year and 500-year return periods).

Subjectively large uncertainties were indicated in the group fragility estimates, reflecting a combination of differences in interpretation and, as revealed through calibration questions, differences between experts in their inherent assessments of uncertainties.

Increasing assumed levels of resourcing for monitoring and scour assessment translated into reductions in the experts' estimates of annual or flood-event failure probabilities, but these reductions were small relative to the experts' overall judgements of uncertainty, which were affected very little by those different assumptions. This finding appears to indicate some tension between qualitative statements, which stressed the importance of monitoring and assessment as a vital plank in scour risk management, “best” estimates of failure probabilities, which reflect these statements to some extent, and judgements of uncertainty, which appear to remain very conservative under the three assumed levels of resourcing that we tested.

The workshop format stimulated strong debate about the problem definition, and the different assumptions relevant in different countries, in particular relating to the age profile and physical scale of bridges and rivers when comparing, say, the UK with North America. As part of this process, the group had time during the workshop to debate and modify the elicitation questions, although the time available was necessarily constrained.

Some of the panel members commented during the workshop and in subsequent feedback that it would have been useful to define the context for each elicitation question in more detail. For instance, assumptions made about inspection and maintenance protocols may have led to differences in how individual experts interpreted those questions. If experts assumed that bridges are routinely inspected after any flood event, then the occurrence of a sequence of events might be viewed as less important than other vulnerability factors because any problems found in the inspection would be addressed in a manner commensurate with the nature and extent of the problem. Under these circumstances, past flooding experience may not have been regarded as an important primary indicator of increased vulnerability. Feedback after the workshop also indicated that there could be differences of interpretation relating to the physical and engineering context for a particular structure. For example, the questions did not specifically distinguish between channels with cohesive versus non-cohesive sediments or tidal versus non-tidal flows.

Following informal feedback and discussions with some of the group, we conclude that there would be merit in holding some form of initial consultation prior to an elicitation workshop of this type to establish whether an expert group feels the intended target questions are defined precisely enough and with sufficient supporting contextual information to be interpreted unambiguously. Bearing in mind that the aim of an elicitation is to gather evidence of experts' judgements about uncertainties, rather than their capacity to access information from the literature or other resources, there then would be a further challenge to provide sufficient but not excessive context material without inducing prejudgement influences, such as availability bias.

When individual experts' estimates of failure probabilities were combined according to their uncertainty judgement weights and validated against a set of control questions in the classical model analysis, the pooled uncertainty bounds became narrower relative to those produced by unweighted averaging, particularly for situations in which a bridge is inherently resilient (i.e. lower failure probability cases); this appears to reflect a less tentative, less precautionary judgement about uncertainty for the most resilient asset types when compared with a naïve, uncritical appraisal of all experts' responses.

There are intangible benefits to be gained from fostering communication and discussion between internationally diverse groups of experts from various different sectors, and the workshop, with its structured elicitation process, provided a constructive – and stimulating – forum for such exchanges.

In this study, the factors identified as important in assessments of scour risk are broadly consistent with industry guidance (summarised with a UK focus, but including reference to international good practice, by Kirby et al., 2015). Factors considered by the expert group that do not have obvious counterparts within industry guidance, for either screening or detailed assessments, related to sequences of events, expressed here in terms of the number of floods in recent years, construction date of a bridge, angle of the approach flow and removal of weirs in the vicinity of a bridge (although the latter is considered in various contexts by Kirby et al., 2015 and Arneson at al., 2012). The expert group ranked none of the above factors within the nine most important factors.

This study was informed by a framework for risk analysis predicated on a probabilistic treatment of hazards and fragility, extending further than the design event concept adopted within most industry guidance. In UK scour management guidance, a detailed scour assessment involves estimating potential scour depth for a design event and comparing this with foundation depth. Starting from the perspective that failure probability is conditional on loading, which could be defined in many different ways, the study has explored formulations for a more general, probabilistic failure function and the associated uncertainties about estimates of failure probabilities over a wide spectrum of load events. In assessing possible definitions of the load condition, the duration of a flood event and the possibility of sequences of events increasing the chance of a failure are regarded as important considerations, in addition to measures of peak hydraulic load. Flood return period, or exceedance probability, was considered as a standardised, probabilistic expression for the load condition in a fragility function.

Knowledge and data uncertainties are considered within industry guidance through a combination of qualitative and quantitative measures. Here, a more explicit quantification of expert judgements about uncertainty was possible through the application of structured elicitation methods. Pooled judgements about uncertainty in scour failure probabilities are more tightly constrained by taking account of the empirical calibration of individual experts' accuracy in assessing uncertainties, although this effect diminished as more extreme, and therefore rarer, flood events were considered.

The experts' pooled estimates of failure probability reduced when considering scenarios involving increasing levels of resources invested in scour assessment and maintenance. This appears to be consistent with the widespread use in practice of tiered risk management approaches involving generalised, high-level screening followed by selective detailed assessments to enhance confidence in the mitigation of scour risk on a prioritised basis.