A Process-based Flow Model for Assessing Direct and Indirect Damages to Flooded Roads in Great Britain

Reliable road infrastructure is vital for daily commuters and economic activities in the UK, yet it faces growing flood risks due to climate change. Effective flood risk management requires an integrated approach that includes pre-disaster traffic flow modelling, direct damage estimation, disruption and recovery analysis to quantify systemic failure impacts. Indirect costs from traffic disruptions are frequently oversimplified, often estimated as multipliers of direct damages. While traffic flow rerouting models are applied in current research, they often overlook critical factors, such as traffic flow constraints and road capacity limitations, instead assigning origin-destination flows to least-cost paths without accounting for congestion. Moreover, the recovery process, which is critical for understanding how restored road and bridge capacities reduced isolated flows and indirect damages, is rarely modelled.

To address these gaps, we developed an open-source modelling framework for Great Britain that integrates a process-based flow model with a stress-testing model to assess road flood damages. Our framework starts with simulating passenger-to-work flows at a national scale by modelling the lifeline connections between physical road networks and demographic factors (e.g., population and economic activities). The flow model employs an iterative approach to simulated congested equilibrium flow assignments, dynamically accounting for road capacities and flow speeds until all traffic is accommodated without causing overflow.

We stress-tested the road networks using 18 historical UK flood events and one synthetic flood event. To model flood-induced disruptions, we developed a speed-flood depth function that restricts maximum flow speeds on flooded roads based on floodwater depth. We applied 30cm and 60cm separately in disruption analysis as threshold for road closure for uncertainty analysis. In each scenario, flood impacts on traffic flows were evaluated by comparing edge flows under floods with those under base flow condition. Direct damages were calculated using generalised damage curves (i.e., function to estimate damage fractions based on floodwater depth), and cost functions (i.e., function to estimate unite asset cost, million £/length or area) for different road types (e.g., bridges, tunnels, ordinary roads) and flood types (e.g., surface floods, river floods). Indirect damages were quantified by calculating rerouting costs due to road closures, including additional fuel costs, tolls, and time-equivalent costs.

We introduced a novel recovery analysis to dynamically evaluate indirect damages by designing various road capacity recovery rates, accounting for road types and damage levels. The recovery process identifies disrupted flows resulting from missing routes or reduced speeds, and reallocates these flows as road capacities are restored on a daily basis. The analysis captures the evolving number of isolated flows, rerouting costs and asset repair costs, offering a more realistic representation of dynamic indirect damages.

Overall, this research advances large-scale flow modelling by integrating capacity constraints, disruption dynamics, and recover processes. It provides actionable insights to enhance the resilience of the UK’s road infrastructure. The framework can be adapted to contexts beyond UK, different spatial scales, multi-modal transport systems, and multi-hazard scenarios, supporting more comprehensive risk assessments and decision-making.