Modest flooding can trigger catastrophic road network collapse due to compound failure

Infrastructure networks are essential for societal functioning but are increasingly stressed by population growth and flood disruptions. Population increases drive demand and congestion that degrade road network service quality, while global flood exposure is projected to triple by 2050 due to development in flood-prone areas. Transportation networks are particularly vulnerable to flooding, which can trigger abrupt regime shifts in performance, with climate change and sea-level rise further exacerbating vulnerability. Although transportation robustness has received wide attention, most studies model only a single failure type, typically modifying topology or functional attributes in isolation. Real flooding causes simultaneous structural failures (road closures due to inundation), functional failures (reduced travel speeds and congestion), and topological failures (intact links becoming isolated from the giant component). This compound effect can amplify individual failures and lead to more catastrophic connectivity loss than singular failures. The study aims to elucidate transportation network robustness under compound flooding-induced failures by employing percolation modeling to capture phase transitions in connectivity and quantify how structural, functional, and topological failures interact during Hurricane Harvey in Harris County, Texas.

Prior work has demonstrated transportation networks’ vulnerability to urban flooding and the increasing magnitude of flood disruptions under climate change. Research on transportation network robustness and resilience often focuses on single-mode failures, altering either topology or flow attributes, and typically overlooks compound, simultaneous disruptions. Studies using network percolation have shown phase transitions in connectivity under link removals, but applications that integrate structural inundation, congestion-induced functional degradation, and resulting topological isolation remain limited. The paper positions itself to bridge this gap by integrating network science and high-resolution empirical traffic data to model compound failures during a major flood event.

Study area and data: Harris County, Texas, during Hurricane Harvey (August–October 2017). High-resolution travel speed data (15-minute intervals) were obtained for major roads in August (pre-Harvey), September (during and immediate post-Harvey), and October (post-Harvey). The transportation network comprises 19,712 links and 15,390 nodes (noted also as 1,712 links in the narrative; baseline construction references 19,712). Flooding information is used to identify inundated (closed) roads over time. Definitions of failures: (i) Structural failure (SF): road closure due to flood inundation; (ii) Functional failure (FF): road segments whose link quality falls below a threshold; (iii) Topological failure (TF): intact and functional links that become disconnected from the giant component (GC) due to SF and FF. Link quality: For road i at time t, quality r_i(t) = v_i(t)/v_ref,i, where v_i(t) is observed travel speed and v_ref,i is a reference speed for that link. Links with r_i below a threshold q_r are considered low quality (congested) and removed for robustness evaluation. Network construction per time t: (1) Remove inundated links (SF). (2) Remove links with r_i ≤ q_r (FF). The remaining links form the residual network; GC size indicates connectivity. Percolation modeling: At each time snapshot, links are ranked by quality r_i. Percolation proceeds by removing links in ascending order of r_i and tracking GC and second-largest component (SC). The percolation critical threshold q_c is identified at the peak of SC and indicates the quality threshold at which the GC fragments. Because congestion dynamics vary temporally, the fraction of links removed at a given q_r can differ by time; thus, robustness is also analyzed as a function of the fraction removed. Fraction-based analysis: Define α as the fraction of lowest-quality links removed at a time t. GC behavior is examined as a function of α, revealing how much removal is needed to cause large connectivity loss. Define β as the fraction of links with quality below q_c. Combining α (quantity) and β (quality) provides a comprehensive robustness assessment. Temporal stability metrics: Daily averages and moving averages of q_c and a derived threshold λ_c are tracked across pre-, during-, and post-Harvey phases. Statistical testing: Two-sample t-tests compare q_c distributions before vs. during Harvey to assess significance of robustness degradation. Scenario engineering and AUC robustness: Percolation-based robustness curves (GC size vs. removal fraction) are summarized by area under the curve (AUC) as an aggregate robustness measure. Flooding scenarios manipulate the order of link removals: (a) empirical flooding (inundated links removed first, then low-quality links), (b) no-flooding (f = 0, remove by quality only), and (c) random-flooding (f = 1, inundated-equivalent fraction removed at random first, then by quality). Differences in AUC between empirical and synthetic scenarios quantify flood impact over selected periods (August 25–September 8). Spatial analysis: Failures (SF, FF, TF) and GC are mapped at selected times (e.g., Mondays at 16:00) to illustrate spatial distribution and compounding effects. Robustness indicators reported include maximum SF, FF, TF, minimum GC, percolation thresholds q_c before/during/after, and α required for fragmentation across phases.

- Compound effects: Even modest flooding can trigger large connectivity losses when combined with congestion. As little as 2.2% flood-induced compound failure is associated with up to a 17.7% reduction in the GC size. - Extent of failures during Harvey: Maximum inundation (SF) reached 2.6% of roads; FF rose to 46.3%; TF reached 30.2%. The GC dropped sharply to a minimum of 21.6% during Harvey. At the start of post-Harvey, GC temporarily increased to 39.2% while FF and TF dropped to 37.2% and 23.3%, respectively, reflecting reduced demand and ongoing safety concerns. - Percolation thresholds: During Harvey, extensive link quality deterioration produced catastrophic fragmentation when removing links below q_r = 0.69. By comparison, q_c values were higher before (q_c ≈ 0.81) and after (q_c ≈ 0.87) Harvey, indicating better robustness in those periods. - Fractional removals: Before Harvey, approximately α = 0.72 of links needed removal to cause large connectivity loss; during Harvey, only α = 0.48 sufficed, demonstrating increased fragility. - Statistical significance: Independent two-sample t-tests on q_c before vs. during Harvey indicate significant drops (reported p-values 0.001 and 0.004). - Scenario comparisons: Synthetic no-flooding scenarios exhibited mixed robustness relative to empirical flooding depending on period, while random flooding generally yielded worse robustness than empirical flooding. This suggests empirical flooding patterns behaved between localized attacks and random failures, influencing the timing of GC disintegration. - Spatial compounding: When Harvey landed, SF amplified FF and TF, causing large-scale fragmentation and minimal GC (e.g., under q = 0.8, FF alone removed 51.3% of links with GC ≈ 12.9%; during Harvey, SF ≈ 22.9% with FF ≈ 63.7% and TF ≈ 32.6%, leaving GC ≈ 1.5%). - Persistence: Post-Harvey thresholds increased but did not immediately return to baseline, consistent with lingering impairments (debris, closures) and altered mobility patterns.

The findings show that urban flooding not only directly removes capacity via inundation (SF) but also indirectly reduces link quality (FF) and isolates intact links (TF), leading to compounding impacts and abrupt losses in network connectivity. Small increases in SF at low levels disproportionately increase FF and TF, accelerating GC collapse. The degradation of percolation thresholds during Harvey and the reduced fraction of links needed for fragmentation underscore the system’s fragility under compound stresses. The impacts persist beyond immediate flooding due to debris, partial closures, and changed travel behavior, delaying reversion to baseline robustness. Scenario analyses reveal that random flooding is particularly damaging, while empirical flooding patterns suggest a mix of localized and random characteristics. These insights emphasize the necessity of accounting for compound failures, not just structural inundation, in risk assessments and planning. Interventions that manage congestion (e.g., public transit, demand management, detours with capacity) can mitigate the amplification pathway from SF to FF and TF, enhancing resilience during flood events.

This study develops and applies a network-theory-based percolation framework to quantify compound structural, functional, and topological failures in a real-world transportation network during Hurricane Harvey. Results demonstrate that modest flooding can precipitate catastrophic connectivity loss when combined with congestion; for example, about 2.2% flood-induced compound failure can cause up to a 17.7% decrease in GC size. Critical robustness thresholds deteriorated during Harvey and only partially recovered afterward, indicating lasting impacts. Comparisons with synthetic no-flooding and random-flooding scenarios show the flood-inundated traffic scenario is less robust than traffic-only, with random flooding being the most damaging. The work highlights the meta-stability of transportation networks under compound flood scenarios and provides a holistic approach for assessing mobility and accessibility during floods. Future work should extend the framework to other cities, infrastructure systems, and hazard types, integrating richer meteorological and mobility datasets and considering additional compound disruptions (e.g., evacuations, special events).

- Case specificity: Analysis is limited to Harris County during Hurricane Harvey; results may not generalize to regions with different geomorphologies, infrastructures, or hazard regimes. - Data scope: Traffic data cover major roads at 15-minute resolution; local streets and multimodal interactions may be underrepresented. Data are not publicly available, constraining reproducibility. - Metric and threshold choices: Link quality based on speed ratios and selected thresholds (q_r, q_c) influence failure classification and percolation outcomes; alternative formulations (e.g., capacity, flow, reliability) could yield different sensitivities. - Flood representation: Structural failures are inferred from inundation/closures; spatial-temporal precision of flood extent and duration affects SF identification. - Scenario simplifications: Synthetic flooding scenarios manipulate removal sequences but cannot capture all behavioral adaptations (route choice, demand shifts) or network control actions (contraflow, incident management). - Single-network focus: Interdependencies with other lifelines (power, telecom, drainage) are not explicitly modeled, potentially underestimating cascading effects.