Road-network terminal reliability analysis needs link reliabilities as inputs, yet for natural-disaster environments few methods exist to estimate them. Fujita and Wakabayashi (2021) proposed a framework in which a slope-failure product model, a Gaussian conversion of deterministic flood-hazard-map depths, and a fuzzy-set pilot study on the Hida-region highway network (Japan) supply link reliabilities, and they explicitly identified five unresolved issues: heuristic (non-objective) assignment of fuzzy numbers and membership functions; uncontrolled vagueness expansion under repeated fuzzy arithmetic; breakdown of the independence assumption in the slope-failure product model under correlated events such as major earthquakes; neglect of link-length weighting and of spatial clustering of failure points; and uncalibrated model choices when converting deterministic hazard maps into probability distributions. The problem of a defensible, standardized method for estimating road-link reliability under natural disasters, combining aleatory disaster correlation with epistemic uncertainty from sparse records, remains open.

Background

In transportation network reliability analysis, the terminal (node-to-node) reliability of a road network is computed from a predefined set of link reliabilities, each link reliability being the probability that the link provides a required service level over a given period; this two-phase structure goes back to the terminal-reliability framework of Wakabayashi, Iida and colleagues (e.g., Iida, Wakabayashi and Fukushima 1989). The first phase (network-level computation) is well developed; the second phase — actually estimating the link reliabilities — is the bottleneck under natural disasters, because historical loss data per link are sparse and each hazard behaves differently. Fujita and Wakabayashi (2021) addressed this second phase. For slope failures on mountainous links, they modeled a link containing nn discrete slope locations as a series system: with RaiR^{a_i} the probability that location ii fails and blocks the link, the link reliability is ra=∏i=1n(1−Rai)r_a=\prod_{i=1}^{n}(1-R^{a_i}), derived under the explicit assumption that the nn local failure events are statistically independent. For inland flooding, they took the deterministic depth μ\mu reported in a government inland-water hazard map (a map of expected inundation areas and example depths) as the mean of a Gaussian flood-depth variable D∼N(μ,σ2)D\sim\mathcal{N}(\mu,\sigma^2) and defined link reliability through the probability that DD stays below a vehicle-passability threshold DcD_c (e.g., 30 cm, from engineering guidance on vehicle running conditions). For earthquakes, where link-level records are too sparse for frequentist estimation, they applied fuzzy set theory: a fuzzy number is a quantity whose possible values carry graded membership in [0,1] rather than a single probability, so that epistemic uncertainty from sparse evidence can be carried explicitly; arithmetic on such quantities is performed via the extension principle with α-level decomposition (Nguyen 1978), where an α-cut is the set of values with membership at least α. In their pilot on a 9-node, 12-link Hida-region network, each link's fuzzy reliability was assigned by a heuristic rule on the α=0.9 level (A0.9′=0.03A'_{0.9}=0.03 for links with recorded past failures, A0.9′=0.09A'_{0.9}=0.09 otherwise), and fuzzy link reliabilities were propagated through the terminal-reliability functional, with the resulting membership functions widening as the number of combined fuzzy inputs grows (vagueness expansion). The authors state that the independence assumption of the product model is invalid under subordinate or large-scale correlated events such as major earthquakes, and that these methods cannot be standardized or used for defensible large-scale infrastructure prioritization until the issues below are resolved. Adjacent literatures treat pieces of the problem but not this objective: correlated component failures in seismic highway networks are modeled for bridges through spatially correlated ground-motion intensity measures (scalars such as peak ground acceleration that summarize earthquake shaking at a site) and fragility curves (functions giving a component's probability of failure as a function of shaking intensity) (Ghosh et al. 2014; Rokneddin et al. 2014), and systemic seismic risk frameworks for road networks exist (Argyroudis et al. 2015); empirical link reliabilities have been estimated from historical disruption records for precipitation (Qiao et al. 2023) and floods (Dong et al. 2023); and earthquake-induced-landslide resilience of regional road networks has been proposed at framework level (Xiong et al. 2023; Louagie et al. 2025). None of these derives fuzzy parameters objectively from sparse records, controls vagueness propagation, or integrates probabilistic scenario earthquakes with correlated slope failures into a link-reliability estimator.

Problem Statement

Develop a defensible, standardized method for estimating road-link reliabilities under natural-disaster environments — the input layer required by terminal (node-to-node) reliability analysis for large-scale road-infrastructure prioritization — that resolves the five linked deficiencies identified by Fujita and Wakabayashi (2021) in their framework. The method must: (1) derive the fuzzy numbers and membership functions from engineering evidence by an objective, reproducible procedure rather than heuristic expert-linguistic choice (replacing the pilot's rule of A0.9′=0.03A'_{0.9}=0.03 for links with prior failures and A0.9′=0.09A'_{0.9}=0.09 otherwise), so that different practitioners reach the same inputs from the same records; (2) control or quantify the vagueness expansion (widening of membership functions) caused by repeated fuzzy arithmetic through the network terminal-reliability functional, so that propagated epistemic uncertainty remains interpretable; (3) replace the independence assumption of the slope-failure product model ra=∏i=1n(1−Rai)r_a=\prod_{i=1}^{n}(1-R^{a_i}) with an explicit treatment of dependence among slope failures triggered by subordinate or large-scale correlated events such as major earthquakes, or otherwise integrate probabilistic scenario earthquakes into the fuzzy framework; (4) incorporate link geometry — length weighting of failure probabilities, the spatial distribution and clustering of multiple failure points along a link, and heterogeneous local vulnerability — instead of treating failure locations as uniformly distributed and equally consequential; and (5) convert deterministic hazard-map information (e.g., single-depth inland-water maps) into proper probability distributions whose model choices (the standard deviation σ\sigma, the distributional form) are calibrated objectively from local hydrologic or other physical data. These five requirements are facets of one scientific objective: an estimator that simultaneously represents aleatory disaster randomness, including correlation across a triggering event, and epistemic uncertainty from sparse historical records, and that is validated to the point of being usable for defensible, reproducible infrastructure prioritization. The scientific objective is a single estimator that is fully determined by its stated inputs and that jointly resolves all five points above.

References

  1. Fujita, Mamoru; Wakabayashi, Hiroshi (2021). "Estimation of Link Reliability under Natural Disaster Environment." Transportation Research Procedia 52, 597-604. DOI 10.1016/j.trpro.2021.01.071, https://doi.org/10.1016/j.trpro.2021.01.071
  2. Iida, Yasunori; Wakabayashi, Hiroshi; Fukushima, Hiroshi (1989). "A Comparative Study of Approximation Methods of Terminal Reliability Analysis for Road Networks." Doboku Gakkai Ronbunshu 1989(407), 107-116. DOI 10.2208/jscej.1989.407_107, https://doi.org/10.2208/jscej.1989.407_107
  3. Nguyen, Hung T. (1978). "A note on the extension principle for fuzzy sets." Journal of Mathematical Analysis and Applications 64(2), 369-380. DOI 10.1016/0022-247X(78)90045-8, https://doi.org/10.1016/0022-247X(78)90045-8
  4. Ghosh, Jayadipta; Rokneddin, Keivan; Padgett, Jamie E.; Duenas-Osorio, Leonardo (2014). "Seismic Reliability Assessment of Aging Highway Bridge Networks with Field Instrumentation Data and Correlated Failures, I: Methodology." Earthquake Spectra 30(2), 795-817. DOI 10.1193/040512eqs155m, https://doi.org/10.1193/040512eqs155m
  5. Rokneddin, Keivan; Ghosh, Jayadipta; Duenas-Osorio, Leonardo; Padgett, Jamie E. (2014). "Seismic Reliability Assessment of Aging Highway Bridge Networks with Field Instrumentation Data and Correlated Failures, II: Application." Earthquake Spectra 30(2), 819-843. DOI 10.1193/040612eqs160m, https://doi.org/10.1193/040612eqs160m
  6. Argyroudis, Sotirios; Selva, Jacopo; Gehl, Pierre; Pitilakis, Kyriazis (2015). "Systemic Seismic Risk Assessment of Road Networks Considering Interactions with the Built Environment." Computer-Aided Civil and Infrastructure Engineering 30(7), 524-540. DOI 10.1111/mice.12136, https://doi.org/10.1111/mice.12136
  7. Koks, E. E.; Rozenberg, J.; Zorn, C.; Tariverdi, M.; Vousdoukas, M.; Fraser, S. A.; Hall, J. W.; Hallegatte, S. (2019). "A global multi-hazard risk analysis of road and railway infrastructure assets." Nature Communications 10, 2677. DOI 10.1038/s41467-019-10442-3, https://doi.org/10.1038/s41467-019-10442-3
  8. Qiao, Ningning; Liu, Kai; Wang, Ming; Ni, Xiaoyong; Yang, Yongsheng (2023). "Reliability Assessment of Road Network to Precipitation Based on Historical Recorded Disruptions." Natural Hazards Review 24(4), 05023010. DOI 10.1061/nhrefo.nheng-1733, https://doi.org/10.1061/nhrefo.nheng-1733
  9. Dong, Shangjia; Gao, Xinyu; Mostafavi, Ali; Gao, Jianxi; Gangwal, Utkarsh (2023). "Characterizing resilience of flood-disrupted dynamic transportation network through the lens of link reliability and stability." Reliability Engineering & System Safety 232, 109071. DOI 10.1016/j.ress.2022.109071, https://doi.org/10.1016/j.ress.2022.109071
  10. Xiong, Min; Hu, Hongqiang; Huang, Yu (2023). "From slope seismic resilience to regional road network resilience: an integrated framework for evaluating the seismic resilience of mountainous road networks." Disaster Prevention and Resilience 2(4). DOI 10.20517/dpr.2023.27, https://doi.org/10.20517/dpr.2023.27
  11. Hosseini, Yaser; Karami Mohammadi, Reza; Yang, Tony Y. (2024). "A comprehensive approach in post-earthquake blockage prediction of urban road network and emergency resilience optimization." Reliability Engineering & System Safety 244, 109887. DOI 10.1016/j.ress.2023.109887, https://doi.org/10.1016/j.ress.2023.109887
  12. Li, Yaqin; Yu, Jia; Zheng, Yuanfan; Shen, Quanyi; Zhou, Yang; Wu, Hangxing; Zhang, Min; Wen, Jiahong (2025). "Allocation and Distribution Path Planning of Emergency Food Materials Under Flood Scenarios: A Case Study in Fengxian District, Shanghai, China." International Journal of Disaster Risk Science 16(6), 1011-1028. DOI 10.1007/s13753-025-00678-7, https://doi.org/10.1007/s13753-025-00678-7
  13. Louagie, Maxim; Aloschi, Fabrizio; Civera, Marco; Miano, Andrea; Chiaia, Bernardino; Prota, Andrea (2025). "A Framework for Assessing the Earthquake-Induced Landslide Resilience of a Road Network in Turin, Italy." Proceedings of the 10th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2025), 1918-1928. DOI 10.7712/120125.12540.24761, https://doi.org/10.7712/120125.12540.24761