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Sustainable and Resilient Infrastructure
可持续与韧性基础设施 IF 2.7 Volume 8, 2023 - Issue sup1: Adaptive Pathways for Resilient Infrastructure
第 8 卷，2023 年 - 增刊 1：韧性基础设施的自适应路径

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Critical facility accessibility and road criticality assessment considering flood-induced partial failure
考虑洪水引发部分失效的关键设施可达性与道路关键性评估

Utkarsh Gangwala Department of Civil and Environmental Engineering, University of Delaware, Newark, DE, USAView further author information

A. R. Sidersb Biden School of Public Policy and Administration, Department of Geography Spatial Sci Ences, University of Delaware, Newark, DE, USA
特拉华大学拜登公共政策与管理学院，地理空间科学系，纽瓦克，特拉华州，美国View further author information
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Jennifer Horneyc College of Health Sciences, University of Delaware, Newark, DE, USAView further author information

Holly A. Michaeld Departments of Earth Sciences & Civil and Environmental Engineering, University of Delaware, Newark, DE, USA
地球科学与土木及环境工程系，特拉华大学，纽瓦克，特拉华州，美国View further author information
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Shangjia Donga Department of Civil and Environmental Engineering, University of Delaware, Newark, DE, USACorrespondencesjdong@udel.edu

https://orcid.org/0000-0003-4280-0500 View further author information

乌特卡什·冈瓦尔，A. R. 西德尔斯，詹妮弗·霍尼，霍莉·A·迈克尔与董尚佳

Pages 337-355 | Received 26 Sep 2022, Accepted 12 Nov 2022, Published online: 25 Nov 2022
第 337-355 页 | 收稿日期：2022 年 9 月 26 日，接受日期：2022 年 11 月 12 日，在线发布日期：2022 年 11 月 25 日

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https://doi.org/10.1080/23789689.2022.2149184
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1. Introduction 1. 引言
2. Literature review 2. 文献综述
3. Methodology 3. 方法论
4. Results 4. 结果
5. Discussions 5. 讨论
6. Conclusion 6. 结论
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ABSTRACT 摘要

This paper examines communities’ accessibility to critical facilities such as hospitals, emergency medical services, and emergency shelters when facing flooding. We use travel speed reduction to account for flood-induced partial road failure. A modified betweenness centrality metric is also introduced to calculate the criticality of roads for connecting communities to critical facilities. The proposed model and metric are applied to the Delaware road network under 100-year floods. This model highlights the severe critical facility access loss risk due to flood isolation of facilities. The mapped post-flooding accessibility suggests a significant travel time increase to critical facilities and reveals disparities among communities, especially for vulnerable groups such as long-term care facility residents. We also identified critical roads that are vital for post-flooding access to critical facilities. The results of this research can help inform targeted infrastructure investment decisions and hazard mitigation strategies that contribute to equitable community resilience enhancement.
本文探讨了社区在面临洪水时对医院、紧急医疗服务和应急避难所等关键设施的可及性。我们采用旅行速度降低来考虑洪水引发的局部道路失效情况。同时，引入一种改进的介数中心性指标，用于计算连接社区与关键设施的道路的关键性。所提出的模型和指标应用于特拉华州道路网络在百年一遇洪水情境下的分析。该模型凸显了因洪水隔离设施而导致的严重关键设施访问损失风险。洪水后的可达性地图显示，前往关键设施的旅行时间显著增加，并揭示了社区间的差异，尤其是对长期护理机构居民等弱势群体的影响。此外，我们还识别了对于洪水后访问关键设施至关重要的关键道路。本研究结果有助于指导有针对性的基础设施投资决策和灾害缓解策略，进而促进社区公平韧性提升。

KEYWORDS: 关键词：

Critical facility accessibility
关键设施可达性
Flood-disrupted transportation network
洪水破坏的交通网络
Critical road identification
关键道路识别

This article is part of the following collections:
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Adaptive Pathways for Resilient Infrastructure
适应性路径：构建韧性基础设施

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1. Introduction 1. 引言

Critical facilities, such as emergency medical service (EMS) stations, hospitals, and emergency shelters, must remain functional and accessible to protect life-saving and life-sustaining activities during and after a disaster (FEMA, Citation2022). Access to these critical facilities is key to the health and well-being of the communities, preventing morbidity and mortality associated with disasters (Esmalian et al., Citation2021a; Twumasi-Boakye & Sobanjo, Citation2021). The road network plays a pivotal role in connecting people to these critical services (Boakye et al., Citation2022; Logan & Guikema, Citation2020). However, road networks often provide unequal levels of accessibility for different communities (Gangwal & Dong, Citation2022). Additionally, critical facilities’ accessibility is constantly challenged by hazard disruptions (Bonilla-Félix & Suárez-Rivera, Citation2019; Esparza et al., Citation2021; Kaiser et al., Citation2021; K. Liu et al., Citation2022a). Disruptions either cut off access to critical facilities or increase travel time. This exacerbates disparities among communities.
关键设施，如急救医疗服务（EMS）站点、医院及应急避难所，在灾害期间及之后必须保持功能性和可达性，以保障生命救援和维持生命的活动（FEMA，2022）。这些关键设施的可达性对社区的健康与福祉至关重要，能预防与灾害相关的疾病和死亡（Esmalian 等人，2021a；Twumasi-Boakye 与 Sobanjo，2021）。道路网络在连接人们与这些关键服务中扮演着关键角色（Boakye 等人，2022；Logan 与 Guikema，2020）。然而，道路网络往往为不同社区提供不平等的可达性水平（Gangwal 与 Dong，2022）。此外，关键设施的可达性持续受到灾害干扰的挑战（Bonilla-Félix 与 Suárez-Rivera，2019；Esparza 等人，2021；Kaiser 等人，2021；K. Liu 等人，2022a）。这些干扰要么切断了对关键设施的访问，要么增加了行程时间，从而加剧了社区间的差异。

Flooding is the most common and costly source of disruption (CRED, Citation2018; NCEI, Citation2019), and its frequency and intensity are expected to grow due to climate change, posing a particularly great threat to coastal communities and beyond (Hauer et al., Citation2016, Citation2021; Sweet et al., Citation2022), as the compound failure from sea-level rise, storm surge, and extensive rainfall escalates. While increased flooding is expected to disrupt road networks, the exact nature and distribution of these disruptions remains unclear. Thus, there is a strong need to map disrupted critical facilities’ accessibility so that equitable infrastructure investments and hazard mitigation strategies can be derived to safeguard coastal communities (Barrette et al., Citation2022; Meerow et al., Citation2019; Nagenborg, Citation2019; Young et al., Citation2021).
洪水是最常见且代价高昂的干扰源（CRED，2018；NCEI，2019），由于气候变化，其频率和强度预计将增加，对沿海社区及更广泛地区构成特别巨大的威胁（Hauer et al.，2016，2021；Sweet et al.，2022），因为海平面上升、风暴潮和广泛降雨的复合失效正在加剧。尽管预计洪水会增加对道路网络的破坏，但这些破坏的确切性质和分布仍不明确。因此，迫切需要绘制受干扰的关键设施可达性图，以便制定公平的基础设施投资和灾害缓解策略，保护沿海社区（Barrette et al.，2022；Meerow et al.，2019；Nagenborg，2019；Young et al.，2021）。

The network-based method is one of the most suitable and frequently used approaches to systematically evaluate critical facility accessibility (W. Wang et al., Citation2019). Dong et al. (Citation2019) proposed a robust component to evaluate if communities can access hospitals after earthquake disruption. Weiss et al. (Citation2020) studied travel time to healthcare facilities globally and examined access to healthcare under no disruption. Gangwal and Dong (Citation2022) examined access to critical facilities such as hospitals during flooding without considering travel time. Novak and Sullivan (Citation2014) examined the accessibility to emergency services using the proposed critical closeness accessibility metric without considering multiple critical facilities scenarios and partial failure effects, such as reduced travel speed due to flooding.
基于网络的方法是系统评估关键设施可达性最为适宜且常用的途径之一（W. Wang 等，2019）。Dong 等（2019）提出了一种稳健组件，用以评估社区在地震破坏后能否到达医院。Weiss 等（2020）在全球范围内研究了前往医疗设施的行程时间，并探讨了无干扰情况下的医疗服务可达性。Gangwal 和 Dong（2022）考察了洪水期间对医院等关键设施的可达性，未考虑行程时间因素。Novak 和 Sullivan（2014）利用提出的关键接近性可达性指标考察了紧急服务的可达性，但未涉及多重关键设施场景及部分失效效应，如洪水导致的行程速度降低。

Despite the invaluable insights learned from the existing efforts, each study only partially addresses the relationship between flooding and partial measures of accessibility, such as increased travel time. This research therefore proposes an integrated network approach that accounts for flood-induced partial failure, multiple critical facilities of different types, and reduced travel time in critical facility accessibility. The scope of this research entails three paradigms. First, we will extend a partial failure integrated road network disruption model by integrating the depth disruption function in travel time calculation. Second, communities’ accessibility to different critical facilities is mapped and disparities are revealed. Third, a modified betweenness centrality metric is developed to identify the critical roads for connecting communities to critical facilities and for recovering critical facility accessibility by identifying flooded roads that would restore isolated communities’ access. We demonstrate the application of the proposed model through a case study of Delaware under the current condition of 100-year floods.
尽管现有研究提供了宝贵的见解，但每项研究仅部分探讨了洪水与部分可达性指标（如增加的行程时间）之间的关系。因此，本研究提出一种综合网络方法，该方法考虑了洪水引发的局部失效、多种不同类型的重要设施以及重要设施可达性中的行程时间缩短。本研究的范围涉及三个范式。首先，我们将通过在行程时间计算中整合深度干扰函数，扩展局部失效综合道路网络干扰模型。其次，绘制社区对不同重要设施的可达性地图，并揭示其中的差异。第三，开发一种改进的介数中心性指标，用于识别连接社区与重要设施的关键道路，并通过识别可恢复孤立社区访问权限的淹没道路来恢复重要设施的可达性。我们通过当前 100 年一遇洪水条件下特拉华州的案例研究，展示了所提模型的应用。

The rest of the paper is organized as follows. Section 2 summarizes prior research in the field of flood-induced network disruption of road networks and critical road identification. Section 3 presents the depth-disruption function used to calculate travel time, the method to calculate road criticality, and the study site of Delaware. Section 4 presents the results of derived redundancy across the network and identified critical roads for both post-flood critical facility access and accessibility restoration. Section 5 presents the discussion and talks about the limitations of the study along with future directions. Finally, section 6 concludes the paper with major findings and their significance.
本文其余部分组织如下。第 2 节概述了道路网络洪水引发网络中断及关键道路识别领域的先前研究。第 3 节介绍了用于计算行程时间的深度-中断函数、计算道路关键性的方法以及研究地点特拉华州。第 4 节展示了整个网络推导出的冗余度结果以及为洪水后关键设施访问和可达性恢复所识别的关键道路。第 5 节进行讨论，探讨了研究的局限性并提出未来研究方向。最后，第 6 节总结了论文的主要发现及其意义。

2. Literature review 2. 文献综述

2.1. Flood-disrupted road network analysis
2.1. 洪水干扰下的路网分析

Flooding becomes increasingly common as the climate and built environment change (Mobley et al., Citation2021; Nofal & Van De Lindt, Citation2022). The impact of flooding on transportation, in particular, is devastating as it impedes people’s access to critical services and affects communities’ well-being (Dong et al., Citation2020a; Esparza et al., Citation2021; Gangwal & Dong, Citation2022; Ramirez-Rios et al., Citation2022; Yuan et al., Citation2022). A growing body of literature focuses on modeling and assessing the performance of flood-disrupted road networks (Bucar & Hayeri, Citation2020; He et al., Citation2021; Morelli & Cunha, Citation2021; Papilloud & Keiler, Citation2021; Wiśniewski et al., Citation2020). For example, Singh et al. (Citation2018) integrated weather-related information and land use patterns into a hydrodynamic model along with the safety speed function to predict road vulnerability. The proposed framework was used to assess the spatial vulnerability for two rainfall events with a 10-year and 100-year return period. Li and Willems (Citation2020) proposed a hybrid model that integrates a suite of lumped hydrological models and logistic regression for fast and probabilistic urban pluvial flood prediction. Using the inundation map produced by hydraulic and hydrologic (H&H) models.
随着气候和建成环境的变迁，洪灾愈发频繁（Mobley 等人，2021；Nofal 与 Van De Lindt，2022）。洪水对交通的影响尤为严重，它阻碍了人们获取关键服务，并影响社区的福祉（Dong 等人，2020a；Esparza 等人，2021；Gangwal 与 Dong，2022；Ramirez-Rios 等人，2022；Yuan 等人，2022）。越来越多的文献致力于模拟和评估受洪水破坏的道路网络性能（Bucar 与 Hayeri，2020；He 等人，2021；Morelli 与 Cunha，2021；Papilloud 与 Keiler，2021；Wiśniewski 等人，2020）。例如，Singh 等人（2018）将天气相关信息和土地利用模式融入水动力模型，结合安全速度函数来预测道路脆弱性。该框架用于评估两个降雨事件的空间脆弱性，分别具有 10 年和 100 年的重现期。Li 和 Willems（2020）提出了一种混合模型，集成了多种集总式水文模型和逻辑回归，以实现快速且概率性的城市地表径流洪水预测。利用水文水力学（H&H）模型生成的淹没图。

Among the various methods used to assess the flood-disrupted transportation systems, network-theory-based models have been widely adopted to study the affected road network (Dong et al., Citation2022, Citation2020b; Duan & Lu, Citation2014; Zhang & Alipour, Citation2019). For example, Alabbad et al. (Citation2021) examined the accessibility to critical amenities under 100 and 500-year flood scenarios using graph theoretical methods. Kermanshah and Derrible (Citation2017) developed a stochastic model to assess the road network robustness in facing flash floods using betweenness centrality and service accessibility. However, the network theory-based analysis often adopts a binary link failure criterion (i.e., either functional or dysfunctional) that does not fully capture the effect of flooding on road functionality, while several studies have shown a nonlinear relationship between disruption and road performance. For example, Liu et al. (Citation2022b) adopted the Bureau of Public Roads (BPR) function to consider the impact of disruption on travel time. Lam et al. (Citation2020) modeled the temporal functional capacity losses of infrastructure and examined the spatio-temporal risk of a road network in Switzerland. To relate flood-depth to travel speed decrease on roads, Pregnolato et al. (Citation2017) developed and calibrated a depth-disruption function that delineates the relationship between the depth of standing water and vehicle speed. Researchers have then extensively used the depth-disruption function to assess partial failure due to flood-water impact on transportation systems. For example, Abdulla et al. (Citation2020) used a network diffusion-based method to capture the impact of floods on a road network and further used the flood depth and vehicle speed to categorize the network into susceptible and impacted. Fereshtehpour et al. (Citation2018) examined the travel time increase and the emergency services coverage area change using the depth-disruption function. Despite the existing effort on flood impact on transportation, there are very limited studies that capture the impact of flooding on different communities’ access to critical facilities considering road partial failure and network isolation. In this research, we bridge this gap by integrating the road partial failure models with network-based methods to assess the impact of flooding on transportation network resilience, with a focus on communities’ access to critical facilities.
在评估洪水破坏的交通系统的方法中，基于网络理论的模型已被广泛采用来研究受影响的道路网络（Dong et al., 2022, 2020b; Duan & Lu, 2014; Zhang & Alipour, 2019）。例如，Alabbad 等人（2021）利用图论方法，在 100 年和 500 年一遇的洪水情景下，考察了关键设施的可及性。Kermanshah 和 Derrible（2017）开发了一种随机模型，使用介数中心性和服务可达性来评估道路网络在面对山洪时的鲁棒性。然而，基于网络理论的分析通常采用二元链接失效标准（即，功能性或功能障碍性），这并未完全捕捉到洪水对道路功能性的影响，而多项研究表明，中断与道路性能之间存在非线性关系。例如，Liu 等人（2022b）采用了公共道路局（BPR）函数来考虑中断对出行时间的影响。Lam 等人（2020）对基础设施的时变功能容量损失进行了建模，并考察了瑞士道路网络的时空风险。为了将洪水深度与道路行驶速度下降关联起来，Pregnolato 等人（2017）开发并校准了一个深度干扰函数，该函数描绘了积水深度与车辆速度之间的关系。随后，研究者广泛利用这一深度干扰函数来评估洪水对交通系统造成的部分失效。例如，Abdulla 等人（2020）采用基于网络扩散的方法来捕捉洪水对道路网络的影响，并进一步利用洪水深度和车辆速度将网络划分为易受影响和已受影响的区域。Fereshtehpour 等人（2018）则通过深度干扰函数考察了旅行时间增加及紧急服务覆盖区域变化的情况。尽管已有研究致力于探讨洪水对交通的影响，但关于考虑道路部分失效和网络隔离情况下，洪水对不同社区获取关键设施途径的影响的研究仍十分有限。在本项研究中，我们通过将道路局部失效模型与基于网络的方法相结合，评估洪水对交通网络韧性的影响，重点关注社区对关键设施的可达性。

2.2. Critical roads identification
2.2. 关键道路识别

All roads are important as they connect people and places, but they do not share equal criticality because of their unique locations in the network. Road criticality has been widely studied to help prioritize infrastructure development. Jafino et al. (Citation2020) summarized seventeen road criticality metrics derived from (i) transport studies and (ii) network theory. The metrics derived from transport studies include weighted and unweighted travel cost (Gauthier et al., Citation2018; Wang et al., Citation2013), user exposure analysis (impact of disruptions experienced by users; Jenelius & Mattsson, Citation2015), weighted and unweighted accessibility (Luathep et al., Citation2011), congestion (Zhou et al., Citation2015), and exposure to disaster (Koks et al., Citation2019; Sohn, Citation2006). On the other hand, the metrics derived from network theory include network-centrality (Geertman et al., Citation2019; Henning et al., Citation2017; Snelder et al., Citation2012), network efficiency (Dehghani et al., Citation2014), and connectivity (Mishra et al., Citation2012; Snelder et al., Citation2012).
所有道路因其连接人与地点的功能而显得重要，但由于在网络中的独特位置，它们的重要性并不均等。道路关键性已被广泛研究，以帮助优先考虑基础设施发展。Jafino 等人（2020 年）总结了从（i）运输研究及（ii）网络理论中得出的十七项道路关键性指标。源自运输研究的指标包括加权与非加权旅行成本（Gauthier 等人，2018 年；Wang 等人，2013 年）、用户暴露分析（用户经历的干扰影响；Jenelius 与 Mattsson，2015 年）、加权与非加权可达性（Luathep 等人，2011 年）、拥堵情况（Zhou 等人，2015 年）以及灾害暴露（Koks 等人，2019 年；Sohn，2006 年）。另一方面，源自网络理论的指标则包括网络中心性（Geertman 等人，2019 年；Henning 等人，2017 年；Snelder 等人，2012 年）、网络效率（Dehghani 等人，2014 年）以及连通性（Mishra 等人，2012 年；Snelder 等人，2012 年）。

These criticality metrics have been further modified to adapt to different study contexts and data types. For example, Li et al. (Citation2020) proposed a traffic flow betweenness index to identify critical roads using origin-destination travel demand. Feng et al. (Citation2019) used GPS trajectory data and combined the physical network with dynamic traffic flow to model a directed weighted road network. The model introduced a new correlation coefficient to evaluate the system performance and identify critical roads. Chen et al. (Citation2012) proposed an impact area vulnerability analysis approach to identify critical roads and assess the impact of road closures while taking into account the varying demand. Gangwal and Dong (Citation2022) identified critical roads corresponding to early warning points for Harris County, Texas, road network under Hurricane Harvey and 500-year floods. Aydin et al. (Citation2019) used the origin-destination betweenness centrality to identify critical intersections for accessing health care services. Helderop and Grubesic (Citation2019) introduced a modified grid-based centrality method to assess the criticality of road segments considering the potential traversability of off-network and whole-landscape features during an extreme event. Mostafizi et al. (Citation2017) proposed criticality of links depending on the impact a link failure might have on an evacuation on foot, which indirectly impacts both safety and mortality rates.
这些关键性指标已进一步修改以适应不同的研究背景和数据类型。例如，Li 等人（2020）提出了一种基于起讫点出行需求的交通流介数指数，用以识别关键道路。Feng 等人（2019）利用 GPS 轨迹数据，将物理网络与动态交通流相结合，构建了一个有向加权道路网络模型，并引入新的相关系数来评估系统性能及识别关键道路。Chen 等人（2012）提出了一种影响区域脆弱性分析方法，旨在识别关键道路并评估道路封闭的影响，同时考虑需求的变化。Gangwal 和 Dong（2022）针对德克萨斯州哈里斯县在飓风哈维及 500 年一遇洪水情况下的道路网络，确定了与早期预警点相对应的关键道路。Aydin 等人（2019）则运用起讫点介数中心性来识别获取医疗服务的关键交叉口。 Helderop 和 Grubesic（2019）提出了一种改进的基于网格的中心性方法，用于评估极端事件期间考虑非网络及整个景观特征潜在可穿越性的道路段关键性。Mostafizi 等人（2017）则根据链接故障对步行疏散可能产生的影响提出了链接的关键性，这种影响间接关系到安全和死亡率。

Identification of critical roads during daily travel or after disruption can help traffic managers anticipate congestion and derive efficient control and routing strategies. But, the roads that connect communities with essential services such as hospitals, emergency medical services, and shelters are more critical because the loss of access to these critical facilities will negatively affect communities’ well-being (Dong et al., Citation2020a). More importantly, the adverse health impact from critical facility access loss will be further exacerbated in a disaster setting, particularly for socially vulnerable communities (Esmalian et al., Citation2021a,Citationb). Identification of the critical roads for accessing critical facilities can also facilitate infrastructure investment decision-making (Dong et al., Citation2021). However, there are few studies on service-oriented critical road identification. To address this research and practice need, this research utilizes a network-based approach to systematically measure road criticality by considering both flood-induced road failure and communities’ access to the critical facility.
在日常出行或遭遇干扰后识别关键道路，有助于交通管理者预见拥堵并制定高效的控制和路线策略。然而，连接社区与医院、急救服务和避难所等基本服务设施的道路更为关键，因为失去对这些关键设施的访问将负面影响社区的福祉（Dong 等，2020a）。更重要的是，在灾难情境下，尤其是对社会脆弱社区而言，因关键设施访问丧失而产生的健康影响将进一步加剧（Esmalian 等，2021a,b）。识别通往关键设施的关键道路还能促进基础设施投资决策的制定（Dong 等，2021）。但目前关于服务导向型关键道路识别的研究甚少。为满足这一研究与实践需求，本研究采用基于网络的方法，系统性地衡量道路关键性，综合考虑了洪水引发的道路失效及社区对关键设施的访问情况。

Roads that enable re-connection between communities and critical facilities are also important. Existing studies mainly use an optimization approach to identify the critical roads for resilience recovery. For example, Liu et al. (Citation2022b) identified the optimal repair strategy using a modified network robustness metric based on travel and repair cost minimization. Merschman et al. (Citation2020) prioritized the repair of four bridges in Mobile, Alabama after disruption considering the travel time and distance, network connectivity, and access to the emergency facility. Aksu and Ozdamar (Citation2014) identified the critical roads for restoration that maximize network accessibility during disaster response and recovery. Akbari et al. (Citation2021) used an online optimization model to derive the road restoration strategy that minimizes the time for a network to regain connectivity. Ulusan and Ergun (Citation2018) developed a mixed-integer programming model and proposed a Cent-Restore heuristic to prioritize the road restoration effort for a disrupted road network. However, existing optimization approaches are more suitable for smaller network exercises and very limited in large-scale network applications. Additionally, the optimization solution only applies to a specific disruption scenario and provides limited insight for long-term general hazard mitigation and resilience planning. In this study, we address this research gap by proposing a weighted road criticality metric that takes into account the restoration of communities’ post-flooding access to critical facilities.
能够促进社区与关键设施重新连接的道路同样至关重要。现有研究主要采用优化方法来识别增强韧性恢复的关键道路。例如，Liu 等人（2022b）基于旅行与修复成本最小化，运用改进的网络鲁棒性指标确定了最优修复策略。Merschman 等人（2020）在考虑旅行时间与距离、网络连通性及紧急设施可达性的基础上，为阿拉巴马州莫比尔市中断后的四座桥梁制定了修复优先级。Aksu 和 Ozdamar（2014）识别了在灾害应对与恢复期间最大化网络可达性的关键修复道路。Akbari 等人（2021）利用在线优化模型推导出使网络恢复连通时间最短的道路修复策略。Ulusan 和 Ergun（2018）开发了一个混合整数规划模型，并提出了一种名为 Cent-Restore 的启发式算法，用于为受扰动的道路网络确定道路修复工作的优先级。然而，现有的优化方法更适用于较小规模的网络实践，在大规模网络应用中极为受限。此外，优化方案仅适用于特定中断情景，对长期普遍性灾害缓解和韧性规划提供的见解有限。本研究通过提出一种加权道路关键性指标来填补这一研究空白，该指标考虑了社区在洪灾后恢复对关键设施的可达性。

3. Methodology 3. 方法论

3.1. Modeling flood-induced road network failure
3.1. 洪水引发道路网络失效的建模

We model flood-induced partial road failure by adopting the depth-disruption function (Pregnolato et al., Citation2017) as follows:
我们通过采用深度干扰函数（Pregnolato 等，2017）来模拟洪水引起的部分道路失效，具体如下：

where $d$ is the flood depth in centimeters. This nonlinear relationship calculates the vehicle’s travel speed limit $v (d)$ of road providing different flood depths. Here, we consider a maximum of 30 cm as the flood depth limit for safe travel (Pyatkova et al., Citation2019; Yin et al., Citation2016). Next, the estimated travel speed limit $v_{d}$ is compared with the free flow speed ( $v_{f}$ ) of the road and the smaller one is adopted for link travel time calculation. The travel time is derived using the length of the road as shown in EquationEq. 1(1) $t = \frac{l}{s}$ (1) .
其中， $d$ 表示洪水深度，单位为厘米。该非线性关系用于计算在不同洪水深度下道路的车辆行驶速度限制 $v (d)$ 。在此，我们考虑将 30 厘米作为安全行驶的洪水深度上限（Pyatkova 等，2019；Yin 等，2016）。随后，估算的行驶速度限制 $v_{d}$ 将与道路的自由流速度（ $v_{f}$ ）进行比较，取两者中的较小值用于路段行驶时间计算。行驶时间根据道路长度得出，如公式 1 所示。

(1)

t = \frac{l}{s}

(1)

where $l$ is the length of the road and $s = m i n (v_{d}, v_{f})$ . The depth-disruption function in and EquationEq. 1(1) $t = \frac{l}{s}$ (1) is used to estimate the travel time of every link in the road network. The travel time after flooding is used to map accessibility to the closest hospital, emergency shelter, and EMS. The NetworkX library in Python is used to calculate the travel time to the closest critical facility. We also identify the closest node for all properties and approximate their travel time to be same as that of the node.
其中 $l$ 表示道路长度， $s = m i n (v_{d}, v_{f})$ 。图 1 和公式 1 中的深度-中断函数用于估算路网中每条链路的行程时间。洪水后的行程时间用于映射到最近医院、应急避难所和紧急医疗服务(EMS)的可及性。使用 Python 中的 NetworkX 库计算到最近关键设施的行程时间。我们还为所有物业确定最近的节点，并近似其行程时间与该节点相同。

Figure 1. Depth-disruption function.
图 1. 深度干扰函数。

3.2. Betweenness centrality of post-flooding critical facility access
3.2. 洪灾后关键设施通达性的介数中心性

Roads that are frequently used by communities for accessing critical facilities post flooding are deemed important. Conventional network theory-based methods involve studying the mobility and accessibility of disrupted networks using the size of the giant component or the largest connected cluster as the metric (Dong et al., Citation2022). However, the access to critical facilities is not considered. We adopt the metric of robust component (Dong et al., Citation2019) to examine each node’s access to critical facilities. The concept of the robust component is illustrated in ). Before flooding, critical facilities A, B, & C can serve all communities. After flooding, critical facility C is flooded and thus loses serviceability. Facility B is isolated by flooding, so no one can access service here, leaving critical facility A to provide service to the rest of the network.
经常被社区用于洪灾后访问关键设施的道路被视为重要。基于传统网络理论的方法涉及使用巨型组件或最大连接簇的大小来研究中断网络的流动性和可达性（Dong et al., 2022）。然而，这些方法并未考虑对关键设施的访问。我们采用鲁棒组件（Dong et al., 2019）这一指标来检查每个节点对关键设施的访问情况。鲁棒组件的概念在图 2(a)中有所展示。在洪水前，关键设施 A、B 和 C 能够服务于所有社区。洪水后，关键设施 C 被淹没，因此失去了服务能力。设施 B 因洪水而孤立，无人能在此获得服务，导致关键设施 A 成为网络中其余部分的服务提供者。

Figure 2. Heuristic illustration of robust component and edge criticality for system connectivity.
图 2. 系统连通性中鲁棒组件与边缘关键性的启发式示意图。

Once the accessible critical facility is identified, we use a modified weighted betweenness centrality $C_{t}$ to identify critical roads for post-flooding critical facility travel, with critical facilities being the destination and regular nodes as the origin. First, the shortest path between each node and its corresponding closest critical facility is identified. Next, the number of occurrences that a link appeared on the node-facility shortest path is recorded (see, EquationEq. 2)(2) $w_{t} (e_{i j}) = \sum_{s, t \in V} σ (s, t | e_{i j})$ (2) .
一旦确定了可接近的关键设施，我们采用修正的加权介数中心性 $C_{t}$ 来识别洪灾后关键设施通行的关键道路，其中关键设施作为目的地，常规节点作为起点。首先，识别每个节点与其最近关键设施之间的最短路径。接着，记录某条链路出现在节点-设施最短路径上的次数（参见公式 2）。

(2)

w_{t} (e_{i j}) = \sum_{s, t \in V} σ (s, t | e_{i j})

(2)

where $V$ is the set of origin-destination pairs with node as origin and the respective closest critical facility as destination and road $σ (s, t | e_{i j})$ is the number of paths passing through edge $e_{i j}$ . The obtained values are then normalized and the critical roads for accessing critical facilities are identified (see, EquationEq. 3)(3) $C_{t} (e_{i j}) = \frac{w_{t} (e_{i j})}{m a x (w_{t} (e_{i j}))}$ (3) .
其中， $V$ 表示以节点为起点、以其最近的紧急设施为终点的起点-终点对集合，而道路 $σ (s, t | e_{i j})$ 则表示经过边 $e_{i j}$ 的路径数量。所得数值随后进行归一化处理，并识别出通往紧急设施的关键道路（参见公式 3）。

(3)

C_{t} (e_{i j}) = \frac{w_{t} (e_{i j})}{m a x (w_{t} (e_{i j}))}

(3)

3.3. Road criticality for post-flooding access restoration
3.3. 洪灾后通道恢复的道路关键性

Roads whose recovery can restore communities’ access to critical facilities are also important. One approach is to derive the optimal sequences that result in maximum resilience recovery (Kaviani et al., Citation2017; Sohouenou & Neves, Citation2021). However, these approaches mainly focus on small networks and provide limited insights into each road’s contribution to a community’s recovery. In this paper, we propose a weighted road criticality $C_{r}$ that encapsulates its importance to different communities and contribution to critical facility access recovery.
能够恢复社区对关键设施访问的道路同样重要。一种方法是推导出实现最大韧性恢复的最优序列（Kaviani et al., 2017; Sohouenou & Neves, 2021）。然而，这些方法主要关注小型网络，对每条道路对社区恢复的贡献提供有限见解。本文中，我们提出了一种加权道路关键性 $C_{r}$ ，它囊括了道路对不同社区的重要性及其对关键设施访问恢复的贡献。

The heuristic illustration of the post-flooding access restoration criticality measurement is demonstrated in ). First, we will identify the shortest paths (in terms of travel time) that connect each disconnected cluster of nodes to its nearest critical facility, but only focus on the inundated roads that require restoration. ) shows the two disconnected cluster of nodes, $N_{1}$ of size 20 nodes and $N_{2}$ of 8 nodes, with path $a - b - e - f$ and path $c - d - e - f$ on their shortest path to their nearest critical facility, respectively. If a disconnected cluster of nodes has multiple shortest paths, the path that has more overlaps with other clusters paths (primary criteria) or shorter lengths (secondary criteria) is selected. Second, we examine the amount of access that restoration of each link can recover. In this case, roads ‘ $a$ ‘ and ‘ $b$ ‘ are only responsible for 20 nodes’ access recovery. While roads ‘ $e$ ‘ and ‘ $f$ ‘ contribute to the recovery of critical facility access for both cluster of nodes $N_{1}$ and $N_{2}$ , and thus achieves a weight of 28 (20 + 8). The mathematical formulation of the above process can be represented as in EquationEq. 4(4) $w_{r} (e_{i j}) = \sum_{k = 1}^{D} α N_{k}$ (4) :
图 2(b)展示了洪灾后恢复通达性关键度测量的启发式示意图。首先，我们将识别连接每个断开节点群集与其最近关键设施的最短路径（以行程时间计），但仅关注需要恢复的淹没道路。图 2(b)显示了两个断开的节点群集， $N_{1}$ 包含 20 个节点和 $N_{2}$ 包含 8 个节点，分别通过路径 $a - b - e - f$ 和路径 $c - d - e - f$ 通往其最近的关键设施。若一个断开的节点群集存在多条最短路径，则选择与其他群集路径重叠更多（主要标准）或长度更短（次要标准）的路径。其次，我们评估每条道路恢复所能恢复的通达量。在此情况下，道路‘ $a$ ’和‘ $b$ ’仅负责恢复 20 个节点的通达性。而道路‘ $e$ ’和‘ $f$ ’则有助于恢复群集 $N_{1}$ 和 $N_{2}$ 的关键设施通达性，因此获得了 28 的权重（20 + 8）。上述过程的数学表达可以表示为方程式。 4:

(4)

w_{r} (e_{i j}) = \sum_{k = 1}^{D} α N_{k}

(4)

α = \{\begin{matrix} 1 i f P_{k} \cap e_{i j} \neq \emptyset \\ 0 o t h e r w i s e \end{matrix}

where $D$ is the number of disconnected cluster of nodes, $N_{k}$ is the size of cluster $k$ , and $P_{k}$ is the set of flooded links in the shortest path for cluster $k$ to reach critical facility. The obtained values are then normalized and the road criticality for community-critical facility connectivity is identified (see, EquationEq. 5)(5) $C_{r} (e_{i j}) = \frac{w_{r} (e_{i j})}{m a x (w_{r} (e_{i j}))}$ (5) .
其中， $D$ 表示节点断开连接的簇数量， $N_{k}$ 表示簇 $k$ 的大小，而 $P_{k}$ 则是簇 $k$ 到达关键设施的最短路径中被淹没链路的集合。所得数值随后进行归一化处理，进而识别社区与关键设施连通性的道路关键度（参见公式 5）。

(5)

C_{r} (e_{i j}) = \frac{w_{r} (e_{i j})}{m a x (w_{r} (e_{i j}))}

(5)

3.4. Study site 3.4. 研究地点

Delaware has the lowest average elevation of any US state and is highly vulnerable to storm-related flooding, which is expected to become more frequent and intense with climate change. There are 22,000 people at risk of coastal flooding in Delaware, and this number is expected to increase to 31,000 by 2050 (Climate Central, Citation2015). Delaware also faces threats from sea-level rise, with a 1.5-meter increase in sea level projected by the year 2100 (Delaware Sea Grant, Citation2022). Increased frequency of sunny day flooding during high tides provides evidence of these growing threats (Howell, Citation2020).
特拉华州是美国平均海拔最低的州，极易遭受风暴引发的洪水灾害，随着气候变化，此类洪水预计将变得更加频繁和剧烈。特拉华州有 22,000 人面临海岸洪水的风险，这一数字预计到 2050 年将增至 31,000 人（Climate Central, 2015）。此外，特拉华州还面临海平面上升的威胁，预计到 2100 年海平面将上升 1.5 米（Delaware Sea Grant, 2022）。高潮期间晴天洪水的增多频率，正是这些日益严重威胁的明证（Howell, 2020）。

Road network 路网

The state-wide road network acquired from the Delaware Department of Transportation contains 100,887 nodes (i.e., intersections) and 117,491 links (i.e., roads), with 14,512 of them being one way streets. The road network is first mapped in GIS and then modeled as a directed network in Python NetworkX library. Three types of critical facilities collected from HIFLD (Citation2022) are investigated, including 16 hospitals, 142 emergency shelters, 72 emergency medical service (EMS) facilities (as shown in ).
从特拉华州交通部获取的全州道路网络包含 100,887 个节点（即交叉口）和 117,491 条路段（即道路），其中 14,512 条为单行道。该道路网络首先在 GIS 中进行映射，随后在 Python 的 NetworkX 库中被建模为有向网络。研究了从 HIFLD（2022）收集的三类关键设施，包括 16 家医院、142 个应急避难所和 72 个紧急医疗服务（EMS）设施（如图 3 所示）。

Figure 3. Study Site, Delaware, USA. (a) 100-year flood maps overlaid with the road network of Delaware. (b) The spatial distribution of three critical facilities (CF) and communities demarcated based on the social vulnerability index (SVI). The critical facilities include hospitals (16), emergency medical service stations (72), and emergency shelters (142).
图 3. 美国特拉华州研究地点。(a) 特拉华州道路网络与百年洪水地图叠加。(b) 基于社会脆弱性指数(SVI)划分的三个关键设施(CF)及社区的空间分布。关键设施包括医院(16 所)、急救医疗服务站(72 个)和应急避难所(142 处)。

Property data 财产数据

We use the First Street Foundation’s property data and map 422,668 properties in the Delaware road network. The data includes the latitude, longitude, and flood factor of various properties, including residential units.
我们利用 First Street Foundation 的房产数据，在特拉华州路网中绘制了 422,668 处房产。该数据涵盖了各房产的纬度、经度和洪水风险系数，其中包括住宅单元。

Flood risk data 洪水风险数据

The flood risk raster layer is acquired through partnership with the First Street Foundation. They developed a nationwide probabilistic flood model that considers flooding risk due to rainfall (global pluvial), riverine flooding (global fluvial), and coastal surge flooding (Bates et al., Citation2021). The model was upgraded using USGS National Elevation data for topography, and Global Runoff Data for rainfall-runoff. The flood risk projections for both current and future scenarios was estimated using a factor to modify the historic return periods. The First Street flood layer matches fairly closely with the FEMA 1% annual probability flood maps, but we use the First Street layer because it incorporates multiple types of flood risk. We adopted the 100-year flood risk (1% annual flood chance) data for the year of 2020 in this paper. The probability of a 100-year flood occurring during any 30-year period, a common length for mortgages, is 26% (Delaware Sea Grant, Citation2022; USGS, Citation2022), so the likelihood that a resident experiences a 100-year type flood and related road closures is fairly high.
洪水风险栅格图层通过与 First Street Foundation 合作获取。该机构开发了一个全国性的概率洪水模型，考虑了降雨引发的洪水（全球城市内涝）、河流洪水（全球河流泛滥）以及海岸风暴潮洪水（Bates 等，2021）。模型利用美国地质调查局（USGS）的国家高程数据进行地形校正，并结合全球径流数据处理降雨-径流关系。当前及未来情景下的洪水风险预测，是通过调整历史重现期因子来估算的。First Street 的洪水图层与联邦紧急事务管理局（FEMA）的 1%年概率洪水图相当吻合，但我们采用 First Street 图层，因其综合了多种洪水风险类型。本文采用 2020 年的百年一遇洪水风险（即 1%年洪水概率）数据。在任意 30 年期间（抵押贷款常见期限），发生百年一遇洪水的概率为 26%（Delaware Sea Grant，2022；USGS，2022），因此居民遭遇此类洪水及其相关道路封闭的可能性相当高。

Social Vulnerability Index (SVI)
社会脆弱性指数（SVI）

We adopt the social vulnerability index (SVI) created by the Centers for Disease Control and Prevention (CDC) in the study. The SVI considers four categories of community characteristics, including socioeconomic status, household composition disability, minority status language, and housing type transportation. The index is computed by synthesizing the aforementioned variables through the principal component analysis procedure (Cutter et al., Citation2012). The SVI is in the unit of census tract and can help us identify the communities that need support and attention before, during, and after a disaster (Flanagan et al., Citation2011). Because SVI is available at a census tract level, we use census tracts to approximate ‘community’ characteristics. We recognize that census tracts are an imperfect proxy for a community, as census tracts range in size from 1,200 to 8,000 people and may not follow jurisdictional or neighborhood boundaries. However, it is an initial starting point to match demographic traits to road access, and we anticipate this will be an area for improvement in future research.
本研究采用美国疾病控制与预防中心（CDC）创建的社会脆弱性指数（SVI）。SVI 综合考虑了社区特征的四个类别，包括社会经济状况、家庭构成与残疾、少数族裔语言以及住房类型与交通。该指数通过主成分分析法（Cutter et al., 2012）整合上述变量进行计算。SVI 以人口普查区为单位，有助于我们在灾害前、中、后期识别需要支持与关注的社区（Flanagan et al., 2011）。由于 SVI 数据可细化至人口普查区层面，我们利用人口普查区来近似反映“社区”特征。我们认识到，人口普查区作为社区的代理存在局限性，其规模从 1,200 至 8,000 人不等，且可能不遵循行政或邻里边界。然而，这是将人口统计特征与道路通达性相匹配的初步起点，我们预期未来研究在此领域有改进空间。

4. Results 4. 结果

4.1. Assessing post-flooding critical facility accessibility
4.1. 评估洪灾后关键设施的可及性

Accessibility to critical facilities is shown in , both during un-flooded conditions and as the increase in travel time after a 100-year flood (2020). The navy blue nodes in the flood map are inundated and thus have no access to critical facilities. Red nodes are isolated, as shown in , and also have no access to critical facilities. The rest of the nodes are colored based on the travel time to the closest critical facility ()) and the increase in travel time ()). Delaware communities are subject to severe isolation risk from flooding, as red nodes dominate the map. In particular, southern Delaware is exposed to inland flooding (gray nodes), which is the major cause for community isolation.
关键设施的可及性如图 4 所示，既包括未淹没状态下的情况，也包括经历百年一遇洪水（2020 年）后旅行时间增加的情况。洪水图中深蓝色节点表示被淹没，因此无法访问关键设施。红色节点如图 2 所示，处于孤立状态，同样无法访问关键设施。其余节点根据到达最近关键设施的旅行时间（图 4(a)）以及旅行时间的增加（图 4(b)）进行着色。特拉华州社区面临严重的洪水隔离风险，地图上红色节点占据主导地位。特别是特拉华州南部，暴露于内陆洪水（灰色节点）之中，这是导致社区孤立的主要原因。

Figure 4. Access to closest CFs (hospitals, EMS, and emergency shelters). (a) Travel time (in minutes) to the closest CF before flood. (b) The increase in travel time after a 100-year flood (2020) is shown here. The flooded nodes and disconnected nodes to CFs are colored in navy blue and red.
图 4. 获取最近关键设施（医院、急救服务和应急避难所）的途径。(a) 洪水前到达最近关键设施的行程时间（分钟）。(b) 此处展示的是 2020 年百年一遇洪水后行程时间的增加情况。被洪水淹没的节点及与关键设施断开的节点分别以深蓝色和红色标示。

) shows the travel time to critical facilities before flooding. The variation is higher in the case of hospitals than EMS and emergency shelters. This is because there are fewer hospitals compared to the other two types of critical facilities. ) shows the travel time increase after 100-year flood. We calculate the average travel time to the closest critical facility before and after flooding. We notice a significant increase in travel time to critical facilities, including around 118% increase for hospitals, and 66% for both EMS and emergency shelters. We observe a particularly large increase in travel time to hospitals in Dover, Harrington, and Townsend regions. An increase in travel time to EMS and emergency shelters is also observed in the Dover and Townsend regions.
图 4(a)展示了洪水前到达关键设施的行程时间。医院的情况变异系数高于紧急医疗服务(EMS)和应急避难所，这是由于医院数量相较于其他两种关键设施较少。图 4(b)则显示了百年一遇洪水发生后行程时间的增加。我们计算了洪水前后到达最近关键设施的平均行程时间，注意到到达关键设施的行程时间显著增加，其中医院增加了约 118%，EMS 和应急避难所均增加了 66%。我们特别观察到多佛、哈灵顿和汤森地区到达医院的行程时间大幅增加，同时，多佛和汤森地区到达 EMS 和应急避难所的行程时间也有所增加。

Apart from the spatial map of accessibility, we plotted the cumulative distribution of critical facility accessibility in to show the macroscopic accessibility profile. The curve in delineates the number of properties (y-axis) that have access to a critical facility within certain travel time ranges (x-axis). For example, 269,540 properties have access to a hospital within 10 minutes in a before-flooding scenario. This number drastically declines after flooding, as more properties experience longer travel times. The bar plot on the left side shows the number of flooded properties (gray region) and disconnected properties (red region). We observe that around 12% (12,270) of nodes are flooded and directly impact around 12% (50,969) properties. The flooded nodes cut off approximately 48% of nodes’ access to hospitals (2.96 times more than the inundated nodes). In terms of the number of properties, approximately 49% (206,603) of properties are isolated or lose access to hospitals (3.1 times more than flooded properties). The large number of disconnected properties demonstrates how the failure of a small number of roads can lead to severe critical facility accessibility loss during a disaster event. In order to visualize the location of the flooded and isolated properties after a 100-year flood, we spatially map the flooded and isolated nodes where the node color represents the number of properties it serves (see, (c) and (d)). In the case of hospitals, we observe a dense distribution of isolated nodes with high property numbers at Glasgow, Red Lion, and White Creek Manor. In case of EMS and Emergency shelters, there are few isolated nodes with high property numbers at Glasgow and Red Lion due to dense distribution of the critical facilities in these regions.
除了可达性空间图，我们在图 5 中绘制了关键设施可达性的累积分布图，以展示宏观可达性概况。图 5 中的曲线描绘了在特定出行时间范围内（x 轴），能够到达关键设施的房产数量（y 轴）。例如，在洪水前情景下，有 269,540 处房产在 10 分钟内可达医院。这一数字在洪水后急剧下降，因为更多房产面临更长的出行时间。左侧的条形图显示了受洪水影响的房产数量（灰色区域）和断连房产数量（红色区域）。我们观察到，约 12%（12,270）的节点遭受洪水侵袭，直接影响约 12%（50,969）的房产。这些受淹节点切断了约 48%节点对医院的可达性（是受淹节点数量的 2.96 倍）。就房产数量而言，约 49%（206,603）的房产被孤立或失去对医院的可达性（是受淹房产数量的 3.1 倍）。大量断连的物业属性展示了在灾难事件中，少数道路失效如何导致关键设施可达性严重丧失。为了直观显示百年一遇洪水后被淹没和孤立物业的位置，我们对这些被淹没和孤立的节点进行了空间映射，其中节点颜色代表其服务的物业数量（参见图 5(c)和(d)）。就医院而言，我们观察到格拉斯哥、红狮和白溪庄园地区孤立节点密集分布且涉及大量物业。至于紧急医疗服务和应急避难所，由于这些区域关键设施分布密集，格拉斯哥和红狮地区仅有少数孤立节点涉及大量物业。

Figure 5. Distribution of critical facility access redundancy. (a)-(b) The number of properties is aggregated at each intersection in the road network. Travel time values are aggregated to generate a cumulative distribution function between the number of properties (y-axis) and the travel time in minutes (x-axis) (a) before flood and (b) after 100-year flood. The spatial distribution of (c) flooded nodes and (d) isolated nodes is generated where the color of the node represents the number of properties it serves.
图 5. 关键设施接入冗余分布。(a)-(b) 在道路网络的每个交叉口处汇总物业数量。将行程时间值汇总以生成物业数量（y 轴）与行程时间（分钟）（x 轴）之间的累积分布函数，(a) 洪水前和 (b) 百年一遇洪水后。(c) 淹没节点和 (d) 孤立节点的空间分布图，其中节点的颜色代表其服务的物业数量。

Elderly residents and those with pre-existing medical conditions are among the populations expected to be most affected by disrupted access to critical facilities during flooding. Here, we particularly examine long-term care facilities’ (LTCF) access to the critical facilities through spatial mapping, using hospitals as an example in (results of EMS and emergency shelters are included in Supplementary Figure 1). The nodes represent the LTCFs and the color corresponds to the travel time to the closest hospital. Results show 36 LTCFs (out of 87) will likely lose access to hospitals after a 100-year flood, including 4 that were directly inundated (purple) and 32 that were isolated by the flood (red). The estimated maximum travel time for a LTCF resident to reach a hospital after a 100-year flood is 45.32 minutes, compared to 36.7 minutes before flooding. Moreover, there is an average of a 2.23 minutes (around 70%) increase for all the LTCFs to reach a hospital after a 100-year flood.
老年居民及已有医疗状况的人群预计在洪水期间关键设施受阻时受到的影响最为严重。在此，我们特别通过空间映射分析了长期护理机构（LTCF）对关键设施的可达性，以医院为例，如图 6 所示（EMS 和应急避难所的结果包含在补充图 1 中）。节点代表 LTCF，颜色对应于到达最近医院的时间。结果显示，在百年一遇的洪水中，87 家 LTCF 中有 36 家可能失去对医院的访问，其中包括 4 家直接被淹没（紫色）和 32 家因洪水而孤立（红色）。百年一遇洪水后，LTCF 居民到达医院的估计最长旅行时间为 45.32 分钟，而洪水前为 36.7 分钟。此外，百年一遇洪水后，所有 LTCF 到达医院的平均时间增加了 2.23 分钟（约 70%）。

Figure 6. Long-term care facilities’ (LTCF) and minority population access to closest hospitals. (a) Travel time (in minutes) to closest hospital is mapped for LTCF after 100-year flood. (b) Integrated 3D plot of no access to hospitals with minority population map is presented. The bar height denotes the total number of properties in a census tract that has no access to hospitals.
图 6. 长期护理机构（LTCF）及少数族裔群体就近医院可达性分析。(a) 百年一遇洪水后，LTCF 至最近医院的行程时间（分钟）分布图。(b) 综合三维图展示了少数族裔群体分布与无医院可达性的关系，柱高表示某一人口普查区内无医院可达性的房产总数。

We also map Black, Indigenous, and communities of color (BIPOC, i.e., non-white non-Hispanic according to CDC SVI definition) with no access to CFs in ) results of EMS and Emergency shelters are included in Supplementary Figure 2). The total number of properties with no access to hospitals in each census tract is overlaid on the population map. We observe that many properties near Middletown and Bridgeville lose access. Regions such as Wilmington, Bear, Cheswold, Dover, and Woodside East have substantial BIPOC populations but have fewer properties affected. The integrated 3D plot of properties with no access to CFs with elderly population is presented in Supplementary Figure 3.
我们还将无法接触到社区设施（CFs）的黑人、原住民及有色人种社区（BIPOC，即根据 CDC 社会脆弱性指数定义的非白人非西班牙裔群体）在图 6(b)中进行了映射，EMS 和应急避难所的结果包含在补充图 2 中。每个人口普查区内无医院可达性的房产总数叠加在人口分布图上。我们发现，米德尔敦和布里奇维尔附近的许多房产失去了可达性。诸如威尔明顿、贝尔、切斯沃尔德、多佛和伍德斯 IDE 东等地区拥有大量 BIPOC 人口，但受影响的房产数量较少。无法接触到 CFs 的房产与老年人口的集成 3D 图示于补充图 3 中。

4.2. Identifying critical roads for accessing critical facilities
4.2. 识别通往关键设施的关键道路

When accessing the closest critical facilities, some road segments are used more frequently as compared to others. These roads are key to post-flooding critical facility access and thus, of great interest for targeted infrastructure protection. We spatially map the frequency of each road that occurred in communities’ shortest paths to critical facilities. (a-b) shows the identified critical roads for accessing hospitals, both before and after the flooding. The criticality change is observed in ). In doing so, we can identify the roads that emerged as the new critical roads (red) after flooding. The critical roads for accessing EMS and Emergency shelters is presented in Supplementary Figure 4.
在接近最近的紧急设施时，某些路段相较于其他路段使用更为频繁。这些道路对于洪灾后紧急设施的通行至关重要，因此成为基础设施保护的重点关注对象。我们通过空间映射展示了各社区通往紧急设施最短路径上各道路的使用频率。图 7（a-b）分别展示了洪水前后通往医院的重点道路。图 7(c)展示了这些道路重要性的变化。由此，我们得以识别出洪水后新出现的关键道路（红色标记）。补充图 4 则展示了通往急救服务和紧急避难所的关键道路。

Figure 7. Critical roads for access to hospitals. The road criticality is spatially mapped and represented for three cases: (i) before flood; (ii) after 100-year flood; and (iii) change in critical roads. The grey roads in (b) represent the flooded and disconnected links in the system.
图 7. 通往医院的要道。道路关键性在空间上被映射并呈现为三种情况：（i）洪水前；（ii）百年一遇洪水后；以及（iii）要道变化。图（b）中的灰色道路代表系统中被淹没且断开的连接。

To identify critical roads for each community, only roads used by the nodes within that census tract to access critical facilities are considered. We can observe from that some roads are critical for pre-flooding network-wide hospital access, but not necessarily critical for a selected socially vulnerable community. When we derive the difference between network-wide criticality and community-specific criticality in 8(e) (f), we can determine if a road is more critical to the network or a specific community’s access to a hospital, or important in both scenarios. For example, out of 671 roads highlighted for the selected community in before flooding, 46 edges have road criticality greater than 0.1 (critical for the selected community) and 53 edges have road criticality less than −0.1 (critical for the network).
为了识别每个社区的关键道路，仅考虑那些用于该人口普查区内节点访问关键设施的道路。从图 8 中我们可以观察到，某些道路对于洪水前整个网络的医院通行至关重要，但未必对选定的社会脆弱社区同样关键。通过图 8(e)和(f)中展示的网络整体关键性与社区特定关键性之间的差异，我们能够判断某条道路是对整个网络更为关键，还是对特定社区的医院通行更为重要，亦或是在两种情况下都具有重要性。例如，在图 8 中选定社区洪水前的 671 条突出显示的道路中，有 46 条道路的关键性大于 0.1（对选定社区关键），而有 53 条道路的关键性小于−0.1（对整个网络关键）。

Figure 8. Critical roads comparison for access to hospitals in Dover, DE. The road criticality is calculated for access to hospitals before flood and after 100-year flood for a small community in Dover (social vulnerability index (SVI) 0.972). (a) & (b) represents the critical roads for the complete system; (c) & (d) represents critical roads for the community; (e) & (f) represent unique critical roads, i.e., the difference between the overall critical roads and critical roads for a particular community.
图 8. 多佛市医院通道关键道路对比图，特拉华州。针对多佛市一小社区（社会脆弱性指数(SVI)为 0.972），计算了洪水前及百年一遇洪水后通往医院的关键道路重要性。(a)与(b)展示了整个系统的关键道路；(c)与(d)为该社区的关键道路；(e)与(f)则表示独特关键道路，即整体关键道路与特定社区关键道路的差异部分。

4.3. Prioritizing roads for critical facility accessibility restoration
4.3. 优先恢复关键设施可达性的道路

Following the procedure proposed in and EquationEq. 5(5) $C_{r} (e_{i j}) = \frac{w_{r} (e_{i j})}{m a x (w_{r} (e_{i j}))}$ (5) , we identify the roads that are most critical to restore in order to restore critical facility accessibility in . A total of 4,703 roads (around 4% of the total roads in the network) are required to reconnect all the disconnected cluster of nodes to hospitals, increasing accessibility from 40,170 to 91,118 nodes (i.e., intersections), or 165,989 to 379,013 properties. More importantly, the restoration of only 308 roads (out of 4,703 roads) will re-establish hospital access for 33,665 nodes (around 27% of total nodes in the system), or 135,971 properties (around 32% of total properties in the system). This criticality mapping provides important analytical evidence for pre-flooding hazard mitigation and targeted road protection and post-flooding road restoration prioritization to ensure that communities have maximum access to critical services.
根据图 2(b)和公式 5 提出的流程，我们确定了为恢复图 9 中关键设施可达性而需优先修复的道路。总计 4,703 条道路（约占网络中道路总数的 4%）需被修复，以重新连接所有与医院断开的节点群，从而将可达节点数从 40,170 增加到 91,118（即交叉口），或使可达房产数从 165,989 增至 379,013。更为关键的是，仅修复 308 条道路（在 4,703 条道路中），就能为 33,665 个节点（约占系统总节点数的 27%）或 135,971 处房产（约占系统总房产数的 32%）恢复医院访问权限。这一关键性映射为洪水前灾害缓解、有针对性的道路保护及洪水后道路修复优先级划分提供了重要的分析依据，确保社区最大限度地获得关键服务。

Figure 9. Critical roads connecting disconnected properties with hospitals. The road criticality after 100-year flood is calculated for the roads that provide disconnected nodes and corresponding properties access to hospitals. The illustrative example shows that restoration of 3 roads can connect 370 properties (118 nodes) to the hospital.
图 9. 连接断开地产与医院的临界道路。针对为断开节点及其相应地产提供通往医院通道的道路，计算了其在百年一遇洪水后的道路临界度。示例表明，修复 3 条道路即可使 370 处地产（118 个节点）与医院相连。

5. Discussions 5. 讨论

This paper refines existing frameworks and proposes new methods to examine how floods affect the accessibility of critical facilities. Previous work has used network analysis to assess flood impact on road network. This work extends those methods in several ways: by using increased travel time as a measure of accessibility (Arrighi et al., Citation2019; Fereshtehpour et al., Citation2018; Pregnolato et al., Citation2017), rather than binary metrics of passable or impassable (Zhang & Alipour, Citation2019); by considering both inundation of roads (increasing travel time on roads) and isolation (communities who are unable to access critical facilities at all); by combining road networks with census tract-level demographics and social vulnerability metrics; by identifying roads whose restoration is most critical to restoring access, and considering this criticality both to the network as a whole and to specific communities. These methods open the potential for new lines of research, such as the equity implications of road restoration and road protection investments. These methods could also inform more nuanced emergency management plans for disaster risk reduction investments and recovery plans.
本文对现有框架进行了细化，并提出了新的方法来研究洪水如何影响关键设施的可及性。以往的研究利用网络分析评估洪水对道路网络的影响。本研究在这些方法的基础上进行了多方面的拓展：采用增加的行程时间作为可及性的衡量标准（Arrighi et al., 2019; Fereshtehpour et al., 2018; Pregnolato et al., 2017），而非简单的可通行或不可通行二元指标（Zhang & Alipour, 2019）；同时考虑了道路淹没（增加道路行程时间）和孤立（完全无法访问关键设施的社区）两种情况；将道路网络与人口普查区级别的人口统计数据和社会脆弱性指标相结合；识别出恢复最为关键的道路以恢复访问，并考虑这种关键性对整个网络及特定社区的影响。这些方法为新的研究方向开辟了可能性，例如道路修复和道路保护投资中的公平性问题。这些方法还能为灾害风险降低投资和恢复计划的更细致应急管理方案提供信息支持。

For example, the distinction between inundation and isolation has implications for emergency planning and for siting of new critical facilities. The network analysis results show that isolation is a bigger threat (Jasour et al., Citation2022; Logan et al., Citation2022) for Delaware coastal communities than direct inundation (). Isolation in Delaware shows an uneven distribution, with dense pockets of communities losing access to hospitals. This pattern is different for EMS and Emergency shelters because there are more of these facilities. Similarly, urban areas experience less isolation because there are more hospitals, EMS bases, and emergency shelters in these areas, so even if access to one facility is lost, residents are more likely to have access to other facilities. Wilmington and Rehoboth Beach, for example, benefit from numerous facilities.
例如，淹没与隔离之间的区别对应急规划和新关键设施选址具有重要意义。网络分析结果显示，对于特拉华州沿海社区而言，隔离比直接淹没构成更大的威胁（Jasour et al., 2022; Logan et al., 2022），如图 5 所示。特拉华州的隔离现象分布不均，多个社区密集区域面临失去医院通道的风险。这种模式在紧急医疗服务（EMS）和应急避难所方面有所不同，因为这些设施数量较多。同样，城市地区遭受隔离的程度较轻，因为这些区域医院、EMS 基地和应急避难所更为密集，即便某一设施的通道受阻，居民仍有可能获得其他设施的服务。例如，威尔明顿和雷霍博斯海滩得益于众多设施的分布。

Our results suggest that it is important for researchers and practitioners to carefully consider the consequences of isolation and inundation. The consequences of losing access to emergency services and a hospital, for example, may be different, depending on the reason why residents need access. Some populations require access to acute care services such as dialysis or opioid treatment (Kaiser et al., Citation2021; Thompson, Citation2017), while others may depend on reliable post-flooding access to pharmacies (Gangwal & Dong, Citation2022). For some of these facilities, a 3-minute delay in accessibility is not critical (e.g., a pharmacy), while for others it could be life-threatening (e.g., emergency response, ). This is one reason we examined access from long-term care facilities, where residents have a higher risk of experiencing a health emergency (Dong et al., Citation2020a), and why the increased travel time from long-term care facilities should be of concern if on-site emergency staff are not available. These types of nuances in terms of the difference between inundation and isolation and their relative importance for access to different types of critical facilities are an important area for future research to better understand how road closures affect residents’ health outcomes.
我们的研究结果表明，研究人员和从业者需慎重考虑隔离和淹没的后果。例如，失去紧急服务和医院的访问权所带来的后果可能因居民需要访问的原因而异。某些人群需要紧急医疗服务，如透析或阿片类药物治疗（Kaiser 等，2021；Thompson，2017），而其他人可能依赖于洪水后可靠的药店访问（Gangwal & Dong，2022）。对于这些设施中的某些，三分钟的访问延迟并不关键（如药店），而对其他设施则可能是生死攸关的（如紧急响应，图 6）。这就是我们为何考察长期护理机构访问的原因，这些机构的居民面临更高的健康紧急风险（Dong 等，2020a），以及为何当现场无紧急工作人员时，长期护理机构增加的旅行时间应引起关注。这些关于淹没与隔离差异及其对不同关键设施可及性相对重要性的细微差别，是未来研究的重要领域，旨在更深入地理解道路封闭如何影响居民的健康结果。

Just as not all facilities are equally critical, some roads are more critical than others to the network, and their criticality depends on the scale of the analysis. Our results in , for example, highlight that the roads that appear critical at a state level may not be the same roads that are critical at a census tract level. Methods to identify this disparity are an important step towards being able to identify the needs of different communities (e.g., Esmalian et al. (Citation2021a)) and to invest equitably in road protection and restoration (Mostafavi, Citation2018; NASEM, Citation2022). State-level transportation agencies might reasonably focus on state-level analyses of road criticality, but our results suggest that this could introduce unintended consequences and inequities. Initiatives at state and national levels to improve social justice (e.g., the Biden Administration’s Justice 40 initiative to invest 40% of federal funds in disadvantaged communities) will need methods to identify roads that are critical to disadvantaged communities. We used the Centers for Disease Control and Prevention Agency for Toxic Substances and Disease Registry’s social vulnerability index (SVI) as the criteria to identify vulnerable communities, and we used census tract data on race and ethnicity as a proxy for disadvantaged communities, but we recognize that these are far from ideal metrics. Vulnerability may be characterized in multiple ways, and there are limitations in using an index approach. Similarly, race and ethnicity do not always identify communities that have been discriminated against, underserved by government investment, or overburdened with environmental risks and hazards. Future work that draws on research exploring relationships between housing discrimination, migration, and other traits would provide greater nuance (Knighton et al., Citation2021; Maldonado et al., Citation2016; Martinich et al., Citation2013). The methods presented here require refinement, especially in how ‘disadvantaged communities’ are defined, but represent a first step.
正如并非所有设施都同等关键一样，某些道路对于网络的重要性也各不相同，其关键性取决于分析的规模。例如，我们在图 8 和图 9 中的结果表明，在州级层面看似关键的道路，在人口普查区层面可能并非同样关键。识别这种差异的方法是迈向能够识别不同社区需求（如 Esmalian 等人（2021a））并公平投资于道路保护和修复（Mostafavi，2018；NASEM，2022）的重要一步。州级交通机构可能会合理地专注于州级层面的道路关键性分析，但我们的结果表明，这可能会带来意想不到的后果和不公平。州级和国家级的提升社会正义举措（例如拜登政府的“正义 40”计划，旨在将 40%的联邦资金投入弱势社区）将需要方法来识别对弱势社区至关重要的道路。我们采用疾病控制与预防中心下属的有毒物质与疾病登记署的社会脆弱性指数（SVI）作为识别脆弱社区的标准，并利用关于种族和民族的人口普查区数据作为劣势社区的代理指标，但我们认识到这些远非理想的衡量标准。脆弱性可通过多种方式体现，采用指数方法存在局限性。同样，种族和民族并不总能准确识别那些遭受歧视、政府投资不足或承受过多环境风险和危害的社区。未来的研究若能借鉴探讨住房歧视、迁移及其他特征之间关系的研究，将能提供更细致的分析（Knighton 等人，2021；Maldonado 等人，2016；Martinich 等人，2013）。本文所介绍的方法需要进一步完善，尤其是在“劣势社区”的定义上，但作为初步尝试，它们具有一定的参考价值。

Future work can also increase nuance in the range of flood risks considered. We used a 100-year flood map to identify the flooded roads. A flood map is a great tool for resilience planning in general, but it has some limitations in road disruption mapping. A flood map is an aggregation of multiple potential flood scenarios, and each flood scenario corresponds to a disruption pattern dependent on the different meteorological conditions at the time, such as precipitation intensity and location. Each disruption will then result in a unique accessibility profile. However, this study does not provide the accessibility result of each flood, but rather the aggregated accessibility results from all flood scenarios. To enhance the current accessibility mapping results, future work will integrate dynamic flood modeling (Barnard et al., Citation2019; Nofal & van de Lindt, Citation2021) to conduct a scenario-based accessibility analysis in future research. Future studies might also consider how risks will evolve with climate change, as a 100-year flood in 2020 may be a 20-year flood in 2050. By considering the probability of different road disruption scenarios in a range of flooding scenarios, we can derive probabilistic access loss risk maps that can better guide infrastructure investment prioritization. In addition, the 100-year flood map is based on the year 2020 while the road network is based on the Delaware Department of Transportation’s 2022 inventory. We acknowledge that the time gap between the two datasets may create a slight discrepancy in analysis. As road networks and flood risks are both continually changing, especially in response to new development in and near the floodplain and in response to climate change, matching flood maps and road inventories will continue to be a challenge. However, future work will need to consider the effect of inconsistencies in the timing of road data and flood projections.
未来的研究工作可以进一步细化所考虑的洪水风险范围。本研究采用百年一遇洪水图来识别受淹道路。洪水图通常是韧性规划的得力工具，但在道路中断映射方面存在一定局限性。洪水图是多种潜在洪水情景的集合，每种洪水情景对应于依赖当时不同气象条件（如降水强度和位置）的中断模式。每一次中断都将导致独特的可达性状况。然而，本研究并未提供每次洪水的具体可达性结果，而是汇总了所有洪水情景的可达性结果。为提升当前可达性制图结果的精确度，未来研究将结合动态洪水模拟（Barnard et al., 2019; Nofal & van de Lindt, 2021），开展基于情景的可达性分析。未来的研究还可能需要考虑随着气候变化，风险如何演变，例如，2020 年的百年一遇洪水在 2050 年可能变为二十年一遇。通过考虑在多种洪水情景下不同道路中断情况的概率，我们可以得出概率性的通行损失风险图，从而更好地指导基础设施投资的优先级排序。此外，百年一遇洪水图基于 2020 年数据，而道路网络则基于特拉华州交通部 2022 年的清单。我们承认，这两组数据之间的时间差可能在分析中产生细微差异。由于道路网络和洪水风险均持续变化，特别是在应对洪泛区内外的新发展和气候变化时，匹配洪水图与道路清单将继续是一个挑战。然而，未来的工作需要考虑道路数据与洪水预测时间不一致所带来的影响。

Emergency managers, planners, and adaptation professionals frequently make decisions about how to prioritize resource allocation for risk reduction. In transportation terms, government officials at federal, state, and local levels have to identify which roads to prioritize for projects that prevent or reduce inundation or that re-open roads after they are flooded. The methods presented in this paper can assist officials in identifying roads that are most important for restoring access, with the caveats noted above. However, disaster recovery in a real-life situation is a dynamic process. For example, the sequence of road restoration can affect overall network accessibility (Wu & Wang, Citation2021), so the criticality of a road may change after the restoration of its counterparts. Thus, we will extend an optimization model in future work to derive the critical roads whose sequential restoration can rapidly recover the most critical facility accessibility. These types of innovations can inform practitioners both as they consider pre-flood risk reduction measures and as they engage in post-flood recovery.
应急管理、规划及适应性专业人员经常需要就如何优先分配资源以降低风险做出决策。在交通领域，联邦、州和地方各级政府官员必须确定哪些道路应优先用于预防或减少洪水淹没的项目，或在道路被洪水淹没后优先恢复通行。本文提出的方法可帮助官员识别对恢复通行至关重要的道路，但需注意上述注意事项。然而，现实中的灾害恢复是一个动态过程。例如，道路修复的顺序会影响整个网络的可达性（Wu & Wang, 2021），因此某条道路的重要性可能在其他道路修复后发生变化。因此，我们将在未来的工作中扩展一个优化模型，以确定那些按序修复能迅速恢复最关键设施可达性的关键道路。这类创新不仅能为从业者在考虑洪水前风险降低措施时提供参考，也能在灾后恢复工作中发挥指导作用。

6. Conclusion 6. 结论

This paper uses a network approach to examine Delaware coastal communities’ access to critical facilities such as hospitals, EMS, and emergency shelters in the face of a 100-year flood event. In particular, we consider the partial functional failure in flood-induced road disruption characterizations by adopting a non-linear relationship between travel speed and flood depth. Moreover, a modified betweenness centrality is developed to capture the road criticality when considering the communities’ access to critical facilities. We show that communities’ access to critical facilities is differentially affected by the flood, and flood-induced isolation poses greater threats to the accessibility of critical facilities as compared to direct flood impact. Specifically, 36 (out of total 87) long-term care facilities are disconnected from hospitals, with 32 of those being isolated. The flood results in an average increase in travel time to hospitals of 2.23 minutes, which could seriously affect individuals seeking urgent health care (eg. heart patients). We also identified the roads that are most important, particularly for socially vulnerable communities, for accessing critical facilities.
本文采用网络方法，研究特拉华州沿海社区在百年一遇洪水事件中对关键设施如医院、急救医疗服务及应急避难所的可达性。特别地，我们通过引入旅行速度与洪水深度间的非线性关系，考虑了洪水引发道路中断导致的局部功能失效。此外，我们开发了一种改进的介数中心性指标，以捕捉在评估社区对关键设施可达性时道路的关键性。研究表明，洪水对社区关键设施的可达性影响存在差异，且洪水引发的隔离对关键设施可达性的威胁远超洪水直接冲击。具体而言，87 处长期护理设施中有 36 处与医院断开连接，其中 32 处被完全隔离。洪水导致前往医院的平均旅行时间增加 2.23 分钟，这对急需医疗服务的个体（如心脏病患者）可能产生严重影响。我们还识别出对社会弱势社区尤为重要的关键道路，这些道路对于保障关键设施的可达性至关重要。

The methods presented herein will require continued refinement to better capture nuances in how different levels of access to different types of critical facilities affect different groups of residents. This will require additional research on scales of analysis, methods of measuring community characteristics, and consideration of additional types of critical facilities. Future work will also need to incorporate more dynamic methods for assessing flood risk and dynamic recovery efforts. These types of dynamic assessment will be particularly important in the light of climate change. Nevertheless, the methods presented herein represent important advances in understanding how floods affect the provision of health services.
本文所述方法需持续精进，以更精准捕捉不同层级对各类关键设施的访问权限如何影响不同居民群体的细微差别。这要求进一步研究分析尺度、社区特征测量方法，并考虑更多类型的关键设施。未来研究还需纳入更动态的洪水风险评估与动态恢复措施。在气候变化背景下，这类动态评估尤为重要。尽管如此，本文提出的方法在理解洪水如何影响医疗服务供给方面已取得重要进展。

CRediT statements CRediT 声明

Utkarsh Gangwal: Conceptualization, Methodology, Analysis, Visualization, Writing- Original draft preparation. A.R. Siders: Conceptualization, Analysis, Reviewing & Editing, Funding acquisition. Jennifer Horney: Conceptualization, Analysis, Reviewing & Editing. Holly Michael: Conceptualization, Analysis, Reviewing & Editing. Shangjia Dong: Conceptualization, Methodology, Analysis, Visualization, Writing- Original draft preparation, Reviewing & Editing, Supervision, Funding acquisition.
Utkarsh Gangwal：概念构思、方法论、分析、可视化、撰写-原始稿件准备。A.R. Siders：概念构思、分析、审阅与编辑、资金获取。Jennifer Horney：概念构思、分析、审阅与编辑。Holly Michael：概念构思、分析、审阅与编辑。Shangjia Dong：概念构思、方法论、分析、可视化、撰写-原始稿件准备、审阅与编辑、监督、资金获取。

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Acknowledgments 致谢

The authors would like to acknowledge funding support from the University of Delaware Research Foundation (UDRF) project #21A00986 and Delaware Department of Transportation project #T202266002, and the data support from the First Street Foundation and Stephen Pondo-Voigt (Whitman, Requardt & Associates). Any opinions, conclusions, and recommendations expressed in this research are those of the authors and do not necessarily reflect the view of the funding agencies. The authors would also like to thank the Editor and the anonymous reviewers for their constructive comments and valuable insights to improve the quality of the article.
作者感谢特拉华大学研究基金会（UDRF）项目#21A00986 及特拉华交通部项目#T202266002 提供的资金支持，以及 First Street 基金会和 Stephen Pondo-Voigt（惠特曼-雷夸特与合伙人事务所）提供的数据支持。本研究中表达的任何观点、结论和建议均为作者个人意见，并不一定代表资助机构的观点。此外，作者对编辑及匿名审稿人提出的建设性意见和宝贵见解表示感谢，这些意见和见解有助于提升文章质量。

Disclosure statement 披露声明

The Coalition for Disaster Resilient Infrastructure (CDRI) reviewed the anonymised abstract of the article, but had no role in the peer review process nor the final editorial decision.
灾害韧性基础设施联盟（CDRI）审阅了文章的匿名摘要，但在同行评审过程及最终编辑决策中未扮演任何角色。

Supplementary material 补充材料

Supplemental data for this article can be accessed online at https://doi.org/10.1080/23789689.2022.2149184
本文的补充数据可在线访问，网址为 https://doi.org/10.1080/23789689.2022.2149184

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Funding 资金

The Article Publishing Charge (APC) for this article is funded by the Coalition for Disaster Resilient Infrastructure (CDRI).
本文的文章出版费用（APC）由灾害韧性基础设施联盟（CDRI）资助。

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