Risk Management of Rural Road Networks Exposed to Natural Hazards: Integrating Social Vulnerability and Critical Infrastructure Access in Decision-Making

Abstract

Road networks are essential for access, resource distribution, and population evacuation during natural events. These challenges are pronounced in rural areas, where network redundancy is limited and communities may have social disparities. While traditional risk management systems often focus on the physical consequences of hazard events alone, specialized literature increasingly suggests the development of a more comprehensive approach for risk assessment, where not only physical aspects associated with infrastructure, such as damage level or disruptions, but also the social and economic attributes of the affected population are considered. Consequently, this paper proposes a Vulnerability Access Index (VAI) to support road network decision-making that integrates the social vulnerability of rural communities exposed to natural events, their accessibility to nearby critical infrastructure, and physical risk. The research methodology considers (i) the Social Vulnerability Index (SVI) calculation based on socioeconomic variables, (ii) Importance Index estimation (I_imp) to evaluate access to critical infrastructure, (iii) VAI calculation combining SVI and I_imp, and (iv) application to a case study in the influence area of the Villarrica volcano in southern Chile. The results show that when incorporating social variables and accessibility, infrastructure criticality varies significantly compared to the infrastructure criticality assessment based solely on physical risk, modifying the decision-making regarding road infrastructure robustness and resilience improvements.

1. Introduction

Road networks play a crucial role in connecting communities with basic services, such as education and health, especially in rural areas, where network redundancy is uncommon and population accessibility to services and goods may have significant limitations [1,2]. Road networks are fundamental to the development of social and economic systems, enabling the continuity of logistics chains and facilitating daily mobility.

Road networks are complex, large-scale, and spatially distributed systems, making them particularly vulnerable to natural hazards [3]. Traditional risk management systems (RMS) study the risks of road networks by considering the physical damage to road assets and indirect costs. Risk is estimated by evaluating the hazard magnitude and territorial exposure using sophisticated simulations, road asset fragility models, mitigation assessments, and user and recovery cost calculations [4,5]. Recent advances have also explored the use of machine learning to assess post-event road closures, with promising results in detecting accessibility gaps after hurricanes [6].

However, this approach overlooks the broader societal consequences of natural hazards. A key shortcoming of traditional RMS is the limited consideration of how hazards disproportionately affect different population groups based on their socioeconomic conditions [7]. The shift from physical to social vulnerability represents a necessary expansion of the traditional risk assessment framework, including social, economic, and cultural dimensions. Social vulnerability encompasses issues such as poverty, inequality, access to resources, social networks, and institutional capacities, all of which influence a population’s resilience [7]. This integration helps provide a more accurate picture of flood risk and informs equitable risk management decisions [8].

Recognizing these dimensions allows for a more comprehensive and equitable approach to reducing risks. Composite indices, such as the World Risk Index, have proven valuable in visualizing how social vulnerability, exposure, and hazards intersect to create systemic risk [9]. The inclusion of social indicators and the adoption of multidimensional frameworks in risk assessment acknowledge that social diversity can significantly amplify the effects of natural hazards on people. Spatial mapping of social vulnerability has been effective in regions such as the Yangtze River Delta, where socioeconomic indicators highlight local disparities [10]. Consequently, integrating social vulnerability into a risk management framework is essential for designing inclusive and effective strategies to reduce risks and enhance resilience. The systematic review in [11] reinforces the need for integrated adaptation strategies, particularly in regions exposed to compound hazards and climate variability.

Recent research emphasizes that incorporating social vulnerability into disaster risk management frameworks helps address inequalities and social conditions that affect how communities prepare for, respond to, and recover from natural events. While traditional approaches focus primarily on physical aspects, such as exposure and susceptibility, integrating social vulnerability reveals how factors such as poverty, disability, immigration, and socioeconomic disparities increase exposure and susceptibility to harm, hinder recovery, and exacerbate inequalities in post-event scenarios [12,13]. A broader understanding permits inclusive and effective strategies and context-sensitive policies to reduce the impact of natural events, promote resilience, and reduce risk [7].

Chamorro and Tighe [14] included the social dimension in unpaved road network management systems by using the Rural Access Index (RAI) [15]. Subsequently, Chamorro et al. [16] suggested a conceptual framework for road network risk management that considers a sustainable approach by integrating hazard simulation and probabilistic models that assess the physical vulnerability of road assets and the social vulnerability of the population, including users and non-users of road networks.

Transportation networks play an important role in the management of natural events [17,18]. Road networks enable access to emergency services in critical infrastructures such as hospitals during and after extreme natural events, as demonstrated by the 1995 Kobe earthquake, which highlighted the vital role of road networks in emergency response and recovery [10] and facilitated the provision of equipment and humanitarian goods to affected areas [19,20].

The identification of the most important roads, such as those that can cause loss of connectivity to critical infrastructure (CI), including drinking water systems, power grids, and essential services, is a key factor in the evaluation of accessibility [21]. Roads providing access to CI have significant indirect exposure to denial of access and services, especially during floods and earthquakes, due to interdependent infrastructure failures [22] and their potential to facilitate rural emergency travel [23].

The interdependence between road networks and critical infrastructure is extensively recognized in the literature, as shown in [10,17,18,19,20,21,22,23]. Nevertheless, there remains a need for indicators that assess the accessibility of rural populations to critical infrastructure using road networks. This paper proposes a method based on the Vulnerability Access Index (VAI) to evaluate access to critical infrastructure. The index considers the existing road network and integrates the social vulnerability of rural communities exposed to natural events with their accessibility to critical infrastructure.

The proposed index allows for prioritization; for instance, investments to enhance the robustness of road segments are based not on traffic volumes, as is typical, but on their relevance to ensuring equitable territorial access and serving a highly vulnerable population.

The remainder of this paper is organized as follows: The first part reviews the available social vulnerability indicators and methods, including the relevance of critical infrastructure placement. Subsequently, the VAI calculation methodology is presented, which consists of the construction of a Social Vulnerability Index (SVI), development of an Importance Index (I_imp) to evaluate access to critical infrastructure, and calculation of VAI, which is obtained as a combination of the indices estimated in the previous stages. Finally, the VAI is calculated and integrated into a road risk assessment in the influence area of the Villarrica volcano, located in Araucanía, Chile. The results show that the VAI combined with traditional road risk assessment is able to identify the links of the road network that allow access to territories that present accessibility or social vulnerability and therefore require special attention when making decisions about the resilience or robustness of the road network.

2. Road Networks as a Connector for Rural Population

Rinaldi et al. [24] define critical infrastructure (CI) as a network of engineered systems and processes that operate collaboratively to produce and distribute essential goods and services. Examples of critical infrastructure include sanitary systems, drinking water supply networks, and electricity grids. Road networks are critical infrastructures that connect various components of a territory, such as the rural population inhabiting it and other critical infrastructures. Within the context of risk management systems (RMS), the social dimension of a road network’s role in a territory has been considered alongside technical and economic factors.

Furthermore, a review of the state of the art on social vulnerability, used as a proxy for the social dimension, was conducted to better represent rural populations. Because road networks function as vital links between rural communities and essential services provided by critical infrastructure, various methods have been evaluated to assess access to these infrastructures. Social vulnerability in rural areas exhibits specific characteristics, such as limited access to basic services, lower educational attainment, restricted economic opportunities, and underdeveloped infrastructure for disaster preparedness and responses. These factors increase the susceptibility of rural communities to natural hazards and impede their recovery compared with that of urban areas [25].

Understanding the relationship between social vulnerability and road networks is crucial for understanding how communities access critical resources and services during emergencies and natural disasters. An adequate road network can substantially reduce social vulnerability by facilitating mobility, evacuation, and aid distribution, especially in areas with high social vulnerability. Conversely, inadequate road infrastructure may isolate vulnerable communities, exacerbate their exposure, and complicate post-disaster recovery efforts [16].

2.1. The Role of Social Dimension in Vulnerability

The social dimension assessment is a sustainable approach. The quantification of social vulnerability is crucial for planning mitigation measures to address natural hazards and to better understand risks [26,27]. The impact of natural events on physical territory may seem unrelated to social conditions, but that is not the case with disaster impacts, which vary based on the level of development and vulnerability of the local population [28]. Koks et al. [8] propose social vulnerability as a key element for effective, equitable, and acceptable development of risk management strategies.

Social vulnerability has different meanings depending on its application. The literature presents several definitions. Although there is no consensus on a single definition, a common trend in the literature is to associate social vulnerability with the susceptibility of a system—whether individuals, communities, or infrastructure—to be adversely affected by a hazardous event [29,30,31,32]. The United Nations Office for Disaster Risk Reduction [33] defines social vulnerability as the conditions determined by physical, social, economic, and environmental factors or processes that increase the susceptibility of an individual, community, asset, or system to the impacts of hazards. Most definitions agree on approaching vulnerability as a function of potential loss and capacity for recovery, often conceptualized through resilience [34].

In recent decades, studies on vulnerability, particularly social vulnerability, have expanded significantly [35,36,37]. Unlike biophysical vulnerability, which focuses on physical exposure, social vulnerability examines pre-existing social and economic conditions that influence a population’s capacity to prepare for, respond to, and recover from disasters [38,39]. Studies have shown that low-income populations, the elderly, children, women, immigrants, and socially marginalized groups generally face higher recovery costs and inhabit areas with greater exposure to hazards [40,41].

Various methodological approaches have been developed to assess social vulnerability, including hierarchical weighting, thematic pillars, cluster-based profiling, and inductive models based on factor analysis [42]. Among these, the Social Vulnerability Index (SoVI^®) developed by Cutter et al. [38] is widely applied. This index allows for the quantification and visualization of spatial patterns of social vulnerability using variables derived from census data, socioeconomic indicators, and environmental data. It has been used in Brazil [28], Portugal [43], China [44], and Chile [7].

Although the SoVI^® has been widely applied in various contexts, including Brazil and Portugal, its direct use in rural environments may present certain limitations. The index was originally developed based on sociodemographic variables derived from urban or densely populated environments, which may not fully capture the distinct facets of rural community vulnerability, such as geographic isolation, limited access to services, and sparse infrastructure. Furthermore, rural areas often have low population densities and informal economies that are not always well represented in the conventional datasets used to estimate social vulnerability.

The SoVI^® and similar indices are valuable tools for reducing the complexity of vulnerability studies, providing insight into multiple dimensions through composite indicators [45]. However, they are often limited to descriptive or inductive analyses and do not always allow for the examination of the underlying social processes that generate vulnerability [46,47]. Furthermore, although widely replicated, mostly at the local or municipal level, national-level applications remain limited, despite their importance in informing public policies and prioritizing resource allocation [48,49,50].

Consensus exists regarding the dimensions to be considered, such as the lack of access to information, knowledge, or technological sources; limited access to political power or its representation; social capital, including social networks and connections; beliefs and traditions; housing and its age; disabled or dependent persons; and the type and quality of infrastructure [51,52]. However, discrepancies exist between authors regarding the variables that should be used to measure social vulnerability. In general, social vulnerability indices depend on the availability of data. Although indicators such as the SoVI^® have been applied in various societies, their heterogeneity necessitates local calibrations. This calibration is particularly relevant in countries such as Chile, where territorial and social disparities directly impact vulnerability to natural hazards [7].

2.2. Access of Rural Population to Critical Infrastructure

The concept of critical infrastructure has received special attention at the global level. Many nations and international organizations have developed their own definitions. For example, the group of countries forming the Critical Five (Australia, Canada, New Zealand, the United Kingdom, and the United States) defines critical infrastructure as systems, assets, facilities, and networks that provide essential services necessary for national security, economic security, prosperity, and the health and safety of their respective nations [53]. The Chilean Chamber of Construction [54] classifies the national critical infrastructure into three groups: basal infrastructure (water resources, power, and telecommunications), logistical support infrastructure (interurban roads, airports, ports, and railroads), and infrastructure for social use (urban roads, public spaces, education, hospitals, and prison infrastructure).

The services provided by critical infrastructure are key to the daily lives of the population. These services become even more important after natural events. The Federal Emergency Management Agency (FEMA) prioritizes access to natural hazards for certain critical infrastructures, such as emergency operations and supply distribution centers [55]. When an event occurs, the evacuation of people or access to emergency services in the affected area is crucial to ensure a rapid response to the event. Thus, road infrastructure and its conditions are key to providing accessibility after extreme natural hazards [23]. Road links that provide access to critical infrastructure, particularly those associated with emergency services such as hospitals or police stations, play an important role in responding to extreme natural events [56].

Ghavami [3] introduced the concept of the strategic road as the road that provides an adequate emergency response in a disaster situation and the failure of which has high negative impacts. Other authors have considered the criticality of road links as an indicator of road performance [57,58,59,60]. If the road link is weak, the road components are critical [3].

Accessibility to critical infrastructure is measured in the literature in terms of walkable distance, which delimits an area of influence that varies between urban and rural contexts. The Rural Access Index (RAI) [15] established 2 km as the maximum walkable distance in rural areas. In an urban context, Yang and Diez-Roux [61] proposed a walkable distance of up to 400 m.

Neither of these accessibility proxies is linked to natural hazard contexts. However, they show variables and methods for considering access to critical infrastructure that are relevant to the proposed methodology in this study. Some relevant parameters for measuring accessibility are as follows:

• The Rural Access Index [15] evaluates access to health services in rural areas using spatial accessibility, health needs, and mobility. In particular, the spatial accessibility index, group populations, and healthcare services within floating catchment areas were examined. It measures the distance to services, number of services, and size of the population at each location [62].
• The total number of opportunities (places for dining, entertainment, shopping, or personal errands) available to individuals within their activity spaces is another measure of accessibility [63]. A potential activity space is defined as the longest distance covered within an individual’s daily trips from their origin or destination to their home. Social variables such as youth, coming from small households, having driver’s licenses, stable jobs, living in urban environments, and willingness to travel long distances increase the number of opportunities in the activity space and the accessibility [63].
• The Infrastructure Density Index [37] detects the concentration of critical infrastructure within a certain area of influence. It is calculated through equal weighting and simple addition of two infrastructure categories: (i) supply infrastructure, such as power plants or water supply systems, and (ii) contamination infrastructure, such as refineries, dumpsites, and water treatment plants. The index values ranged from zero to one. Higher values indicate greater infrastructure density and accessibility [37].
• Travel time during normal operations is a standard measure of accessibility. A comparison with travel time after a natural event affects infrastructure and facilities and can explain the loss of accessibility from a territorial unit of analysis to some critical services (for instance, healthcare facilities). It permits the creation of buffer areas around facilities in terms of travel time to access before and after natural events and a comparison with the desirable access time [64].

3. Methodology Proposed for Assessing Social Vulnerability and Access to Critical Infrastructure

The proposed method integrates the social vulnerability of rural communities exposed to natural events and their accessibility to nearby critical infrastructure to estimate a Vulnerability Access Index (VAI) for each community. The VAI describes the relevance of the road network for accessing critical infrastructure or services, given their social vulnerability and the relative importance of routes used by communities to access critical infrastructure or services. The VAI provides information to decision-makers to prioritize investments to enhance road robustness, considering the physical vulnerability of the infrastructure and the social vulnerability of the population.

3.1. Conceptual Framework

Figure 1 illustrates the conceptual framework of the VAI calculation. The input data are those that permit the configuration of the explanatory variables of the SVI and I_imp. Data can be obtained from population censuses, socioeconomic surveys, critical infrastructure surveys, and road network inventories. Data disaggregation depended on the scale of the territorial unit being analyzed. Stages one, two, and three describe the procedures used to obtain each index. The output data are each index (SVI, I_imp, and VAI). Because all variables and data are spatial, the output of each index is represented by maps, which can be overlapped with physical vulnerability maps of road assets to produce a risk map from which critical road links can be easily identified.

The proposed method consists of three stages. Stage 1 involves the construction of the SVI based on socioeconomic variables using principal component analysis (PCA) to identify the most determining dimensions of social vulnerability in terms of explained variance. SVI calibration is similar to the procedure used to calibrate the SoVI^® [38].

In Stage 2, the Importance Index (I_imp) is estimated in terms of traffic, redundancy, and the length of the different routes used by the population to access critical infrastructure. The procedure consists of obtaining the location of the existing CI in the territory under analysis, defining the road network under analysis and its attributes, and specifying the area of influence around each CI. These activities are conducted using GIS software (arcGIS Version 10.8).

Stage 3, the calculation of the VAI, combines the SVI and I_imp. The next sections explain the conceptual framework and each step of the method used to obtain the VAI. This index associates each link in the road network with the vulnerability of the population and their accessibility to nearby critical infrastructure.

3.2. Social Vulnerability Index

The main objective of Stage 1 is to perform the necessary steps to calculate the SVI adapted for decision-making on spatially distributed infrastructure, such as road networks. The SVI variables are obtained using a factor analysis that reduced the number of variables from the input data according to the characteristics of the study area.

The variables required to evaluate vulnerability were defined by reviewing the literature and available databases. In addition, the rural population of Chile inhabits very large, low-density territories. Moreover, agricultural activities or activities related to the environment and natural resources are dominant. This information helps determine the social variables that define rural Chilean society to develop an index that clarifies the conjunction of these variables.

Regarding socioeconomic variables, it should be mentioned that an indicator associated with critical infrastructure in the studied territory was incorporated into the principal component analysis (PCA). In particular, the variable of critical infrastructure density within each unit of analysis was designed considering the interurban highway system, healthcare facilities, educational infrastructure, power sector, water system, and citizen security services. This modification is based on the revised literature and infrastructure density variables.

Once the data for each unit of analysis were collected, the values were normalized through percentages and then standardized using the Z-score to obtain variables with a zero median and unitary standard deviation. The components of the SVI are obtained by applying PCA and “varimax” rotation. The number of principal components is obtained using the Kaiser criterion, which suggests retaining components with eigenvalues higher than 1.0. The final SVI score for each territorial unit is a component addition, considering their scores and cardinality.

3.3. Importance Index of Road Infrastructure

The aim of Stage 2 was to design and construct the Importance Index (I_imp). The procedure used to assess society’s dependence on critical infrastructure focuses on accessibility. The selected critical infrastructure systems were healthcare facilities, educational infrastructure, power systems, rural drinking water systems, citizen security, and emergency services. The interurban highway network was the main infrastructure in the analysis because it connects the services provided by the selected critical infrastructure.

An area of influence of 2 km was determined around the infrastructure and highway network links selected based on [15]. The 2 km threshold corresponds to the maximum reasonable walking distance in rural areas with limited transportation alternatives. If a road segment within this buffer zone is disrupted, residents may still be able to reach the critical infrastructure by foot. This threshold has been widely applied in previous studies examining rural areas [65,66,67,68,69,70]. Chillón et al. [71] empirically validated the 2 km distance as a reasonable walking range in the context of education. However, this threshold is context-dependent, as the physical effort required to walk 2 km varies significantly between flat and mountainous areas and is influenced by individual physical capacity. Despite these limitations, this study adopted the 2 km threshold because of its widespread use in the literature and the lack of a locally calibrated alternative for the study area. Importantly, the proposed methodology remains flexible and can accommodate alternative thresholds appropriate to the context.

The average annual daily traffic (AADT; vehicles/day-year) and road network link lengths were also collected. These two variables strengthen the functional and spatial importance of each road type. AADT reflects the level of use of each road (roads with higher AADT are assumed to be more critical) [72]. AADT is also a proxy for socioeconomic dependence on a particular road segment. Roads with higher AADT are more critical for people’s mobility and goods transportation [73]. Road length captures spatial coverage. Longer road segments are likely to serve broader areas, particularly in regions with low road network density. By combining these two variables, the index accounts for both the intensity of use and the geographic significance of each link, which is particularly relevant for rural areas with limited connectivity and infrastructure redundancy [74].

The normalized weighted sum of Equation (1) yields the dimensionless value of the I_imp by weighing the average annual daily traffic (AADT) by the link length (L) and dividing it by the total number of links (L_T) that provide access to the same infrastructure and the total traffic (AADT_T). This index highlights rural links that connect wide areas with mostly low road-network densities.

$$I_{imp}=1+{\sum }_j^m{\displaystyle \frac{L_i\times A{ADT}_i}{L_{T_j}\times A{ADT}_{T_j}}}$$

(1)

In Equation (1), i is the analyzed link, j is the critical infrastructure accessed by link i, and m is the total infrastructure accessed by link i. The T_j sub-index refers to the total number of links that provide access to infrastructure j and the total traffic on the road links that provide access to infrastructure j. L is the length of the link (km), and AADT is the traffic (vehicles/day-year) on link i.

3.4. Vulnerability Access Index

The VAI is obtained by multiplying the SVI by the I_imp, as shown in Equation (2). The variables and subscripts have already been described and are the same as those in Equation (1).

$$VAI=SVI(I_{imp})=SVI\left(1+{\sum }_j^m{\displaystyle \frac{L_i\times A{ADT}_i}{L_{T_j}\times {AADT}_{T_j}}}\right)$$

(2)

For the spatial estimation of the VAI, the following considerations should be considered: the purpose of the VAI is to identify the arcs of the road network that are relevant for providing accessibility to critical infrastructure. Therefore, it is important to distinguish between links in the road network that provide access to critical infrastructure and those that do not. The links of the road network that provide accessibility will have SVI and I_imp values corresponding to the territorial unit in which each link is located. The links that do not provide accessibility, on the other hand, will have as their only attribute the value of SVI corresponding to the territorial unit in which each link is located, whereas I_imp will have a value of 1. In both cases, Equation (2) is valid.

4. Case Study: Integrating the VAI to Road Network Exposed to Volcanic Hazards

This case study illustrates the estimation of the VAI and its integration into the risk assessment of road networks exposed to volcanic hazards. The road network near the Villarrica volcano in southern Chile was selected. The Villarrica volcano is one of the most active volcanoes in Chile. The territory comprises the municipalities of Villarrica, Pucón, Curarrehue, and Panguipulli (see Figure 2), which are within the influence area of a volcanic complex dominated by the Villarrica volcano. The population and infrastructure are highly exposed to volcanic hazards. It is a mountainous region close to the border with Argentina, with lakes and volcanoes. The location and topography of the study area restrict the existence of a dense and redundant road network, limiting the mobility and accessibility of the people living there.

The study area has intense tourist activities, encouraged by a diverse landscape of lakes, volcanoes, forests, and hot springs. The environment enables trekking and winter sports, which are mainly concentrated in the municipalities of Villarrica and Pucón. Agricultural and forestry activities are predominant in Panguipulli and Curarrehue, respectively. These municipalities have a low population density and low-density road network, producing a certain level of isolation. There was also a strong presence of native indigenous people in the study area during the survey.

4.1. Estimation of Social Vulnerability

Data were obtained from the 2017 Chilean National Census performed by the Chilean National Statistics Institute (INE) and the 2017 CASEN survey conducted by the Social Observatory of the Ministry of Social Development [75,76]. The 2017 census was Chile’s most recent national census. Although a new census was conducted in 2024, the results will not be available until 2025. Therefore, while acknowledging that significant social and economic changes have occurred over the last eight years, especially due to the COVID-19 pandemic and 2019 social unrest, the 2017 census remains the primary official dataset for nationwide demographic and social information in Chile [77].

The 18 variables used to obtain the SVI, grouped by the representative dimensions of social vulnerability, are listed in

Table 1. Variables of social vulnerability used to estimate the SVI.

Id	Dimension	Variable
1	Gender	% of Women
2	Age	% Population ≤ 15 years
3		% Population ≥ 65 years
4	Migration	% Non-resident population in this municipality
5	Education	% Population w/o studies
6		% Population with primary education
7	Ethnicity	% Native Population
8	Socioeconomic status	% Population in situation of multidimensional poverty
9		% Households with no support and social participation
10		Total average income per capita of household
11	Employment-occupation	Dependency Ratio
12		% Population Primary Sector
13		% Population Secondary Sector
14		% Non-active Population
15	Quality of built environment	% Non-recoverable Housing
16		% Housing w/o direct access to water (w/o connection to public network or well)
17		% Housing with medium or critical overcrowding
18	Critical infrastructure	Density of critical infrastructure and road network

. The dimensions of social vulnerability were based on the literature and the data available in the Chilean Census and CASEN survey: gender, age, migration, education, ethnicity, socioeconomic status, employment occupation, quality of the built environment, and critical infrastructure density.

Principal component analysis (PCA) was conducted to identify the main dimensions underlying social vulnerability, as characterized by the variables in Table 1. Seven principal components with eigenvalues greater than one were retained, explaining 73.8% of the total variance in the dataset. These components represent the dominant factors influencing social vulnerability in the study area. The seven components and variables associated with PCA were as follows (the numbers inside brackets are the variable weights, and the signum is the effect on the SVI):

• Socioeconomic Status: average income (+0.955)
• Dependent Population: dependency ratio (+0.829)
• Women and Children: women and young children (+0.855)
• Education and Unemployment: population with primary education (+0.882)
• Occupation: secondary sector (−0.811)
• Household and Housing Quality: non-recoverable housing unit (+0.801)
• Access to Critical Infrastructure: CI density (+0.870)

The SVI is the sum of seven principal components categorized into five levels according to the standard deviation thresholds proposed by Cutter [39].

The SVI map (Figure 3) shows the prevalence of medium-to-high-social-vulnerability areas. Curarrehue and Panguipulli predominated in terms of high levels of social vulnerability. In Curarrehue, none of the territories reached low or very low vulnerability. This is consistent with the scatter of the sparse population, which is mainly rural, evidencing an isolation level higher than that of the rest of the neighboring regions. In contrast, low and very low social vulnerability were mainly present in Pucón and Villarrica, which is consistent with their high development levels compared to the other municipalities. Both places have a strong tourist presence and, in recent years, have attracted people with a greater economic capacity to travel to this area because of its great tranquility and intriguing landscapes.

4.2. Estimation of Road Network Importance Index

The main inputs for estimating the I_imp are the road network and critical georeferenced infrastructure (health system, educational infrastructure, power sector, rural drinking water system, citizen security, and emergency services). This information is available in the Chilean Geospatial Data Infrastructure (IDE-Chile) database. Data can be visualized and downloaded as shape files from the online viewer provided by IDE-Chile.

A 2 km buffer was created around each critical infrastructure site. These buffers identify road links that are relevant to accessibility. Equation (1) was used to estimate the relative importance of these connections. Figure 4 summarizes these results. Dark red represents links with “very high” importance. Red represents links with “high” importance. The orange color represents links with “medium importance.” No link was categorized as having “low” or “very low” importance. Figure 4 shows that the links with “very high” importance are placed in the same territories in which the SVI values were “high” (See Figure 3). These territories are likely to have the highest vulnerability indices.

4.3. Estimation of Vulnerability Access Index

The SVI and I_imp indices are introduced in Equation (2) to obtain the VAI. Figure 5 shows the VAI of each road link and the SVI of each territorial unit. An increase in the vulnerability level of the links located in the most vulnerable territories can be observed. The eastern area of Curarrehue has the highest social vulnerability (higher SVI) and the most important links in terms of accessibility to critical infrastructure. These roads are the only ones providing access to the region’s infrastructure, which explains the high VAI increase in that region, accounting for 954 points in the most vulnerable segment.

In contrast, Pucón and the surrounding areas concentrate on critical infrastructure and exhibit a denser road network and low SVI values. Both patterns indicate that most links present “medium” VAI levels, and the links closest to the city have “low” and “very low” VAI levels. In terms of investment to improve accessibility, the eastern Curarrehue and western Panguipulli territories should be prioritized, considering that their vulnerability could increase the consequences of link interdiction by a Villarica volcano eruption and affect the physical part of the road network.

Figure 5 also shows the predominance of less impacted links, but with a very high dispersion range in relation to higher values because of the juxtaposition of high-vulnerability territory and the importance of accessibility. The links that finally emerge for their criticality are those present in more isolated areas and with a low density of the road network, such as the Reigolil route that connects Curarrehue from the south to the north. In this situation, contrary to isolation, links that traverse urban centers with extensive coverage of critical infrastructure emerge.

4.4. Integration of Physical Risk with the Vulnerability Access Index

The next question is how to introduce a VAI model into the risk assessment of road networks exposed to natural hazards. This section describes the procedure applied to volcanic hazards in the same territory where the VAI was calculated.

Under normal conditions, the VAI was obtained using the previously described procedure. Once a natural event physically affects a road network, several links can be disabled, partially affected, or unaffected by the event. Consequently, traffic is reassigned, increasing the total travel time in the road network. Traditionally, the total travel time is considered a proxy for physical risk [78]. The magnitude of the travel time increase depends on exposure to natural hazards, the magnitude of the hazard, and infrastructure fragility.

Therefore, as the travel time increases, accessibility to critical infrastructure decreases, and VAI magnitude increases. This increase is represented as a weight greater than 1, which multiplies the VAI obtained using Equation (2), as shown in Equation (3).

$$VA{I}_w=w_{i}VA{I}_i=w_{i}SVI\left(I_{imp}\right)$$

(3)

where i is the road link under study and w_i is the weight that represents the travel time due to an increase in travel time due to a natural event, which in this case study corresponds to an eruption of the Villarrica volcano.

The increase in travel time is the difference between the travel time under normal conditions and the travel time under restrained conduction provoked by a natural event. In both normal and restrained conditions, the travel time was estimated using the BPR travel time model [79,80,81] and traffic assignment models.

The first step in estimating the weight w_i is to define the volcanic scenarios. These scenarios were obtained from the study of the National Hydraulic Institute (INH), which modeled lahar flows of the Villarrica volcano [81]. The INH modeled three scenarios of eruptive dynamics: Hawaiian–Strombolian, sub-Plinian, and Plinian eruptions that produced lahar flows from the Villarica volcano to Villarrica Lake. Each scenario considered winter and summer conditions, respectively.

Infrastructure damage induced by lahar flows modeled by INH was computed using the fragility curves calibrated by Dagá et al. [82]. Fragility curves estimate the failure probability of bridges exposed to lahar flows, and for extension, the interruption probability of the links at which bridges are affected by lahars. This procedure permits the identification of links that are totally or partially interrupted and the operative links configuring a “damaged road network,” which is different from road networks operating under normal conditions. The incremental traffic assignment (ITA) algorithm described in [83] and the BPR travel time model were applied to estimate the travel time increase. The origin–destination and traffic data necessary to apply the ITA were obtained from the National Traffic Survey of the Chilean Ministry of Public Works (MOP). This methodology has been applied under extreme conditions resulting from natural event disruptions [84,85,86].

Figure 6 shows the area within the integration of physical risk and the VAI. This area includes a road network connecting Villarrica and Pucón (Figure 6A). This road network is directly connected to lahar flows from the Villarrica volcano (see the shaded area in Figure 6B). Each road in Figure 6B is represented by a different thickness. The black dots represent road bridges. Greater thickness indicates a greater physical risk in terms of increased travel time and, therefore, a higher weight. These links correspond to those directly affected by the lahar flow. The paths of the lahar flow modeled by the INH are represented by green, blue, yellow, and cyan.

Figure 7 shows the effect of integrating the VAI and physical risk. Figure 7A shows the VAI obtained for the road network without considering physical risk. The model estimates the same VAI level, independent of the presence of volcanic hazards and considering only the importance of the links. Figure 7B shows that when physical risk is included in the VAI calculation, three links directly affected by lahar flow increase the VAI level.

5. Results and Discussion

This study aimed to develop and apply a composite index, the Vulnerability Access Index (VAI), to assess the significance of road network segments by integrating social vulnerability with access to critical infrastructure. The results show that incorporating social indicators significantly changes the prioritization of road links compared with traditional methods that rely solely on physical risk or traffic volumes. In this section, we discuss the implications of these findings, emphasizing how the proposed methodology promotes more equitable and resilient infrastructure planning, particularly in rural areas exposed to natural hazards. The first part of the discussion addresses methodological issues, and the next covers the implications of the findings on the treatment and interpretation of risk, considering social vulnerability.

From the principal component structure of the SVI, seven components explained 73.8% of the total variance. The first (“Socioeconomic Status”, +0.955 loading) and third (“Women and Children”, +0.855) jointly accounted for 42% of the variance. Components five (“Occupation”, −0.811) and seven (“Access to CI”, +0.870) are antagonistic: territories specializing in secondary sector employment paradoxically exhibit lower social vulnerability, but only where critical infrastructure (CI) density is relatively high.

In terms of the functional and spatial importance of roads, only 11.3% of links are of “high” or “very high” importance, yet they serve over half (≈54%) of the resident population, confirming empirical findings that traffic volumes in rural areas are a reasonable—though imperfect—proxy for socioeconomic dependence. In addition, when the SVI and I_imp are fused, 17.7% of the links shift out of the “medium” band—either upward (Curarrehue east, Panguipulli west) or downward (Pucón urban core). The VAI thus surfaces latent inequities: low-traffic roads in socially fragile areas are revealed to be more critical than high-volume arterials in resilient municipalities.

Table 2. Number and links percentage categorized by SVI and I_imp level.

Index		Very Low	Low	Medium	High	Very High	Total
SVI	Number of Segments	8	52	74	70	3	207
SVI	Percentage of Segments	3.90%	25.10%	35.70%	33.80%	1.40%	100%
Iimp	Number of Segments	0	0	338	26	17	381
Iimp	Percentage of Segments	0.00%	0.00%	88.70%	6.80%	4.50%	100%

presents a summary of the road network Importance Index intervals. Because the index has a great dispersion, the extreme categories do not account for 5% of the total. The category associated with links with very low and low importance regarding their accessibility to CI has a value of zero because the calculation process estimates only the network links with some kind of infrastructure nearby (within a radius of 2 km); the remainder are excluded from the analysis. Table 2 also indicates that 88.7% of the road segments fall into the “medium” importance category, with only 11.3% classified as high or very high. Notably, no segments fell under the low or very low category, as the analysis excluded roads beyond the 2 km buffer from any critical infrastructure. This middle-heavy distribution suggests a spatially consistent reliance on road segments for accessing essential services, validating the 2 km accessibility threshold.

By analyzing the indicators directly associated with the road network, it can be observed that medium-category cases predominate (see Figure 4 and Figure 5). This result is primarily due to the distribution of the values of both indices. In the case of the I_imp, most of the links in the lower category (medium) are those that are not located within the area of influence of any CI. Figure 8 shows the distributions of the different I_imp and VAI categories.

As shown in Figure 8, most road links exhibit medium values of the Vulnerability Access Index (VAI), accounting for 82.3% of the segments. This reflects a high degree of homogeneity across the area, largely driven by uniform levels of social vulnerability, where the medium and high categories represent nearly 70% of the population, and there is a widespread medium level of access to critical infrastructure (88.7%). These two factors suggest that the region has a relatively uniform vulnerability. The proposed methodology can also be applied to identify spatial heterogeneities or disparities in social vulnerability and infrastructure access within exposed areas.

Figure 8 overlaps the categorical distributions: while 88.7% of links lie in “medium” I_imp, 82.3% remain “medium” in terms of the VAI—evidence that social weighting amplifies only a subset of segments. This selective amplification matters because traditional cost–benefit logic (traffic × damage) would dismiss low-AADT links, the and VAI demonstrates their outsized equity benefits. This application can also serve to detect service deprivation thresholds: links serving settlements where travel time to the nearest hospital exceeds 60 min (n = 5, all in Curarrehue) are flagged as “very high” VAI even though they carry <350 veh/day-year, aligning with accessibility literature that prioritizes time-critical services over traffic.

For the I_imp, only the links in the three most critical categories were found: medium, high, and very high. The most critical links were concentrated in the urban areas around the two main cities, Villarrica and Pucón. This is because urban areas concentrate most of the critical infrastructure; despite having less social vulnerability, they are hotspots for critical services. In addition, more isolated areas emerge in terms of road density, such as those located east of the municipalities of Curarrehue and Panguipulli.

The results of this study highlight the crucial importance of incorporating social vulnerability into road vulnerability assessments, particularly in rural areas that are vulnerable to natural hazards. Identifying critical road links should not rely solely on physical or functional attributes, such as traffic volume or direct hazard exposure, but must also consider the social conditions of the communities that depend on them. As observed in municipalities such as Curarrehue and Panguipulli, high levels of social vulnerability amplify the consequences of connectivity loss, as these populations face greater challenges in accessing essential services and recovering from disruptions. This approach contributes to the design of more resilient and inclusive transportation networks that better serve the disadvantaged population.

Integrating a natural hazard model (lahars in this case) into the VAI revealed that values can change significantly. As shown in Figure 7B, three road links shifted from medium to high vulnerability owing to their significant impact on travel time when disrupted. However, these results are highly sensitive to both the consequence and hazard models used in the analysis. This study quantified the consequences solely in terms of increased travel time, prioritizing road links that would result in longer detours if disrupted. Alternative consequence models, such as economic loss or gas emissions, can be incorporated to provide a broader understanding of each road disruption, potentially leading to different prioritizations of road disruptions.

Similarly, the hazard model determines the likelihood and spatial distribution of disruptions. The lahar model used in this paper has two characteristics: (i) a well-defined source (the Villarrica volcano) and (ii) a clearly delineated lahar path influenced by topography. As such, potentially affected roads are located within the known lahar paths. In contrast, natural hazards such as earthquakes can impact broader areas and therefore require a more extensive spatial hazard modeling approach. Therefore, when using the VAI for decision-making under single-hazard scenarios, road agencies must interpret the results carefully, considering the limitations and assumptions embedded in the chosen hazard and consequence models.

The study confirms a growing consensus in the literature that infrastructure risk assessment must move beyond physical vulnerability alone to incorporate socioeconomic and functional dimensions of access [8,9]. Traditional assessments prioritize roads based on structural condition or traffic volumes [10,78], yet the VAI introduces a third axis—social vulnerability—which reorders priority to include segments that serve structurally isolated and economically fragile communities. This finding aligns with Murray and Grubesic [59], who emphasized criticality from a systems-of-systems perspective. In the case study, roads like the Reigolil route (Curarrehue) would typically rank low in a purely physical-risk model but are highlighted as high-priority due to their role in connecting high-SVI populations to basic services.

The results obtained empirically support Cutter’s argument [31,51] that social vulnerability is not merely additive to hazard risk but structurally shapes the outcomes of hazard exposure. We observed how similar hazard exposure levels (e.g., roads under lahar threat) produced different VAI outcomes depending on the socioeconomic profile of the surrounding communities.

6. Conclusions and Recommendations

This study proposes a method for creating an index associated with a road network that considers social vulnerability and access to critical infrastructure. The VAI provides a multidimensional and sustainable approach when integrated into road network risk management systems.

Social vulnerability was evaluated by developing an SVI based on the SoVI^® structure. Through an exhaustive bibliographical review and the identification of available databases, we determined the socioeconomic variables that define rural Chilean society in the case study area, which are nationally representative. The inclusion of infrastructure density as a variable within the SVI allows for the consideration of the built territory by including several critical infrastructures in the analysis. This allows an engineering perspective to be integrated into the traditional socioeconomic approach to variables.

The Importance Index (I_imp) associated with the links in the road network was calculated. This index evaluates accessibility to various infrastructures, where the road network is the connecting point. It considers variables such as the length of links, their AADT, and the number of accesses to each of the analyzed infrastructures. Thus, the links can be categorized based on their level of importance in terms of accessibility to critical facilities.

Although the 2 km threshold adopted from the World Bank Rural Access Index (RAI) provides a standardized and widely used measure of rural accessibility, it may not fully reflect the actual conditions in certain areas. In some areas, walking 2 km can be significantly more difficult owing to steep slopes, natural barriers, and limited pedestrian infrastructure. Consequently, applying a uniform 2 km radius may lead to an overestimation of the effective accessibility to critical infrastructure in some regions. Nonetheless, this threshold was used in the present study for the entire study area to ensure consistency. Future research could refine this approach by incorporating changes in walking distance, which may reflect local conditions.

Finally, these two indices were combined into a single index, the Vulnerability Access Index (VAI). This index jointly values the road network in terms of its importance (I_imp) and the social vulnerability (SVI) of the population living in the territory through which the road network under study runs. This information was reflected in a case study conducted in the vicinity of the Villarrica volcano.

In this way, the developed methodology evaluates social vulnerability and identifies territories whose state of vulnerability of access to their own resources and infrastructure makes them the focus of attention in favor of better public policies. Regarding the methodology developed to analyze the location of critical infrastructure in the territory and its accessibility, this method identified links in the road network that allow access to territories with extreme accessibility needs and which therefore require special attention. This method also identifies areas where the density of road infrastructure that provides access to critical assets is minimal and practically without redundancy. Thus, even before the failure of the links with these characteristics, the population of such a sector is isolated with respect to its critical services. However, the methodology also highlights the links that run through areas with high critical infrastructure density. In this case, these are links of great value because a failure, despite these links having greater redundancy, would leave much critical infrastructure unattended.

Applying the developed methodology allows prioritization differently from traditional practice, which is based on the traffic of individual roads. Instead, this methodology prioritizes roads according to their relevance to the territory, considering the rural population and access to other critical infrastructure.

This methodology is presented as a road-network management tool. It can be easily incorporated into the decision-making process, as shown in the application case. This index enables the consideration of critical criteria associated with the population and territory beyond road infrastructure itself.

The Vulnerability Access Index is a tool that helps re-order investment priorities toward territorial equity. By exposing hidden interdependencies between social vulnerability and infrastructural centrality—and by remaining sensitive to dynamic hazard regimes—the VAI offers practitioners a defensible and data-driven basis for allocating scarce resilience funds where they matter most. According to this idea, the policy and planning implications of the VAI can be focused on equity-centered prioritization, adaptive redundancy, dynamic monitoring, and interaction between sectors such as healthcare, highways, and education.