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date: 24 March 2018

# Physical Resilience in Cities

## Summary and Keywords

In the early 21st century, achieving the sustainability of urban environments while coping with increasingly occurring natural disasters is a very ambitious challenge for contemporary communities. In this context, urban resilience is a comprehensive objective that communities can follow to ensure future sustainable cities able to cope with the risks to which they are exposed.

Researchers have developed different definitions of resilience as this concept has been applied to diverse topics and issues in recent decades. Essentially, resilience is defined as the capability of a system to withstand major unexpected events and recover in a functional and efficient manner. When dealing with urban environments, the efficiency of the recovery can be related to multiple aspects, many of which are often hard to control. Mainly it is quantified in terms of the restoration of urban economy, population, and built form (Davoudi et al., 2012). In this article, engineering resilience is defined in relation to cities’ capability to be sustainable in the phase of an extreme event occurrence while reconfiguring their physical configuration. In this view, a city is resilient if it is sustainable in the occurrence of a hazardous event.

Accordingly, in an urban context, a wide range of nonhomogeneous factors and intrinsic dynamics have to be accounted for, which requires a multi-scale approach, from the single building level to the urban and, ultimately, the global environmental scale. As a consequence, cities can be understood as physical systems assessed through engineering metrics. Hence, the physical dimension represents a starting point from which to approach resilience. When shifting the focus from the single structure to the city scale, human behavior is revealed to be a critical factor because social actors behave and make choices every day in an unpredictable and unorganized manner, which affects city functioning. According to the ecosystem theory, urban complexity can be addressed through the ecosystem theory approach, which accounts for interrelations between physical and human components.

# Introduction

The term resilience is derived from the Latin resilire, meaning “to bounce back.” The word dates back to the 19th century, when it was used in physics to indicate the ability of materials to withstand impulsive loads without suffering damage. The concept was then also used in medicine (Lotka, 1924; Pfeiffer, 1929), psychology (Garmezy, 1991; Werner, 1971), and biology (Holling, 1973).

Recently, the notion of resilience has triggered growing interest when referring to communities and urban systems in relation to natural and human-induced disasters. This approach found its basis in the 1980s, when Timmerman referred to the term as “the ability of human communities to withstand external shocks or perturbations to their infrastructure and to recover from such perturbations” (Timmerman, 1981).

The advent of the concept of resilience in this context is the result of an increasing need for a response to new and more intense threats to modern societies. In fact, growing interdependencies, exposure, and the complexity of contemporary cities, along with more severe events caused by climate change, are leading modern societies to seek prevention, preparedness, damage reduction, and rapid recovery strategies—in other words, resilience. This urgent need is pushing the scientific community to discuss how to define and integrate resilience in disaster risk processes and how to quantify it.

Many studies address resilience by interpreting urban environments as complex systems composed of dynamic relationships between the physical environment and communities. According to a general definition, cities can be regarded as resilient if they are able to cope with extreme events without suffering devastating losses and damage to their physical systems or a reduced quality of life for their inhabitants (Godschalk, 2003). However, a comprehensive definition is still not available, given the complexity of defining the behavior of urban systems in a deterministic fashion.

So, what are the real processes taking place in urban systems? What is meant by urban damage and functionality for urban systems after extreme events? Does the optimal response of urban systems to extreme events, i.e., the “resilient” response, depend on the type of event and/or the city configuration? These are just some of the questions that make the concept of disaster resilience explode with different and multidisciplinary meanings. One of these is related to the engineering understanding of the resilience concept according to the ecosystem theory.

To date, a growing number of structural systems are clustered in disaster-prone areas worldwide. Hence, whenever a catastrophic event occurs, a civil engineering approach is needed to assess urban structural performances. According to some authors, a resilient structure plays a critical role within the urban environment. In fact, it can enhance the resilience of the local community because of its capability to ensure essential services and emergency response and shelter for deallocated citizens. Furthermore, severe economic and human losses can be expected due to the damage to and collapse of buildings in the face of shocking events. As a result, designing and erecting disaster-resilient buildings and infrastructures has a positive outcome, allowing also social and economic issues to be addressed.

Furthermore, structures and infrastructures within the urban environment are interrelated upstream and downstream with other components and actors, causing uncontrollable cascade effects and consequences at different levels. Physical, geographic, and societal links exist between the urban components ruling dynamics, which are peculiar to each considered system.

An innovative, transdisciplinary field of research, the ecosystem theory, developed around the study of cities. According to a holistic point of view, cities are complex systems comprised of physical and human components that are correlated and interacting. Consequently, just like ecosystems, cities can be understood as systems that are subjected to dynamic equilibrium states and are continuously exposed to external changes.

Accordingly, ecosystem theory and engineering approaches can be collaterally developed when dealing with urban resilience to natural disasters. These are disciplines able to assess the response capability of physical systems and the indirect consequences on social agents in the face of catastrophes contextually in terms of the service function. In parallel, resilience is a critical aspect contributing to sustainability. In fact, a resilient urban environment is one that is capable of withstanding external stresses while reestablishing the economic and social equilibrium between inhabitants and the built environment.

In this article diverse approaches to the resilience definition and quantification are presented. In particular, attention is focused on the engineering resilience understood as a function of infrastructure function in cities. Multiple aspects and urban dynamics related to resilience are investigated. Finally, different methodologies to quantify resilience are discussed, highlighting the importance of strengthening the understanding of physical resilience in cities as part of the ecosystem theory according to different perspectives.

# Theories and Perspectives on Urban Resilience

## Understanding Urban Resilience

The theoretical construct of resilience is innovative when applied to the context of urban systems. The basic principle refers to the capacity of a system composed of several nonhomogeneous components (e.g., a person and his or her body, the human brain, the microstructure of a material). These interact and coexist within the same organism (e.g., material structure, ecosystems, human or animal, communities, and cities) to enable the system to face an extreme event and bounce back from adversity. This general definition can be adapted to diverse complex systems such as ecosystems, economics, the human body, and urban environments, as is the case in many studies in the relevant literature (Zhou, Wang, Wan, & Jia, 2010).

On the other hand, cities can be subjected to diverse event typologies, each of which needs a specific approach to define resilience. Nonetheless, it is not easy to identify unique patterns for such processes to be shared worldwide and to be applied in each urban context. This is because each city has specific weaknesses and strengths and is threatened by different hazard typologies. In the case of climate-related events, for instance, the most effective mitigation techniques are indirect and to be undertaken on a global scale through the reduction of CO2 emissions and the implementation of environmental protection measures. On the other hand, in terms of seismic events, each area in the world exhibits diverse vulnerability and exposure, meaning that actions have to be assessed and applied on the local scale.

Given the wide range of perspectives on resilience and the multidisciplinary and multidimensional understandings of it, several diverse definitions can be found in the literature. In fact, none of these excludes the others, but, simply, each definition is better applied to one context than another.

According to Francis and Bekera (2014), some main areas of interest can be recognized based on the specific system resilience studied: infrastructure systems, safety management systems, organizational systems, social-ecological systems, economic systems, social systems, and a further category described as “uncategorized.”

Recently, a further field of study has gained the attention of scientists when it comes to addressing disaster resilience: community resilience. Community resilience is dependent on all the dimensions and fields of interest proposed by Francis and Bekera, and so it is the merger of them in line with the interpretation by Cutter et al. (2008).

Many authors, particularly in the field of civil engineering, address resilience in the face of natural disasters by integrating a humanitarian perspective. This enables us to account for the ability of the physical urban system to deal with extreme events while indirectly considering its interrelation with the social system in terms of the service function (Bruneau et al., 2003; Cimellaro, Reinhorn, & Bruneau, 2010; Chang & Chamberlin, 2004; Cutter et al., 2008; Davis, 2014; Decò, Bocchini, & Frangopol, 2013; Franchin & Cavalieri, 2015; Frazier, Arendt, Cimellaro, Reinhorn, & Bruneau, 2010; Frazier, Thompson, Dezzani, & Butsick, 2013; Miles, 2015). Based on a literature review, the main properties contributing to disaster resilience can be recognized according to the area of interest to which they are applied, as shown in Table 1.

Table 1. Main Aspects Contributing to Resilience, According to Area of Interest

 Resilience of ecological systems Biodiversity, redundancies, response diversity, spatiality, and governance and management plans (Adger, 2000; Cumming et al., 2005; Folke, 2006; Gunderson et al., 2002; Gunderson & Holling, 2002; Holling, 1973; Holling, 1996; Kinzig et al., 2006; Pimm, 1984) Social resilience Communications, risk awareness, and preparedness, development and implementation of disaster plans, purchase of insurance, and sharing of information to aid in the recovery process; some of these are a function of the demographic characteristics of the community and its access to resources (Adger, 2000; Allenby & Fink, 2005; Pelling, 2003) Economic resilience Loss estimation models, business disruption post-event, employment, value of property, wealth generation, municipal finance/revenues (Cardona, 2008; Fiksel, 2006; Perrings, 2006; Rose, 2004) Organizational resilience Institutions and organizations and requires assessments of the physical properties, how organizations manage or respond to disasters such as organizational structure, capacity, leadership, training, and experience (Fujita, 2006; Grote, 2008; Haimes, 2009; Kendra & Wachtendorf, 2003; Risk Steering Committee—U.S. Department of Homeland Security–, 2010; Woods & Cook, 2006) Infrastructure resilience Lifelines and critical infrastructure, transportation network, residential housing stock and age, commercial and manufacturing establishments as well as their dependence and interdependence on other infrastructure (Berkeley & Wallace, 2010; Commonwealth of Australia, 2010; McCarthy, 2007; Tokgoz & Gheorghe, 2013) Safety management system Vulnerability and exposure assessment, risk management, recovery planning, adaptation and mitigation (Chen et al., 2008; Geis, 2000; Mileti, 1999; Risk Steering Committee—U.S. Department of Homeland Security, 2010; Woods et al., 2012) Community resilience Ecological, social, economic, institutional, infrastructure, community competence indicators being merged with population wellness, quality of life, and emotional health, pre- and post-disaster community functioning (Asprone & Manfredi, 2015; Bozza et al., 2015b; Bruneau et al., 2003; Cardona, 2008; Carpenter et al., 2001; Cavallaro et al., 2014; Comfort, 1999; Cutter et al., 2008; Horne & Orr, 1997; Kendra & Wachtendorf, 2003; Kimhi & Shamai, 2004; Mallak, 1998; Mileti, 1999; Paton et al., 2000; Rockström, 2003; Timmerman, 1981; UNESCAP, 2008; UNISDR, 2009)

## The Scale of Resilience

According to the 2015 Global Assessment on Disaster Risk Reduction, losses due to intensive risks in 85 countries and territories were equivalent to a total of \$250–300 billion per year with reference to the decade 2005–2015 (UNISDR, 2015). In particular, natural hazards threaten infrastructure conservation, land use, economic and social development, and human safety. Most people, in fact, reside in cities (Crane & Kinzig, 2005) as a consequence of the unprecedented demographic scale of the urbanization (United Nations, 2015). Nonetheless, opportunities and challenges arise from the modern urbanization phenomenon in terms of future sustainable development scenarios. In keeping with this, resilience can potentially be the long-awaited answer to the challenge of understanding and predicting how and to what extent urbanization dynamics will affect interrelations between society, the built environment, and nature.

With this aim, and according to the general definition of resilience, the capability of urban systems to cope with and bounce back from external shocks has to be guaranteed at all levels. Hence, it has to be considered that each urban system is characterized by a great range of diverse features, which are highly variable place by place, resulting in the immense diversification of geographic and organizational factors and human activities.

Accordingly, it is evident that studying resilience and sustainability on a global scale would not enable the local features that allow urban behaviors to be captured. This is because cities are typical examples of fractals, i.e., they show the same patterns at all levels, reflecting statistical self-similarity (Batty, 2008; Bettencourt, Lobo, Helbing, Kühnert, & West, 2007).

Despite the acknowledged effectiveness of studying urban dynamics on an urban scale, a wide range of heterogeneous components and complex interrelations must be accounted for. Consequently, cities can be understood as ecosystems (Botkin & Beveridge, 1997) characterized by dynamics involving both physical and social components (Kates & Parris, 2003). In particular, according to complex network theory, as a city’s behavior is neither regular nor random, it can be asserted that it is ruled by a small-world principle (Latora & Marchiori, 2001; Milgram, 1974). In this view, cities can be modeled by considering their physical components and the mutual links existing between them to finally compute urban resilience according to an engineering perspective. Consequently, when approaching the study of resilience in the face of natural hazards, a multiscale approach should be pursued, starting from single buildings, e.g., the physical dimension to model their isolated and then collective behavior, in order to finally define the city as a whole as a complex system. In other words, merging complex systems, i.e., ecosystem and civil engineering perspectives, resilience must be approached in a systemic manner, broadening typical performance-based standards from the level of the single building to the interconnected infrastructures and, finally, the urban system.

Given the configuration of the urban fabric, resilience can be evaluated at different levels:

• - The single structure scale, where the measure depends on the strength and resisting capacity of the single structure, as well as other critical parameters such as ductility, durability and robustness

• - The single infrastructure system (e.g., urban lifelines) scale, which arises from the efficiency of the services provided to citizens through robustness and redundancy properties

• - The urban scale, which is the overall complex system that depends on the city efficiency, the physical bouncing back, and copying capacity of all the components

• - The super-urban scale, namely the global scale, which is understood here as the level at which resilience is evaluated according to national and/or international mitigation and adaptation policies aimed at enhancing resilience and sustainability from economic, political, and environmental perspectives

## Opportunities and Challenges to Resilience

Key tests for resilience-related practice and thinking concern opportunities and challenges, which can arise from resilience-oriented approaches and actions. These result in the need for integration, namely the development of a common language to discuss multichallenges and multidisciplinary issues in a more joined-up way. In this context, understanding and the sharing of knowledge among both scientific researchers and institutional officers and international coordination actors are critical. In keeping with this, a focus is proposed on opportunities and challenges around resilience and the consequential need for their mutual integration.

The great attention paid to the resilience concept from communities worldwide has reinvented the discussion around how to support development. With this, the potential of this topic to rally different stakeholders around a common interest in enhancing development is highlighted, thanks to the ability of this topic to pull together different disciplines, people, and goals.

As a consequence, many more actors are engaged in promoting the development of resilience on both a local and a global scale. In particular, resilience should not be merely understood as a philosophy, it should be effectively operationalized. In this context, the stakeholders involved in the management and the maintenance of urban environments appear as the key actors that can guarantee for building resilience. In fact, a higher proactivity of such stakeholders—politicians, risk managers, local institutions, etc.—would ensure the resilience concept to be really included in the process of urban management (Bosher, 2014). In keeping with this, limits can be represented by target and budget constraints, informed by politics, that can shift the focus from the understanding of other urban systems dynamics (Armitage, Béné, Charles, Johnson, & Allison, 2012). Such political and financial constraints cannot be forecast and are often characterized by a high degree of uncertainty. On the other hand, in case of disaster, policymakers have the power to address priorities for recovery and address them, according to the resilience pillars. In this view, engineering-based approaches can help policymakers in assessing the controlling variables supporting human development, governance, or political economy. They can use methodologies to quantify resilience to evaluate the effects and consequences of diverse potential actions to be undertaken. In each case, resource allocation can be evaluated according to the local availability, starting from the restoration of the physical environment aimed at feeding the population. Hence, domains of resilience are more likely to emerge, finding a synergy of the existing political structures, agents, and physical systems (Badahur & Tanner, 2014; Moench, 2014). Resilience would become an imperative both in peacetime and in case of a disaster, in the former case in planning and implementing mitigation actions and in the latter by developing adaptation methodologies and integrating disaster risk reduction into the recovery process of the built environment.

Hence, novel approaches have been encouraged to track progress toward moving targets, above all when dealing with vulnerability-based perspectives, which are often approached as static. Value has been added to the traditional risk assessment methodologies, which account for the high variability of hazards, exposure, and vulnerability to natural disasters.

Resilience is currently being integrated in many disparate contexts, such as economics, politics, and land management, and to address actions toward sustainability.

Current efforts around resilience highlight the need to consider specific features of each investigated system, promoting subjectivity and local identity. Nonetheless, the disastrous events that may occur, along with related cascade effects, should also be accounted for.

The importance of tackling multiple hazards is today widely recognized, but it is a very difficult issue to deal with. In this sense, some national agencies and bodies have reneged on resilience framing due to the constraints of existing institutions and practices. This is due to the lack of a common language to share between diverse stakeholders and is both a potential opportunity and a great practical challenge. Many institutions have undertaken effective actions in this sense. This is the case of the local interventions for disaster resilience purposes fostered by the Rockefeller Foundation (Asian Cities’ Climate Change Resilience Network), Arup (100 Resilient Cities Framework), Iclei (Resilient Cities), the United Nations (City Resilience Profiling Programme), the World Bank (Increasing Resilience to Climate Change and Natural Hazards), and many other institutions.

Global communities are constantly working to find convergence in terms of building capacity for disaster risk reduction, social protection, and climate adaptation purposes. Governmental and research institutions are committing to reduce risks from natural disasters while also enhancing withstanding capacities. Such evidence can help us understand the potential of the concept of resilience to remain not just a metaphor but to reveal interconnections between the components of the built environment and their indirect link with the society. Resilience issues are already stimulating discussions among international institutions and can effectively open new debates in the modern society’s structure of political power (Vale, 2014).

## A Novel Understanding of Resilience: Closing the Loop Between Resilience and Sustainability

A very important issue within the modern scientific debate concerns the methodology to best measure the resilience level of a system.

When dealing with engineering and economic systems, a quantitative assessment is necessary to measure the effectiveness of the recovery process and to recognize synthetic indicators that represent the system’s wellness. In this case, resilience is the measure of the ability of the system to bounce back from a shock event to its previously steady equilibrium condition. This is “engineering resilience” (Bruneau et al., 2003; Holling, 1996; O’Neill, 1986; Pimm, 1984). On the other hand, resilience becomes almost qualitative when dealing with the systems subjected to dynamic equilibrium states. Ecosystems are a typical example, and their resilience is defined as the measure of a system’s capability to reach a different, even new, dynamic equilibrium condition when subjected to external shocks (Holling, 1973, 1986, 1996, 2001).

Looking at the typical structure of a city, one can argue that a city can be assimilated into an ecosystem, the resilience of which can be assessed according to the ecosystem approach. As explained by McDaniels, Chang, Cole, Mikawoz, and Longstaff (2008), the city system has to be conceived as a physical system being linked to social and institutional systems, as well as to the economic and environmental systems embedded within the urban context.

An urban system is, in fact, difficult to study in isolation (Bettencourt & West, 2010). In addition, cities’ subsystems are continuously changing and functioning in many different configurations, which are potential equilibrium stages.

Each of these new post-event stages can be better or worse than the previous one. Consequently, an engineering approach is needed to evaluate the “goodness” of each new configuration.

According to this approach, authors propose merging the two definitions of resilience and defining urban resilience as ecosystem resilience on the basis of an engineering perspective. In keeping with this, urban resilience is defined as the capability of a city to absorb external shocks and reach a dynamic equilibrium stage. This can be at least the same as the pre-event condition but also a new, different stage, provided that the critical indicators giving a measure of the efficiency and quality of the system’s performances have at least the same values as those in the pre-event configuration (Asprone & Manfredi, 2015; Bozza, Asprone, & Manfredi, 2015a; Cavallaro, Asprone, Latora, Manfredi, & Nicosia, 2014; Dalziell & McManus, 2004).

Measuring the urban capability to exhibit a positive response to external stresses is still difficult for contemporary cities. The economic, energy, and human resources employed to reach equilibrium must be considered in relation to the urban and environmental equilibrium. The social, economic, and environmental sustainability of each action thus has to be assessed. In particular, the measure of a “good” state is given by its level of sustainability within all the above-mentioned systems.

Finally, it can be asserted that ideally a positive response is the one enabling a city to meet the appropriate equilibrium condition between the natural and the built environment, that is, reaching sustainability goals. Practically, this is hard to manage and to measure at a city-scale level, but indicators and measures that are proxies of it can be used. This is the case in carbon dioxide emissions, life cycle assessment of industrial processes, the ecological footprint, etc. Consequently, it stresses the correlation between resilience and sustainability, as already widely accepted (Adger, 1997, 2000; Dovers & Handmer, 1992; Fiksel, 2006; Perrings, 2006; UN, 1992, 1997; UNESCAP, 2008). This emphasizes the concept that a truly sustainable city also needs to be resilient (Adger, 1997; Asprone & Manfredi, 2015; Bozza et al., 2015a; UNISDR, 2009; World Summit on Sustainable Development, 2002). This concept is a very general one that embraces several nonhomogeneous factors. As a consequence, it is also difficult to measure. Nonetheless, institutions and researchers are currently working on this, according to different topics, each of them developing methodologies that enable to measure the included variables because of the diverse understandings of the problem, and the diverse use of it, according to the position of actors that study it. For example, academic researchers from economics focus on economic development, disaster, and capital indices and metrics (Cardona et al., 2008; Miles, 2015; Vugrin, Warren, & Ehlen, 2011), whereas authors from social sciences focus on mobility, historic memory, and institutions (Adger, 2000; Olick & Robbins, 1998; Ruitenbeek, 1996; Tyler & Moench, 2012). Conversely, researchers from scientific fields try to quantify resilience engineering, assessing disaster risk, damages from adverse events, and the connectivity of urban systems (Bruneau et al., 2003; Cavallaro et al., 2014; Chang & Shinozuka, 2004; Cimellaro et al., 2010; Franchin & Cavalieri, 2013).

Although many factors contributing to sustainability can be quantified in a scientific fashion, the understandings of the concept of sustainability are still related to ecological principles (mass balance, conservation of resources, allocation trade-offs of assimilated resources) (Gunderson & Holling, 2002). Also, actors that can decide how to relate such principles refer to social, political, and power relationships as well as to the understanding of the functioning of biological and physical systems. In this context, quantifying resilience becomes fundamental to supporting political decisions to drive urban management (Pickett et al., 2014).

The connection between the concept of city resilience and that of city sustainability remains faithful to the approach that addresses the complexity of sustainability. In engineering, in particular regarding industrial products and processes, the notion of a sustainability assessment refers to each phase of the entire life cycle of the investigated system.

The same kind of framework can be applied to the city. Therefore, in dealing with the life-cycle assessment of the city, one can analyze the transformations over the built environment. Apart from the construction, operation, maintenance, and disposal phase, a further phase can be considered—hazardous event occurrence (HEO). In this phase, as a result of which a hazardous event takes place (Asprone & Manfredi, 2015; Bozza et al., 2015a), both the direct (damage and losses) and indirect (due to the post-event recovery process) effects have to be evaluated in terms of their economic, environmental, and social burdens. For instance, a structure or infrastructure is considered to be truly resilient if the negative effects of an extreme event are minimized, that is, sustainability in the HEO phase is maximized. For this reason, a city is deemed resilient if it is sustainable during the HEO phase, which is the period during which the city suffers an extreme event and tries to reconfigure both its physical and social systems, with the primary aim being to reach an equilibrium state. Accordingly, resilience becomes one of the main factors contributing to sustainability—i.e., for a city to be sustainable it has to be resilient too.

# The Importance of Quantifying Resilience

## Quantifying Resilience

The growing interest in resilience requires methodological frameworks to assess it. Measuring disaster resilience would help the physical resilience of urban systems to natural risks to be understood and improved and would enable the most effective strategies to be implemented. In view of this goal, different studies have been developed that propose operational frameworks to quantify disaster resilience and other related properties.

In general, resilience is assessed according to two main types of approach: qualitative and quantitative. In parallel with this, most of the methodologies available in the scientific literature can also be divided into two kinds of approach: physical resilience and social-economic resilience. In the former, attention is focused on the performances of physical systems, e.g., single structures, urban lifelines, and transportation systems, and how they are related to the service function. In this case, resilience is measured as the capability of physical components and systems to effectively operate and recover their functionality in the case of disruption. Mainly, these methods are developed within the engineering community. In this field, novel approaches have recently been proposed based on a new understanding of systems, namely as the merger between their main constituents, and by accounting for their mutual relationships. This is the case with graph theory, in which the systems analyzed are modeled as complex networks.

In the latter case, attention is focused on social systems, and resilience is measured as the capability of communities to recover a good quality of life. These are the methods proposed in the social science community and that will not be investigated within this study.

### Approaches to the Assessment of Physical Resilience

One of the most cited approaches is that of Bruneau and the MCEER research group, and it forms the basis of most of the studies in the literature on the quantification of resilience. Bruneau et al. (2003) provided a conceptual framework that defines and quantifies the seismic resilience of communities.

Bruneau et al. (2003) moved from a qualitative to a quantitative and comprehensive conceptualization of resilience through developing the notion of a “resilience triangle.” In keeping with this, a unified framework is developed based on three complementary and quantifiable factors within the notion of system resilience, namely the reduction of failure probability, the cascade effects of failure, and the time needed to recover.

According to this approach, different methods have been proposed, the final scope of which is to compute resilience as the ability to cope with degradation in a system’s performance over time, $Q(t)$, evaluated as:

$Display mathematics$
(1)

where $Q∞$ represents the capacity of the studied structural system when it is fully functioning, $Q0$ is the post-event capacity, $b$ is an empirically derived parameter (from restoration data following the event), and $t$ is the post-event time (in days). Usually, $Q(t)$ is normalized by dividing both sides of the relationship by $Q∞$. Limit cases are recognized by the upper and lower bounds of the interval in which $Q(t)$ is defined. Meanwhile, $Q(t)=1$ indicates a fully operable system and $Q(t)=0$ an inoperable one. Values in between these two represent varying degrees of system operability.

Furthermore, the ratio of $(Q∞−Q0)$ to $Q∞$ is suggested as a measure of system robustness. In addition, the parameter $b$ is proposed as a measure of the rapidity of the recovery process. Finally, resilience can be quantified through the integration of the area under the curve $Q(t)$ (O’Rourke, 2007) divided by the time needed to restore the pre-event performance (Fig. 1) (Bruneau, 2006; Bruneau & Reinhorn, 2006):

$Display mathematics$
(2)

where $t 0$ and $t 1$ are the endpoints of the time interval under consideration.

Click to view larger

Figure 1. Physical resilience

(Bruneau et al., 2003).

Meanwhile, $t0$ is the time of the event and $t 1$ the time to completely recover the pre-event performance. This approach has been applied to buildings (Bruneau & Reinhorn, 2007), bridges (Decò et al., 2013), road networks (Arcidiacono, Cimellaro, Reinhorn, & Bruneau, 2012), and urban infrastructure systems (Franchin & Cavalieri, 2013; Ouyang & Dueñas-Osorio, 2012) using different performance functions $Q(t)$.

Based on the TOSE framework, Chang and Shinozuka (2004) also proposed a seismic resilience metric for communities.

This makes two significant refinements to the Bruneau et al. model: it outlines a more succinct series of resilience measures and reframes them in a probabilistic context. Resilience is quantified as the probability of an investigated system meeting both robustness and rapidity standards (that is the maximum acceptable loss and the maximum acceptable recovery time) in the case of the occurrence of a certain event, I, of magnitude i (for instance, an earthquake).

According to the resilience components defined by Bruneau et al. (2003), Cimellaro et al. (2010) also quantify resilience as the area under the quality curve, which also depends on the direct and indirect losses caused by the event. These authors focus on rapidity and robustness and introduce two new control variables: the control and the recovery time. The main difference with respect to the study by Bruneau et al. (2003), as also highlighted by Bocchini and Frangopol (2011), is that the former assess the loss of resilience, while Cimellaro et al. (2010) quantify it. The authors suggest that each of the proposed metrics can be used depending on the particular elements one wants to highlight, stressing the evidence of the major versatility of the approach proposed by Cimellaro et al. (2010).

Similar to Cimellaro et al. (2010), the rapidity resilience dimension is also defined by Decò et al. (2013) within the implementation of a resilience assessment framework and following the approaches by Bruneau et al. (2003), Cimellaro et al. (2010), and Bocchini and Frangopol (2011). Attention is also paid to the way in which the recovery process should be represented, namely by accounting for all the involved variables (Miles & Chang, 2006) and integrating different types of information (Chang & Shinozuka, 2004).

Further attempts have been made to integrate a probability-based procedure within the resilience assessment, given the aleatory nature of natural hazards. This is the case for Ouyang and Dueñas-Osorio (2012, 2014), who propose a methodology for quantifying the hurricane resilience of electric power systems and estimating economic losses. This is a probabilistic modelling approach that brings together four different model typologies: hurricane hazard, component fragility, power system performance, and system restoration.

Ouyang, Dueñas-Osorio, & Min (2012) enable the annual expected resilience to be quantified by accounting for multiple types of event, according to a probability-based approach. A time-dependent expected annual resilience (AR) metric is introduced, based on the correlation between the target system’s performances and the hazard frequency. This metric is different from that proposed by Bruneau et al. (Bruneau et al., 2003), Cimellaro et al. (2010), Reed, Kapur, and Christie (2009), Vugrin et al. (2011), and O’Rourke (2007), although they all seem to have the same functional form. The difference, in fact, lies in the time interval that such relationships refer to. While other authors quantify resilience as starting from the instant time in which the event occurs, Ouyang and Dueñas-Osorio (2014) also consider the system’s pre-event condition.

Essentially, the ability of a system to face adverse events is, in fact, also provided by its performance before the event occurs. For instance, where the quality function is low pre-event, the damage induced by an external shock will certainly be more severe than in the case where such a function is higher before the event. Consequently, the restoration process will be more burdensome. So one can conclude that resilience has to be evaluated with reference to all the phases experienced by a system, i.e., pre-event, HEO, emergency, and recovery (Bozza et al., 2015a).

Further work has been conducted on this topic and focuses on different urban systems and performance functions $Q(t)$. However, most of the research in the recent literature shares the theoretical scheme in Eq. (1) or Eq. (2) in order to compute resilience.

### Approaches to the Resilience Assessment of Networked Systems

Recent applications in the field of civil engineering approach resilience assessments according to graph theory by accounting for physical system city components, integrating the mutual interrelations (O’Rourke, 2007; Reed et al., 2009; Vugrin et al., 2011).

Major efforts to assess resilience to seismic catastrophes have been made by Cavallaro et al. (2014), Bozza et al. (2015a), and Franchin and Cavalieri (2013, 2015). These authors modeled physical graphs and used the efficiency of the network in the city’s graph nodes as the performance metric, $Q(t)$, with the aim being to measure the capability of the physical systems to serve their end users. In fact, the power of human agents is often neglected or not treated as central in engineering and ecology, partly because concepts from social sciences are hard to effectively engineer, as are symbols, social identity, and politics (Vale, 2014). While these concepts cannot be properly addressed by natural hazards science, the approaches presented can support decision-makers. With this, the human component of an urban system can be indirectly accounted for by considering fictitious links between physical and social components in a hybrid system. According to the approaches by Cavallaro and Bozza (Cavallaro et al., 2014; Bozza et al., 2015b), different cities’ graph nodes are modeled, and these represent diverse urban components. There are in fact nodes that represent the distribution nodes of urban facilities, or “service nodes.” Other nodes represent the residential buildings where a certain percentage of citizens being served by each service node resides, or “social nodes.” These nodes are modeled in two different planar graphs. The former is comprised of the service nodes (for example, schools, shops, energy distribution structures, and hospitals) and the links connecting them, while the latter is composed of the social nodes (residential buildings) and the links connecting them to the service nodes. The two graphs are then overlapped and merged in a hybrid social-physical network (HSPN), for which resilience is evaluated. With this, whenever a catastrophic event occurs, the probability of the network being disrupted is acquired by assessing the fragility of the service nodes representing urban infrastructures. Accordingly, in the aftermath of a catastrophe, knowledge of the number of urban infrastructures that have been affected by the event enables the number of city inhabitants whose quality of life is undermined in relation to the service function to be evaluated.

This makes it possible to evaluate the performance level of physical infrastructures and contextually assess the indirect effect on quality of life related to the efficiency of the city functioning. Resilience is assessed following the approach of Cavallaro et al. (2014), based on the notion of efficiency of a HSPN according to Latora and Marchiori (2001). These studies present the common feature of considering resilience as dependent on the structural behavior of the city’s physical components and on the connectivity between them. In particular, the infrastructure network is represented through the modeling of the buildings and of the street network because the efficiency of most urban services is typically dependent on the performance of the critical infrastructures that provide them and the urban street patterns that link them. As a result, this simplification enables us to study the interactions between the city inhabitants residences and services by modeling only two planar graphs.

In addition, these approaches make it possible to model a different kind of city considering the availability of information about the geographical configuration of the street patterns and the number and the typology of buildings. These are data that can be acquired from national databases and surveys or from databases available on the Internet.

Consequently, approaches to resilience according to hybrid complex networks enable us to quantify resilience as a multidimensional parameter. Conversely, potential issues when dealing with large urban centers might arise when collecting the information needed with regard to the built environment. These are models that typically integrate fragility models to compute the structural vulnerability of physical components. Fragility models might not be available for all the infrastructure typologies and hazards typologies to be studied. In addition, the behavior of social agents is not accounted for, and it is only indirectly embedded through the consideration of the buildings where people live and their connection with service infrastructures.

The use of graph theory to quantify resilience has also been proposed by other researchers. Mensah and Dueñas-Osorio (2015) proposed a framework for quantifying the resilience to hurricane hazards of electric grids and distributed wind generation. Distribution networks are modeled as minimum spanning trees (MSTs). Resilience is assessed with the same functional form proposed by Ouyang and Dueñas-Osorio (2014) and is particularized with reference to the fraction of customers served or not served by the electrical power systems after a hurricane occurs. Mensah and Dueñas-Osorio (2015) and Ouyang and Dueñas-Osorio (2014) assessed resilience based on the aleatory uncertainty in the hazard’s variables for natural disasters.

The functional form of the proposed metric is conceptually similar to others. It is based on the stochastic modeling of an iterative process, which considers hazard occurrence, restoration, and the recovery process. The strength of this approach is that it enables one to quantify a system’s resilience under multiple hazards. In addition, it refers to a period time that include the pre-event system behavior. Consequently, the metric provides an overview of the entire life cycle of a system. In fact, the measure of the efficiency of a city’s restoration process is given by the comparison with the pre-event condition. Conversely, this approach also has weaknesses, in that it focuses only on the technical dimension of resilience and the multiple hazards effects are considered as non-correlated.

Todini (2000) considered urban water distribution systems and designed them as a series of interconnected closed and undirected loops through which water flows are analyzed. The problem is formulated as a vector optimization issue, with cost and resilience as two objective functions. Hence, it is a heuristic design approach that refers to a target value of resilience in order to identify the pipe diameters for each connection between couple of nodes. As a consequence, esilience is assessed in relation not to the performances of the water distribution system but to its physical features. This approach does not enable one to evaluate urban resilience as overall city efficiency. In fact, it only focuses on the single physical components, without considering their interrelations with other urban systems. Leu, Abbass, and Curtis (2010) proposed an approach for quantifying resilience in transportation networks, which were modeled as graphs. Based on GPS data, these authors modeled a network composed of three interacting layers representing the physical structure, the service function, and the cognitive properties, i.e., the human dimension. In this methodology, no agent-based models are integrated. Hence, human behaviors are not realistically accounted for. In addition, different metrics are evaluated for the diverse layers modeled, and combining them in a unique resilience indicator might be complicated, as also highlighted by authors.

Murray-Tuite (2006) focused on the resilience of transportation networks and proposed multiple metrics by measuring adaptability, mobility, safety, and recovery using a large set of different metrics for each dimension. The studies from Leu et al. (2010) and Murray-Tuite (2006) present the same issues, which are related to the integration, interpretation, and comparisons between heterogeneous indicators. Hence, these approaches are mostly methodological, but no effective implementation can be foreseen in real practice.

Berche, Von Ferber, Holovatch, and Holovatch (2009) analyzed the resilience of public transportation networks (PTNs) under different attack scenarios. They mapped the PTNs as graphs and so used network connectivity metrics to define random attack scenarios. Resilience is evaluated as a proxy for the mathematical features of the graph without considering information with regards to the vulnerability of the physical system. Consequently, the authors evaluated only the connectivity between physical components within an urban context. They did not consider their performances in the face of a catastrophic event, which is fundamental in order to integrate the probability of disruption of the urban network.

Dorbritz (2011) combined the approach of Bruneau et al. (2003) with the network analysis proposed by Berche et al. (2009) for quantifying resilience. The consequences of node removals in transportation networks are modeled from a topological and operational perspective. Software is used to quantify such consequences and to measure resilience according to the approach of Cimellaro et al. (2010). The main weakness of this approach is related to the topological measures performed, which do not account for network dynamics or characterize network disruption. Omer, Nilchiani, and Mostashari (2009) proposed a quantitative approach to define and measure resilience using a network topology model. They defined base resilience as the ratio of the value delivery of the network after disruption to its value delivery before the disruption occurs. The value delivery is defined as the amount of information to be carried through the network.

Miller-Hooks, Zhang, and Fautrechi (2012) quantified resilience as the maximum expected system throughput in order to improve preparedness and recovery activities against potential system disturbances. Both of these methodologies can be understood as important methodological advancements, but they might not be computationally affordable for real systems.

Paredes and Dueñas-Osorio (2015), meanwhile, developed an integrated resilience-based modeling approach to assess the seismic resilience of coupled networked lifeline systems. Here, capacity, fragility, and response actions, including those informed by engineering and community-based policy, are considered as inputs.

Time-dependent seismic resilience is used to perform connectivity assessments for the lifelines being modeled as complex networks. Hence, the proposed metric is substantially similar to those proposed by other authors. On the other hand, it integrates information from engineering and community-based policies. They are stakeholders and experts, whose opinion is fundamental in case of occurrence of a catastrophic event.

Heaslip et al. (2009) developed a method to assess and quantify resilience using fuzzy inference systems (FIS). They developed a framework that introduced two main concepts: the resilience cycle and the system performance hierarchy. They rank the performance levels of the system according to the theory of the hierarchy of human needs. The combination of these concepts in a Cartesian plane results in a time-dependent curve that represents the system’s performance levels during the resilience cycle. The resilience metric is defined by developing a diagram of the hierarchy of the variables. Similar to Heaslip et al. (2009), Freckleton, Heaslip, Louisell, and Collura (2012) developed a framework that builds the dependency diagram directly between indicators describing a system’s critical attributes. These metrics are classified according to their area of interest: the individual, the community, the economic, and the recovery metric groups.

Advancements are also produced by these studies, highlighting the importance of introducing a methodology that makes it possible to integrate heterogeneous components contributing to resilience. Conversely, their implementation in real practice might be tricky because of the greater number of variables, and consequently a higher computational burden.

González, Dueñas-Osorio, Sànchez-Silva, and Madaglia (2015) introduced the Interdependent Network Design Problem (INDP). This focuses on the resilience of a partially destroyed infrastructure network system, which is assessed based on the reconstruction strategy that costs the least. Budget, resources, operational constraints, and interdependencies are also accounted for in the evaluation process. In this case, economic variables are considered, which are typically critical to the choice of the best recovery strategy to be implemented in the aftermath of a catastrophic event. Nonetheless, it does not consider the effective structural vulnerability of the city’s physical components. Hence, it might be potentially used only right after the event, when the damage scenario is known. Consequently, it might not be used in order to implement mitigation actions and planning policies, which are critical to the resilience enhancement.

Davis (2014) understands the resilience of a water system as its ability to provide post-earthquake services to other lifeline and emergency operations, such as hospitals, emergency operation centers, and evacuation centers, in a manner that does not significantly disrupt their critical operations to help improve community resilience. He maintains that the resilience of a water system can be measured not only by the service-time lost but also by how it helps to improve overall community resilience. This is a novel approach to infrastructure assessment and makes it possible to take into account interrelations between critical infrastructures, which might be fundamental to achieve an efficient response of the urban system. He outlined that water system resilience can be measured not only by the service time lost but also by how it helps to improve the overall community resilience.

# Conclusion

The concept of resilience is very innovative due to its application to modern research fields, even though its definition has distant roots back in the 19th century. In last few decades, the notion of resilience has been widely investigated and refined and applied to multidimensional and multidisciplinary topics.

Several definitions of resilience are available in the literature, depending on the topics and issues to be addressed. The factors contributing to resilience, and influencing it, are recognized to be numerous, with each of them gaining weight according to the application discipline.

This is one of the main peculiarities of disaster resilience within the modern research society from which challenges and opportunities arise. On the one hand, the availability of a wide range of different definitions of resilience enables us to choose the one that best fits the needs related to the specific field of interest. On the other hand, the existence of so many definitions could lead to misunderstandings between diverse stakeholders involved in the same process. For instance, whenever a natural disaster occurs, economists, engineers, disaster managers, and urban officers are convened to power up discussions about how to best to manage its effects. Accordingly, in the aftermath of the event, i.e., the emergency phase, and, later, when a recovery strategy has to be chosen and implemented, knowledge and experience from all of these actors is required. Approaching resilience in a heterogeneous fashion means that each actor would give value to different aspects of it, thus producing challenges in terms of reaching a common view of the problem and so a common strategy for recovering from it. Although such efforts in terms of communication could be difficult, they could also boost collaboration among stakeholders to find a common understanding of resilience.

The need to share experiences and understandings of resilience presents the same issues as when dealing with the available methodologies for its quantification. In this article, resilience is understood as strictly related to the physical dimension of urban environments, i.e., as a function of infrastructural performances and service function. The methodologies proposed in the literature largely enable us to understand that resilience can also be examined on different scales.

In particular, the physical resilience perspective, which also embeds the most recent approach to the resilience quantification of networked systems, is focused on the urban scale. Physical infrastructures are, in fact, different from city to city, and their management is usually entrusted to local authorities. In fact, when dealing with the efficiency of the recovery after an adverse event, it should be considered that citizens and urban environments experience disasters differentially. Hence, the recovery can be efficient in a local context rather than another one, highlighting the importance of studying such dynamics at the urban level.

In keeping with this, it is important to integrate different understandings of the resilience concept. Relevant social dimensions of urban systems should be included within the assessment of the engineering resilience. They include political and economic power relations, social identity and change, economics of production and consumption, the nature of livelihood and lifestyle, and questions of social justice and vulnerability (Grove et al., 2006). This shift in the scientific frameworks and the broadening of urban ecological approaches can help advance the understanding of city resilience because both biophysical and social structures and processes are components of these hybrid systems (Cadenasso & Pickett, 2008).

Many researchers worldwide are working on the integration of variables affecting disaster resilience and heterogeneous information with respect to the studied systems, with the goal being to develop a unique resilience indicator that enables a prompt, synthetic judgment to be made. Such indicators have the potential to support policymakers in assessing urban resilience quickly prior to and after the event occurrence, to set priorities and plans for action, which can be effective if the localized system’s characteristics are considered (Moench, 2014). In this way, metrics leading to the development of a resilience index can help in assessing urban features that can be engineered in a rigorous fashion. Paralleling this, political issues, justice, and fairness can be included through the integration of local managers’ expertise.

Social indicators, economic indexes, and engineering metrics are difficult to process together and so need to be normalized to be interpreted effectively. This has already been done with the fuzzy logic and event trees approaches, although further experimentation and validation is required. In keeping with this, despite the important methodological advancements made with the development of valuable heuristic approaches, integrating social and engineering variables is still theoretical.

A further issue to be considered is related to the modern urbanization processes. With this, cities are continuously increasing in size and asset exposure. In fact, the bigger the city, the higher the concentration of economic activities and physical assets established. Hence, a city’s topological configuration can change, as can its functioning. Accordingly, the resilience trend needs to be studied in relation to such dynamics to enable urban behaviors to be assessed and forecast (Bozza, Asprone, Fiasconaro, Latora, & Manfredi, 2015b).

As for the definition of resilience, the diverse way in which it is approached, and the great heterogeneity of the available methods for its quantification could constitute a benefit for cooperation and development, but also a disadvantage in terms of the lack of a common language between stakeholders.

Future directions for resilience-oriented approaches in several diverse fields can be fostered, as can the development of a common language, although to date this represents a limitation in this area of research. On the other hand, and above all when focusing on urban environments, novel approaches are currently being implemented in diverse disciplines, promoting subjectivity and local identity, which can be crucial when facing catastrophes due to natural events. With this in mind, instruments are provided to disaster managers and local officers to prepare cities to withstand external stresses according to their own features and specific conditions.

Integration and a unique interpretation are, however, required in terms of both the definition and quantification of resilience, and this has the potential to encourage the sharing of knowledge between stakeholders. Recent evidence has, in fact, proved that the great attention paid to resilience, and its close link with sustainability, has reinvented the discussion on the best way to support development according to these principles.

Basically, the quantification of resilience is possible thanks to the development of rigorous approaches, although there is still much to do to integrate specific factors, such as socio-political ones, that are hard to quantify. In addition, efforts are also needed to integrate such methodologies with current practices on both the urban and supranational levels.

The perception of risk needs to be stimulated, too. This is currently being done by several national and international institutions and associations, which constantly stress the central role of resilience in natural disasters in terms of guaranteeing sustainable development and population well-being (IPCC, 2014; UN, 2015a, 2015b, 2015c, 2015d; Swilling et al., 2013; UNEP-DTIE, 2013). Several organizations like affected and donor members have been taking part in this discussion, such as the World Bank, the International Monetary Fund (IMF), the Organisation for Economic Co-operation and Development (OECD), the United Nations Development Programme (UNDP), and the United Nations International Strategy for Disaster Reduction (UNISDR).

Further experimentation is still required on these studies to prove their effectiveness and persuade institutions of the importance of integrating such processes within their disaster risk reduction and management procedures.The validation of real case study data can also be carried out and integrated with judgments from experts and outcomes of rigorous scenario analyses.

Common goals and directions are currently incentivized by international organizations for local communities worldwide to undertake work toward disaster resilience while also improving sustainability. In conclusion, it can be asserted that, while the definition of resilience needs to be globally defined in a unique way, approaches to its quantification should continue to be customized according to the local environment to which they are applied. The quantification of resilience should be conducted using a bottom-up approach to guarantee respect toward and understanding of the modern self-organization processes taking place in cities.

At the same time, new paths toward disaster resilience should be addressed according to a top-down approach. This requires supranational authorities to support and help local communities undertake actions to enhance resilience and sustainability, as the former have many more resources and are capable of powerful decision-making.

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