Measuring the Seismic Resilience of Housing Systems in Italy

Abstract

In recent decades, one of the most interesting innovations has undoubtedly been the application of resilience principles to the study and mitigation of seismic risk. However, although new rigorous mathematical models have become available in the context of seismic resilience assessment, their applications to real case studies focus on a local scale, or even single structures. Consequently, new models and procedures are absolutely necessary to adopt resilience measurements in the formulation of mitigation strategies on a national or subnational scale. Given the crucial role of residential buildings in the global resilience of Italian cities against major earthquakes, a new framework for large-scale applications is proposed to roughly measure the seismic resilience of communities through the integration of an empirical recovery function based on the reconstruction process of housing systems in the aftermath of the 2012 Northern Italy Earthquake. As a first attempt, the framework is applied to housing systems in the southern regions of Italy by modelling their physical damage with vulnerability curves defined on the basis of macroseismic approaches. The main results are presented and discussed in terms of average functionality levels over time in order to compare and understand the recovery capacity of the considered housing systems.

1. Introduction

In 1973, the resilience concept was first used by Holling [1] to describe ecological systems. Subsequently, resilience was introduced in other research areas, becoming a hot topic nowadays, especially in the engineering field, that offers solutions to the problem of disaster prevention and mitigation (e.g., [2,3,4]). Nevertheless, the resilience concept may be perceived as ambiguous because its acceptance changes depending on the specific field of study. For example, in an analysis of the most common definitions of resilience [5],over forty explanations for this term can be identified. In the disaster-recovery field, resilience is commonly understood as the ability of a community to absorb, adapt and respond to adverse events, rapidly recovering from possible disruptions and emergencies caused by them. A comprehensive review of state-of-the-art approaches to quantify community resilience and their applications to case studies may be found in recent works (e.g., [6,7]).

The seminal work of Bruneau et al. [8] built a general framework to quantify the seismic resilience of communities through quantitative measures of robustness, rapidity, resource availability and redundancy. Based on this work, several models and conceptual frameworks have been proposed (e.g., [9]) by including socioeconomic aspects, housing issues and infrastructure systems (electricity, transportation and water). The main objective is to analyze the recovery of community functionality and related operational levels. The integration of economic, organizational, social and technical aspects together with dimensions of infrastructure and facility systems (such as critical facilities, energy, transportation, water) is conceptually considered to have a key role in resilience assessment (e.g., [9]).

The PEOPLES resilience framework [10,11,12] is conceptually derived from Bruneau et al. [8] and considers seven dimensions (i.e., physical infrastructures, economic development, organized governmental services, population, lifestyle, ecosystem and environment, and social capital) to measure community resilience. Based on the PEOPLES framework, a software was developed by Arcidiacono et al. [13] to quantify disaster community resilience. In particular, through a comparison between four different recovery scenarios, this software was tested in Italy on the case study of the 2009 L’Aquila earthquake.

A resilience simulation model called ResilUs was implemented and run inside a modelling software to help educate users about the alternative approaches to enhance recovery and resilience [14]. Such a model was built upon the prototype model of Miles and Chang [9]. It defines hazard-related damage and recovery over time of buildings and lifelines using parameters calibrated on the basis of the 1994 Northridge earthquake data. The ResilUS model works with a macro-subdivision of area (i.e., neighborhoods of a broader community) and uses fragility curves and Markov chains to model damage/loss and recovery over time, respectively. Although the modules to model lifeline recovery were not evaluated (more details in this direction are provided by Miles [15]), the recovery model for both households and businesses requires some data (i.e., amount of disaster aid per household, savings and structural mitigation of household and business, building year, tenure and building’s type of business) to be simulated.

To improve the resilience of communities, the National Institute of Standards and Technology (NIST) proposed an approach/methodology that allows local governments a six-step planning process [16]. It helps communities prioritize resilience actions for buildings and infrastructure systems. In this regard, the resilience of infrastructure systems can be measured in terms of time to recover functionality, including the following aspects [17]: ability to recover rapidly, damage and loss of functionality, existing system condition, and hazard intensity.

Ellingwood et al. [18] develops the Centerville Virtual Community in order to build an integrated decision-making model capable of interacting with physical and social infrastructure systems. It aims to enable fundamental resilience assessment algorithms considering the natural hazards to which the community is exposed, the physical infrastructure within the community, and the population demographics. Then, Zhang and Nicholson [19] applied their multi-objective optimization model to the Centerville Virtual Community. By starting with a group of residential and commercial buildings and assigning them a given budget, this optimization model is able to analyze the trade-offs between direct economic loss and the goal of minimizing immediate population dislocation.

An IdealCity model is presented by Battegazzore et al. [20] to simulate and study the disaster resilience of communities at the urban level for post-earthquake scenarios. The model is based on the PEOPLES resilience framework and considers the mutual interaction between different model layers (i.e., built environment, road network, generated debris, and agents), the effect of debris on evacuees’ walking speed, as well as the simulation of the emergency response network (ambulances, hospitals, shelters). The building stock, population and its distribution in the IdealCity are representative of a typical Italian building portfolio, while occupancy and physical characteristics of structures and infrastructures (i.e., road transportation network, building archetype, year of construction, height classifications) reflect the characteristic of the town of Turin. Working with the IdealCity, an integrated platform was developed by Marasco et al. [21] to evaluate the seismic resilience of communities. The platform analyses different layers (i.e., road transportation networks, buildings, water distribution networks, power grid, and socio-technical networks) using specific models to simulate their interdependency. However, in the current state of the platform, the recovery of damaged structures and infrastructure cannot be considered.

Sharma et al. [22] developed a stochastic formulation that is able to measure the resilience of engineering systems by estimating the impact of recovery activities and possible recovery interruptions on the damage state of these systems. To this aim, a reliability-based definition of damage levels was also proposed. The formulation was applied to investigate the resilience of a reinforced concrete (RC) bridge retrofitted with fiber-reinforced polymer. In the work of Jiang et al. [23], a new framework for the seismic resilience evaluation of single buildings is proposed to build resilient buildings. It was applied to a ten-story RC moment-resisting frame structure located in Shanghai.

Currently, some elements now seem clear. Resilience models are conceptually very similar. However, they must be adapted to the context under consideration [24,25]. The data and assessment models must also be specific to the community under consideration. They strongly affect evaluations, particularly in assessing initial conditions, defining recovery time and recovery functions, down time, and so on. As a result, procedures can vary widely in practical applications, and specific studies of community subparts (facilities, residential buildings, etc.) are needed (e.g., [26,27]). While rigorous mathematical frameworks for resilience analysis are being developed, applications of these frameworks to real case studies focus on a local scale (neighborhood, district, city), or even single structures.

The first large-scale resilience assessments have only recently been defined by mapping Urban Limit Conditions (ULCs) in southern Italy according to the seismic robustness of housing systems and specific ULC thresholds [28]. ULCs were formulated for the first time by several authors [29,30,31] and correspond to different urban functionality loss levels for earthquakes of increasing intensity [32]. Then, in the study of Basaglia et al. [33], ULC thresholds were quantitatively defined for housing, education, economy, healthcare, governance and social system. Based on the reference literature [28,29,30,31,33], ULCs can be identified and described as follows:

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The Operational Limit Condition (OLC) is reached when the housing system’s functionality is greater than 99.5%. In such a condition, the housing system is fully functional or has a slight local loss that is not significant at the urban level.

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The Damage Limit Condition (DLC) is characterized by a functionality greater than 90% but less than or equal to 99.5%, for which the housing system suffers a provisional and localized limitation and the overall urban functionality (considering all urban sub-systems) undergoes a temporary or partial reduction.

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Life Safety Limit Condition (LSLC) is experienced when the housing system functionality is greater than 70% but less than or equal to 90%. This condition corresponds a partial functionality limitation, while the overall urban functionality exhibits a significant or prolonged loss without invalidating its general performance.

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The Collapse Limit Condition (CLC) is attained if the housing system functionality is greater than 50% but less than or equal to 70%. This implies that the housing system and many other urban sub-systems are damaged in the medium or long term, while the residual urban functionality is retained by some sub-systems.

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The Emergency Limit Condition (ELC) is attained when the housing system functionality is less than or equal to 50%. For this last condition, urban resilience could be more challenging because the housing system is totally compromised and its recovery is not obvious. Only emergency areas and strategic buildings and infrastructures could continue to function in the urban settlement.

The peculiarity of the Italian condition, particularly in southern regions, has always highlighted the key role of residential building stock in the general assessment of community resilience [24,34]. Because of this, studies on the large-scale seismic behavior of Italian residential buildings have increased in recent years (e.g., [28,35,36,37,38,39]). By following an empirical, analytical or hybrid approach [35], these studies develop fragility curves in terms of vulnerability and height classes that allow users to estimate the expected damage of masonry and RC buildings in seismic risk analysis performed with poor census data. For urban applications, an innovative procedure has also been recently proposed to derive fragility curves of road networks from the seismic damage of nearby residential buildings [40].

The key role of residential buildings is now unanimously recognized, and studies on community resilience are strongly tied to them and their quantitative assessments. For this reason, this article focuses on residential building stock. The realization that residential building stock is only a component (that is very relevant) of the general measurement of community resilience is embodied in the proposed procedure and its operational choices. The latter depend strongly on the large spatial scale considered. However, the assessment at that territorial scale (and its corresponding approximations) is fundamental to the overall governance of supra-regional territories.

In the present work, a new framework is proposed to quantify the community’s resilience to seismic hazards in large-scale applications. It is based on previous studies in which restoration data are derived from the 2012 Northern Italy Earthquake. Policymakers can leverage this study’s findings to make decisions about future mitigation strategies and training programs in disaster preparedness. The first part of the article briefly describes the proposed framework. It is then applied to all municipalities in five regions of southern Italy. Finally, the main results in terms of average functionality levels over time and concerning ULCs are discussed, highlighting advantages, limitations, and future research directions in the conclusions.

2. Resilience Measurement

According to the resilience definition provided by some authors [10,11,41] and widely adopted in resilience assessment studies (e.g., [13,26,34,42]), the resilience index R of a community can be defined as the area underneath the functionality function of a given system normalized by the control time (T_LC) for the period of interest. Analytically, R is commonly defined as follows:

$$R={\displaystyle \underset{t_{0E}}{\overset{t_{0E}+T_{LC}}{\int }}Q(t)}/T_{LC}dt$$

(1)

where t_0E is the time instant when the disastrous earthquake happens, T_LC is the analyzed control time and Q(t) is the functionality function of the considered system (urban sub-system, city, city’s system, region). The latter can be evaluated considering all the sub-systems of the PEOPLES resilience framework, or only some of them.

As evidenced in some studies [26,28], this R index is geometrically equivalent to an average height. In fact, a height is obtained by normalizing the area underneath the functionality function Q(t) with a control time that represents the base of this area (see Figure 1). Consequently, the resilience of a system can be considered as an average functionality on the assigned control time over which the area underneath the functionality function is assessed and normalized.

Generally, the functionality function Q(t) of a system is a piecewise function in which its constituent functions are continuous on the corresponding time intervals (subdomains) and there is no discontinuity at each endpoint of the subdomains within that interval. As shown in Figure 1, after a disastrous earthquake, the theoretical functionality of a resilient system can be described through four main intervals: (i) at t=0, a drop in functionality linked to the seismic risk of the exposed assets in which a residual functionality (robustness) is obtained through the usable structures and infrastructures; (ii) a pseudo-horizontal phase (downtime) comprising the emergency management, the seismic damage evaluation and the planning and implantation of preparatory activities for starting the reconstruction process; (iii) a third phase of recovery with a progressive increase in functionality thanks to the gradual allocation of funds and the consequent restoration works; and (iv) a fourth phase in which pre-earthquake functionality is roughly restored.

The different urban subsystems of a city can be considered as dominant or non-dominant according to their impact on urban resilience. In particular, during the downtime and recovery phase, the global functionality of a city depends on the functionality of its dominant urban subsystems, which work in series (i.e., when one dominant subsystem fails, the urban system fails). As a result, the urban functionality is most affected by the more vulnerable dominant subsystem. Investigating the resilience of Italian cities against earthquakes, Vona et al. [24] highlight that the vulnerability of residential buildings is predominant in determining the resilience of cities, especially for longer control times. These buildings were the main source of economic losses, fatalities, injuries, and disruptions due to Italian earthquakes.

Thus, several interesting studies were performed to analyze the functionality of housing systems during the reconstruction process that took place after the 2009 L’Aquila Earthquake [25,34,43] or the 2012 Northern Italy Earthquake [44]. For most of these studies, the functionality function of a housing system in the recovery phase is similar in shape and slope to the temporal curve of the cumulative financial grant allocated to cope with the disaster.

Based on the empirical formulations proposed in a preceding article [45], the functionality function Q(t) of a housing system during the restoration time T_RB (i.e., the recovery function) can be assessed as follows:

$$Q\left(t\right)=100-p(t)=r+100\cdot \left(1-e^{-0.033\cdot t}\right), \mathrm{if} 0 \le t\le T_{\mathrm{RB}}$$

(2)

where r is the seismic robustness of the considered housing system (i.e., the residual functionality in the time instant when the catastrophic event happens, expressed as the expected percentage of residents in usable buildings), t is the month following the disastrous earthquake, and p(t) is the percentage of the population still displaced in the tth month [45]. The latter was defined by generalizing the main results obtained by Basaglia et al. [44] in the study of residents still displaced in the reconstruction process of two cities severely hit by the 2012 Northern Italy Earthquake during the period from May 2012 to May 2019.

Mathematically, r can be formulated as follows:

$$r=100\cdot \frac{E_{TOT}}{P_{TOT}} (\%)$$

(3)

where E_TOT is the total number of expected residents in usable buildings and P_TOT is the total number of the population in the considered area. In particular, E_TOT can be evaluated through a probabilistic seismic risk analysis using the procedure suggested by Anelli et al. [28]. As depicted in Figure 1, T_RB is the sum of the downtime and the recovery time. According to Anelli et al. [45], it is expressed in months and can be roughly estimated as follows:

$$T_{RB}=-30.\overline{30}\cdot \ln \left(\frac{\max \left(r;100\cdot e^{-5.313}\right)}{100}\right)$$

(4)

By substituting Equation (2) into Equation (1) and integrating Equation (1) with respect to t between the limits 0 to T_LC (with 0 < T_LC ≤ T_RB), the resilience of a generic housing system can be evaluated as follows (Figure 1a):

$$R=r+100\cdot \left(1+\frac{e^{-0.033\cdot T_{LC}}-1}{0.033\cdot T_{LC}}\right), \mathrm{if} 0 < T_{\mathrm{LC}}\le T_{\mathrm{RB}}$$

(5)

where T_RB and T_LC are both expressed in months. As illustrated in Figure 1b, the R index is equal to the robustness for a short control time (T_LC≈0). Analytically, this condition can be written as follows:

R = r, if T_LC = 0

(6)

On the other hand, as shown in Figure 1c, the subdomain of the functionality function at the end of the restoration time should also be considered in the R index estimation for a long control time (T_LC > T_RB). In this case, the R index can be estimated by integrating Equation (1) with respect to t between the limits 0 to T_RB and T_RB to T_LC, and using the corresponding functionality function valid for these subdomains (Equation (2) for 0 ≤ t ≤ T_RB, and Q(t) = 100 for T_RB ≤ t ≤ T_LC). Mathematically, this can be expressed as follows:

$$R=\frac{{\displaystyle {\int }_0^{T_{RB}}r+100\cdot \left(1-e^{-0.033\cdot t}\right)}dt+{\displaystyle {\int }_{T_{RB}}^{T_{LC}}100dt}}{T_{LC}}$$

(7)

By solving Equation (7), the R index for a control time greater than the restoration time (T_LC > T_RB) can be obtained as follows:

$$R=\frac{\left(r+100\right)\cdot T_{RB}+3030.\overline{30}\cdot \left(e^{-0.033\cdot T_{RB}}-1\right)+100\cdot \left(T_{LC}-T_{RB}\right)}{T_{LC}}, \mathrm{if} T_{\mathrm{LC}}>T_{\mathrm{RB}}$$

(8)

Depending on the calculated robustness value, the seismic resilience of a housing system can be estimated for any control time using Equations (5), (6) and (8). In addition, the functionality at the end of the considered control time may also be assessed from Equation (2) by replacing t with the control time. However, in Equation (4) there is an additional condition that limits the minimum robustness value to be greater than 0.49% for the restoration time calculation. This condition was proposed by Anelli et al. [45] to take into account the maximum restoration time defined in the study of Basaglia et al. [44], which was evaluated as 161 months (or 13 years and 5 months) after the earthquake. The main novelty of the proposed framework is twofold: (i) the introduction of an empirical recovery function for large-scale applications (deduced from previous studies), which is governed by the seismic robustness of the housing system and the months following the disastrous earthquake; and (ii) the definition of new resilience formulations that are obtained through the timeintegration of the aforementioned function considering different control and restoration times.

3. Application to Housing Systems in Southern Italy

The proposed resilience measurement framework has been applied to the housing systems of all municipalities in Apulia, Basilicata, Calabria, Campania, and Sicily regions. To estimate their seismic robustness, a probabilistic risk analysis has been performed through the convolution of vulnerability, exposure, and hazard models. In recent works [28,45], these models have been used to assess and define Urban Limit Conditions (ULCs) and resilient mitigation strategies of specific Territorial Contexts (TCs) defined according to the emergency planning exigencies of Italian Civil Protection.

The vulnerability curves proposed by Anelli et al. [28,35] have been considered as vulnerability models. Such curves were obtained from the macroseismic approach of Lagomarsino and Giovinazzi [46], referring to their probable vulnerability values (V− and V+) for masonry and RC building types, and using the I-PGA correlation law of Guagenti and Petrini [47] or Bilal and Askan [48]. As shown in Figure 2 and Figure 3, the considered vulnerability curves correlate the damage factor (i.e., the expected repair cost ratio as a percentage of the building replacement cost) with the hazard intensity measure expressed in terms of Peak Ground Acceleration (PGA), considering four masonry vulnerability classes (A, B, C1 and D1) and two RC vulnerability classes (C2, D2), together with two height classes (L= 1–2 stories and MH ≥ 3 stories). To take into account the structural response uncertainties of the different building types associated with a specific vulnerability class, two different vulnerability models have been adopted. These vulnerability models were defined according to the repair cost ratios of buildings in L’Aquila [49] and work well with exposure models developed at large scales (e.g., regional or national scales), which are usually based on poor census data aggregated at the municipality level.

The exposure model of the considered residential building stock and its occupants has been obtained from the national census data on buildings and population [50]. These data are disaggregated at the sub-municipal level according to census sections that cover the entire national territory. The main characteristics of buildings include structural material, construction age, and number of stories. Referringto the criteria used in the National Risk Assessment [51], vulnerability classes are derived from structural material and construction age. Consequently, the considered residential buildings have been grouped in twelve taxonomies (one for each vulnerability and height class), combining their structural material and construction age with their number of stories. In this way, the residential assets have been appropriately sampled and spatially linked to the corresponding vulnerability models taking into consideration their geographic coordinates together with their structural material, construction age, number of stories and occupants, built area, and structural and non-structural replacement cost. Such cost has been assumed constant among the twelve taxonomies and equal to 1200 EUR /m², which represents the mean reconstruction cost of buildings in L’Aquila [49]. It can be assigned to the entire portfolio because the repair cost ratios used in the vulnerability curves definition refer to buildings in L’Aquila. These repair cost ratios strictly depend on the seismic damage suffered by buildings rather than on the hazard intensity [49].

The hazard model has been developed according to the Italian reference model, known as MPS04 [52,53] and incorporated in the current Italian seismic code [54], including the stratigraphic amplification effects. Thus, the ZS9 seismic source zone model of Italy [55] has been employed together with the seismicity rates of the Italian Parametric Earthquake Catalogue CPTI04 [56]. To incorporate the stratigraphic amplification effects into the hazard model, the new generation of the Ground Motion Prediction Equation (GMPE) proposed by Bindi et al. [57] has been adopted, jointly with the shear-wave velocity to a 30 m depth (Vs30) provided by Mori et al. [58]. More specifically, hazard curves in terms of PGA for multiple return periods have been computed at the exposure site model through an event-based analysis conducted with OpenQuake-engine software [59], version 3.13.0.

Using the same software with a probabilistic event-based risk calculator and the aforementioned models, loss exceedance curves and probabilistic loss maps have been developed and an aggregate loss curve of assets with the same taxonomy classification has been calculated for each municipality taking into consideration a return period of 100, 250, and 500 years. Then, the procedure suggested by Anelli et al. [28] has been followed to estimate the robustness of each municipality for the different vulnerability models and return periods. In this way, all assets that experience a slight damage (loss ratios below 15%) and the 60 percent of the assets that experience a moderate damage (loss ratios equal to 15% but less than 50%) have been considered as usable buildings and their occupants have been computed for each municipality and taxonomy.The robustness of each municipality has been therefore evaluated for each vulnerability model and return period using Equation (3), which expresses in percentage terms the ratio between the total number of expected residents in usable buildings (taking into account all taxonomies) and the total number of the population.

Finally, for each vulnerability model and return period, the restoration time T_RB has been estimated through Equation (4), and the seismic resilience of housing systems in the study area has been assessed by means of Equations (5), (6) and (8), investigating different control times. Figure 4, Figure 5 and Figure 6 summarize the resilience measurements obtained considering a control time equal to 12, 24, 36 and 60 months and averaging the respective values of two vulnerability models for each return period.

4. Discussion

As can be deduced from Figure 4, Figure 5 and Figure 6, resilience values decrease by increasing the return period while increasing the control time. The reduction in value is due to the lower robustness associated with a higher return period, while the increase in value is connected to the greater recovery for a longer control time. This is intuitive but can also be proved mathematically by applying Equations (5), (6) and (8) for different return periods and control times.

As underlined in Section 2, the resilience of a system can be defined as its average functionality level over the considered control time. Accordingly, in addition to indicating time-averaged functional levels, Figure 4, Figure 5 and Figure 6 may also be viewed as average ULCs over time, which may be recovered during the reconstruction process. Thus, to provide a practical resource of information for policymakers, the obtained results are discussed in terms of average ULCs over the considered control times, referring to the ULC thresholds described in Section 1.

For a return period of 100 years (Figure 4), the towns of San Marco in Lamis, Carbone, Marzi, Sassinoro, and Castelvecchio Siculo are the least resilient of Apulia, Basilicata, Calabria, Campania, and Sicily regions, respectively. Conversely, the towns of the Province of Lecce and Brindisi (together with the southeastern towns in Taranto Province), Policoro, Montegiordano, Castellabate (together with Perdifumo and closed towns), and those of the Province Trapani, Caltanisetta, Agrigento (including part of the Enna Province) are the most resilient of the same regions, respectively. According to the ULC thresholds specified in Section 1, OLC can be experienced in many towns of the five regions for different control times. However, due to the low resilience values (<50%) of some towns in the Calabria and Campania regions (highlighted in red in Figure 4a), ELC can be experienced over a control time of 12 months. For these towns, CLC and LSLC could be expected over a control time of 36 (Figure 4b,c) and 60 (Figure 4d) months, respectively. Considering the first 12 months (Figure 4a), CLC can be exhibited in the critical towns of Basilicata and Sicily, while LSLC can be experienced in the most vulnerable towns of Apulia. On the other hand, considering a control time of 60 months (Figure 4d), LSLC could be obtained in the same towns of Basilicata and Sicily, while DLC in those of the Apulia region.

Referring to a return period of 250 years (Figure 5), the towns of Carpino, Castelluccio Superiore, Albi, Pietraroja and Alì become the least resilient of Apulia, Basilicata, Calabria, Campania, and Sicily regions, respectively. In these towns and their surroundings, ELC is expected over a control time of 12 months (Figure 5a), and whenincreasing the control time (Figure 5b–d), better ULCs are obtained, especially for the towns of Apulia followed by those of Sicily, where LSLC is expected considering a control time of 60 months. The critical towns of Basilicata and Campania exhibit ELC for a control time of 24 months and CLC for a control time of 36 and 60 months. In the most critical town of Calabria, ELC is experienced for a control time of 24 and 36 months, while CLC is expected to have a control time of over 60 months. For each control time, the most resilient towns of the analyzed regions (highlighted in light green, green and dark green in Figure 5) exhibit a DLC in Basilicata and Campania and an OLC in Apulia, Campania and Sicily.

Finally, for a return period of 500 years (Figure 6), the towns of Celenza Valforte, Carbone, San Basile, Sassinoro and Mandanici can be considered as the least resilient of Apulia, Basilicata, Calabria, Campania, and Sicily regions, respectively. These critical towns and their surroundings exhibit ELC for the first 36 months (Figure 6a–c) and experience CLS over a control time of 60 months (Figure 6d). On the other hand, the less resilient towns of Apulia exhibit ELC for the first 12 months (Figure 6a), as well as CLS and LSLC over a control period of 24–36 (Figure 6b,c) and 60 (Figure 6d) months, respectively. LSLC and DLC is expected in the town of Calabria with higher resilience values (i.e., Rocca Imperiale) for a control time of 12 and 24–60 months, respectively. The most resilient towns of the Basilicata and Campania regions (i.e., Nova Siri and Perdifumo, respectively) exhibit a DLC for the different control times. Only in Apulia and Sicily are there towns exhibiting OLC over the considered control times. As shown in Figure 6, these towns fall within the provinces of Bari, Brindisi, Lecce, Taranto, Agrigento and Trapani.

Note that the most critical towns may change for different return periods. This is due to the different values of the vulnerability curves as the seismic intensity increases. However, thinking in terms of average ULCs over time, although small differences in the resilience values can be appreciated, all the aforementioned critical towns present the same ULC for the analyzed return period and control time. Obviously, the estimated ULC represents an average urban functionality over the considered control time; therefore, the functionality and its ULC at the end of the control time (obtained from Equation (2) by replacing t with the control time) is certainly higher than the corresponding average value. Furthermore, by referring to these ULCs over time, useful insights can be gleaned for other urban subsystems through the ULC description summarized in Section 1.

The obtained results are very helpful to compare and understand the different recovery capacities of the considered towns. These capacities are presented and discussed in terms of average ULC over time to gain greater awareness from resilience measurements. According to the different ULCs over time among towns and the acceptable performance levels at an urban and/or higher scale, policymakers may plan mitigation strategies and/or training programs in disaster preparedness [28].

5. Conclusions

In this article, a framework to roughly quantify the seismic resilience of communities on a national/sub-national scale is proposed. It uses probabilistic risk analysis to estimate the robustness of cities against possible earthquakes by focusing on housing systems and neglecting the functional interdependencies of urban sub-systems. The inaccuracy of this approximation is due to the large spatial scale considered in this study and the key role of residential buildings in Italian territories, especially in the southern regions. The resilience measurements are then obtained through the time integration of an empirical recovery function considering different control times.

Recovery function is evaluated at an urban level according to the seismic robustness of housing systems for different return periods. This function describes the housing functionality recovery over time of a city and is defined on the basis of the empirical formulations suggested by Anelli et al. [45] to generalize the housing recovery observed by Basaglia et al. [44] after the 2012 Northern Italy Earthquake. It is able to combine the drop in functionality linked to the seismic risk of the exposed assets with the emergency management and recovery phases, as well as the integration and social cohesion of communities during these phases. In this way, the different dimensions of resilience may be more easily analyzed according to recent findings on Italian reconstruction processes.

The proposed framework is applied to the housing systems of all municipalities in five regions of southern Italy to provide resilience measurements for a return period of 100, 250 and 500 years, and a control time of 12, 24, 36 and 60 months. These measurements may help policymakers in comparing and understanding the recovery capacities of the analyzed municipalities in order to foster good practices and policies in risk governance and management at a local, regional and interregional level.

Notwithstanding the developed work is based on one of the most recent post-disaster reconstruction processes in Italy, the calculated resilience measurements could be optimistic when used to quantify the resilience of poor communities. This is due to the fact that they refer to productive realities in which it is reasonable to foresee a great boost to the local economy by the investments of national and multinational companies, as well as small- and medium-sized businesses. Such investments have brought greater integration and social cohesion during the emergency management and recovery phases, but they could not occur in the poor communities of many cities in southern Italy, where the willingness to pay for seismic retrofitting of their properties may also be very low [60]. In fact, in these communities, depopulation phenomena already occur in peacetime and greater risks of abandonment may arise in the aftermath of a disastrous earthquake.

The different seismic response of Italian communities is linked to the territorial differences in terms of production system, labor market, corporate financing and other factors, such as infrastructure and public services, socio-economic conditions, quality of institutional context and public administration, and diffusion of organized crime. Consequently, specific recovery functions could be estimated to better reproduce the reconstruction process of poor communities. In this direction, the authors are working to fine-tune more accurate resilience measurements for vulnerable communities.

Although the proposal may be intended as a simple and pragmatic way to analyze the community’s resilience to Italian seismic events, it could easily beimplemented in other earthquake-prone countries in order to carry out preliminary resilience assessments and then make comparisons and initial choices. However, more robust resilience assessments may be conducted in such countries by applying specific data and modifications to the recovery function. In particular, for these countries, empirical recovery functions should be developed based on their restoration data derived from past earthquakes. Obviously, in these cases, their corresponding hazard, exposure and vulnerability models should be used to perform the risk analysis.