Damage to Churches after the 2016 Central Italy Seismic Sequence

: The present study focuses on seismic damage to 36 masonry churches observed after the 2016 Central Italy earthquake. In the sample, recurrent architectural and structural features were identiﬁed and accurately described. In order to classify the churches in the sample based on their safety level, their seismic vulnerability was assessed by adopting the simpliﬁed procedure proposed in the current Italian standards for cultural heritage. The observed damage, directly detected by the authors during the post-earthquake surveys, is presented and carefully described, highlighting the evolution of the damage. An analysis of the damage suffered by the inspected churches highlighted the most frequent causal mechanisms and the most vulnerable macroelements. Particular attention was devoted to computation of a damage index based on the observed damage as well as on the macroelements present in the surveyed churches. Moreover, a judgment of usability, i.e., whether a church could be occupied after a seismic event, was made using the ofﬁcial survey form and related to both the seismic intensity experienced and the observed damage index. An analysis of the collected data enabled consideration of the usability judgment with respect to the damage index values, computed according to the Italian standards.

The seismic performance of historical masonry constructions is influenced by an insufficient connection between horizontal and vertical bearing elements; a crack pattern subdivides the structure into distinct macroelements with autonomous behavior, such that box behavior cannot occur [30][31][32]. Due to the architectural feature particular to churches, such as large halls, slender walls, lack of intermediate horizontal floors, and heavy, thrusting structures-such as domes and vaults-local collapse mechanisms are emphasized. Analysis of the damage occurring after the most significant Italian earthquakes (Friuli, 1976;Irpinia, 1980; Umbria-Marche, 1997; Molise, 2002; L'Aquila, 2009; Emilia, 2012) highlighted that the seismic performance of masonry churches was governed by the autonomous responses of single architectural portions [33][34][35][36], and the related damage depended on both their architectural morphology and their construction details [37,38]. Both these features vary from country to country and from region to region. Nevertheless, considerable amount of observed data extracted from survey forms was collected in the second group of papers [70][71][72][73][74][75], focusing on the development of predictive models for the seismic damage of historical churches, also by means of complex methodologies. The first paper defining empirical fragility curves for masonry churches was proposed by Hofer et al. [70], who collected 196 survey forms of churches with the aim of deriving fragility curves based on the observed mean global damage index, and with the aim of identifying the structural peculiarities of Italian "Apennine churches". Subsequently, De Matteis and Zizi [71,72] estimated the vulnerability indexes of a homogeneous sample of 68 one-nave churches according to the simplified approach proposed by the Italian guidelines [76]. Moreover, in [71,72], observed damage was compared to the values estimated through the predictive function proposed in [36], and a revised formulation for the expected average damage based on the peak ground acceleration (PGA) instead of the macroseismic intensity level (I MCS ) was proposed. Canuti et al. [73] considered a sample of 514 churches for computing damage probability matrices with respect to both the global damage index and the single mechanism. The churches' vulnerability indexes were finally derived by introducing the observed mean global damage index in the model of observational vulnerability proposed in [36]. Cescatti et al. [74] performed a statistical analysis of 889 inspections to assess the main seismic vulnerabilities of churches in Central Italy. The deep analysis of the survey's forms highlighted that most of Central Italian religious buildings are simple (one-nave churches with or without apse), as was also remarked in [70]. Therefore, based on such homogeneous vulnerability, and using data from a class composed of 633 churches, damage probability matrices were defined for different damage levels, and empirical fragility curves were derived. Finally, Morici et al. [75] statistically processed the damages of 514 religious buildings belonging to the Archdiocese of Camerino-San Severino, with the main aim of deriving the expected damage scenarios for the Marche region.
In the present paper, the damages of 36 churches during the 2016 Central Italy earthquake are presented. After a brief description of the historical and architectural features of the inspected churches, their vulnerability was assessed according to the simplified procedure of the Italian standards, as proposed in [76]. Then, the global damage index, based on the observed damage collected during the surveys, was evaluated, according to [57,76]. The dependence of the observed damage by the seismic intensity suffered by the churches was investigated considering both peak ground acceleration (PGA) and macroseismic intensity (I MCS ) as seismic intensity measures. Finally, the damage index was compared with the usability judgment for each inspected church and some drawbacks on the definition of the damage index are shown.

Inspected Churches
After an earthquake, the post-emergency Civil Protection Department activities include the identification of the most stricken and damaged areas-the "red zones"-and the evaluation of the structural safety of the damaged buildings. This knowledge is necessary to ensure the safety of the people involved in the seismic event. The architectural heritage is also analyzed in the post-emergency stage, with the following primary aims: (i) evaluating the usability of the buildings; (ii) implementing provisional measures to ensure the safety of citizens and users; (iii) drawing up a priority of the provisional safety operations; (iv) preserving the pieces of art which are in danger; (v) estimating realistic levels of national funding for the reconstruction phase.
After the 2016 Central Italy earthquakes, the authors, as ReLUIS members, participated in the activities surveying monumental buildings, which were coordinated by the Italian Civil Protection Department and the Ministry of Cultural Heritage. In this framework, a total of 36 churches were inspected starting from September 17: 11 were in the municipalities of Accumoli and Amatrice (near the epicenter of 24 August); 20 were near the city of Teramo (approximately 40 km away from the 24 August epicenter); the 5 farthest away are located near Macerata, in the northern surveyed area, or in the proximity of L'Aquila All the examined monuments belong to the Italian Cultural Heritage, representing tremendous cultural and sociological value for the inhabitants of the localities and for history. The largest number of surveyed churches was founded in the XV-XVI century, as is the case of the Dome in Campli (Figure 2a). The oldest surveyed church is the Romanic Abbey of Holy Mary in Montesanto near Teramo (Figure 2b), which-according to the popular tradition-was founded in the VI century AD by Saint Benedict from Norcia. Contrarily, historical sources suggest that the Abbey was founded during the XI century, becoming one of the most powerful Benedictine Monasteries of the region in the medieval period. The following sections briefly analyze the surveyed churches in terms of historical features, plan configuration, and masonry quality. A simplified vulnerability assessment was carried out according to the Italian guidelines provisions on the assessment and the mitigation of seismic risk on cultural heritage [76]. All the examined monuments belong to the Italian Cultural Heritage, representing tremendous cultural and sociological value for the inhabitants of the localities and for history. The largest number of surveyed churches was founded in the XV-XVI century, as is the case of the Dome in Campli (Figure 2a). The oldest surveyed church is the Romanic Abbey of Holy Mary in Montesanto near Teramo (Figure 2b), which-according to the popular tradition-was founded in the VI century AD by Saint Benedict from Norcia. Contrarily, historical sources suggest that the Abbey was founded during the XI century, becoming one of the most powerful Benedictine Monasteries of the region in the medieval period. The following sections briefly analyze the surveyed churches in terms of historical features, plan configuration, and masonry quality. A simplified vulnerability assessment was carried out according to the Italian guidelines provisions on the assessment and the mitigation of seismic risk on cultural heritage [76].

Historical and Architectural Features
The investigated churches were founded in five distinct temporal-architectonic intervals ( Figure 3a). In detail, 22.22% of the sample is composed of medieval churches, characterized by poor decoration, in accordance with the main peculiarity of Central Ital-

Historical and Architectural Features
The investigated churches were founded in five distinct temporal-architectonic intervals ( Figure 3a). In detail, 22.22% of the sample is composed of medieval churches, characterized by poor decoration, in accordance with the main peculiarity of Central Italian medieval churches [77,78]. A proportion of 29.17% of the inspected churches were founded between the XV and the XVI centuries (the Renaissance period), including the meaningful example of the Dome in Campli (Figure 2a). The religious buildings belonging to the Baroque period (from the XVI to the XVII century) are characterized by impressive facades, with interiors animated by aisles, vaults, and often rich frescoes-such churches constitute 26.39% of the sample. The architecture of the Neoclassical cluster (12.50% of the sample) is inspired by Classical Era principles; therefore, the spatial characterization is marked by stuccoes, producing a well-balanced dynamism that never exhibits contrasting tensions. The last set (9.72% of the sample) was built in the Modern Age, i.e., in the XX century, and it is composed of churches of smaller dimensions and often characterized by less refined masonry (irregular texture characterized by stone elements).

Historical and Architectural Features
The investigated churches were founded in five distinct temporal-architectonic intervals ( Figure 3a). In detail, 22.22% of the sample is composed of medieval churches, characterized by poor decoration, in accordance with the main peculiarity of Central Italian medieval churches [77,78]. A proportion of 29.17% of the inspected churches were founded between the XV and the XVI centuries (the Renaissance period), including the meaningful example of the Dome in Campli (Figure 2a). The religious buildings belonging to the Baroque period (from the XVI to the XVII century) are characterized by impressive facades, with interiors animated by aisles, vaults, and often rich frescoes-such churches constitute 26.39% of the sample. The architecture of the Neoclassical cluster (12.50% of the sample) is inspired by Classical Era principles; therefore, the spatial characterization is marked by stuccoes, producing a well-balanced dynamism that never exhibits contrasting tensions. The last set (9.72% of the sample) was built in the Modern Age, i.e., in the XX century, and it is composed of churches of smaller dimensions and often characterized by less refined masonry (irregular texture characterized by stone elements). Among the different architectural key features, the main distinction that characterized the seismic response is the plan configuration according to the approach already  Among the different architectural key features, the main distinction that characterized the seismic response is the plan configuration according to the approach already adopted by other authors [21][22][23]43,60,[70][71][72][73][74][75]. According to the characteristics of the surveyed churches, the considered layouts comprise the following: single-nave typology (SN), one nave with transept (SNT), three naves and transept (3NT), and central plan configuration (C). It can be observed that the single nave configuration, that of SN and SNT, is the most frequent layout, while only 12% of the sample presents a more complex architectural conformation ( Figure 4a). Such results are in line with the remarks of other authors [70,74]. In Figure 4, some examples of inspected churches with different plan configurations are reported.
(SN), one nave with transept (SNT), three naves and transept (3NT), and central plan configuration (C). It can be observed that the single nave configuration, that of SN and SNT, is the most frequent layout, while only 12% of the sample presents a more complex architectural conformation (Figure 4a). Such results are in line with the remarks of other authors [70,74]. In Figure 4, some examples of inspected churches with different plan configurations are reported.  To summarize, the single nave without transept (SN) category comprises the larger sample, i.e., 80% of the inspected churches. Among them, 27.59% were built in the Medieval era, 24.14% in the Renaissance, and 20.69% in the Neoclassical period. The churches characterized by a single nave and built in the Baroque or Modern period comprise 13.79% of the clusters in both cases. All the churches characterized by the single nave without transept are moreover characterized by the following features: (i) a façade with a rose window over the entrance and a triangular or rectangular gable; (ii) a double pitched timber roof; (iii) a belltower beside the church. These typical features depict the "Apennine church" typology, as defined in [44,67,70,74] after the Central Italy earthquake. An example of a surveyed "Apennine church" is the St. Maxim Oratory in Collalto (Amatrice), sketched in Figure 5.
of the clusters in both cases. All the churches characterized by the single nave without transept are moreover characterized by the following features: (i) a façade with a rose window over the entrance and a triangular or rectangular gable; (ii) a double pitched timber roof; (iii) a belltower beside the church. These typical features depict the "Apennine church" typology, as defined in [44,67,70,74] after the Central Italy earthquake. An example of a surveyed "Apennine church" is the St. Maxim Oratory in Collalto (Amatrice), sketched in Figure 5.

Structural Features
The inspected churches are characterized by different masonry typologies, depending on their geographic location and the importance attributed to the church by the community ( Figure 6). The typical masonry walls often consist of local irregular stones, frequently characterized by a double layer and a poor-quality mortar (Figure 6a), as also observed by other authors analyzing the churches stricken by the Central Italy earthquake [74]. In the case of medium-importance structures, i.e., St. Savino in Gualdo, the prevailing availability of irregular calcareous stones result in a medium-quality wall ( Figure 6b); however, in the case of seismic action, it could easily crumble. Among the surveyed churches, the cases of good-quality masonry are rare and observed only in important monuments, i.e., the Abbey of Holy Mary in Montesanto, in which calcareous bricks, regular in size and shape, can be observed (Figure 6c).

Structural Features
The inspected churches are characterized by different masonry typologies, depending on their geographic location and the importance attributed to the church by the community (Figure 6). The typical masonry walls often consist of local irregular stones, frequently characterized by a double layer and a poor-quality mortar (Figure 6a), as also observed by other authors analyzing the churches stricken by the Central Italy earthquake [74]. In the case of medium-importance structures, i.e., St. Savino in Gualdo, the prevailing availability of irregular calcareous stones result in a medium-quality wall ( Figure 6b); however, in the case of seismic action, it could easily crumble. Among the surveyed churches, the cases of good-quality masonry are rare and observed only in important monuments, i.e., the Abbey of Holy Mary in Montesanto, in which calcareous bricks, regular in size and shape, can be observed ( Figure 6c).    Several churches present domes ( Figure 7) and vaults (Figure 8), among these, the false camorcanna vaults (Figure 8a) and the more vulnerable in folio vaults ( Figure 8b) were observed. In the case of inspectable roofing, a non-pushing timber light roof was typically detected (47% of the sample); only in one church-the Virgin of Rescue in Campli-was the gable roof made of one-way ribbed slab.

Simplified Vulnerability Assessment
In order to evaluate whether the church sample was composed of homogenous data in terms of structural features and seismic responses, the surveyed churches' vulnerability was assessed according to the simplified LV1 procedure proposed by the Italian guidelines on the assessment and the mitigation of the seismic risk on the cultural heritage [76]. The methodology analyses the constructive details and features according to the procedure proposed in [36], through the direct observation of the existing macroelements, including 28 mechanisms (M), as shown in Table 1. The principal advantage of the approach is the limited amount of data necessary, which is essential for a quick assessment. The LV1 methodology allows having a first seismic vulnerability classification of the church based on the assessment of a vulnerability index that ranges from 0 (if the church does not present seismic vulnerability) to 1 (if the church has a high vulnerability). The vulnerability index, iv, is defined as a weighted sum of the vulnerability indicator assigned to all possible local mechanisms that could occur in the structure, regardless of the probability of their contemporary activation. According to [76], the vulnerability index can be estimated as follows: where vki is the indicator of vulnerability attributed to the k-th mechanism associated with a specific macroelement, and vkp is the indicator of vulnerability assigned to the seismic protection devices of the same mechanism (i.e., tie rods, buttresses, etc.). Both these indi-

Simplified Vulnerability Assessment
In order to evaluate whether the church sample was composed of homogenous data in terms of structural features and seismic responses, the surveyed churches' vulnerability was assessed according to the simplified LV1 procedure proposed by the Italian guidelines on the assessment and the mitigation of the seismic risk on the cultural heritage [76]. The methodology analyses the constructive details and features according to the procedure proposed in [36], through the direct observation of the existing macroelements, including 28 mechanisms (M), as shown in Table 1. The principal advantage of the approach is the limited amount of data necessary, which is essential for a quick assessment. The LV1 methodology allows having a first seismic vulnerability classification of the church based on the assessment of a vulnerability index that ranges from 0 (if the church does not present seismic vulnerability) to 1 (if the church has a high vulnerability). The vulnerability index, i v , is defined as a weighted sum of the vulnerability indicator assigned to all possible local mechanisms that could occur in the structure, regardless of the probability of their contemporary activation. According to [76], the vulnerability index can be estimated as follows: where v ki is the indicator of vulnerability attributed to the k-th mechanism associated with a specific macroelement, and v kp is the indicator of vulnerability assigned to the seismic protection devices of the same mechanism (i.e., tie rods, buttresses, etc.). Both these indicators vary between 0 and 3 and are evaluated according to an expert's judgment: v ki increases with the vulnerability of the macroelement, and v kp increases with the effectiveness of the seismic protection device. Therefore, v ki = 0 means that the kinematic mechanism cannot be activated (i.e., the macroelement is absent), while v kp = 0 means that the aseismic protection devices are ineffective or absent. On the contrary, the value 3 is assumed for highly vulnerable macroelements or when the devices can inhibit the associated kinematic mechanisms. For all the analyzed churches, the obtained vulnerability indexes are listed in Table 2 and reported in Figure 9. It is worth underlining that the vulnerability index cannot be evaluated for the collapsed churches (C12, C26-C29), since the inspections were realized only after the earthquake when the collapses had occurred. The results of the LV1 procedure (Table 2, Figure 9) show a predominant low-medium vulnerability of the inspected churches: 39% of the sample is characterized by a low vulnerability index (lower or equal to 0.40), 36% had medium vulnerability (the vulnerability index ranges between 0.40 and 0.60), and 25% were marked by high vulnerability. (facade, elements of the nave or the apse, triumphal arches, and belltower), as well as being reliant on the occurrence of activation of the related kinematic mechanism. Instead, the vulnerability index evaluated according to the LV1 approach disregards proper coefficients of combination to consider the non-simultaneous triggering of the kinematic mechanisms. Consequently, the vulnerability index perceives the possibility of contemporary activation of all possible mechanisms, even if distinct macroelements can independently move and collapse when an earthquake shakes an ancient masonry church. Although each element should be properly weighted to account for their different rule in the seismic response, according to [76], almost all macroelements are considered of equal importance; therefore, the weight affects the final value of iv only in a limited way. In this perspective, the LV1 approach was recently criticized [77,78], and a more flexible definition of the adopted weights was suggested. It is worth noting that the attained vulnerability index could not be fully representative of the effective seismic vulnerability of the church, although the score assigned to the indicators of vulnerability is a key factor for the final assessment of i v . In fact, the church vulnerability is strictly related to the vulnerability of the most relevant macroelements (facade, elements of the nave or the apse, triumphal arches, and belltower), as well as being reliant on the occurrence of activation of the related kinematic mechanism. Instead, the vulnerability index evaluated according to the LV1 approach disregards proper coefficients of combination to consider the non-simultaneous triggering of the kinematic mechanisms. Consequently, the vulnerability index perceives the possibility of contemporary activation of all possible mechanisms, even if distinct macroelements can independently move and collapse when an earthquake shakes an ancient masonry church.
Although each element should be properly weighted to account for their different rule in the seismic response, according to [76], almost all macroelements are considered of equal importance; therefore, the weight affects the final value of i v only in a limited way. In this perspective, the LV1 approach was recently criticized [77,78], and a more flexible definition of the adopted weights was suggested.

Observed Damages
The earthquake which occurred on 30 October 2016 was the strongest Italian seismic event in the last 40 years [79]: the event, with an epicenter located 5 km away from the municipality of Norcia, recorded 6.5 magnitude. The shock was a part of a wider sequence, called "Central Italy Earthquake 2016", and started on 24 August with a first earthquake of 6.0 magnitude and an epicenter near the municipality of Accumoli.
In the survey activities promoted by the Civil Protection Department and the Italian Cultural Heritage Ministry, the authors directly observed the damages caused by the two mainshocks of 24 August and 30 October. According to the lessons from the Friuli earthquake and the Emilia-Romagna earthquake [42], the cumulative damages in the Central Italy earthquake were significant and, in several cases, dramatic. Evidence of the damage evolution due to multiple seismic events is represented in Figure 10, where the evolution of damage in the St. Lawrence and St. Paul Church in Accumoli (C29) is depicted: the shock, which occurred on the 24 August, activated the rocking motion of the gable of the façade up to its collapse ( Figure 10b); then, when the shock of the 30 October occurred, the church totally disintegrated (Figure 10c). quake and the Emilia-Romagna earthquake [42], the cumulative damages in the Central Italy earthquake were significant and, in several cases, dramatic. Evidence of the damage evolution due to multiple seismic events is represented in Figure 10, where the evolution of damage in the St. Lawrence and St. Paul Church in Accumoli (C29) is depicted: the shock, which occurred on the 24 August, activated the rocking motion of the gable of the façade up to its collapse ( Figure 10b); then, when the shock of the 30 October occurred, the church totally disintegrated (Figure 10c). Upon the first examination, the more recurrent damages suffered by the inspected "Apennine church", i.e., the typical religious building typology in the analyzed geographical context, concern the façade. As also remarked by several authors, based on the collected aftershock data analysis [21][22][23]34,42,44,47,48,74], the façade is the most frequently damaged macroelement, and the overturning is the most dangerous mechanism. Analogously, the crack patterns observed in the St. Francis Church in Amatrice (C10), before and after the 24 August shock, evidence that the damages mainly struck the façade macroelement (Figure 11a,b). The results of the St. Peter and St. Paul Church inspections in Accumoli (C27) point out the same evidence of this out-of-plane mechanism ( Figure  12a,b). It is worth noting that if the connection between the wall leaves is poor, as in the case of the St. Elpidio church in Gualdo (C9, Figure 13), where an opening under the arch was closed by a poor-quality masonry wall, and the out-of-plane mechanism appears as a detachment of the external masonry layer, since the masonry does not express any monolithic behavior. Therefore, a wall can experience a partial disruption for seismic acceleration values lower than the one corresponding to the activation of the kinematic motion of the entire wall. Upon the first examination, the more recurrent damages suffered by the inspected "Apennine church", i.e., the typical religious building typology in the analyzed geographical context, concern the façade. As also remarked by several authors, based on the collected aftershock data analysis [21][22][23]34,42,44,47,48,74], the façade is the most frequently damaged macroelement, and the overturning is the most dangerous mechanism. Analogously, the crack patterns observed in the St. Francis Church in Amatrice (C10), before and after the 24 August shock, evidence that the damages mainly struck the façade macroelement (Figure 11a,b). The results of the St. Peter and St. Paul Church inspections in Accumoli (C27) point out the same evidence of this out-of-plane mechanism (Figure 12a,b). It is worth noting that if the connection between the wall leaves is poor, as in the case of the St. Elpidio church in Gualdo (C9, Figure 13), where an opening under the arch was closed by a poor-quality masonry wall, and the out-of-plane mechanism appears as a detachment of the external masonry layer, since the masonry does not express any monolithic behavior. Therefore, a wall can experience a partial disruption for seismic acceleration values lower than the one corresponding to the activation of the kinematic motion of the entire wall.
With specific reference to the out-of-plane motion of the façade, it is worth noting that the 2016 Central Italy earthquake presents a strong directionality, as suggested by the acceleration response spectra of the two main events (Figure 14). In particular, the higher seismic acceleration struck the region in the east-west direction, corresponding to the so-called "sacred direction" of the churches (east-west axis), until the II Vatican Council (1960). As an explanatory case, the example of the Saint George Church in Terracino (C35) is given, for which the overturning mechanism of the façade is evident (Figure 15).
Aside from the façade mechanism, the overturning mechanism causes the abrupt displacement of the imposts of arches and vaults or domes; these structures, frequently made with bricks arranged in folio, can easily move into the minimum thrust condition, and then collapse, as in the example of St. Savino church in Gualdo (C36, Figure 16). With specific reference to the out-of-plane motion of the façade, it is worth noting that the 2016 Central Italy earthquake presents a strong directionality, as suggested by the acceleration response spectra of the two main events (Figure 14). In particular, the higher seismic acceleration struck the region in the east-west direction, corresponding to the socalled "sacred direction" of the churches (east-west axis), until the II Vatican Council (1960). As an explanatory case, the example of the Saint George Church in Terracino (C35) is given, for which the overturning mechanism of the façade is evident (Figure 15). Aside from the façade mechanism, the overturning mechanism causes the abrupt displacement of the imposts of arches and vaults or domes; these structures, frequently made with bricks arranged in folio, can easily move into the minimum thrust condition, and then collapse, as in the example of St. Savino church in Gualdo (C36, Figure 16). With specific reference to the out-of-plane motion of the façade, it is worth noting that the 2016 Central Italy earthquake presents a strong directionality, as suggested by the acceleration response spectra of the two main events (Figure 14). In particular, the higher seismic acceleration struck the region in the east-west direction, corresponding to the socalled "sacred direction" of the churches (east-west axis), until the II Vatican Council (1960). As an explanatory case, the example of the Saint George Church in Terracino (C35) is given, for which the overturning mechanism of the façade is evident (Figure 15). Aside from the façade mechanism, the overturning mechanism causes the abrupt displacement of the imposts of arches and vaults or domes; these structures, frequently made with bricks arranged in folio, can easily move into the minimum thrust condition, and then collapse, as in the example of St. Savino church in Gualdo (C36, Figure 16). The clerestory walls, typically present in three naves churches, are characterized by a high vulnerability to out-of-plane action. These structural elements correspond to the short walls of the central nave located above the arches separating the central nave from the lateral nave. Since they should support only the weight of the roof structures, the clerestory walls are typically slenderer than the other walls; moreover, they are often marked by full-height windows, allowing the appropriate brightness for the religious building. Both these aspects, coupled to the vertical amplification of seismic motion, promote the formation of splitting cracks spreading on the top and lower sections of the element, as observed in the example of the Dome of Campli (C34, Figure 17). It is interesting to recall The clerestory walls, typically present in three naves churches, are characterized by a high vulnerability to out-of-plane action. These structural elements correspond to the short walls of the central nave located above the arches separating the central nave from the lateral nave. Since they should support only the weight of the roof structures, the clerestory walls are typically slenderer than the other walls; moreover, they are often marked by fullheight windows, allowing the appropriate brightness for the religious building. Both these aspects, coupled to the vertical amplification of seismic motion, promote the formation of splitting cracks spreading on the top and lower sections of the element, as observed in the example of the Dome of Campli (C34, Figure 17). It is interesting to recall that similar damages were recorded after the Emilia earthquake [42]. The clerestory walls, typically present in three naves churches, are characterized by a high vulnerability to out-of-plane action. These structural elements correspond to the short walls of the central nave located above the arches separating the central nave from the lateral nave. Since they should support only the weight of the roof structures, the clerestory walls are typically slenderer than the other walls; moreover, they are often marked by full-height windows, allowing the appropriate brightness for the religious building. Both these aspects, coupled to the vertical amplification of seismic motion, promote the formation of splitting cracks spreading on the top and lower sections of the element, as observed in the example of the Dome of Campli (C34, Figure 17). It is interesting to recall that similar damages were recorded after the Emilia earthquake [42]. The belltowers frequently present damages in the pinnacles, in the bell cell, and along the tower. In particular, the damage on the stem can be detected when the variation of the vertical stiffness in the structure is significant, i.e., for towers connected to the church (Figure 18). Instead, the most damaged element becomes the cell when the variation in stiffness is more gradual. In fact, in all inspected cases these elements are characterized by the presence of large openings and by vertical bearing elements with reduced thickness, since the working loads that they should sustain are low. Consequently, the cells can experience The belltowers frequently present damages in the pinnacles, in the bell cell, and along the tower. In particular, the damage on the stem can be detected when the variation of the vertical stiffness in the structure is significant, i.e., for towers connected to the church ( Figure 18). Instead, the most damaged element becomes the cell when the variation in stiffness is more gradual. In fact, in all inspected cases these elements are characterized by the presence of large openings and by vertical bearing elements with reduced thickness, since the working loads that they should sustain are low. Consequently, the cells can experience a shear failure, as in the case of the St. Savino church in Gualdo (C36), where a significant crack pattern on the piers was detected (Figure 19a). Finally, when the piers are strong enough, the damages are localized on the upper part of the cell (Figure 19b).   Among the mechanisms frequently detected in the post-seismic survey activities, the in-plane shear mechanism in the façade or in the lateral walls ( Figure 20a) and the roof cover mechanism with the sliding of the timber beams ( Figure 20b) must be mentioned. This mechanism could be very dangerous due to the possible loss of the support for the timber beams with the consequent roof collapse. Among the mechanisms frequently detected in the post-seismic survey activities, the in-plane shear mechanism in the façade or in the lateral walls ( Figure 20a) and the roof cover mechanism with the sliding of the timber beams ( Figure 20b) must be mentioned. This mechanism could be very dangerous due to the possible loss of the support for the timber beams with the consequent roof collapse.

Possible and Activated Collapse Mechanisms
In this section, a synthesis related to the possible and the activated mechanisms observed during the inspection is given for the 36 Apennine churches inspected by the authors after the Central Italy earthquake. Specifically, during the surveys, the first point was to identify whether the macroelement was present in the church, and then, if present, to identify whether it was damaged. Figure 21 shows the relative presence and occurrence of the mechanism activation for each macroelement-recalled following the nomenclature used in Table 1. Observing the red bars, in more than 90% of the surveyed churches the façade, (M1, M3), the gable (M2), the nave (M5-M6), and its roof (M19) were present, as expected. In more than 60% of the cases, plano-altimetric irregularities (M25) and the standing-out elements (M26) were observed. The vaults were present in different positions inside the church, such as in the nave, the transept, etc., for about 42% of the cases; however, if consideration is limited to the more relevant elements, characterized by weight ρk = 1 (i.e., M8 and M9 according to Table 1), this proportion reduces to 31% of the cases. The other macroelementsthe belltower (25%), transept (11%), dome (8%), and chapel (3%)-were registered with significantly lower frequency.

Possible and Activated Collapse Mechanisms
In this section, a synthesis related to the possible and the activated mechanisms observed during the inspection is given for the 36 Apennine churches inspected by the authors after the Central Italy earthquake. Specifically, during the surveys, the first point was to identify whether the macroelement was present in the church, and then, if present, to identify whether it was damaged. Figure 21 shows the relative presence and occurrence of the mechanism activation for each macroelement-recalled following the nomenclature used in Table 1. Observing the red bars, in more than 90% of the surveyed churches the façade, (M1, M3), the gable (M2), the nave (M5-M6), and its roof (M19) were present, as expected. In more than 60% of the cases, plano-altimetric irregularities (M25) and the standing-out elements (M26) were observed. The vaults were present in different positions inside the church, such as in the nave, the transept, etc., for about 42% of the cases; however, if consideration is limited to the more relevant elements, characterized by weight ρ k = 1 (i.e., M8 and M9 according to Table 1), this proportion reduces to 31% of the cases. The other macroelements-the belltower (25%), transept (11%), dome (8%), and chapel (3%)-were registered with significantly lower frequency.
to identify whether it was damaged. Figure 21 shows the relative presence and occurrence of the mechanism activation for each macroelement-recalled following the nomenclature used in Table 1. Observing the red bars, in more than 90% of the surveyed churches the façade, (M1, M3), the gable (M2), the nave (M5-M6), and its roof (M19) were present, as expected. In more than 60% of the cases, plano-altimetric irregularities (M25) and the standing-out elements (M26) were observed. The vaults were present in different positions inside the church, such as in the nave, the transept, etc., for about 42% of the cases; however, if consideration is limited to the more relevant elements, characterized by weight ρk = 1 (i.e., M8 and M9 according to Table 1), this proportion reduces to 31% of the cases. The other macroelementsthe belltower (25%), transept (11%), dome (8%), and chapel (3%)-were registered with significantly lower frequency.  Since the presence of the macroelement does not imply the mechanism activation, in distinct macroelements, the frequency of observed damages was calculated as the ratio of the number of churches showing the activation of the specific mechanism over the number of churches where the macroelements was present. For this purpose, it is important to underline that, in the case of destroyed churches, all mechanisms concerning the main macroelements (such as the façade, the nave, and the roof) were assumed to be activated. Similarly, if the collapse of a single macroelement was observed, all the related mechanisms were considered activated.
Concerning the activated mechanisms involving the façade (M1, M2, and M3), the following frequencies are detected:

•
Overturning of the façade (M1)-it occurred in 24 churches, i.e., in 69% of cases in which the macroelement could be activated; • Overturning of the gable (M2)-it was detected in the 50% of the possible cases; • Shear mechanism in the façade (M3)-observed in the 60% of the reduced sample.
The fourth mechanism (M4) involves the porch or the narthex, architectural components found only in 11% of the inspected churches, which exhibited a negligible vulnerability level, since their activation percentage was 25%. As far as the nave is concerned, the mechanism should be distinguished between those affecting the vertical elements and those affecting the vaults. The first group includes the transversal vibration of the nave (M5) and the shear mechanism on the nave lateral walls (M6), mechanisms possible in all the surveyed churches, but triggered only in 56% and in 58% of the sample, respectively. Only 14% of the inspected religious buildings had a colonnade, but their longitudinal response (M7) was activated in 80% of the possible cases. The transept was present only in the 11% of the sample and its associated mechanisms cannot be regarded as representative, since the overturning (M10) was never triggered, and the shear failure (M11) was activated only in half of the possible cases. Only 39% of the inspected churches present triumphal arches, but the related mechanism (M13) was activated in 89% of the cases. Regarding the apses and presbytery walls, we can observe the following:

•
The apse overturning (M16) could be developed in 15 churches, i.e., in 42% of the sample, and among them the activation frequency was the 60%; • The shear failure of apse walls (M17) was triggered only in 27% of the possible cases.
The vaults, present in 42% of the sample, were mainly detected in the nave, the presbytery, and the apse. In detail, vaults of the central nave (M8) and in the presbytery and apse (M18) were observed in 10 churches (i.e., 28% of the sample). Concerning the vaults of the central nave (M8), the mechanism was triggered in 60% of the cases. Instead, more vulnerable were the vaults of the presbytery and the apse (M18), the mechanism of which was activated in 70% of the inspected buildings. Finally, the vaults of the aisles (M9) and of the transept (M12) are negligible since they characterize only 6% of the inspected churches. Nevertheless, in all cases the aisle vaults (M9) mechanism was activated, while the damage in the vaults of the transept (M12) occurred in only 50% of cases.
The dome and the lantern (M14) can be found only in three churches of the sample, but the related mechanism was always enabled. On the contrary, the collapse mechanism of the lantern (M15) was never triggered, but the related macroelement was observed in only one church. Among the most occurring mechanisms, hammering and damage in the roofs were very frequent, as follows:

•
Damage on the nave roof (M19) could be verified in 94% of the sample, but it was activated only in 41% of the possible cases; • The mechanisms in the transept roof (M20) were possible in only 14% of the churches and they had an occurrence probability of 40%; • On the roof of the apse and the presbytery (M21), the mechanisms occurred in 36% of the religious buildings, and they took place only in 8% of the reduced sample.
The mechanisms related to the chapels (overturning, the shear failure of the walls, and the collapse of the vaults, i.e., M22, M23, and M24, respectively) seem to be extremely rare, since these components were present only in one inspected church; in this sample, only the overturning mechanism (M22) was triggered.
The interaction between elements characterized by different behaviors (M25) was verified in 69% of inspected buildings, and the related mechanism was effectively activated in 68% of the possible cases. Analogously, standing-out elements were observed in 61% of the sample, and their overturning (M26) developed in 50% of the cases.
Finally, belltowers were detected in 31% of the structures, and the related mechanisms-the global collapse (M27) and that of the bell cell (M28)-had trigger frequencies of 55% and 45%, respectively.
In summary, the most damaged architectural elements were the façade, the vaults, and the standing-out elements. Moreover, the damage caused by the interaction between elements, characterized by different behaviors, was frequent. Finally, even though domes were present in only three churches, in all these cases they were strongly damaged.
After identifying the activation of one of the mechanisms, the damage level reached was evaluated. Congruently to the approach adopted for assessing the mechanism activation, the maximum damage level was assumed for all collapsed macroelements and their related mechanisms. As an example, in the case of C10-St. Francis church-in which the façade collapsed (Figure 11), a damage level equal to 5 was assumed for all mechanisms concerning the façade (M1, M2, M3). In Figure 22, the mean damage level of each mechanism is represented by a scale from 1 to 5. The weight of the damage mechanisms is assessed according to the manual for the compilation of the survey In order to properly analyze the observed damaged mechanism, it is particularly interesting to relate the frequency of a given mechanism activation to the exposure of the related macroelement, i.e., the frequency of the presence of the macroelement in the surveyed churches.
concerning the façade (M1, M2, M3). In Figure 22, the mean damage level of each mechanism is represented by a scale from 1 to 5. The weight of the damage mechanisms is assessed according to the manual for the compilation of the survey In order to properly analyze the observed damaged mechanism, it is particularly interesting to relate the frequency of a given mechanism activation to the exposure of the related macroelement, i.e., the frequency of the presence of the macroelement in the surveyed churches. It can be observed that the mechanisms M19 (nave roof), M21 (roof of apse and presbytery), and M26 (standing-out elements) are characterized by a higher mean damage level. However, damage of nave rooves, and the standing-out elements can be considered particularly serious because of their frequency of occurrence and, above all, because of their relevance in the churches' seismic performances. On the contrary, the apse was rarely present in the sample; therefore, the damage in its roof could not be considered meaningful. Among the mechanisms with an observed mean damage level higher than 3, the risk seems significant only for the façade (M1, M2, M3), the nave (M5 and M6), and the walls of the presbytery and the apse (M17). In fact, the vaults of the presbytery and the apse It can be observed that the mechanisms M19 (nave roof), M21 (roof of apse and presbytery), and M26 (standing-out elements) are characterized by a higher mean damage level. However, damage of nave rooves, and the standing-out elements can be considered particularly serious because of their frequency of occurrence and, above all, because of their relevance in the churches' seismic performances. On the contrary, the apse was rarely present in the sample; therefore, the damage in its roof could not be considered meaningful. Among the mechanisms with an observed mean damage level higher than 3, the risk seems significant only for the façade (M1, M2, M3), the nave (M5 and M6), and the walls of the presbytery and the apse (M17). In fact, the vaults of the presbytery and the apse (M18), as well as the roof of the transept (M20), were infrequent in the sample, as previously indicated.
If macroelement is present in the church and the activation of the corresponding mechanism is observed, then it can be stated that the vaults of the presbytery and apse (M17) are slightly unsafe, and that the most critical mechanisms involve the façade and the related sidewalls (wall of the nave). In detail, concerning the elements composing the central nave, we can observe the following:

•
The façade overturning (M1) simultaneously presents a 100% probability of occurrence, a probability of activation of 69%, and a mean damage level higher than 3. Specifically, through deeply analyzing the survey form, it can be detected that 44% of the sample is characterized by a damage level higher than 3 (serious damage). This percentage reduced to 28% if only those values higher than 4 (very serious damage) are considered.

•
The gable overturning (M2) has a 94% probability of occurrence, and simultaneously, a 50% probability of activation and a mean damage level higher than 3. However, only 31% of the sample is characterized by a damage level higher than 3, and it should be considered that the façade collapsed in only 19% of cases.

•
The shear mechanism of the façade (M3) was simultaneously characterized by a 100% probability of occurrence, a 60% probability of activation, and a mean damage level higher than 3. In detail, churches presenting a damage level higher than 3 comprise 42% of the sample, but when considering only very serious damages and collapses, this percentage reduces to 25%.

•
The transversal vibration of the nave (M5) has a probability of occurrence of 100%, a probability of activation of 56%, and a mean damage level higher than 3. Additionally, in this case, 42% of the sample presents a damage level higher than 3, while the percentage decreases to 36% if accounting for only those values higher than 4.

•
The shear mechanism in the nave sidewalls (M6) is characterized by a 100% probability of occurrence, 58% probability of activation, and a mean damage level higher than 3.
A proportion of 39% of the sample is characterized by damage levels higher than 3, while only 28% suffered the worst damages.
In conclusion, the overturning of the facade was the most dangerous mechanism we observed in the "Apennine church".

The Damage Index: Relationship with IMs and Usability Judgment
The above-described damage data were used to evaluate the average level of damage suffered by each church. According to [81], the index accounts for all possible kinematic mechanisms that can develop (the blue bars in Figure 21), regardless of their actual activation (red bars in Figure 21). Following the Italian post-seismic damage form, specifically designed for churches [57], the mean damage index can be evaluated as follows: where d k is the damage level of the k-th mechanism, defined by expert judgment, ranging from 0 (if any damage is observed) to 5 (in case of collapse); n is the number of the mechanisms that may be potentially activated when the related macroelement is present. Alternatively, the Italian guidelines on the assessment and the mitigation of the seismic risk on cultural heritage [76] suggests estimating the damage index through a weighted sum of the damages occurred in all kinematics mechanisms, as follows: where ρ k is the weight assigned to each activable mechanism according to the importance of the considered macroelement on the seismic performance of the church, according to the LV1 approach. For each mechanism, their possible values are the same as those reported in Table 1 [76]. For each inspected church, the following data are reported in Table 3: the seismic intensity of the measures suffered by the churches; the damage indexes, evaluated according to Equations (2) and (3); the usability judgment assigned to each church. Concerning the values of the damage indexes, it is interesting to note that Equations (2) and (3) led to very similar values for the considered sample, despite the application of specific weights in Equation (3) to account for the importance of some mechanisms. This result can be attributed to the peculiarities of the Apennine churches, composed mainly of basic macroelements associated with a unit weight according to the actual standards [76]. Instead, the weights assume a value of ρ k = 0.5, only in the few cases of the less frequent macroelements. Undoubtedly, completely different values of i dW could be presumed if the relative geometrical proportion of macroelements also is considered in the computation of the weighted observed damage index, as suggested in [77]. However, since the actual procedure of the post-seismic inspections disregards the measurement of the geometrical dimensions of the macroelements, a proper comparison between the damage index evaluated according to the actual Italian guidelines [76] and the one derived by the methodology proposed in [77] cannot be carried out. Table 3. Church identification number (ID), peak ground accelerations (PGA), and macroseismic intensities (I MCS ), derived from ShakeMaps according to the geographical location of the church, the vulnerability index i v , the observed and weighted observed damage index (i d and i dW , respectively), and the usability judgment.  Due to the similarity of the global and weighted damage indexes for the considered sample, only the global damage index, i d (Equation (2)), is considered in the following. Concerning the obtained results, it could be concluded that:

ID
• 25% of the inspected churches were severely damaged or collapsed; • 17% of the dataset experienced extended damage and consequently observed damage indexes ranging from 0.3 to 0.6; • 58% of the inspected churches were characterized by limited damage (i.e., observed damage index from 0 to 0.3).
To evaluate a relationship between the damage index and the maximum intensity measures suffered by the churches, the damage index, i d , was represented versus two seismic intensity measures: the observed Mercalli-Cancani-Sieberg macroseismic intensities, I MCS , and the PGA. The I MCS , deduced from [82], is defined according to an empirical qualitative scale representative of the effects of an earthquake on people, objects, buildings, and environment, evaluated by observing the percentage of buildings damaged or destroyed and the behavior of people. Therefore, it is not a measure in the strict sense, and it could not characterize the effective severity of an earthquake in less urbanized areas, such as those in which many of the surveyed churches are placed. The PGA, instead, is the actual measurement of the maximum acceleration exerted by an earthquake on the ground, and it is punctually recorded by means of the accelerometers belonging to the finalized Italian Strong Motion Network. A synthetic representation of the PGA suffered by a region after an earthquake is depicted by the ShakeMaps [83], developed by the Italian National Institute of Geophysics and Volcanology, according to proper attenuation laws; this is particularly accurate in sites where the geognostic and geophysical investigations are available.
Analyzing the relationship between i d and the macroseismic intensity (Figure 23a), it can be observed that, for lower intensities (I MCS = V), the distribution of the observed damage index spreads between 0 and 0.43; meanwhile, higher values (I MCS > VII), cataloged as ruinous-destructive for ordinary buildings, according to the I MCS scale, were suffered by churches whose damage index is above 0.8, except for one case, with i d equal to 0.78. Concerning I MCS values equal to VI, the damage index is very scattered. Since there is not a direct correlation between the observed I MCS and the PGA, some overlapping can be observed in Figure 23b. Noteworthy aspects related to the inspected churches and seismic intensity measures are the following:

•
The locations of most of the inspected churches are characterized by the V degree of the I MCS scale, corresponding to PGA values between 0.02 g and 0.08 g (except for one struck by a PGA of 0.12 g).

•
Even if the VI degree of the I MCS corresponds to a wide range of PGA (from 0.08 g to 0.48 g), only 5 churches of the inspected sample are in such an area.

•
The degrees of I MCS greater than VI are associated with high PGA values, ranging between 0.44 g and 0.76 g. Concerning the usability assessment, the church form considers six possible categories, selected among the following: usable; partially usable, i.e., only a portion of the structure can be used safely; usable after local interventions; temporarily unusable, i.e., requiring a more detailed investigation; unusable; unusable due to external hazard. In Figure  24, the usability judgment is represented with respect to the observed PGA (Figure 24a), the global damage index (Figure 24b), and the vulnerability index (Figure 24c). For the following analysis, the "Usable after local intervention" outcome, consisting of only two churches, was added to the "Partially usable" group, composed of three churches. Analyzing the usability outcomes presented in Figure 24a and  Concerning the usability assessment, the church form considers six possible categories, selected among the following: usable; partially usable, i.e., only a portion of the structure can be used safely; usable after local interventions; temporarily unusable, i.e., requiring a more detailed investigation; unusable; unusable due to external hazard. In Figure 24, the usability judgment is represented with respect to the observed PGA (Figure 24a), the global damage index (Figure 24b), and the vulnerability index (Figure 24c). For the following analysis, the "Usable after local intervention" outcome, consisting of only two churches, was added to the "Partially usable" group, composed of three churches. Analyzing the usability outcomes presented in Figure 24a and All usable and partially usable churches suffered a PGA value lower than 0.08 g, with the limited exception of one church (C21), for which the assigned PGA was equal to 0.48 g. It is worth noting that this church is in a small village, in which the masonry buildings experienced minor seismic damages in the surrounding areas. • Unusable churches suffered a PGA ranging from 0.04 to 0.77 g; in detail, 10 churches were characterized by PGA > 0.40 g, whilst 13 churches were struck by PGA ranging between 0.04 and 0.12 g.

•
Overall, all churches with a PGA > 0.08 g were unusable and seriously damaged, with the only exception of 1 usable building. • It is difficult to identify a proper correlation between the intensity measure and the usability judgment for low values of PGA. In fact, church vulnerability plays a key role in the judgment of damages and usability.
Geosciences 2022, 12, 122 24 of 29 2016, even in the face of a PGA equal to 0.08 g. However, it is worth underlining that the low id obtained in the above cases is due to highly localized damages (C18) or to the significant number of macroelements present in the structures compared with the activated mechanism (C20, C33).
Finally, concerning the usability outcomes in relation to the vulnerability index (Figure 24c, Tables 2 and 3), the following can be observed: • Usable churches had a maximum vulnerability index equal to 0.39, with an average value of 0.30. According to the obtained results (Figure 24b), the usability judgment shows a low correlation with the mean damage index. Conversely, it has become well established that id does not frequently depict the actual scale of the suffered damages and the usability assessment of ancient masonry churches [77,84], the seismic behavior of which is not characterized by the activation (progressive or simultaneous) of all local mechanisms. When only one macroelement collapses, or a very limited number of kinematic mechanisms are triggered, one finds that the church is declared unusable, and the observed damage index, id, results are exceptionally low. This is, for example, the case of C23 (Holy Mary Abbey in Montesanto) (Figure 25), where the roof was completely collapsed: the church was clearly unusable, but the observed damage index is equal to 0.35. Similarly, the churches characterized by a preexisting crack pattern as a consequence of the 2009 L'Aquila Earthquake-in the case of the structures located in the Abruzzo region-or due to the consecutive earthquakes of the 2016/2017 seismic sequence, show worsening conditions affecting the already damaged macroelements. In this situation, the church is declared unusable due to the overall observed damage pattern-the result of several shakes occurring over a long time-even when the mean damage index, id, is low, and when the seismic accelerations of the main earthquake occurring before the inspection were small. Analyzing the usability outcomes in relation to the damage index (Figure 24b and  Table 3), the following should be noted:

•
The damage index varies from 0 to 1, with a mean value equal to 0.081 and 0.550 for usable and unusable churches, respectively; all churches with a damage index greater than 0.2 are unusable. • Usable and partially usable churches are characterized by damage index varying between 0 and 0.2.

•
Unusable churches can be subdivided in two families: 20 churches characterized by i d > 0.2, and 3 churches (C18, C20, C33) with lower values. The latter suffered the 2009 L'Aquila earthquake, and the previous damages were eventually unrepaired (C18 and C33). Therefore, such moderately vulnerable churches (i v falls in the range of 0.36-0.46) had their preexisting crack pattern enlarged after the seismic sequence in 2016, even in the face of a PGA equal to 0.08 g. However, it is worth underlining that the low i d obtained in the above cases is due to highly localized damages (C18) or to the significant number of macroelements present in the structures compared with the activated mechanism (C20, C33).
Finally, concerning the usability outcomes in relation to the vulnerability index (Figure 24c, Tables 2 and 3), the following can be observed: According to the obtained results (Figure 24b), the usability judgment shows a low correlation with the mean damage index. Conversely, it has become well established that i d does not frequently depict the actual scale of the suffered damages and the usability assessment of ancient masonry churches [77,84], the seismic behavior of which is not characterized by the activation (progressive or simultaneous) of all local mechanisms. When only one macroelement collapses, or a very limited number of kinematic mechanisms are triggered, one finds that the church is declared unusable, and the observed damage index, i d , results are exceptionally low. This is, for example, the case of C23 (Holy Mary Abbey in Montesanto) (Figure 25), where the roof was completely collapsed: the church was clearly unusable, but the observed damage index is equal to 0.35. Similarly, the churches characterized by a preexisting crack pattern as a consequence of the 2009 L'Aquila Earthquake-in the case of the structures located in the Abruzzo region-or due to the consecutive earthquakes of the 2016/2017 seismic sequence, show worsening conditions affecting the already damaged macroelements. In this situation, the church is declared unusable due to the overall observed damage pattern-the result of several shakes occurring over a long time-even when the mean damage index, i d , is low, and when the seismic accelerations of the main earthquake occurring before the inspection were small. As a matter of fact, the mean damage index is not a reliable representation of the actual earthquake damage to a church since it is evaluated in the hypothesis of contemporary activation of all possible mechanisms. Therefore, generally, small values could characterize the mean damage index, id, defined according to the guidelines in force, even in the presence of severe but localized damages; moreover, such low values do not reflect the usability judgment.
Among the critical issues in the definition of the mean damage index, id, two factors which are disregarded seem to be crucial-the peaks of the damage and the effects of the directionality of the seismic action. To overcome such a criticism, Lagomarsino et al. [77] introduced new additional damage scores: two considering the directionality of the response (differentiated for the two main directions of the church) and one to evaluate the presence of peaks of damage. However, it is worth noting that Lagomarsino et al. [77] introduced a new form that could account for 150 potential mechanisms, to be as general and flexible as possible. Moreover, the weights evaluated from the macroelement geometrical size are suggested rather than fixed, based on the element's importance in the structural context. Unfortunately, due to the absence of certain data, such updates make the application of the approach proposed in [77] impossible, since only the content of the actual damage surveys [57] is available. As a matter of fact, the mean damage index is not a reliable representation of the actual earthquake damage to a church since it is evaluated in the hypothesis of contemporary activation of all possible mechanisms. Therefore, generally, small values could characterize the mean damage index, i d , defined according to the guidelines in force, even in the presence of severe but localized damages; moreover, such low values do not reflect the usability judgment.

Conclusions
Among the critical issues in the definition of the mean damage index, i d , two factors which are disregarded seem to be crucial-the peaks of the damage and the effects of the directionality of the seismic action. To overcome such a criticism, Lagomarsino et al. [77] introduced new additional damage scores: two considering the directionality of the response (differentiated for the two main directions of the church) and one to evaluate the presence of peaks of damage. However, it is worth noting that Lagomarsino et al. [77] introduced a new form that could account for 150 potential mechanisms, to be as general and flexible as possible. Moreover, the weights evaluated from the macroelement geometrical size are suggested rather than fixed, based on the element's importance in the structural context. Unfortunately, due to the absence of certain data, such updates make the application of the approach proposed in [77] impossible, since only the content of the actual damage surveys [57] is available.

Conclusions
This work presents the results of the survey inspections carried out after the 2016 Central Italy seismic sequence on 36 historical masonry churches, with the aim of identifying the structural damages and assessing their eventual usability. The analyzed monuments were located between 5 and 50 km from the epicenter, and most of them presented similar architectural features depicting the typical "Apennine church": a single nave, a simple facade with a rose window over the entrance, a triangular/rectangular gable, a double pitched timber roof, and a belltower beside the church. The typical masonry walls consist of a double layer of local irregular stones and poor-quality mortar. The post-seismic damage assessment provided data about the architectural morphology, the most frequently observed damage mechanisms, and the usability judgment for each church. These data were carefully analyzed, and they were employed to evaluate the seismic vulnerability of each church, defined according to the simplified LV1 procedure, proposed by the Italian guidelines.
Concerning the results obtained for the vulnerability indexes, a predominant low-medium vulnerability was observed for the considered sample (i v ≤ 0.6). This could explain the absence of a proper correlation between the usability index and the seismic intensities for low values of PGA. In such cases, the church vulnerability plays a key role in the damages and, therefore, influences the judgment of the usability. On the other hand, the authors' inspections outline that, for 11 cases out of 18, the unusable churches were characterized by a vulnerability index higher than 0.50; considering the entire sample of the unusable churches, the estimated average value of the vulnerability index was 0.56.
Regarding the post-earthquake damage observation, the churches declared unusable usually presented a damage level greater than 3 in at least one macroelement. Moreover, the high vulnerability of the façade was observed. The out-of-plane mechanism of the façade occurred in 69% of cases, causing serious damages in 44% of the sample. The shear mechanism of the façade showed a similar percentage (42% of the sample was characterized by a damage level higher than 3), but it occurred less frequently, i.e., in 60% of cases.
Even if the number of presented churches is low, the analysis of the sample made it possible to highlight some critical issues of the actual definition of the damage index, the global damage index, i d , and its poor correlation with the final usability judgment.
According to the Italian guidelines on the assessment and the mitigation of the seismic risk of the cultural heritage, the damage index, i d , accounts for all mechanisms which could develop in a church. Therefore, concentrated damages have a low impact on the i d value, which is often not representative of the effective damage state, as has been observed by other authors. In the considered sample, the usable churches present a mean value of 0.081, while all churches with a damage index greater than 0.2 were declared unusable. Moreover, i d shows a low association with usability assessment.
Of course, since the main outlined findings are related to a small sample of 36 churches, the observed outcomes should be confirmed by using a more extensive database of churches located in the region struck by the 2016 Central Italy earthquake.

Data Availability Statement:
The raw/processed data required to reproduce these findings cannotbe shared at this time as the data also forms part of an ongoing study.