buildings

Article Failure Analysis of Apennine Masonry Churches Severely Damaged during the 2016 Central Seismic Sequence

Francesco Clementi

Department of Civil and Building Engineering, and Architecture, Polytechnic University of , 60131 , Italy; [email protected]; Tel.: +39-071-220-4569

Abstract: This paper presents a detailed study of the damages and collapses suffered by various masonry churches in the aftermath of the seismic sequence of Central Italy in 2016. The damages will first be analyzed and then compared with the numerical data obtained through 3D simulations with eigenfrequency and then nonlinear static analyses (i.e., pushover). The main purposes of this study are: (i) to create an adequately consistent sensitivity study on several definite case studies to obtain an insight into the role played by geometry—which is always unique when referred to churches—and by irregularities; (ii) validate or address the applicability limits of the more widespread nonlinear ap- proach, widely recommended by the Italian Technical Regulations. Pushover analyses are conducted assuming that the masonry behaves as a nonlinear material with different tensile and compressive strengths. The consistent number of case studies investigated will show how conventional static approaches can identify, albeit in a qualitative way, the most critical macro-elements that usually trigger both global and local collapses, underlining once again how the phenomena are affected by the geometry of stones and bricks, the texture of the wall face, and irregularities in the plan and   elevation and in addition to hypotheses made on the continuity between orthogonal walls.

Citation: Clementi, F. Failure Keywords: collapses; masonry churches; Central Italy earthquake; damage; nonlinear static analysis Analysis of Apennine Masonry Churches Severely Damaged during the 2016 Central Italy Seismic Sequence. Buildings 2021, 11, 58. 1. Introduction https://doi.org/10.3390/buildings 11020058 The Architectural Heritage (AH) of European countries, which includes iconic build- ings like churches, historical palaces, towers, monuments, as well as historical bridges, Academic Editors: Maria Polese and wall, small villages, etc., is a pillar of the societal identity and among the most strategic Marco Gaetani d’Aragona world’s economic assets, making its preservation a commitment towards future gener- Received: 7 January 2021 ations. Many countries of the Mediterranean area are characterized by a high level of Accepted: 4 February 2021 seismicity, which constantly puts at risk AH structures. This is especially true in Italy, Published: 8 February 2021 which hosts the largest number of towers, churches, fortresses, etc., in the world, and where some earthquakes, which occurred in the last few decades (Umbria-Marche 1997–1998, Publisher’s Note: MDPI stays neutral Abruzzo 2009, Emilia-Romagna 2012, Central Italy 2016), dramatically damaged several with regard to jurisdictional claims in unique pieces of the AH. In particular, the Central Italy seismic sequence leads to a total of published maps and institutional affil- 299 fatalities, 386 injured and about 4800 homeless [1]. iations. The effects of the earthquake are such as to produce considerable damage, especially in the AH, with catastrophic loss of income from cultural tourism in some areas, with both social and economic inconveniences for local communities. Moreover, the loss of the AH can lead to the dispersion of collective memory and European identity, and the accessibility Copyright: © 2021 by the author. to AH usually leads to a significant improvement of the economics, enhancing social Licensee MDPI, Basel, Switzerland. uniqueness. For these reasons, ensuring historical buildings to be safe and functional, This article is an open access article along with infrastructures, will certainly enhance their usability and therefore the livability distributed under the terms and of cities. conditions of the Creative Commons Simple and efficient tools are the basis for a correct assessment of seismic safety. Attribution (CC BY) license (https:// Structural Health Monitoring (SHM) and non-destructive (ND) testing play a major role, creativecommons.org/licenses/by/ providing information on the building condition and existing damage, and allowing us to 4.0/).

Buildings 2021, 11, 58. https://doi.org/10.3390/buildings11020058 https://www.mdpi.com/journal/buildings Buildings 2021, 11, 58 2 of 17

define adequate remedial measures. Numerical tools, however, can be used to complete or partially replace them, requiring expert judgment in most cases. AH’s structural assessment is one of the most complex part of structural engineering and is an active research area [2], exhibiting the constituting materials significant variations in properties and internal structure, which affect local and global behaviors. These aspects are reflected in the conservativeness of the reference values of the resistances that the manuals, guidelines, or codes [3–6] impose for the existing structures. The different tensile and compressive strengths, in addition to the strong nonlinear behavior of the masonry, require the use of challenging modeling techniques, some of them requiring the use of anisotropic constitutive laws. The mechanical behavior of masonry shows that the nonlinear phase is predominant and characterized mainly by crack opening, splitting the structures into macro-blocks. The decrease in the masonry’s strength in the inelastic phase is generally considered with an elastic plastic damage constitutive law [7–11]. Nonetheless, numerical analysis itself is still a challenging issue, especially working with high-dimensional problems. [12–14]. There are two distinct methods that can be established [15–17]. The continuous approach discretizes the masonry’s walls by means of Finite Element Method (FEM), using beam, shell and solids elements [18,19]. The discrete approach, alternative to the first, considers the masonry as an assembly of blocks that can impact, and slide between them [20–23]. In this paper, referring to FEM, it was possible to recognize the mechanical per- formance of six different churches, supplying helpful data for conservation, repair and strengthening interventions of AH [24–26]. Above all, the FEM is the most powerful and frequently used modelling approach for structural seismic response, and for this reason the results obtained in this paper will be of greater use also for practitioners and not just for academics. The paper is scheduled as follows. In Section2, both the historical developments and the main features of the selected case studies are reported. In Section3, after a brief illustration of the modelling strategy, modal analyses are reported and compared with response spectra of the three main shocks of Central Italy seismic sequence of 2016 [27,28], in order to have a first inside on the main structural portions that are most involved during a seism. In Section4, a comparison between the real and the numerical damages are reported and discussed. The paper ends with some conclusions (Section5).

2. Apennine Churches The churches that characterize the Apennine area of central Italy have a very different plano-volumetric configuration from those sited in the inhabited areas heavily damaged by the earthquakes of L’Aquila 2009 and Emilia-Romagna 2012. This is mainly linked to the peculiar orographic conformation of the territory that paved the way to small, sparsely populated villages, between hills and narrow valleys, characterized by a main urban center and many hamlets, mostly scattered on the peaks of the surrounding hills and mountains. For this reason, it was impossible to build monumental churches that belonged only to the main urban center, thus favoring the development of many smaller churches both in the main villages and in the hamlets. An example is the Municipality of Castelsantangelo sul Nera, characterized by a total of 246 inhabitants scattered in eight hamlets, and which hit the headlines for the enormous destruction suffered by the 2016 earthquake. The strong propensity of the area to earthquakes has led to design churches and other buildings of the cultural heritage with very strict rules, leaving no impetus towards the construction of majestic structures. Specifically, the churches were built starting from a small medieval core, with minor expansions made in different centuries, most of them in the shape of side chapels and altars whose design was encouraged after the Catholic Counter-Reformation, as well as adjustments made after strong earthquakes. An example is the Collegiate Church of Santa Maria in [29], characterized by a beautiful but equally rare bell tower that stands out from the church. In fact, the churches in the Apennine Buildings 2021, 11, 58 3 of 17

Buildings 2021, 11, x FOR PEER REVIEW 3 of 19 area are almost entirely built with a single nave, with not very high walls, and with small annexes surrounding them where the sacristies or ancillary rooms are concentrated. Thesmall facades annexes are oftensurrounding adorned them with where a rose the window sacristies and or ancillary a triangular rooms tympanum. are concentrated. In place of theThe bell facades tower are it is often common adorned to find with a a bell-gable rose window along and the a triangular walls of thetympanum. nave and In supportingplace a smallof the bell. bell tower The walls it is common of the naveto find are a bell embellished‐gable along with the walls small of windows, the nave and with support roofs‐ with woodening a small trusses. bell. The The presence walls of the of apsesnave are is rare. embellished with small windows, with roofs withFinally, wooden it trusses. is important The presence to stress of apses the factis rare. that in the main cities at the base of the ApennineFinally, areas, it is the important classic churchesto stress the typologies fact that in widely the main analyzed cities at the in literature base of the are Ap clearly‐ visible,ennine but areas, which the willclassic represent churches the typologies subject widely of future analyzed works. in literature are clearly vis‐ ible,In but the which following will represent paragraph, the asubject concise of descriptionfuture works. of the main historical and geometri- cal featuresIn the of following the analyzed paragraph, “Apennine a concise Churches” description is of provided. the main historical Furthermore, and geomet in Figure‐ 1 is possiblerical features to observe of the analyzed the churches’ “Apennine locations Churches” inside is provided. the Marche Furthermore, region (Central in Figure Italy) 1 and is possible to observe the churches’ locations inside the Marche region (Central Italy) and respect to the epicenters of the seismic sequence of 2016. respect to the epicenters of the seismic sequence of 2016.

FigureFigure 1. Churches’ 1. Churches’ locations locations respect respect to to the the Epicenters Epicenters ofof Central Italy Italy seismic seismic sequence sequence of 2016: of 2016: Madonna Madonna of Valcora of Valcora Sanctuary in (a), Sant’Anna Church in (b), Sant’Antonio Church in (c), San Francesco Church Sanctuary in Fiuminata (a), Sant’Anna Church in Camerino (b), Sant’Antonio Church in Ussita (c), San Francesco Church in in (d), San Francesco Church in (e), Santissimo Crocifisso in Arquata del (f). Sarnano (d), San Francesco Church in Montefortino (e), Santissimo Crocifisso in Arquata del Tronto (f). 2.1. San Francesco Church in Montefortino (Marche Region, Fermo Province) 2.1. SanSan Francesco Francesco Church Church in was Montefortino built in the (Marche15th century Region, on remains Fermo of Province) ancient Santa Maria of Girone church. The church is Romanesque‐Gothic’s style, with a unique nave of 20.36 m lengthSan and Francesco 10.89 m Churchwidth, and was a maximum built in the height 15th of century 15.53 m. on The remains apse has of 9.36 ancient m length Santa and Maria of Girone7.1 m width church. dimensions, The church covered is Romanesque-Gothic’sby a barrel vault. On the north style, façade, with a there unique is a belfry nave ofwith 20.36 m lengtha height and of 10.89 24.24 m m. width, Different and retrofitting a maximum interventions height of occurred 15.53 m. after The the apse Umbria has 9.36‐Marche m length andearthquake 7.1 m width happened dimensions, in September covered 1997, by asince barrel the vault. church On highlighted the north serious façade, damages there is on a belfry withthe a façade, height on of the 24.24 apse’s m. vault Different and on retrofittingthe bell cell. In interventions general, the church’s occurred walls after are realized the Umbria- Marcheby disordered earthquake rubble happened stone masonry, in September while the roof 1997, is made since by thewooden church beams. highlighted serious damagesDuring on the the façade, seismic sequence on the apse’s of 2016, vault major and cracks on appeared the bell cell.on the In barrel general, vaultthe of the church’s wallsapse, are decorated realized by with disordered rich stuccos rubble (v. Figure stone masonry,2a). The presence while the of roof a crack, is made between by wooden the bell‐ beams. towerDuring and the apse, seismic suggest sequence the possibility of 2016, of major the activation cracks appearedof a bell tower on the rotation. barrel Dif vault‐ of theferent apse, minor decorated cracks with developed rich stuccos on the (v.connections Figure2a). between The presence the façade of and a crack, nave’s between walls, the bell-tower and the apse, suggest the possibility of the activation of a bell tower rotation. Different minor cracks developed on the connections between the façade and nave’s walls, Buildings 2021, 11, 58 4 of 17 Buildings 2021, 11, x FOR PEER REVIEW 4 of 19

between the north wall and the bell-tower, on the middle of façade, on the triumphal arch andbetween the connection the north wall between and the it and bell the‐tower, walls on surrounding. the middle of façade, on the triumphal arch and the connection between it and the walls surrounding.

FigureFigure 2. Main 2. Main damages damages in: in: San San Francesco Francesco Church Church in in Montefortino Montefortino (a), San Francesco Church Church in in Sarnano Sarnano (b (),b ),Sant’Anna Sant’Anna Church in Camerino (c), Sant’Antonio Church in Ussita (d), Madonna of Valcora Sanctuary in Fiuminata (e), Santissimo Church in Camerino (c), Sant’Antonio Church in Ussita (d), Madonna of Valcora Sanctuary in Fiuminata (e), Santissimo Cro- Crocifisso in Arquata del Tronto (f). cifisso in Arquata del Tronto (f). Buildings 2021, 11, 58 5 of 17

2.2. San Francesco Church in Sarnano (Marche Region, Province) The San Francesco church was built in the 14th century. It was renovated in 1833 and a light barrel vault was placed thanks to a general elevation of 4 m, finally adding some Ionic columns. The building has a unique nave of dimensions 22.87 m × 11.26 m (length × width) with a maximum height of 16 m and the tower has dimensions of 5 m × 6.5 m and a height of 28 m. A little rectangular chapel of 12.34 m × 6.95 m (length × width) relates to the church on the south-west. The church has a timber roof. The church’s walls are realized by disordered rubble stone masonry covered by a solid bricks’ masonry layers. The church underwent renovations between 2014–2015. During the seismic sequence of 2016 suffered minor damage (v. Figure2b). Differ- ent cracks appeared on the nave’s light camorcanna vault both in the middle and near the façade, although little cracks are noticeable on the apse’s light barrel vault and on the triumphal arch.

2.3. Sant’Anna Church in Camerino (Marche Region, Macerata Province) The church’s unique nave of 14.92 m × 8.53 m (length × width) has a maximum height of 16 m. The walls’ thicknesses are between 0.7–0.8 m. Disordered rubble stone masonry composed the main walls, as well as in the previously described case study; the façade is covered by brick masonry. The triumphal arch, embedded in a brickwork board, separates the apse from the nave area. A rectangular annex is placed in on side of the church, with dimensions of 12.18 m × 4.29 m and a height of 8.46 m. The current features are due to the heavy collapses suffered during the earthquake of 1799. Subsequently, after the seismic sequence of 1997, the church showed structural failure of the foundation, then restored in 1999. During the seismic sequence of 2016, the façade was affected by heavy cracks (Figure2c) mainly due by the activation of a composed overturning mechanism, with cracks that appeared between it and the nave’s walls and along it. Diagonals cracks also appeared on the south façade.

2.4. Sant’Antonio Church in Ussita (Marche Region, Macerata Province) The little church of Sant’Antonio was built during the 17th century. A unique rectan- gular nave (10.96 m × 6.25 m) characterizes the church with a maximum height of 7 m. The walls’ thickness is about 0.60 m. Disordered rubble stone masonry composes the main walls. The nave and the apse are isolated by a triumphal arch with a gothic molding. The church is covered by a wooden roof and a light vault is placed in the apse. An annex used as a sacristy is placed in one side. It has dimensions of 4.3 m × 4.4 m and height of 3.6 m. It suffered several damages during through the years, mainly referred to the Umbria-Marche seismic sequence of 1997. Sant’Antonio’s church is one of the two most damaged churches among the six analyzed since it is very near to the epicenter of the event occurred on the 26 October 2016. Extensive damages are present in all its walls. The collapse of the ball-gable led to the failure of the apse. A smeared cracking of the façade near the windows, and on the connection between the nave’s walls completes the report of the damages (Figure2d).

2.5. Madonna of Valcora Sanctuary in Fiuminata (Marche Region, Macerata Province) The church is located in a hamlet of Fiuminata. It was built in the first half of the 15th century and successively extended in 1728. The sanctuary has a single nave with dimensions 16.2 m × 9.16 m (length × width) with a gable roof. The walls’ thicknesses range between 0.5 m to 0.8 m. Limestone masonry composes the main walls. During the seismic sequence that stroke Central Italy in 2016, major cracks appeared on the barrel vault of the apse. Minor cracks are widespread all over the complex. An over- turning mechanism is also activated due to the presence of a crack between the church and the bell-gable (see Figure2e). Buildings 2021, 11, 58 6 of 17

2.6. Santissimo Crocifisso in Arquata del Tronto (Marche Region, Province) The church of Santissimo Crocifisso is located in a hamlet of Arquata del Tronto. The first documents date back to the 15th century. It has a unique nave of 11.94 m × 7.24 m (length × width). The façade has essential features, with a travertine stone gate and a big window above it. Disordered rubble stone masonry composes the main walls. During its life, it has suffered several damages from intense earthquakes; thus, it underwent subsequent restorations. The Umbria-Marche seismic sequence of 1997 heavily damaged the church. Between the years 2014–2015, a seismic retrofitting was executed using the restoration technique of unstitching and stitching of the masonry walls, introducing curb steel on the principal façade and reinforcing the camorcanna vaults. At the same time, the recesses were reopened, and a new wood roof was built. During the Central Italy seismic sequence of 2016, different overturning mechanisms were activated in the façades, and several collapses were observed due to disintegrations of the walls (v. Figure2f).

3. The Numerical Models The numerical models are realized in accordance to a detailed relief of the variations Buildings 2021, 11, x FOR PEER REVIEW 7 of 19 in walls’ thicknesses, on geometrical and structural irregularities and on wall connections. Finally, the main openings of the churches are reproduced (Figure3).

Figure 3. Numerical models of San Francesco Church in Montefortino (a), San Francesco Church in Sarnano (b), Sant’Anna Figure 3. Numerical models of San Francesco Church in Montefortino (a), San Francesco Church in Sarnano (b), Sant’Anna Church in Camerino (c), Sant’Antonio Church in Ussita (d), Madonna of Valcora Sanctuary in Fiuminata (e), Santissimo Church in Camerino (c), Sant’Antonio Church in Ussita (d), Madonna of Valcora Sanctuary in Fiuminata (e), Santissimo Cro- Crocifisso in Arquata del Tronto (f). cifisso in Arquata del Tronto (f). Table 1. Main characteristics of the numerical models of the six churches analyzed. The characterization of the materials strictly follows the data collected during the sur- Church veys, and the main mechanicalElements parameters are takenNodes directly fromDegrees Italian Regulations of freedom [3 ,4]. San Francesco Church in MontefortinoIn Table1, the main characteristics16466 of the numerical5243 models of the six churches15033 analyzed San Francesco Church inare Sarnano synthetized. 57889 16623 48516 Sant’Anna Church in Camerino 29706 8471 24336 Sant’Antonio Church in Ussita 5642 1859 6597 Madonna of Valcora Sanctuary in Fiuminata 24814 7358 20964 Santissimo Crocifisso in Arquata del Tronto 169935 38499 112899

Figure 4. Stress–strain constitutive relations used for the simulations: masonry uniaxial compression (a), masonry uniaxial tension (b), shear behavior (c).

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Buildings 2021, 11, x FOR PEERTable REVIEW 1. Main characteristics of the numerical models of the six churches analyzed. 7 of 19

Church Elements Nodes Degrees of Freedom San Francesco Church in Montefortino 16,466 5243 15,033 San Francesco Church in Sarnano 57,889 16,623 48,516 Sant’Anna Church in Camerino 29,706 8471 24,336 Sant’Antonio Church in Ussita 5642 1859 6597 Madonna of Valcora Sanctuary in Fiuminata 24,814 7358 20,964 Santissimo Crocifisso in Arquata del Tronto 169,935 38,499 112,899

In this paper, the nonlinear behavior of the masonry is considered within a continuum mechanics theory, based on a smeared crack approach implemented in MIDAS FEA© where the cracks are not labelled one by one but are in its place continuously spread inside the continuum affecting (reducing) the average stiffness [30]. The used macro- modelling technique offers a variety of possibilities, ranging from fixed single to fixed multidirectional and rotating crack approaches. Here, the distinction lies in the orientation of the crack, which is either kept constant, updated in a stepwise manner, or updated continuously [31,32]. The masonry’s complex behavior is considered by the selected constitutive laws: in compression by means of a parabolic hardening rule and a parabolic softening branch following the peak of resistance, while in tension by a linear hardening branch followed by a nonlinear softening branch (see Figure4). The fracture energies in compression ( Gc) and tension (Gf) are reported in Table2, and h is the mean dimension of the mesh. The shear retention factor (β) gives the shear stiffness after cracking, which can be a constant (low) value between 0 and 1, or a value depending on the crack opening. Here, a constant value equal to 0.05 was adopted like requested in [31]. For a broader and more detailed use of the method, see [12,13,30,33]. Figure 3. Numerical models of San Francesco Church in Montefortino (a), San Francesco Church in Sarnano (b), Sant’Anna Table 2. Mechanical characteristics of the main elements of the numerical models of the six churches analyzed. Church in Camerino (c), Sant’Antonio Church in Ussita (d), Madonna of Valcora Sanctuary in Fiuminata (e), Santissimo Crocifisso in Arquata del Tronto (f). f f γ E ν G G h Church m t v c f (MPa) (MPa) (kN/m3) (MPa) (−) (N/mm) (N/mm) (mm) Table 1. Main characteristics of the numerical models of the six churches analyzed. San Francesco Church in Montefortino 0.741 0.074 18 870 0.49 0.938 0.009 400 San FrancescoChurch Church in Sarnano 2.000 0.200Elements 22 1500Nodes 0.49 1.880Degrees 0.019of freedom 700 San FrancescoSant’Anna ChurchChurch in in Camerino Montefortino 0.741 0.07416466 19 8705243 0.49 0.93815033 0.009 400 San Francesco Church in Sarnano 57889 16623 48516 Sant’Antonio Church in Ussita 1.007 0.101 18.5 948 0.49 1.163 0.012 200 Sant’Anna Church in Camerino 29706 8471 24336 Madonna of Valcora Sanctuary in Fiuminata 1.007 0.101 18.5 948 0.49 1.163 0.012 200 Sant’Antonio Church in Ussita 5642 1859 6597 MadonnaSantissimo of CrocifissoValcora Sanctuary in Arquata in del Fiuminata Tronto 1.482 0.14824814 20 12307358 0.40 1.52420964 0.015 200 Santissimo Crocifisso in Arquata del Tronto 169935 38499 112899

Figure 4. Stress–strain constitutive relations used for the simulations: masonry uniaxial compression (a), masonry uniaxial Figure 4. Stress–strain constitutive relations used for the simulations: masonry uniaxial compression (a), masonry uniaxial tension (b), shear behavior (c). tension (b), shear behavior (c).

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The main mechanical parameters are assumed according to Table C8.5.I of [4], for the knowledge level 1, and they are reported in Table2.

3.1. Eigenfrequency Analysis An eigenfrequency analysis is firstly performed on the 3D FE models to identify the main frequencies, the related modal shapes and the effective modal masses (%Meff) of each mode of the six considered Apennine Churches. We opted for the Block Lanczos method to estimate the modal shapes, as we need to consider different modes to have more than 85% of excited mass, since churches are generally affected by many local modes: • 34 modes for San Francesco Church in Montefortino; • 271 modes San Francesco Church in Sarnano; • 30 modes Sant’Anna Church in Camerino; • 28 modes for Sant’Antonio Church in Ussita; • 40 modes Madonna of Valcora Sanctuary in Fiuminata; • 52 modes for Santissimo Crocifisso in Arquata del Tronto. In order to have a first insight on the churches’ most vulnerable to seismic actions areas, while remaining in the linear elastic field, the frequencies of the six churches will be compared with the spectra obtained from the accelerations recorded in the three epicenters of the seismic sequence of central Italy in 2016:

• 24 August 2016 with ML = 6.0 and MW = 6.0 (AMT station in Italian Ac- celerometric Archive (ITACA)), • 26 October 2016 Campi with ML = 5.9 and MW = 5.9 (CMI station in ITACA), • 30 October 2016 Forca Canapine ML = 6.1 and MW = 6.5 (FCC station in ITACA). The spectra are freely accessible from the site http://itaca.mi.ingv.it/ItacaNet_30/#/home.

3.1.1. San Francesco Church in Montefortino It can be noted (see Figure5) that the first ( T = 0.497 s) and second (T = 0.396 s) modes involve mainly the belfry with the largest %Meff equal to 30.69% and 21.41% in the north and east directions, respectively. The other modes with higher participation masses are the sixth mode (T = 0.182 s) that is quite spread (%Meff is 12.33% in north and 13.78% in east directions) involving the main façade, the belfry, and the apse. The seventh mode (T = 0.179 s) is always spread like the sixth but presents a main %Meff in the north direction equal to 26.76%. The main modes corresponding to the acceleration’s peaks, involved separately the nave’s walls and the façade but are not reported in Figure5 only for sake of clarity. The %Meff are always around 10% and, therefore, they are not negligible, being carriers of very localized damage that can activate classic overturning mechanisms.

3.1.2. San Francesco Church in Sarnano The main period and modal shapes are reported in Figure6. The first ( T = 0.281 s) and third modes (T = 0.214 s) involve mainly the belfry and the nave’s wall, and they are associated with a %Meff equal to 18.62% in north and 14.41% in east directions, respectively. They are close to the peaks of acceleration which involves a possible localized damage in these portions. The third mode seems very dangerous for both the triumphal arch and the bell cell. Buildings 2021, 11, 58 9 of 17 Buildings 2021, 11, x FOR PEER REVIEW 9 of 19

FigureFigure 5. Distribution 5. Distribution of modal of modal shapes shapes in in the the longitudinal longitudinal and transversal transversal directions directions and and comparison comparison with withthe pseudo the pseudo-‐ acceleration response spectra of the three main shocks of Central Italy seismic sequence of 2016 for San Francesco Church accelerationin Montefortino response (Fermo, spectra Central of the threeItaly). main shocks of Central Italy seismic sequence of 2016 for San Francesco Church in Buildings 2021, 11, x FOR PEER REVIEW 10 of 19 Montefortino (Fermo, Central Italy). 3.1.2. San Francesco Church in Sarnano The main period and modal shapes are reported in Figure 6. The first (T = 0.281 s) and third modes (T = 0.214 s) involve mainly the belfry and the nave’s wall, and they are associated with a %Meff equal to 18.62% in north and 14.41% in east directions, respec‐ tively. They are close to the peaks of acceleration which involves a possible localized dam‐ age in these portions. The third mode seems very dangerous for both the triumphal arch and the bell cell. The other modes with higher participation masses are the fourth (T = 0.191 s) and the eleventh (T = 0.144 s) that involve mainly the façade and the two nave’s walls (%Meff is 11% in north and 8.60% in east directions) involving the main façade, the belfry, and the apse. The %Meff is for both around 10% and, therefore, they are not negligible, being car‐ riers of very localized damage that can activate classic overturning mechanisms.

Figure 6. Distribution of modal shapes in the longitudinal and transversal directions and comparison with the pseudo‐ Figure 6. Distribution of modal shapes in the longitudinal and transversal directions and comparison with the pseudo- acceleration response spectra of the three main shocks of Central Italy seismic sequence of 2016 for San Francesco Church accelerationin Sarnano response (Macerata, spectra Central of the Italy). three main shocks of Central Italy seismic sequence of 2016 for San Francesco Church in Sarnano (Macerata, Central Italy). 3.1.3. Sant’Anna Church in Camerino The main period and modal shapes are reported in Figure 7. The first (T = 0.272 s) and second (T = 0.214 s) modes involve the nave in the two orthogonal directions in plan and are characterized by a %Meff equal to 56.01% in east and 45.59% in north directions, respectively. They are close to the peaks of acceleration which involve a possible localized damage. In both modes, the most vulnerable elements are the facade and the bell gable. The other modes with higher participation masses are the third (T = 0.215 s) and the ninth (T = 0.105 s), mainly involving the façade and the triumphal arch (%Meff is 13.73% in north and 11.93% in east directions). The %Meff is for both around 12% and, therefore, they are not negligible, carrying very localized damage that can activate the most common overturning mechanisms. Buildings 2021, 11, 58 10 of 17

The other modes with higher participation masses are the fourth (T = 0.191 s) and the eleventh (T = 0.144 s) that involve mainly the façade and the two nave’s walls (%Meff is 11% in north and 8.60% in east directions) involving the main façade, the belfry, and the apse. The %Meff is for both around 10% and, therefore, they are not negligible, being carriers of very localized damage that can activate classic overturning mechanisms.

3.1.3. Sant’Anna Church in Camerino The main period and modal shapes are reported in Figure7. The first ( T = 0.272 s) and second (T = 0.214 s) modes involve the nave in the two orthogonal directions in plan and are characterized by a %Meff equal to 56.01% in east and 45.59% in north directions, Buildings 2021, 11, x FOR PEER REVIEWrespectively. They are close to the peaks of acceleration which involve a possible localized11 of 19 damage. In both modes, the most vulnerable elements are the facade and the bell gable.

FigureFigure 7. 7. DistributionDistribution of of modal modal shapes shapes in in the the longitudinal longitudinal and and transversal transversal directions directions and and comparison comparison with with the the pseudo pseudo-‐ acceleration response spectra of the three main shocks of Central Italy seismic sequence of 2016 for Sant’Anna Church in acceleration response spectra of the three main shocks of Central Italy seismic sequence of 2016 for Sant’Anna Church in Camerino (Macerata, Central Italy). Camerino (Macerata, Central Italy).

3.1.4. TheSant’Antonio other modes Church with in higher Ussita participation masses are the third (T = 0.215 s) and the ninthThe main (T = period 0.105 and s), mainly modal involvingshapes are thereported façade in and Figure the 8. triumphal The second arch (T = (%M 0.088eff s)is and13.73% third in (T north = 0.085 and s) 11.93% modes in involve east directions). the nave in The the %Mtwoeff orthogonalis for both directions around 12% in plan and, andtherefore, are characterized they are not negligible,by the biggest carrying %Meff very equal localized to 60.03% damage in north that can and activate 33.79% the in mosteast directions,common overturning respectively. mechanisms. Given the small size of the church, both in plan and in height, it is much rigid than the previous ones and, for this reason, the main modes are not posi‐ tioned3.1.4. Sant’Antonionear the peaks Church of spectral in Ussita acceleration of the most dangerous shock of 30 October 2016. TheHowever, main period they are and close modal to the shapes peaks are of reported the seismic in Figure acceleration8. The second of 26 October ( T = 0.088 2016 s) whoseand third epicenter (T = 0.085 was s)close modes to the involve church’s the location. nave in the It is two important orthogonal to stress directions the fact in planthat theand most are characterizedvulnerable element by the for biggest the first %M twoeff equalmodes to is 60.03% the bell in gable. north and 33.79% in east directions,The other respectively. modes with Given higher the smallparticipation size of the masses church, are both the first in plan (T = and 0.105 in height,s) and the it is thirteenthmuch rigid (T than = 0.041 the s) previous that involve ones and,mainly for the this bell reason, gable the and main the modestriumphal are notarch positioned (%Meff is 28.5%near the in east peaks and of 5.79% spectral in north acceleration directions). of the There most are dangerous very localized shock modal of 30 October shapes that, 2016. even in these cases, can activate classic overturning mechanisms, as their periods are al‐ ways very close to the peaks of the shock of 26 October 2016. Buildings 2021, 11, 58 11 of 17

However, they are close to the peaks of the seismic acceleration of 26 October 2016 whose Buildings 2021, 11, x FOR PEER REVIEWepicenter was close to the church’s location. It is important to stress the fact that the12 most of 19

vulnerable element for the first two modes is the bell gable.

Figure 8. Distribution of of modal shapes in in the longitudinal and and transversal directions directions and and comparison comparison with with the the pseudo pseudo-‐ acceleration responseresponse spectra spectra of of the the three three main main shocks shocks of of Central Central Italy Italy seismic seismic sequence sequence of 2016 of 2016 for Madonnafor Madonna of Sant’Antonio of Sant’An‐ tonio Church in Ussita (Macerata, Central Italy). Church in Ussita (Macerata, Central Italy).

3.1.5. TheMadonna other modesof Valcora with Sanctuary higher participation in Fiuminata masses are the first (T = 0.105 s) and the thirteenthThe main (T = period 0.041 s) and that modal involve shapes mainly are the reported bell gable in Figure and the 9. triumphal The first ( archT = 0.234 (%M effs) andis 28.5% fourth in ( eastT = 0.143 and 5.79%s) modes in north involve directions). the nave in There the two are orthogonal very localized directions modal in shapes plan andthat, are even characterized in these cases, by can the activate biggest classic%Meff overturningequal to 36.66% mechanisms, in north and as their 52.79% periods in east are directions,always very respectively. close to the This peaks is ofa more the shock rigid of church 26 October respect 2016. to Montefortino and Sarnano and it is characterized by short periods close to the peaks of the seismic acceleration of 26th3.1.5. October Madonna 2016. of ValcoraIt is important Sanctuary to instress Fiuminata the fact that the most vulnerable element for the firstThe two main modes period are and the nave’s modal walls, shapes the are triumphal reported arch in Figure and the9. The façade. first ( T = 0.234 s) and fourthThe other (T = modes 0.143 s)with modes higher involve participation the nave masses in the two are orthogonalthe fifth (T = directions 0.134 s) and in plan the thirteenand are ( characterizedT = 0.087 s) that by involve the biggest mainly %M theeff bellequal gable to 36.66% and nave’s in north wall andin the 52.79% out‐of in‐plane east directionsdirections, (%M respectively.eff is 16.29 This and is7.18%, a more and rigid both church in north respect directions), to Montefortino and they and can Sarnanoactivate classicand it isoverturning characterized mechanisms. by short periods close to the peaks of the seismic acceleration of 26th October 2016. It is important to stress the fact that the most vulnerable element for the first two modes are the nave’s walls, the triumphal arch and the façade. The other modes with higher participation masses are the fifth (T = 0.134 s) and the thirteen (T = 0.087 s) that involve mainly the bell gable and nave’s wall in the out-of-plane directions (%Meff is 16.29 and 7.18%, and both in north directions), and they can activate classic overturning mechanisms. Buildings 2021, 11, 58 12 of 17 Buildings 2021, 11, x FOR PEER REVIEW 13 of 19

Figure 9. Distribution of modal shapes in the longitudinal and transversal directions and comparison with the pseudo‐ Figure 9. Distribution of modal shapes in the longitudinal and transversal directions and comparison with the pseudo- acceleration response spectra of the three main shocks of Central Italy seismic sequence of 2016 for Madonna of Valcora accelerationSanctuary response in Fiuminata spectra (Macerata, of the three Central main Italy). shocks of Central Italy seismic sequence of 2016 for Madonna of Valcora Sanctuary in Fiuminata (Macerata, Central Italy). 3.1.6. Santissimo Crocifisso Church in Arquata del Tronto The main period and modal shapes are reported in Figure 10. The first (T = 0.219 s) 3.1.6.and Santissimo third (T = 0.144 Crocifisso s) modes Church involve in mainly Arquata the nave, del Tronto the façade and the bell gable and areThe characterized main period by a and %M modaleff equal shapes to 38.41% are in reported east and 27.71% in Figure in north 10. Thedirections, first ( reT‐= 0.219 s) andspectively. third (T = 0.144 s) modes involve mainly the nave, the façade and the bell gable and are Buildings 2021, 11, x FOR PEER REVIEW The other modes with higher participation masses are the seventh (T = 0.093 s)14 andof 19 characterized by a %M equal to 38.41% in east and 27.71% in north directions, respectively. the eleventh (T = 0.074eff s) that involve mainly the bell gable and the facade in the out‐of‐ plane directions (%Meff is 30.28 and 14.39% in east and in north directions, respectively), and they can activate classic overturning mechanisms, given the concomitance of the structural periods with that of the spectral acceleration peaks.

Figure 10. Distribution of modal shapes in the longitudinal and transversal directions and comparison with the pseudo‐ Figure 10.accelerationDistribution response of modal spectra shapes of the three in the main longitudinal shocks of Central and Italy transversal seismic sequence directions of 2016 and for comparison Santissimo Crocifisso with the pseudo- accelerationchurch response in Arquata spectra del Tronto of the (Ascoli three Piceno, main Central shocks Italy). of Central Italy seismic sequence of 2016 for Santissimo Crocifisso church in Arquata del Tronto (Ascoli Piceno, Central Italy). 4. Damage Assessment by Nonlinear Static Analysis The nonlinear static analysis method, also known as pushover analysis, was used to properly analyze the seismic behavior of the six churches, by monotonically increasing horizontal loads and keeping gravity loads constant. A total of two systems of perpendic‐ ular horizontal forces, acting at different times, were used to consider seismic loads. These systems lead to two load distributions that may be considered two limit states of the build‐ ing capacity, one related to the masses on each floor by direct proportion (PushMass) and one equivalent to the superposition of main modes involving at least the 85% of partici‐ pating masses in both directions (PushMode). As can be clearly remarked by considering the above described load distributions, the pushover analysis performed is merely conventional, i.e., loads applied to the building are kept constant while the structure progressively degrades during the loading, so grad‐ ual changes in modal frequencies caused by yielding and cracking on the structure during loading are not considered. Even though the invariance of static loads may lead to an overestimation in assessing masonry buildings’ seismic capacity, mostly on structures af‐ fected by a high or non‐uniform impairment, a conventional pushover analysis ensures a less computationally expensive alternative to nonlinear dynamic analyses. It also provides substantial data on the progressive damage occurring to buildings under seismic loads, such as cracking. In the following sections, a comparison between the real and the numerical damages is reported, and discussed, in order to assess the numerical methods and the main vulner‐ abilities of the six analyzed churches.

4.1. San Francesco Church in Montefortino The nonlinear static analyses confirm the results obtained from the eigenvalue anal‐ ysis. Widespread damage, with the probable occurrence of an active failure mechanism, Buildings 2021, 11, 58 13 of 17

The other modes with higher participation masses are the seventh (T = 0.093 s) and the eleventh (T = 0.074 s) that involve mainly the bell gable and the facade in the out-of-plane directions (%Meff is 30.28 and 14.39% in east and in north directions, respectively), and they can activate classic overturning mechanisms, given the concomitance of the structural periods with that of the spectral acceleration peaks.

4. Damage Assessment by Nonlinear Static Analysis The nonlinear static analysis method, also known as pushover analysis, was used to properly analyze the seismic behavior of the six churches, by monotonically increasing horizontal loads and keeping gravity loads constant. A total of two systems of perpen- dicular horizontal forces, acting at different times, were used to consider seismic loads. These systems lead to two load distributions that may be considered two limit states of the building capacity, one related to the masses on each floor by direct proportion (PushMass) and one equivalent to the superposition of main modes involving at least the 85% of participating masses in both directions (PushMode). As can be clearly remarked by considering the above described load distributions, the pushover analysis performed is merely conventional, i.e., loads applied to the building are kept constant while the structure progressively degrades during the loading, so gradual changes in modal frequencies caused by yielding and cracking on the structure during loading are not considered. Even though the invariance of static loads may lead to an overestimation in assessing masonry buildings’ seismic capacity, mostly on structures affected by a high or non-uniform impairment, a conventional pushover analysis ensures a less computationally expensive alternative to nonlinear dynamic analyses. It also provides substantial data on the progressive damage occurring to buildings under seismic loads, such as cracking. In the following sections, a comparison between the real and the numerical dam- ages is reported, and discussed, in order to assess the numerical methods and the main vulnerabilities of the six analyzed churches. Buildings 2021, 11, x FOR PEER REVIEW 15 of 19

4.1. San Francesco Church in Montefortino The nonlinear static analyses confirm the results obtained from the eigenvalue analysis. isWidespread registered damage,in the upper with part the probableof the walls occurrence of the façade of an activeand the failure apse, mechanism, see Figure 11, is regis-con‐ firmingtered in this the upperarea as part the of most the wallsvulnerable of the one. façade A heavy and the numerical apse, see Figuredamage 11 is, confirming evident at thisthe interfacearea as the between most vulnerable the triumphal one. arc A and heavy the numerical apse’s vault, damage in the is middle evident of at the the triumphal interface arc,between and in the the triumphal connection arc between and the apse’sthe belfry vault, and in the nave’s middle wall, of the and triumphal immediately arc, and over in thethe main connection entrance between with a thequasi belfry‐vertical and crack the nave’s in the wall, main and façade. immediately All numerical over damages the main properlyentrance reproduce with a quasi-vertical what is reported crack in in the Figure main 2a. façade. All numerical damages properly reproduce what is reported in Figure2a.

Figure 11. 11. NumericalNumerical damage damage for for San San Francesco Francesco Church Church in Montefortino in Montefortino (Fermo, (Fermo, Central Central Italy) Italy) for PushMass for PushMass + x (a), + Push x (a),‐ MassPushMass − x (b−), PushMassx (b), PushMass + y (c), + PushMass y (c), PushMass − y (d).− y (d).

4.2. San Francesco Church in Sarnano Widespread damage, with the probable occurrence of an active failure mechanism, is registered in the upper part of the walls of the façade, of the nave’s walls, and of the apse, see Figure 12, confirming the results obtained from the eigenvalue analysis. A heavy numerical damage, always obtained with nonlinear static analysis, is evident in the con‐ nection between the belfry and the nave’s wall, and immediately over the windows of the façade with a quasi‐vertical crack in the middle. The bell cell presents cracks in the col‐ umns, and in general the nonlinear static analysis well replicates what is reported in Fig‐ ure 2b.

Figure 12. Numerical damage for San Francesco Church in Sarnano (Macerata, Central Italy) for PushMass + x (a), Push‐ Mass − x (b), PushMass + y (c), PushMass − y (d).

4.3. Sant’Anna Church in Camerino A clear diagonal crack in the main façade is correctly reproduced, with the probable occurrence of its active failure mechanism, see Figure 13, confirming both the real damage and the results obtained from the eigenvalue analysis. A similar inclined crack in the up‐ per part of the secondary façade is also well reproduced, also with a clear activation of the out‐of‐plane mechanism of the bell gable. A heavy numerical damage is evident in all the connections between orthogonal walls, with a widespread cracking of the nave’s wall not supported by the annex. Even in this case, the nonlinear static analysis well replicates what is reported in Figure 2c. Buildings 2021, 11, x FOR PEER REVIEW 15 of 19

is registered in the upper part of the walls of the façade and the apse, see Figure 11, con‐ firming this area as the most vulnerable one. A heavy numerical damage is evident at the interface between the triumphal arc and the apse’s vault, in the middle of the triumphal arc, and in the connection between the belfry and the nave’s wall, and immediately over the main entrance with a quasi‐vertical crack in the main façade. All numerical damages properly reproduce what is reported in Figure 2a.

Buildings 2021, 11, 58 14 of 17 Figure 11. Numerical damage for San Francesco Church in Montefortino (Fermo, Central Italy) for PushMass + x (a), Push‐ Mass − x (b), PushMass + y (c), PushMass − y (d).

4.2. San San Francesco Francesco Church Church in Sarnano Widespread damage, with the probable occurrence of an active failure mechanism, isis registered registered in in the the upper upper part part of of the the walls walls of of the the façade, façade, of ofthe the nave’s nave’s walls, walls, and and of the of apse,the apse, see Figure see Figure 12, confirming 12, confirming the results the resultsobtained obtained from the from eigenvalue the eigenvalue analysis. analysis.A heavy numericalA heavy numerical damage, damage,always obtained always obtainedwith nonlinear with nonlinear static analysis, static analysis,is evident is in evident the con in‐ nectionthe connection between between the belfry the and belfry the and nave’s the nave’swall, and wall, immediately and immediately over the over windows the windows of the façadeof the façade with a with quasi a‐ quasi-verticalvertical crack crackin the in middle. the middle. The bell The cell bell presents cell presents cracks cracks in the in col the‐ umns,columns, and and in general in general the thenonlinear nonlinear static static analysis analysis well well replicates replicates what what is reported is reported in Fig in‐ ureFigure 2b.2 b.

Figure 12. Numerical damage damage for for San San Francesco Francesco Church Church in Sarnano in Sarnano (Macerata, (Macerata, Central Italy)Central for Italy) PushMass for PushMass + x (a), PushMass + x (a),− Pushx (b),‐ PushMassMass − x (b +), y PushMass (c), PushMass + y− (cy), (PushMassd). − y (d).

4.3. Sant’Anna Church in Camerino 4.3. Sant’AnnaA clear diagonal Church crack in Camerino in the main façade is correctly reproduced, with the probable occurrenceA clear of diagonal its active crack failure in mechanism, the main façade see Figure is correctly 13, confirming reproduced, both with the thereal probable damage andoccurrence the results of its obtained active failure from mechanism,the eigenvalue see analysis. Figure 13 A, confirmingsimilar inclined both thecrack real in damage the up‐ perand part the resultsof the secondary obtained from façade the is eigenvalue also well reproduced, analysis. A similar also with inclined a clear crack activation in the upperof the outpart‐of of‐plane the secondary mechanism façade of the is bell also gable. well reproduced,A heavy numerical also with damage a clear is evident activation in all of the connectionsout-of-plane between mechanism orthogonal of the bell walls, gable. with A heavya widespread numerical cracking damage of isthe evident nave’s inwall all not the connections between orthogonal walls, with a widespread cracking of the nave’s wall not Buildings 2021, 11, x FOR PEER REVIEWsupported by the annex. Even in this case, the nonlinear static analysis well replicates16 of 19 whatsupported is reported by the in annex. Figure Even 2c. in this case, the nonlinear static analysis well replicates what is reported in Figure2c.

Figure 13. Numerical damage damage for for Sant’Anna Sant’Anna Church Church in Camerino in Camerino (Macerata, (Macerata, Central Central Italy) Italy) for PushMass for PushMass + x (a), + PushMass x (a), PushMass− x (b), PushMass− x (b), PushMass + y (c), PushMass + y (c), PushMass− y (d). − y (d).

4.4. Sant’Antonio Church in Ussita 4.4. Sant’Antonio Church in Ussita The bell gable is always the most vulnerable part of the church, and this is also con‐ firmedThe by bell the gablenonlinear is always analyses, the see most Figure vulnerable 14, and part not only of the by church, the eigenvalue and this analysis is also whoconfirmed see it byas thethe nonlinear main source analyses, of the see structural Figure 14 collapse., and not A only heavy by the numerical eigenvalue damage analysis is evidentwho see in it all as the mainconnections source between of the structural orthogonal collapse. walls, with A heavy a widespread numerical cracking damage of is theevident nave’s in wall all the not connections supported by between the annex, orthogonal this latter walls, clearly with damaged a widespread in all its cracking walls. The of the nave’s wall not supported by the annex, this latter clearly damaged in all its walls. main façade presents three main vertical cracks immediately over the openings as also clearly visible in Figure 2d.

Figure 14. Numerical damage for Sant’Antonio Church in Ussita (Macerata, Central Italy) for PushMass + x (a), PushMass − x (b), PushMass + y (c), PushMass − y (d).

4.5. Madonna of Valcora Sanctuary in Fiuminata The most damaged points are the main façade in correspondence with the openings which, as previously pointed out, create the trigger for almost vertical cracks (Figure 15). Widespread cracks are present in all the connections between the nave’s walls and the façade, confirming once again the overturning mechanism of the facade as the most likely, as well as what affects the bell gable (see Figure 2e). Possible tilting mechanisms can be triggered in the walls of the nave. In this case a direct reference with the real damage is not possible as the site of Valcora suffered attenuated effects given the distance of the epicenters.

Buildings 2021, 11, x FOR PEER REVIEW 16 of 19

Figure 13. Numerical damage for Sant’Anna Church in Camerino (Macerata, Central Italy) for PushMass + x (a), PushMass − x (b), PushMass + y (c), PushMass − y (d).

4.4. Sant’Antonio Church in Ussita The bell gable is always the most vulnerable part of the church, and this is also con‐ Buildings 2021, 11, 58 firmed by the nonlinear analyses, see Figure 14, and not only by the eigenvalue analysis15 of 17 who see it as the main source of the structural collapse. A heavy numerical damage is evident in all the connections between orthogonal walls, with a widespread cracking of the nave’s wall not supported by the annex, this latter clearly damaged in all its walls. The Themain main façade façade presents presents three three main main vertical vertical cracks cracks immediately immediately over overthe openings the openings as also as also clearlyclearly visible visible in in Figure Figure2 d.2d.

FigureFigure 14. Numerical 14. Numerical damage damage for Sant’Antonio for Sant’Antonio Church Church in Ussita in Ussita (Macerata, (Macerata, Central Central Italy) Italy) for for PushMass PushMass + x + ( xa ),(a PushMass), PushMass− x (b), PushMass− x (b +), y PushMass (c), PushMass + y (c−), PushMassy (d). − y (d). 4.5. Madonna of Valcora Sanctuary in Fiuminata 4.5. MadonnaThe most of Valcora damaged Sanctuary points are in the Fiuminata main façade in correspondence with the openings which,The mostas previously damaged pointed points out, are create the main the trigger façade for in almost correspondence vertical cracks with (Figure the openings15). Widespread cracks are present in all the connections between the nave’s walls and the which, as previously pointed out, create the trigger for almost vertical cracks (Figure15). façade, confirming once again the overturning mechanism of the facade as the most likely, Widespread cracks are present in all the connections between the nave’s walls and the as well as what affects the bell gable (see Figure 2e). Possible tilting mechanisms can be façade,triggered confirming in the walls once of again the nave. the overturning In this case a mechanism direct reference of the with facade the real as damage the most is likely, as well as what affects the bell gable (see Figure2e). Possible tilting mechanisms can be Buildings 2021, 11, x FOR PEER REVIEWnot possible as the site of Valcora suffered attenuated effects given the distance 17of of the 19 triggeredepicenters. in the walls of the nave. In this case a direct reference with the real damage is not Buildings 2021, 11, x FOR PEER REVIEW 17 of 19 possible as the site of Valcora suffered attenuated effects given the distance of the epicenters.

Figure 15. Numerical damage for Madonna of Valcora Sanctuary in Fiuminata (Macerata, Central Italy) for PushMass + x Figure 15. Numerical damage for Madonna of Valcora Sanctuary in Fiuminata (Macerata, Central Italy) for PushMass + x (a), PushMass − x (b), PushMass + y (c), PushMass − y (d). (Figurea), PushMass 15. Numerical − x (b), PushMassdamage for + Madonnay (c), PushMass of Valcora − y ( dSanctuary). in Fiuminata (Macerata, Central Italy) for PushMass + x (a), PushMass − x (b), PushMass + y (c), PushMass − y (d). 4.6. Santissimo Crocifisso in Arquata del Tronto 4.6. Santissimo Crocifisso in Arquata del Tronto 4.6. SantissimoWidespread Crocifisso damage, in Arquatawith the del probable Tronto occurrence of an active failure mechanism, Widespread damage, with the probable occurrence of an active failure mechanism, is registeredWidespread in the damage, upper part with of the the probable walls of occurrencethe façade, ofof anthe active nave’s failure walls, mechanism, and of the is registeredapse,is registered see Figure in in the the16, upper confirmingupper partpart the of the results walls walls obtained of of the the façade,from façade, the of eigenvalue the of the nave’s nave’s analysis. walls, walls, and A heavyof and the of the apse,numericalapse, see see Figure Figure damage 16 16,, confirming is confirming evident in thethethe resultsconnection results obtained obtained between from from the the bell the eigenvalue gable eigenvalue and analysis. the analysis. nave’s A heavy wall, A heavy numericalandnumerical a clear damage damageactivation is is evident evidentof an out inin of the plane connection connection mechanism between between of the the south the bell bell façadegable gable and is also andthe numerically nave’s the nave’s wall, wall, andconfirmed.and a clear a clear activation activationIn the same of of an anwall, outout clear of plane plane vertical mechanism mechanism cracks areof ofthe replicated the south south façade by façade the is alsononlinear is numerically also numerically static confirmed.analysisconfirmed. well In In theas the possible same same wall, comparewall, clear in verticalFigure vertical 2f.cracks cracks are are replicated replicated by the by thenonlinear nonlinear static static analysisanalysis well well as as possible possible compare compare in Figure Figure 2f.2f.

Figure 16. Numerical damage for Santissimo Crocifisso in Arquata del Tronto (Ascoli Piceno, Central Italy) for PushMass + x (a), PushMass − x (b), PushMass + y (c), PushMass − y (d). FigureFigure 16. Numerical 16. Numerical damage damage for Santissimo for Santissimo Crocifisso Crocifisso in Arquata in Arquata del del Tronto Tronto (Ascoli (Ascoli Piceno, Piceno, Central Central Italy) Italy) for for PushMass PushMass + x (a), + x (−a), PushMass − x (b), PushMass + y (c), −PushMass − y (d). PushMass x (b), PushMass + y5. (c Conclusions), PushMass y (d). 5. ConclusionsIn the present paper, six masonry churches damaged by the 2016 Central Italy seismic sequenceIn the were present numerically paper, six analyzed. masonry churchesEigenfrequency damaged analyses by the are2016 firstly Central used Italy with seismic real spectrasequence derived were numericallyby the accelerometer analyzed. registeredEigenfrequency near the analyses three epicenters;are firstly usedthe nonlinear with real staticspectra analyses derived are by then the accelerometerapplied with aregistered smeared cracknear themodel, three being epicenters; masonry the a nonlinear material withstatic low analyses tensile are strength then applied and softening with a insmeared tension crack but also model, in compression. being masonry The a final material aim ofwith the low numerical tensile investigationstrength and softeningcarried out in in tension this study but also is to in put compression. at disposal theThe results final aim of aof sensitivity the numerical analysis investigation led on a satisfactorily carried out ingreat this sample study is to to establish put at disposal if the simplifications the results of adopteda sensitivity in a analysisclassical leddesign on a may satisfactorily be always great observed sample as reliableto establish or not. if the simplifications adoptedThe needin a classical to analyze design several may case be always studies observed derives from as reliable the peculiar or not. characteristics of masonryThe churches,need to analyze in particular several those case studiesof the Apennine derives from area the of Centralpeculiar Italy, characteristics whose geo of‐ metricmasonry variabilities churches, andin particular irregularities, those as of well the Apennineas the architectural area of Central intricacy Italy, can whose give ageo vi‐‐ brantmetric knowledge variabilities on and the irregularities,existence of discrepancy as well as the between architectural real and intricacy numerical can damages.give a vi‐ Frombrant anknowledge overall analysis on the ofexistence the results of discrepancy obtained, the between following real remarks and numerical may be made:damages. From Classical an overall eigenfrequency analysis of the analyses results obtained, associated the with following natural remarks spectra may from be real made: earth ‐  quakesClassical can, eigenfrequency even qualitatively, analyses identify associated the possible with areasnatural or betterspectra macro from‐ blocksreal earth that‐ couldquakes cause can, evencollapse qualitatively, during a seismic identify event. the possible However, areas such or better analyses macro turn‐blocks out to that be defectivecould cause when collapse masonry during is loaded a seismic beyond event. the However, elastic limit. such analyses turn out to be defective when masonry is loaded beyond the elastic limit. Buildings 2021, 11, 58 16 of 17

5. Conclusions In the present paper, six masonry churches damaged by the 2016 Central Italy seismic sequence were numerically analyzed. Eigenfrequency analyses are firstly used with real spectra derived by the accelerometer registered near the three epicenters; the nonlinear static analyses are then applied with a smeared crack model, being masonry a material with low tensile strength and softening in tension but also in compression. The final aim of the numerical investigation carried out in this study is to put at disposal the results of a sensitivity analysis led on a satisfactorily great sample to establish if the simplifications adopted in a classical design may be always observed as reliable or not. The need to analyze several case studies derives from the peculiar characteristics of masonry churches, in particular those of the Apennine area of Central Italy, whose geomet- ric variabilities and irregularities, as well as the architectural intricacy can give a vibrant knowledge on the existence of discrepancy between real and numerical damages. From an overall analysis of the results obtained, the following remarks may be made: • Classical eigenfrequency analyses associated with natural spectra from real earth- quakes can, even qualitatively, identify the possible areas or better macro-blocks that could cause collapse during a seismic event. However, such analyses turn out to be defective when masonry is loaded beyond the elastic limit. • Nonlinear static analyses appear to be able to represent the failure mechanisms with a more truthful detail, and to replicate case by case the geometric specificities of each church. Despite the large amount of approximations introduced, collapse mechanisms seem in reasonable agreement with reality. Finally, the presented sensitivity analysis allows asserting that the seismic assess- ment of such peculiar structures should be always estimated through diverse procedures, including standard eigenfrequency and nonlinear static analyses. All these strategies are affected by different levels of precision and intricacy, but they may eventually lead to a convincing representation of the structural weakness when performed together.

Funding: This research received no external funding. Data Availability Statement: Not applicable. Conflicts of Interest: The author declares no conflict of interest.

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