Seismic response and damage patterns of masonry churches: Seven case studies in Ferrara, Italy

Engineering Structures 177 (2018) 809–835

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Seismic response and damage patterns of masonry churches: Seven case studies in Ferrara, Italy Marco Valente, Gabriele Milani

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Department of Architecture, Built Environment and Construction Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

ARTICLE INFO

ABSTRACT

Keywords: Emilia earthquake Masonry church Crack pattern 3D FE model Macro-element Non-linear dynamic analysis Damage distribution

The seismic performance assessment of historical masonry structures is still a complex issue in civil engineering. This paper investigates the seismic response of seven masonry churches, which are located in the province of Ferrara (Northern Italy) and suffered extensive damage during the 2012 Emilia earthquake. Different field surveys, which were conducted after the earthquake to collect information on typical damage patterns, provided a preliminary knowledge of utmost importance for developing detailed FE models of the churches and for better understanding the results of advanced numerical simulations. First, modal analyses were performed to have a preliminary insight into the dynamic behavior of the churches. Then, non-linear dynamic analyses with different peak ground accelerations were carried out in order to obtain the damage distribution in the churches and to identify the most vulnerable macro-elements. The results highlighted the influence of morphological and geometrical characteristics on the seismic behavior of the different macro-elements composing the churches.

1. Introduction The conservation and preservation of cultural heritage are a topic of great interest in seismic-prone regions, such as Italy [1–7]. Recent Italian earthquakes (Umbria-Marche 1997, L’Aquila 2009, Emilia 2012, Central Italy 2016) showed the high vulnerability of older masonry constructions to seismic actions [8–17]. In particular, historical masonry churches proved to be highly vulnerable to horizontal loads [18–23]. Post-earthquake damage surveys carried out after past seismic events highlighted that one of the main causes of vulnerability for such structures is associated with local failure modes, mainly due to the outof-plane response of macro-elements [24–26]. This paper investigates the seismic response of seven masonry churches, which are located in the province of Ferrara (Northern Italy) and suffered extensive damage during the 2012 Emilia earthquake. In May–June 2012 a seismic sequence of Magnitude ML = 5.9 (May 20) and 5.8 (May 29) struck Northern Italy: the epicenter of the major event was located at few kilometers from the towns of Mirandola, Finale Emilia and Bondeno, and about 30 km west of the city of Ferrara. The affected area was characterized by a high number of industrial buildings and masonry constructions that were severely hit by the seismic sequence. Among these, masonry churches were especially damaged due to their particular structural and architectonical features, such as slender perimeter walls, absence of adequate connections between the

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various parts, lack of intermediate horizontal floors. Within a research agreement between Politecnico di Milano and Curia di Ferrara after the 2012 Emilia earthquake, an extensive campaign of investigations on the damaged churches was performed by the authors. Several on-site surveys were carried out on the churches in order to identify critical parts, typical damage patterns and vulnerable elements. Moreover, the available information from visual inspections and on-site surveys provided a preliminary knowledge of utmost importance for developing detailed finite element (FE) models of the structures and for better understanding the results of advanced numerical simulations. A careful seismic performance assessment of the churches damaged by earthquakes is one of the most effective ways to understand the structural weaknesses of this type of constructions. In such a context, advanced non-linear FE simulations may represent useful tools for a proper evaluation of the seismic safety [27–32]. Detailed FE models of the churches were created and non-linear dynamic analyses were performed using the real accelerogram registered in Mirandola during the seismic event on 29 May 2012. A damage plasticity material model, exhibiting softening in both tension and compression, was used for masonry. The main aims of this study are: (1) to assess the seismic response of masonry churches by means of advanced non-linear dynamic analyses with different peak ground accelerations identifying the damage

Corresponding author. E-mail address: [email protected] (G. Milani).

https://doi.org/10.1016/j.engstruct.2018.08.071 Received 31 March 2018; Received in revised form 4 August 2018; Accepted 20 August 2018 0141-0296/ © 2018 Elsevier Ltd. All rights reserved.

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distribution and the most vulnerable macro-elements; (2) to point out the influence of the morphological and geometrical characteristics on the seismic behavior of the different macro-elements composing the churches, by using detailed 3D FE models.

2.2. Natività di Maria Vergine Church in Stellata (Church 2) Natività di Maria Vergine Church in Stellata, a small hamlet of the municipality of Bondeno that is located about 15 km northwest of Ferrara, was built in 1448. The gabled façade, which is about 14 m high and 0.55 m thick, is subdivided by decorative pilasters into three parts and presents a rectangular window above the main door. The church consists of a single nave, which is over 13 m high. The overall length and width of the church are about 35.6 m and 17.2 m, respectively; the main nave is 28.8 m long and 14.3 m wide. On the right side of the nave, there are four rectangular chapels that are separated from each other: the height of the chapels walls is about 8 m. On the other hand, the left side of the church, without side chapels, is characterized by four rectangular windows and a secondary entrance. The presbytery, which is raised a few steps, is separated from the nave by the triumphal arch and presents side walls that are about 7 m high; the back wall behind the altar, which is about 11 m high, exhibits two elongated windows. The bell tower, which is 17 m high, is incorporated into the presbytery, on the left side of the church.

2. Description of the churches under study Seven masonry churches located in the province of Ferrara (EmiliaRomagna region) and damaged during the seismic events of May–June 2012 are analyzed in this study:

• Church 1: San Giovanni Battista Church in Denore; • Church 2: Natività di Maria Vergine Church in Stellata; • Church 3: San Benedetto Abate Church in Ferrara; • Church 4: Natività di Maria Vergine Church in Cassana; • Church 5: San Giovanni Battista Church in Bondeno; • Church 6: Sant’Antonio da Padova Church in Bondeno; • Church 7: San Bartolomeo Apostolo Church in San Bartolomeo in Bosco.

These churches have been selected because they may be representative of the architectural and constructive practice of the area. A general view of the seven churches is shown in Fig. 1. In this section a concise geometrical architectural description of the churches is provided. The drawings with the relevant geometrical features and the main geometrical dimensions of the churches are presented from Figs. 2–8.

2.3. San Benedetto Abate Church in Ferrara (Church 3) San Benedetto Abate Church in Ferrara was built between 1496 and 1553. During the Second War World the church was severely damaged and partially destroyed: it was reconstructed following the original drawings and completed in 1954. The church presents remarkable geometrical sizes both in plan and elevation: the overall length is about 60 m and the height of the dome is equal to 28 m. The façade, which is subdivided into three parts by pilasters with Corinthian capital, has a large rose window in the upper part and three doors of different size: the large central door is about 4.5 m high. The church presents a Latin cross plan, with three naves separated by two rows of columns. On both the sides of the aisles, which are 31.8 m long, there are six semicircular chapels with a radius equal to about 2.5 m. The nave walls are approximately 18 m high and present a circular opening of diameter equal to 2.4 m at about mid-length. The aisles walls are 11 m high, while each side chapel is 8 m high and presents rectangular openings. The transept of the church is almost 45 m long and 18 m high as the nave: the two side chapels of the transept exhibit two side windows. The dome is built on the circular tholobate. The end part of the church consists of a semicircular apse and two small side apses, which have the same dimensions as the side chapels of the naves. The semicircular apse has a radius of almost 6 m and presents two elongated windows.

2.1. San Giovanni Battista Church in Denore (Church 1) San Giovanni Battista Church in Denore, a small hamlet of Ferrara, dates back to the first decades of the fourteenth century, but it was rebuilt in 1617. The church, which is characterized by a Romanesque architecture, consists of a single nave with several side chapels and annexes: the façade, which is about 17 m high and 0.45 m thick, presents a large door and is marked by pilasters. The whole church presents an overall length of about 33 m and a maximum width of 24 m. The nave walls, which are over 14 m high and 0.6 m thick, are supported by columns and exhibit several rectangular windows in the upper part. The side chapels are about 8 m high, present several small openings and are separated by transversal walls. On the two sides of the presbytery there are the sacristy and a room. The semicircular apse, which is about 14 m high and presents a radius equal to about 4 m, is surmounted by a semi-dome and shows two small side openings.

Church 1

Church 5

Church 2

Church 3

Church 6 Fig. 1. General views of the churches under study. 810

Church 4

Church 7

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Fig. 2. Drawings and main geometrical dimensions of San Giovanni Battista Church in Denore (Church 1).

2.4. Natività di Maria Vergine Church in Cassana (Church 4)

church, there is the sacristy, which was probably built later than the church and presents several openings on both the sides.

Natività di Maria Vergine Church in Cassana, a small hamlet of Ferrara, dates back to the fourteenth century. The façade, which is about 11 m high and 0.65 m thick, presents a narrow upper part with pediment and is characterized by four pilasters highlighting the different parts of the church: above the main door, which is flanked by two niches, there is a square window. The church consists of a single nave exhibiting a rectangular plan, which is about 13 m long and 8 m wide. On the right side of the nave there are the small baptistery and a chapel, while on the left side there are two chapels and a storeroom. The nave of the church, as well as the adjacent annexes, has a double pitched roof supported by a wooden truss. The presbytery is separated from the central nave by a triumphal arch. The apse is semi-circular with a radius of about 2 m and presents two tall narrow windows: next to the apse, on the right side, there is a rectangular chapel. The bell tower, which is about 14 m high and presents a side of 2.6 m, is located on the left side and is incorporated into the church. In addition, on the left side of the

2.5. San Giovanni Battista Church in Bondeno (Church 5) San Giovanni Battista Church in Bondeno, a small city located about 15 km northwest of Ferrara, is about 33 m long and 16 m wide. The façade, which is approximately 18.5 m high, 11.5 m wide and 0.5 m thick, is characterized by baroque decorations: it presents a door, which is flanked by two niches, a large opening in the upper part and an oculus in the tympanum. The church consists of a single nave with rectangular chapels on each side: the interior shows baroque decorations, which were presumably made after the construction of the complex. On both the sides of the façade, in correspondence with the chapels, there is a small door. The nave walls, which are about 15 m high, 10 m wide and 0.5 m thick, present two openings in the upper part. The side chapels, which are about 9 m high, are separated by transversal walls. The presbytery and the apse, which are about 10 m

Fig. 3. Drawings and main geometrical dimensions of Natività di Maria Vergine Church in Stellata (Church 2). 811

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Fig. 4. Drawings and main geometrical dimensions of San Benedetto Abate Church in Ferrara (Church 3).

long, are slightly less wide than the central nave: the presbytery presents a small door on one side and the apse exhibits two small windows. The bell tower on the left side of the church is adjacent to the side chapels and incorporated into the sacristy, which was probably built in more recent times. The bell tower, which is over 27 m high and has a characteristic onion dome, exhibits four openings in the belfry and three windows at about mid-height.

polygonal apse that is about 3.3 m long. The salient façade, which is about 14.7 m high and 15 m wide and presents a thickness of about 0.45 m, exhibits a central pointed arch portal and two side narrow pointed arch windows in correspondence with the aisles: in the upper part of the façade there is a large rose window. The church is subdivided into three naves separated by two rows of columns; the width of the central nave is approximately equal to 7 m and double than that of the aisles. The aisles walls, which are about 7 m high and 0.45 m thick, present some tall narrow pointed arch windows. The nave walls, which are about 12 m high and 0.45 m thick, exhibit some small circular openings in the upper part, in correspondence with the windows of the aisles walls. At the end of the two aisles there are two rectangular chapels with a small door on one side. The chorus is as wide as the nave

2.6. Sant’antonio da Padova Church in Bondeno (Church 6) Sant’Antonio da Padova Church in Bondeno, a small city located about 15 km northwest of Ferrara, was built in 1597. The church has a rectangular plan, which is about 15.3 m wide and 20.2 m long, with a

Fig. 5. Drawings and main geometrical dimensions of Natività di Maria Vergine Church in Cassana (Church 4). 812

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Fig. 6. Drawings and main geometrical dimensions of San Giovanni Battista Church in Bondeno (Church 5).

Fig. 7. Drawings and main geometrical dimensions of Sant’Antonio da Padova Church in Bondeno (Church 6). 813

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Fig. 8. Drawings and main geometrical dimensions of San Bartolomeo Apostolo Church in San Bartolomeo in Bosco (Church 7).

and ends with a polygonal apse. The apse, which is about 11.9 m high, presents three tall narrow pointed arch windows, similar to those on the aisles walls; the window located on the apse central wall is now walled up.

3. Damage survey Several field surveys were conducted by the authors on the churches under study after the 2012 earthquake. On-site inspections are fundamental to collect information on the presence of local damage and its extension. In this paper, only a short description of the main damage observed in four churches is provided and some schematic drawings showing the main crack patterns are reported.

2.7. San Bartolomeo Apostolo Church in San Bartolomeo in Bosco (Church 7) San Bartolomeo Apostolo Church in San Bartolomeo in Bosco, a small hamlet of Ferrara, was built in 1959 over the earlier church dating back to the eighteenth century that was destroyed during the Second World War. The church presents an elongated rectangular plan that ends with a semicircular apse flanked by two small chapels: the overall length of the church is about 33.5 m. The façade, which is about 15.8 m wide and 17.5 m high, presents a main door, flanked by two columns, and two smaller side doors: moreover, it exhibits a large circular rose window with a diameter of about 2 m at mid-height and a smaller circular window in the upper part. The church consists of a single large volume with a rectangular plan, although the decorative motifs with arches and pilasters of the walls recall the presence of chapels or aisles. The two nave walls, which are about 10 m high with a thickness of about 0.45 m, present six small round arch windows: moreover, three doors are present on the left nave wall and one door on the right one. The back wall of the nave, which connects the presbytery, raised a few steps, and the apse, is about 14 m high. The semicircular apse, which is 9.85 m high with a radius of about 3.5 m, is flanked by two smaller semicircular chapels, which are about 7 m high with a radius of about 1.5 m. The apse presents two tall narrow windows and each side chapel has a small circular opening on the external side.

3.1. San Giovanni Battista Church in Denore (Church 1) Fig. 9 presents a summary of the main cracks observed in Church 1 during the field survey. The survey brought out the presence of: (a) vertical and diagonal cracks in the central part of the façade, above the main door, visible also inside the church; (b) vertical and diagonal cracks in the annex buildings; the apse does not present any remarkable damage; (c and d) vertical and diagonal cracks near the openings of the perimeter longitudinal walls; (e and f) diagonal shear cracks in the nave walls, originating mainly above the door near the façade; (g and h) diagonal shear cracks along the whole height of the transversal walls of the side chapels. 3.2. Natività di Maria Vergine Church in Stellata (Church 2) Fig. 10 shows a summary of the main cracks observed in Church 2 during the field survey. The survey highlighted the presence of: (a) vertical cracks in the central part of the façade, in particular along the sides of the window, above the door and in the tympanum; small diagonal cracks near the openings of the belfry; 814

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Fig. 9. Church 1. Crack patterns observed during on-site inspections. (a) north side; (b) south side; (c) east side; (d) west side; (e) longitudinal section 1; (f) longitudinal section 2; (g) transversal section 1; (h) transversal section 2.

(b) several cracks in the back walls of the apse and the naves; vertical and diagonal cracks along the body and in the belfry of the bell tower; (c) vertical cracks in the bottom part of the bell tower and near the opening of the belfry; vertical cracks in the lateral walls, mainly near the façade; (d) horizontal cracks in the upper part of the side chapels; (e) widespread cracks in the internal side of the lateral northern wall, near the arches and the supports of the roof truss beams; (f) cracks in the internal side of the lateral southern wall, near the windows and the supports of the roof truss beams; (g) extensive cracks in the upper part of the apse, in the triumphal arch

and near the supports of the roof truss beams; (h) horizontal and vertical cracks, mainly originating from the openings, in the internal side of the façade. 3.3. Natività di Maria Vergine Church in Cassana (Church 4) Fig. 11 shows a summary of the main cracks observed in Church 4 during the field survey. The survey brought out the presence of: (a) vertical cracks located in the facade near the door and the window, spreading up to the tympanum; two horizontal cracks near the corners of the openings at the base of the belfry; diagonal cracks in 815

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Fig. 10. Church 2. Crack patterns observed during on-site inspections. (a) east side; (b) west side; (c) south side; (d) north side; (e) longitudinal section 1; (f) longitudinal section 2; (g) transversal section 1; (h) transversal section 2.

Fig. 11. Church 4. Crack patterns observed during on-site inspections. (a) west side; (b) east side; (c) north side. 816

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Fig. 12. Church 5. Crack patterns observed during on-site inspections. (a) north side; (b) south side; (c) east side; (d) west side;

the left edge of the façade, mainly in correspondence with openings. (b) some small diagonal cracks spreading from the opening of belfry; slight diagonal cracks at the edge of the apse and in adjacent walls; (c) horizontal and diagonal cracks in the belfry; some cracks in bottom part of the sacristy walls.

the analysis of concrete structures under static or dynamic loading, but it may be also applied to describe the behavior of masonry structures, see, among the others, [13,27,36]. The CDP is a continuum plasticitybased damage model that assumes tensile cracking and compressive crushing as main failure modes: it allows analyzing materials with different strength in tension and compression, assuming distinct damage parameters. Fig. 14 shows the constitutive behavior adopted in tension and compression for masonry. It is worth mentioning that the model is based on the concepts of isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to represent the material inelastic behavior. Masonry is characterized by an orthotropic behavior, both in the linear and non-linear fields. However, experimental results reported by Page on regular masonry wallets [37] show that such a material exhibits a moderate orthotropy ratio (around 1.2) under biaxial stress states. Moreover, the application of complex orthotropic damage models for the analysis of large-scale historical masonry structures appears to be ineffective due to their high computational effort. On the other hand, due to the chaotic and random texture of historical masonry, an orthotropic model appears as questionable as an isotropic one. For these reasons, the use of isotropic damage models for sophisticated dynamic analyses of full-scale complex masonry structures is widely accepted [38,39], after an adaptation of the parameters to fit an average behavior between vertical and horizontal compression. In this study, the same masonry material is assumed for all the models, considering that all the churches, belonging to the same territorial area, are made of solid masonry bricks and lime mortar, as also emerged from field surveys. Moreover, it is important to observe that some parts of the churches under study were rebuilt over the centuries. Nevertheless, in this study the same material properties are used for all the parts of each church because the purpose of this work is a qualitative comparison of the individual churches with a particular emphasis on their geometrical details and macro-elements features. In the absence of experimental tests results, the main mechanical properties of masonry were assumed referring to the indications provided in the Italian recommendations for existing buildings and built heritage [40–42]. The following assumptions have been taken into account for a masonry made of solid bricks and lime mortar: (i) the density and the elastic modulus are equal to 1800 kg/m3 and 1500 MPa, respectively; (ii) the compressive strength is equal to σcu = 2.4 MPa. The tensile strength is assumed equal to σto = 0.1 MPa, obtaining a ratio between the tensile and compressive strength equal to about 0.04.

the the the the

3.4. San Giovanni Battista Church in Bondeno (Church 5) Fig. 12 provides a summary of the main cracks observed in Church 5 during the field survey. The survey showed the presence of: (a) vertical cracks in the façade, spreading from the door, near the openings and at the top of the tympanum; diagonal cracks running across a window at the mid-height of the bell tower; (b) vertical and diagonal cracks near the openings of the apse and at the mid-height of the bell tower; (c an d) vertical and diagonal cracks in the nave walls, in the connection regions with the façade and in the apse, mainly near the openings. 4. FE models and material model adopted A detailed geometric characterization of the seven churches based on the existing documentation made available by the Curia di Ferrara, along with accurate on-site surveys and wide photographic documentations carried out by the authors, allowed for the definition of 3D FE models of the churches. Fig. 13 shows some general views of the geometrical and FE models of the seven churches developed directly in the commercial code Abaqus [33]. The 3D FE discretization was based on four-node tetrahedron elements: the choice of the element size was done in order to share the advantages of sufficiently reliable results and numerical efficiency during the non-linear dynamic analyses. It is worth mentioning that some simplifications were introduced into the numerical models in order to limit the computational effort: for this reason, some details were not modelled due to their secondary structural function. Moreover, masonry vaults, semi-domes and timber roofs, when they are present, were not modelled, but included in the models by considering the corresponding mass: their membrane stiffness is safely assumed negligible for horizontal loads, as well as the box behavior induced by their presence in the FE models. Such a conservative assumption is due to the lack of available accurate geometrical data and is motivated by the presence of wooden truss beams and by the poor strength and stiffness of the masonry forming the vaults. The non-linear behavior of masonry was modeled using the Concrete Damaged Plasticity model (CDP), which is available in ABAQUS/Standard [33]. The model, proposed by Lubliner et al. [34] and extended by Lee and Fenves [35], provides a general capability for

5. Modal analysis and non-linear dynamic analyses In order to obtain a preliminary assessment of the dynamic behavior of the churches under study, an eigen-frequency analysis is performed on the three-dimensional FE models, which allows identifying the deformed shapes of the main vibration modes characterized by a high 817

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Church 7

Church 6

Church 5

Church 4

Church 3

Church 2

Church 1

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Fig. 13. General views of the geometric and FE models of the churches under study.

seismic sequence; moreover, they approximately correspond to the maximum horizontal acceleration (ag) prescribed for that region at the Life Safety Limit State (SLV) according to Italian Code [40]. In this study, the seismic performance assessment of the churches is carried out, for two different peak ground accelerations (PGA = 0.1 g and PGA = 0.15 g), in terms of tensile damage distribution and maximum values of normalized displacement for the different macro-elements. In fact, the structural behavior of complex masonry constructions under seismic actions can be analyzed referring to different meaningful structural portions, called macro-elements, which are characterized by an almost autonomous structural behavior in comparison with that of the rest of the structure. In particular, past earthquakes have shown that

participating mass ratio (PMR) as well as the corresponding periods. Then, non-linear dynamic analyses are carried out on the FE models of the churches, using the real accelerogram registered in Mirandola during the seismic event on 29 May 2012. It is worth mentioning that from such a registration a part of duration equal to 10 s is considered due to the high computational effort required by the numerical simulations. Fig. 15 shows the two horizontal components of the real accelerogram used in the non-linear dynamic analyses and the corresponding response spectra: the same peak ground acceleration (PGA) is adopted for the two orthogonal directions. It is worth mentioning that the highest values of the PGA used in the non-linear dynamic analyses are similar to the ones registered in that region during the 2012 Emilia 818

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Fig. 14. Representation of the masonry constitutive behavior in (a) tension and (b) compression.

Fig. 15. Horizontal components and corresponding response spectra of the real accelerogram used in the non-linear dynamic analyses: longitudinal direction (left) and transversal direction (right).

the seismic response of churches exhibits a recurrent behavior that is characterized by local damage and collapse mechanisms of the different macro-elements [43–44]. Consequently, the FE models of the churches under study are subdivided into suitable macro-elements that are structurally recognizable and recurrent in the different churches. The meaning of the labels used in this study for the different macro-elements is the following: F stands for façade, A refers to the apse, RNW and LNW denote the right and left nave walls, REW and LEW refer to the right and left external walls, TA indicates the triumphal arch, BT refers to the bell tower (if it is present) and RSC and LSC denote the right and left side chapels.

10.9% and 13%, respectively, in the transversal direction. The fifth mode (T = 0.231 s) concerns the nave walls and the apse with a PMR equal to 9.1% in the transversal direction, the seventh mode (T = 0.185 s) involves the façade and the nave with a PMR equal to 9.5% in the longitudinal direction. The highest PMR (37%) in the longitudinal direction is related to the eighth mode (T = 0.179 s) involving the façade and the nave. Fig. 17 shows the tensile damage distribution for Church 1 at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. – A significant widespread damage, which can be clearly observed even under PGA = 0.1 g, is registered in the upper part of the façade. It can be noted that the façade presents a very high slenderness, only one opening (the main door) and a small height difference between the top of the tympanum and the nave walls (about 1.8 m). Moreover, considerable vertical damage is detected in the connection regions between the façade and the nave walls, above all

5.1. San Giovanni Battista Church in Denore (Church 1) Fig. 16 shows the modal deformed shapes of the main vibration modes characterized by a PMR larger than 5% and the corresponding periods for Church 1. It can be noted that the first (T = 0.494 s) and the second (T = 0.360 s) modes involve the nave walls with a PMR equal to 819

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Fig. 16. Church 1. Distribution of the first one hundred modes in the longitudinal and transversal directions. Deformed shapes of the first main modes with corresponding periods and participating mass ratios in the longitudinal and transversal directions.

under PGA = 0.15 g. It can be noted that the numerical model shows a more widespread damage than the real case, particularly with regard to the upper part of the façade. – Under PGA = 0.1 g, the nave walls, which are characterized by several openings in the upper part and relevant height (about 15 m), exhibit vertical damage and typical X-shaped cracks near the openings and the arches, in agreement with the on-site survey: such damage patterns become more marked under PGA = 0.15 g. Furthermore, vertical damage is observed in the transversal walls of

the side chapels, mainly near the nave walls, even under PGA = 0.1 g: it is pretty similar to what has been observed during the field survey. – The apse presents some vertical cracks in the upper part and near the corners of the two small side windows: conversely, no remarkable damage was observed during the on-site survey.

PGA=0.15g

PGA=0.1g

Fig. 18 shows the maximum normalized displacements registered for the main macro-elements of Church 1 in the two orthogonal

Fig. 17. Church 1: tensile damage distribution at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. 820

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Fig. 18. Church 1: maximum normalized displacements registered for the main macro-elements in the longitudinal and transversal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. A large increase of the normalized displacements can be observed in the case of PGA = 0.15 g. Under PGA = 0.1 g, the maximum normalized displacement is registered for the façade (0.25%) in the longitudinal direction and for the left nave wall (0.35%) in the transversal direction. Under PGA = 0.15 g, the maximum normalized displacements in the transversal direction are computed for the nave walls (0.88% for the left nave wall), which are characterized by small thickness and significant height and length: moreover, it has to be pointed out that transversal walls are not present in the end part, near the transept. The façade, which exhibits a small thickness and is higher than the nave walls by about 1.8 m, presents normalized displacements larger than 0.45% in the longitudinal direction.

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5.2. Natività di Maria Vergine Church in Stellata (Church 2) Fig. 19 shows the modal deformed shapes of the main vibration modes characterized by a PMR larger than 5% and the corresponding periods for Church 2. It can be noted that the first mode (T = 0.487 s) involves the nave wall without lateral chapels with a PMR equal to 10.8% in the transversal direction. The second mode (T = 0.315 s) concerns the façade in the longitudinal direction and the nave wall without lateral chapels with a PMR equal to 6.9% in the longitudinal direction. The highest PMR (15.4%) in the transversal direction is related to the fourth mode (T = 0.217 s) involving the bell tower and the adjacent apse and triumphal arch. The fifth mode (T = 0.212 s) concerns the nave wall with lateral chapels in the transversal direction with a PMR equal to 7.1% in the transversal direction. The highest PMR (9.9%) in the longitudinal direction is related to the sixth mode (T = 0.197 s) involving the bell tower and the adjacent apse and triumphal arch. Fig. 20 shows the tensile damage distribution for Church 2 at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

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–

–

about 3.5 m. Under PGA = 0.1 g a widespread damage is registered in the upper part of the façade, near the central window: such damage increases considerably under PGA = 0.15 g. Significant vertical damage is observed near the connection regions between the nave walls and the façade, indicating a possible overturning mechanism of the façade. As emerged from the on-site survey, a quite widespread damage can be observed in all the sides of the bell tower, with peculiar diagonal cracks, probably due to the torsional effects induced by the earthquake: it has to be noted that the bell tower, which exhibits a small height (about 16 m) and a small thickness of the walls, is restrained by the walls of the choir and the apse. It can be noted that the nave walls are characterized by relevant length and several openings: moreover, lateral chapels are present only on the right side. The left nave wall without lateral chapels shows horizontal damage near the base, which propagates diagonally at the edges near the façade and the back wall: moreover, extensive damage can be observed near the openings. It is important to observe that the weakness of the left nave wall is confirmed by the results obtained from modal analysis: the first vibration mode clearly involves such a macro-element. The right nave wall presents widespread horizontal and diagonal cracks above the side chapels. The right side chapels exhibit severe vertical damage in the transversal walls near the nave walls under PGA = 0.1 g; under PGA = 0.15 g, vertical cracks appear also at the external edges of the transversal walls, indicating a possible overturning mechanism of the side chapels external walls. The back wall of the apse exhibits two vertical cracks in the upper part under PGA = 0.1 g, as emerged from the on-site survey: a considerable increase of damage characterized by diagonal shear cracks near the openings can be observed under PGA = 0.15 g. The triumphal arch shows vertical damage in the central part and marked diagonal cracks at the edges: it is in a good agreement with the surveyed damage.

Fig. 21 shows the maximum normalized displacements registered for the main macro-elements of Church 2 in the two orthogonal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. Under PGA = 0.1 g, the maximum normalized displacement is

– It is important to point out that Church 2 is characterized by a small (14.1 m) wide (17.2 m) gabled façade, which presents a central door and a rectangular window in the upper part: moreover, the height difference between the top of the tympanum and the nave walls is 821

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Fig. 19. Church 2. Distribution of the first one hundred modes in the longitudinal and transversal directions. Deformed shapes of the first main modes with corresponding periods and participating mass ratios in the longitudinal and transversal directions.

registered for the left nave wall without lateral chapels (0.21%) in the transversal direction and for the façade (0.16%) in the longitudinal direction. Under PGA = 0.15 g, a large increase of normalized displacements can be observed: the maximum normalized displacement of the left nave wall in the transversal direction becomes very high (1.72%). It is worth mentioning that the left nave wall presents relevant length (about 28 m) and is not out-of-plane restrained by lateral

chapels. The façade presents normalized displacements larger than 0.55% in the longitudinal direction. The normalized displacements of the bell tower are smaller than 0.2% in both the orthogonal directions. 5.3. San Benedetto Abate Church in Ferrara (Church 3)

PGA=0.15g

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Fig. 22 shows the modal deformed shapes of the main vibration

Fig. 20. Church 2: tensile damage distribution at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. 822

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Fig. 21. Church 2: maximum normalized displacements registered for the main macro-elements in the longitudinal and transversal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

Fig. 22. Church 3. Distribution of the first one hundred modes in the longitudinal and transversal directions. Deformed shapes of the first main modes with corresponding periods and participating mass ratios in the longitudinal and transversal directions.

modes characterized by a PMR larger than 5% and the corresponding periods for Church 3. It can be noted that the first mode (T = 0.732 s) involves the nave walls of the central nave with a PMR equal to 15.3% in the transversal direction. The third mode (T = 0.444 s) concerns the central nave and the façade with the highest PMR (47.9%) in the longitudinal direction. The highest PMR (31.8%) in the transversal direction is related to the eighth mode (T = 0.271 s) involving the nave, the transept and the apse. The ninth mode (T = 0.258 s) concerns the

chapels of the transept with a PMR equal to 12.1% in the longitudinal direction. Fig. 23 shows the tensile damage distribution for Church 3 at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. – Under PGA = 0.1 g the façade shows a quite widespread damage that significantly increases under PGA = 0.15 g. The façade, which is characterized by a large central door, two small lateral doors and 823

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Fig. 23. Church 3: tensile damage distribution at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

a central rose window in the upper part, presents significant vertical damage between the top of the tympanum and the central window and in the connection regions with the nave walls: moreover, diagonal cracks are registered near the two side doors. It is important to point out that the façade is very wide (27.85 m) and presents relevant slenderness: moreover, the height difference between the top of the tympanum and the nave walls is about 3.9 m. – The nave walls, which are supported by slender columns and a series of arches, present widespread vertical damage in the upper part, mainly near the central opening, and in correspondence with the arcades. Some vertical cracks starting from the openings can be observed in the upper part of the side chapels located near the façade and the transept chapels. – The apse exhibits vertical cracks in the upper part and diagonal cracks near the openings; moreover, vertical damage can be observed in the upper part of the two transept chapels.

Fig. 24 shows the maximum normalized displacements registered for the main macro-elements of Church 3 in the two orthogonal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. Under PGA = 0.1 g, the maximum normalized displacement is registered for the nave walls (0.46%) in the transversal direction and for the façade (0.32%) in the longitudinal direction. Under PGA = 0.15 g, the maximum normalized displacement of the left nave wall is equal to 0.69% in the transversal direction, while the façade presents a maximum normalized displacement equal to 0.48% in the longitudinal direction. It can be noted that the normalized displacements of the apse and the triumphal arch are smaller than those of the other macro-elements in both the directions. 5.4. Natività di Maria Vergine Church in Cassana (Church 4) Fig. 25 shows the modal deformed shapes of the main vibration modes characterized by a PMR larger than 5% and the corresponding

Fig. 24. Church 3: maximum normalized displacements registered for the main macro-elements in the longitudinal and transversal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. 824

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Fig. 25. Church 4. Distribution of the first one hundred modes in the longitudinal and transversal directions. Deformed shapes of the first main modes with corresponding periods and participating mass ratios in the longitudinal and transversal directions.

transversal direction is related to the fourth mode (T = 0.118 s) involving the nave walls and the side chapels. Fig. 26 shows the tensile damage distribution for Church 4 at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

PGA=0.15g

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periods for Church 4. It can be noted that the first mode (T = 0.224 s) involves the upper part of the façade with the highest PMR (8.9%) in the longitudinal direction. The second (T = 0.213 s) and the third (T = 0.204 s) modes concern the bell tower and the triumphal arch with a PMR equal to 13.4% in the transversal direction and 7.7% in the longitudinal direction, respectively. The highest PMR (21.5%) in the

Fig. 26. Church 4: tensile damage distribution at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. 825

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– Severe damage concentrates in the upper part of the façade with a marked horizontal crack that may cause a probable overturning mechanism of the tympanum under PGA = 0.15 g: it is important to observe that the façade, which is characterized by several openings (the central door with four small lateral windows and a rectangular opening located in the upper part), presents low slenderness due to the small height (10.7 m): moreover, the height difference between the top of the tympanum and the nave walls is about 3.5 m. – In agreement with the on-site survey, negligible damage is registered in the nave walls, which are characterized by small thickness and restrained by side chapels and annexes. – The bell tower, which exhibits small height (about 14 m) and is located inside the structure, shows a damage concentration near the connection regions with the church and in the upper part near the openings of the belfry; such damage is clearly visible even under PGA = 0.1 g. These results are consistent with what has been observed during the field survey. – The triumphal arch presents severe damage near the bell tower and at the edges: such damage significantly increases under PGA = 0.15 g. – -Diagonal cracks can be observed in the back wall of the sacristy, mainly near the openings of the upper storey. The apse shows minor vertical damage near the connection regions with the walls of the sacristy.

direction. 5.5. San Giovanni Battista Church in Bondeno (Church 5) Fig. 28 shows the modal deformed shapes of the main vibration modes characterized by a PMR larger than 5% and the corresponding periods for Church 5. It can be noted that the first and second modes involve the bell tower: the first mode (T = 0.834 s) presents a PMR equal to 13.5% in the transversal direction, the second mode (T = 0.457 s) exhibits a PMR equal to 7.8% in the longitudinal direction. The third mode (T = 0.432 s) concerns the nave walls with a PMR equal to 12.7% in the transversal direction. The fifth mode (T = 0.258 s) involves the nave walls, the bell tower and the apse with the highest PMR (15.4%) in the transversal direction. The highest PMR (21.2%) in the longitudinal direction is related to the thirteenth mode (T = 0.14 s) concerning the façade, the nave walls and the bell tower. Fig. 29 shows the tensile damage distribution for Church 5 at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. It can be noted that a large damage increase occurs in the case of PGA = 0.15 g. – A damage concentration can be observed in the upper part of the façade, which presents high slenderness, two openings (the portal and a large rectangular window in the upper part) and a height difference with the nave walls equal to 3.6 m. In particular, an important vertical crack extends from the door to the top of the tympanum and two notable diagonal cracks propagate from the central window to the edges of the tympanum: such damage is already visible under PGA = 0.1 g. These results are reflected in the main outcomes derived from the on-site survey. – The bell tower exhibits evident vertical and diagonal cracks at midheight in the connection region with the nave walls, on both the transversal sides. It is interesting to observe that the upper part of the bell tower does not present any damage, even under

Fig. 27 shows the maximum normalized displacements registered for the main macro-elements of Church 4 in the two orthogonal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. It can be noted that the maximum normalized displacements are small for all the macro-elements, even under PGA = 0.15 g, except for the façade (0.45%) in the longitudinal direction. The bell tower presents normalized displacements smaller than 0.26% in both the directions and the nave and external walls exhibit normalized displacement smaller than 0.2% in the transversal

Fig. 27. Church 4: maximum normalized displacements registered for the main macro-elements in the longitudinal and transversal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. 826

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Fig. 28. Church 5. Distribution of the first one hundred modes in the longitudinal and transversal directions. Deformed shapes of the first main modes with corresponding periods and participating mass ratios in the longitudinal and transversal directions.

Fig. 29. Church 5: tensile damage distribution at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

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Fig. 30. Church 5: maximum normalized displacements registered for the main macro-elements in the longitudinal and transversal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

PGA = 0.15 g, as emerged from the field survey. – Several vertical cracks, which are consistent with the real damage, can be observed in the apse, mainly in the upper part of the wall and near the two small windows, even under PGA = 0.1 g. – The nave walls, which are characterized by high slenderness due to the small thickness and some openings in the upper part, exhibit some diagonal cracks near the openings under PGA = 0.1 g; under PGA = 0.15 g, damage becomes more marked and consists of severe horizontal cracks in correspondence with the top of the side chapels. These results are consistent with what has been highlighted during the field survey. Marked vertical cracks can be observed in the transversal walls of the side chapels, mainly near the nave walls, already visible under PGA = 0.1 g.

involves the walls of the central nave with the highest PMR (26.4%) in the transversal direction. The third mode (T = 0.225 s) concerns the walls of the central nave, the external walls and the triumphal arch with a PMR equal to 17.9% in the transversal direction. The highest PMR (48.8%) in the longitudinal direction is related to the fourth mode (T = 0.213 s) involving the façade, the central nave and the triumphal arch. Fig. 32 shows the tensile damage distribution for Church 6 at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. It is interesting to highlight that extensive damage can be already observed under PGA = 0.1 g, especially in the façade and in the nave walls. – The façade, which is characterized by high slenderness and several openings (such as the central door with two adjacent narrow side windows and a large central rose window located in the upper part), shows radial cracks around the rose window and marked diagonal cracks starting from the corners of the two narrow side windows: moreover, severe damage can be observed between the rose window and the central door. – The nave walls, which are supported by columns and thus present low stiffness in the longitudinal direction, exhibit a widespread vertical damage starting from the openings, already visible under PGA = 0.1 g. Severe vertical cracks can be registered near the connection regions between the façade and the nave walls, even under PGA = 0.1 g. – The external longitudinal walls present some diagonal cracks near the narrow openings and slight horizontal cracks at the base, above all under PGA = 0.15 g. – The walls of the presbytery show some vertical cracks in the upper part. The triumphal arch exhibits a marked vertical crack at the top under PGA = 0.1 g and widespread damage involving also the edges under PGA = 0.15 g. – The polygonal apse does not present any damage under PGA = 0.1 g: only few diagonal cracks can be observed near the

Fig. 30 shows the maximum normalized displacements registered for the main macro-elements of Church 5 in the two orthogonal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. It can be noted that the normalized displacements are smaller than 0.5% for all the macro-elements. Under PGA = 0.1 g, the maximum normalized displacement is registered for the façade (0.24%) in the longitudinal direction and for the bell tower (0.22%) in the transversal direction. The nave walls exhibit a maximum normalized displacement equal to 0.17% in the transversal direction. Under PGA = 0.15 g, the maximum normalized displacement (0.48%) in the longitudinal direction is registered for the façade. The bell tower presents a maximum normalized displacement equal to 0.45% in the transversal direction: the maximum normalized displacement for the nave wall is equal to 0.37%. 5.6. Sant’antonio da Padova Church in Bondeno (Church 6) Fig. 31 shows the modal deformed shapes of the main vibration modes characterized by a PMR larger than 5% and the corresponding periods for Church 6. It can be noted that the first mode (T = 0.360 s) 828

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Fig. 31. Church 6. Distribution of the first one hundred modes in the longitudinal and transversal directions. Deformed shapes of the first main modes with corresponding periods and participating mass ratios in the longitudinal and transversal directions.

Fig. 32. Church 6: tensile damage distribution at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

corners of the openings under PGA = 0.15 g.

triumphal arch exhibits normalized displacements equal to 0.21%. In the transversal direction the two nave walls present similar values of normalized displacements (about 0.24%).

Fig. 33 shows the maximum normalized displacements registered for the main macro-elements of Church 6 in the two orthogonal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. Under PGA = 0.1 g, the highest normalized displacements are registered for the façade (0.35%) in the longitudinal direction and for the nave walls (0.12%) in the transversal direction. Under PGA = 0.15 g, in the longitudinal direction the maximum normalized displacement (0.75%) is computed for the façade: the

5.7. San Bartolomeo Apostolo Church in San Bartolomeo in Bosco (Church 7) Fig. 34 shows the modal deformed shapes of the main vibration modes characterized by a PMR larger than 5% and the corresponding periods for Church 7. It can be noted that the first mode (T = 0.518 s) 829

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Fig. 33. Church 6: maximum normalized displacements registered for the main macro-elements in the longitudinal and transversal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

Fig. 34. Church 7. Distribution of the first one hundred modes in the longitudinal and transversal directions. Deformed shapes of the first main modes with corresponding periods and participating mass ratios in the longitudinal and transversal directions.

involves the tympanum of the façade with the highest PMR (16.3%) in the longitudinal direction. The second mode (T = 0.485 s) concerns the walls of the nave with a PMR equal to 24.6% in the transversal direction: it can be noted that the church does not present chapels and lateral naves. The highest PMR (25.8%) in the transversal direction is related to the sixth mode (T = 0.217 s) involving the walls of the nave and the

triumphal arch. Fig. 35 shows the tensile damage distribution for Church 7 at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. It can be noted that the church presents considerable damage even under PGA = 0.1 g.

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Fig. 35. Church 7: tensile damage distribution at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

– The façade, which is characterized by a narrow tympanum, a large wall thickness and several openings of different size (such as the central door with two adjacent side doors, a large central windows and a small circular opening located in the upper part), shows extensive damage. Under PGA = 0.1 g, vertical damage concentrates mainly near the large central window and above the two lateral doors. Under PGA = 0.15 g, a considerable increase of damage can be observed at the base of the tympanum, above the large central window, indicating an onset of overturning mechanism of the upper part. – The nave walls, which are characterized by relevant length, several openings (doors and windows) and absence of lateral chapels, exhibit different types of widespread damage: X-shaped cracks near the openings, horizontal cracks at the base near the doors and vertical cracks in the upper part. Significant vertical damage can be observed near the connection regions with the façade, even under PGA = 0.1 g. – The triumphal arch presents vertical damage in the central part and at the edges, already visible under PGA = 0.1 g. – The apse shows quite negligible damage under PGA = 0.1 g: some diagonal cracks can be observed near the corners of the two large openings under PGA = 0.15 g.

6. Comparison and discussion of the numerical results – The numerical results obtained from modal analysis have provided useful preliminary information about the dynamic response of the churches, highlighting a low structural stiffness in the transversal direction and significant out-of-plane deformations of different macro-elements. As a matter of fact, for the majority of the churches, the first main mode with high PMR involves the nave walls in the transversal direction; this occurs mainly when side chapels or lateral naves are not present or in the case of nave walls supported by slender columns. Two churches (Church 4 and Church 7) exhibit the first main mode with high PMR involving the façade in the longitudinal direction; this occurs in the case of slender and narrow tympanum presenting a relevant height difference with the nave walls. As expected, the first two modes of Church 5 involve the tall bell tower with the highest values of period among the churches under study; conversely, it is worth mentioning that the bell towers of Church 4 and Church 2 are small and embedded in the structure (Church 2) and the period values of the corresponding modes are low. It can be noted that all the churches present very few modes with PMR larger than 5%: as a consequence, a large number of modes should be considered to reach significant effective modal masses and thoroughly describe the global response of the churches. Moreover, the period of the first main mode is within the range 0.22–0.51 s for the majority of the churches, except for Church 3 presenting nave walls on slender columns and for Church 5 with a tall bell tower. Consequently, the churches present the modes characterized by high PMR in correspondence with low period values: such a result may explain the extensive damage suffered by the churches in the numerical simulations, taking into account that the first main modes with considerable PMR generally correspond to high amplifications of the spectral acceleration. – Fig. 37 shows the maximum normalized base shear (base shear/ weight) computed for the different churches in the longitudinal and transversal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. It can be noted that the maximum normalized base shear in the longitudinal direction is larger than

Fig. 36 shows the maximum normalized displacements registered for the main macro-elements of Church 7 in the two orthogonal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. Under PGA = 0.1 g, the maximum normalized displacement (0.4%) in the longitudinal direction is registered for the façade, while the other macro-elements (the triumphal arch and the apse) exhibit much smaller displacements; in the transversal direction the largest normalized displacement (0.37%) is observed for the right nave wall. Under PGA = 0.15 g, in the longitudinal direction the façade presents a maximum normalized displacement equal to 0.61%, which may be consistent with an onset of tympanum overturning mechanism; the right nave wall shows normalized displacements equal to 0.55% in the transversal direction.

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Fig. 36. Church 7: maximum normalized displacements registered for the main macro-elements in the longitudinal and transversal directions during the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

that in the transversal direction for the majority of the churches, except for Church 3 and Church 6, which present slender columns at the base of the nave walls and consequently low stiffness in the longitudinal direction. Under PGA = 0.15 g, the values of the normalized base shear range approximately between 0.13 and 0.25 in the longitudinal direction and between 0.15 and 0.2 in the transversal direction. – Fig. 38 shows the energy density dissipated by tensile damage (EDDTD) for the different churches at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. Church 2, Church 6, Church 1 and Church 7 present the highest values of EDDTD: it can be noted that damage is quite uniformly widespread in all the parts of the church. Conversely, Church 4 presents the smallest values of EDDTD: damage is minor and limited to some parts of the church, mainly at the base of the tympanum where a local collapse can activate. Church 3 presents small values of EDDTD due to its large volume. – The numerical results of the non-linear dynamic analyses highlight the extensive damage suffered by the façades of the churches

examined in this study. Significant damage is registered mainly in the upper part of the façade, near the openings and in the connection regions with the nave or external walls. Under PGA = 0.15 g, all the churches exhibit maximum normalized displacements of the façade larger than 0.45%. It is important to highlight that the façades of Church 1, Church 3 and Church 6 present significant slenderness (height/thickness ratio): moreover, the nave walls of such churches are supported by slender columns and present low stiffness in the longitudinal direction. The façade of Church 5 exhibits a high slenderness and a significant height difference between the top of the tympanum and the nave walls, along with a rectangular window in the upper part. It can be noted that the façades of Church 4 and Church 7 are characterized by a narrow upper part and a significant height difference between the top of the tympanum and the nave walls, above all in the case of Church 7: the numerical analyses indicate that a possible overturning mechanism of the tympanum can activate. However, in the case of Church 4 the normalized displacements of the façade are smaller due to the low slenderness of the wall; moreover, damage concentrates mainly at

Fig. 37. Maximum normalized base shear (base shear/weight) registered for the different churches in the longitudinal and transversal directions during the nonlinear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g. 832

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Fig. 38. Energy density dissipated by tensile damage for the different churches at the end of the non-linear dynamic analyses with PGA = 0.1 g and PGA = 0.15 g.

two churches. The nave walls of Church 4 present a small thickness and several side chapels: negligible damage is registered and the normalized displacements of the nave walls are the smallest among the different churches analyzed in this study. It can be noted that the modes involving the nave walls with significant PMR in the transversal direction present a period with a small amplification of the spectral accelerations: moreover, the presence of side chapels limits the displacements in the transversal direction. As already said, Church 5 does not present very large normalized displacements in the transversal direction, despite the high slenderness of the nave walls. It may be justified by the predominant motion of the church in the longitudinal direction, involving the façade. It can be noted that the amplification of the spectral accelerations related to the modes involving the façade is much larger than that related to the nave walls. – The majority of the churches show similar damage patterns in the apse, with vertical cracks originating from the top and extending to the bottom parts. A typical damage can be observed for Church 5, which presents evident cracks in various parts of the apse and the choir. Church 1 and Church 3 present a similar tall and narrow apse with a couple of windows: as expected, damage is similar on the walls of the choir and near the openings. Negligible damage can be observed for Church 6 and Church 4: only in the case of Church 6 a slight damage occurs near the window. Church 2 exhibits a quadrangular choir, without chapels, with two rectangular windows: in this case damage is widespread, with diagonal cracks starting from the upper part to the openings. The normalized displacements of the apse are small (lower than 0.2%) for all the churches: the peak value is registered for the back wall of Church 2. – The majority of the triumphal arches are severely damaged and present similar cracks patterns, with vertical cracks in the central part and diagonal cracks at the edges. Moreover, in the case of Church 4, the triumphal arch exhibits significant damage near the connection regions with the bell tower. The normalized displacements of the triumphal arch are generally small (lower than 0.25%), with a peak value observed for Church 2. – The bell towers suffered visible damage along the body, near the connection regions with the church and, in general, near the openings of the belfry. It is important to highlight that remarkable damage can be observed along the bell tower body when it is connected to the church. The bell towers of Church 2 and Church 4 present small heights (around 16 m and 14 m, respectively) and small walls thickness: moreover, the bell tower of Church 4 is inside the structure and the bell tower of Church 2 is connected to the presbytery and the apse of the church. The bell towers of Church 2 and Church 4 show a damage concentration near the connection region with the church, with peculiar diagonal cracks, probably due also to the torsional effects induced by the seismic action. The bell

the base of the tympanum. It has to be pointed out that the façades of Church 6 and Church 7 are characterized by the presence of several openings: in the case of Church 6 radial cracks start from the large central opening and reach the other parts of the façade, while in the case of Church 7 vertical cracks can be observed above the main and lateral doors. Church 2 exhibits a significant height difference between the top of the tympanum and the nave walls and a rectangular window in the upper part of the façade: a possible overturning mechanism of the tympanum can be expected. Moreover, as regards Church 1 and Church 6, the modes involving the façade with significant PMR in the longitudinal direction present a period with the highest amplification of the spectral accelerations: this result may contribute to explain the large displacements of the façade of such churches in the longitudinal direction. – The upper parts of the central nave walls, above the lateral naves or side chapels, exhibit widespread damage, mainly in the presence of a marked transversal response of the naves, small walls thickness and large openings. It can be noted that horizontal cracks can be observed in the nave walls of Church 2 and Church 5 in correspondence with the top of the lateral chapels. The nave walls of Church 1, Church 6, Church 7 and Church 5 are characterized by several openings and exhibit extensive damage with typical Xshaped cracks. Significant damage can be observed in the connection regions between the façade and the nave walls, even under PGA = 0.1 g, especially for Church 1, Church 6 and Church 7. – Under PGA = 0.15 g, the majority of the churches exhibit normalized displacements of the nave walls larger than 0.5%, except Church 5 and Church 6, which present values around 0.35–0.4%, and Church 4, which shows small values. It is important to highlight that Church 2 and Church 7 present high normalized displacements because lateral naves and chapels are not present, at least on one side. For both the churches, an evident horizontal crack can be observed at the base of the nave walls. A large difference between the normalized displacements of the two nave walls can be observed in the case of Church 2, because only the left nave wall does not present lateral chapels. The nave walls of Church 1, which are characterized by several openings in the upper part and high slenderness, exhibit large displacements in the transversal direction and present severe and widespread damage with typical X-shaped cracks near the openings; moreover, vertical cracks are also observed near the connection regions with the façade. The nave walls of Church 3 and Church 6 are supported by columns and a series of arches: vertical and diagonal cracks start from the top of the arches and then involve a large part of the wall. However, the maximum normalized displacements of the nave walls are different, being larger in the case of Church 3. Such a result may be justified by the different periods of the mode involving the nave walls of the 833

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tower of Church 5 is the tallest one (27.3 m high) among those considered in this study, but it presents less constraints and exhibits smaller damage than the other towers: in any case, typical diagonal cracks can be observed along the body near the connection regions with the church. The maximum normalized displacements of the bell towers of Church 2 and Church 4 are small (lower than 0.25%): larger maximum normalized displacements (around 0.45%) are registered for the bell tower of Church 5. In fact, as already mentioned, the bell tower of Church 5 is less restrained in the transversal direction and consequently undergoes larger displacements than the other bell towers: it can be noted that this occurs despite the main modes related to the bell tower of Church 5 present periods associated with smaller amplifications of the spectral acceleration than the other bell towers.

generally show small displacements, but extensive damage, mainly in the central part and at the edges. – However, in some cases, the geometrical features are not sufficient to comprehensively explain the seismic response and vulnerability of the main macro-elements. Also the dynamic properties of the macro-elements with reference to the characteristics of the accelerogram considered should be taken into account. The results of the modal analyses associated with the response spectra used in this study show that the modes related to the façades generally present higher amplifications of the spectral accelerations than those related to the nave walls. – The results obtained in this study may represent a useful tool to improve the knowledge of the seismic behavior of similar masonry churches located in the same region, providing valuable information for a proper seismic vulnerability assessment at provincial scale: moreover, they can drive future strengthening and consolidation measures to reduce the seismic vulnerability of similar masonry churches. – Finally, it is worth mentioning that some case studies analyzed in this work are not isolated structures, but they are connected to surrounding buildings or annexes. The presence of confining structures can represent an effective constraint for the adjacent parts of the churches and the seismic vulnerability can be influenced by the dynamic interaction with them. The development of global models of the entire complex is therefore highly recommended and further research will be performed on this topic.

7. Conclusions In this study the seismic response of seven masonry churches located in the province of Ferrara (Northern Italy) and damaged during the 2012 Emilia earthquake has been investigated through advanced FE simulations. – The results of the numerical analyses, along with the observation of the widespread damage collected during several on-site surveys and cracks patterns documentations, have shown that the examined structures are highly vulnerable to seismic actions. Extensive damage and large normalized displacements have been registered for the majority of the churches under study, even for PGA = 0.1 g. It can be observed that the modal analysis method can provide preliminary useful information about the main structural weaknesses and critical macro-elements that most probably will activate. Such preliminary results are generally in a good agreement with those obtained through sophisticated non-linear dynamic analyses, which, in any case, are an essential and irreplaceable tool for a deep and detailed knowledge of the seismic behavior of the churches and for future effective strengthening interventions. – Some geometrical features, such as high slenderness, presence of large openings, interaction with adjacent macro-elements, presence of transversal walls, sudden variations of geometry, plan and elevation irregularities, play a crucial role in the seismic performance of the different macro-elements composing the churches. The correlation between local geometrical characteristics and damage distributions in the churches under study has been clearly highlighted by the numerical analyses. – The façade and the nave walls generally undergo the highest normalized displacements in the longitudinal and transversal directions, respectively. The presence of a narrow tympanum, large openings and a significant height difference with the nave walls are detrimental for the seismic performance of the façade. Numerical analyses highlight a considerable damage in the connection regions with the nave walls, indicating a probable overturning mechanism of the façade in the case of poor interlocking. The presence of slender columns at the base of the nave walls decreases the stiffness of the church in the longitudinal direction. On the other hand, high slenderness, large openings and the presence of side chapels or lateral naves are the main factors influencing the seismic performance of the nave walls. Evident horizontal cracks can be observed at the base of the nave walls without side chapels and in correspondence with the top of the side chapels when they are present, indicating a possible global or partial overturning mechanism of the walls. – The results show that the seismic response of the bell tower is largely influenced by the interaction with the church: considerable diagonal cracks are clearly registered along the body of the bell tower in the connection regions with the church. Triumphal arches

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