Seismic assessment of two masonry Baroque churches damaged by the 2012 Emilia earthquake

Engineering Failure Analysis 79 (2017) 773–802

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Seismic assessment of two masonry Baroque churches damaged by the 2012 Emilia earthquake

MARK

Marco Valente⁎, Gaia Barbieri, Luigi Biolzi Department of Architecture, Built Environment and Construction Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

AR TI CLE I NF O

AB S T R A CT

Keywords: Masonry Baroque church Survey Experimental tests FE model Non-linear dynamic analysis

The structural assessment of historical buildings is a complex and articulated problem based on different activities. This paper describes the different phases of an integrated approach to obtain an accurate knowledge of the structural damage and seismic performance of two masonry Baroque churches located in Northern Italy and hit by the 2012 Emilia earthquake. The activities involved historical research, laser scanning survey, diagnostic investigation and structural analysis. The historical research, based on the analysis of written documents and historical maps, aimed at understanding previous structural problems and major changes in the structure over the centuries. The geometrical survey of the churches was performed by means of a laser scanner technique in order to very precisely determine the geometry of the two churches. Experimental tests and visual inspections allowed identifying location and extent of cracks, construction techniques, presence of voids and defects in structural masonry walls, as well as some characteristics of masonry. Based on this information, detailed three-dimensional finite element models of the two churches were developed and non-linear dynamic analyses were performed. The numerical simulations led to the determination of damage distribution and the identification of the most vulnerable elements, highlighting the main structural deficiencies of the churches when subjected to different levels of seismic actions.

1. Introduction The seismic sequence that occurred in Northern Italy in May–June 2012 caused extensive structural damage and several collapses of precast and masonry structures [1–8]. It involved a wide area including the provinces of Modena, Ferrara and Bologna in the Emilia-Romagna region, the Southern portion of the province of Mantua in Lombardia and some municipalities of the province of Rovigo in Veneto. Buildings belonging to the cultural heritage are mostly constituted by unreinforced masonry structures. Even if the sound structural design used by the ancient architects and builders allowed many historical structures to be preserved till nowadays [8] - even in particular conditions [9] - exceptional events involving significant horizontal actions may seriously jeopardize these structures [10]. The high seismic vulnerability of the historical heritage was clearly evident after the 2012 earthquake and the extensive damage found on the monumental buildings - such as churches, fortresses, palaces - was one of the most dramatic effects occurred, as documented, among the others, by [11–13]. In particular, churches were especially damaged for their intrinsic vulnerability to seismic actions, mainly related to particular features, such as large halls, single and double curvature structures such as arches, vaults and domes, high bell towers, presence of annexes [14–17]. For this reason, they have been extensively analyzed over time [18–24] and their preservation and strengthening against earthquakes is of relevant importance for historical, social and artistic

⁎

Corresponding author. E-mail address: [email protected] (M. Valente).

http://dx.doi.org/10.1016/j.engfailanal.2017.05.026 Received 6 September 2016; Received in revised form 2 May 2017; Accepted 3 May 2017 Available online 04 May 2017 1350-6307/ © 2017 Elsevier Ltd. All rights reserved.

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Fig. 1. General view of the two churches under study: (a) Sant'Antonio Abate church in Villa Pasquali; (b) San Erasmo and Agostino church in Governolo.

reasons [25–26]. The structural assessment of historical masonry churches is an articulated problem due to the complexity of the structures and requires a deep knowledge of the history, geometry, materials and structure [27–31]. This paper highlights the importance of an integrated approach in the evaluation of the seismic vulnerability of historical masonry churches damaged by earthquakes. The main purpose of the integrated use of the different methodologies was the improvement of the knowledge of the churches for recognizing structural problems, identifying vulnerable elements and defining future appropriate retrofitting solutions. Two masonry Baroque churches located in the province of Mantua are analyzed in this study: 1) Sant'Antonio Abate church in Villa Pasquali; 2) San Erasmo and Agostino church in Governolo. The two churches suffered a significant and different damage after the seismic events of May–June 2012. Fig. 1 shows a general view of the two churches under study. These buildings have been selected because they can be considered valuable examples of Baroque architecture in the province of Mantua. In particular, the importance of Sant'Antonio Abate church is due to the prestige of its architect, Antonio Galli da Bibiena, and to the peculiar system of masonry perforated vaults, which is an unicum in architectural history, as underlined also in a previous study presented by the Authors [32]. Nevertheless, until now the two churches have not been studied and one of the aims of this study is to give a valuable contribution to fill the gap of knowledge about these two churches. The two churches have been investigated according to a research plan consisting of different phases: (i) documentary and historical research; (ii) geometric survey; (iii) on-site investigations and experimental campaign; (iv) evaluation of crack patterns; (v) structural analysis. The careful application of complementary activities provides the most reliable information for a thorough knowledge of the structural damage and seismic vulnerability of the two churches. The historical research was devoted to the examination of old written documents, by focusing on the history of the churches and on their transformations over the centuries, which could be usefully combined with the data provided by architectural analysis. The geometric survey of the churches was performed by means of a Terrestrial Laser Scanner (TLS) technique and traditional methods. All the data collected during the on-site laser scanning technique were processed to obtain a three-dimensional model by assembling the point clouds surveyed from different station points. This part was fundamental to create a precise reconstruction of the geometry of the two churches. Experimental tests were carried out on masonry structures to qualify the masonry and to locate and quantify degraded or deteriorated areas. This experimental campaign was focused on the acquisition of the data needed for evaluating the structural safety of the two churches. During the field investigations carried out after the 2012 earthquake, the presence of extensive cracks and damage was evaluated for the two churches. The crack patterns and the masonry discontinuities were accurately classified and documented by pictures and schematic drawings. Moreover, the visual inspections led to the identification of materials and to the preliminary evaluation of the state of conservation and decay of the structures. Based on this available information, detailed three-dimensional finite element (FE) models of the two churches have been developed. An isotropic softening model has been adopted for masonry and the main mechanical properties of the materials have been reasonably defined through the results of the experimental tests. The results of the numerical simulations could help in the damage interpretation, highlighting the main structural deficiencies of the churches when subjected to different levels of seismic actions. In what follows, the main results and outcomes of the different phases are presented with the aim of providing useful information about the structural damage and the seismic performance of the two churches.

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2. Historical survey The first phase of the research focused on the analysis of historical documentation, structural changes over time and construction techniques of the two churches. 2.1. Sant'Antonio Abate church in Villa Pasquali The church of Sant'Antonio Abate is located in Villa Pasquali, near Sabbioneta, a small town in the province of Mantua in Lombardia region, about 30 km south-west of Mantua. The first documents proving the existence of a church devoted to Santi Sebastiano e Antonio Abate in Villa Pasquali date back to the second half of the XVI century. It is reported that the first church was smaller, located in the garden that actually is in front of the rectory and surrounded by the cemetery. The documents of the pastoral visit of the bishop in 1635 give a description of the ancient oratory. It pointed toward east and presented a main chapel, partly vaulted and partly covered by paneled ceiling; there was only one nave with a roof composed of wooden planks without arches and moldings; the floor was entirely in cotto tiles and there were also some vaulted chapels. This church had a sacristy and a bell tower, too. In 1647, a Po river flood caused the collapse of the ancient church, which was rebuilt in 1650, probably over the ruins of the previous one. However, due to the important demographic growth of the population, probably in 1764, the ex novo construction of the actual church of Sant'Antonio Abate began. The project was attributed to the internationally renowned architect and scenographer Antonio Galli Bibiena. This new and majestic church arose near the ancient building and it pointed toward north. An important archival document shows that on 19th November 1766, during the construction phase, the central dome suddenly collapsed. This document contains some important information concerning the dynamics of the collapse and the techniques and quality of the materials used. It is reported that no tie-rods or steel reinforcements were adopted, and mortar and clay bricks of all kinds were employed. These bricks surely consisted of reused elements (derived from the demolition of the ancient church or other buildings) or probably of new but undercooked ones with different sizes (perhaps produced by makeshift rudimentary furnaces built to reduce the construction time). For what concerns the dynamics of the collapse, it is recorded that the presbytery and the apse (which were generally the first parts built in holy buildings) stood up and the failure surely involved the central dome and the lateral chapels. There is no information about the involvement of the nave in the collapse. In addition, the damage of the roof of a private house, presumably located on the south-west side of the Bibiena's dome, is reported as a consequence of the dome failure. In Fig. 2 an extract of the Teresian cadastre (last decade of the XVIII century) is showed, with the indication of the private building damaged by the dome collapse (number 1789). The rehabilitation of the church restarted immediately, but only in 1784 the work finished. A document records that the new building was provided with appropriate tie-rods, in order to counteract the thrust of the arches and prevent a second collapse. However, probably due to the reconstruction costs, the church remained unfinished: one of the two bell towers was not built, the exterior remained in exposed brickwork and the interior decorations were completed only during the XIX century. After the construction, the stability of the church was threatened mainly by the not good properties of the soil. Owing to the presence of an aquifer 7.5 m deep under the floor of the church, starting from the third decade of the XX century, some foundation settlements and cracks were documented. In that regard, in the Thirties two tie-rods were inserted in correspondence with the apse. Successively, in the Sixties, some strengthening interventions were suggested at the foundation level to solve the particularly alarming situation of the north-east side of the church. The interventions provided for the execution of a sub-foundation system based

Fig. 2. Sant'Antonio Abate church: extract from the Teresian cadastre.

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Fig. 3. San Erasmo and Agostino church: extract from the Teresian cadastre.

on the insertion of reinforced concrete precast circular section piles (diameter equal to 25 cm), located under the existing foundations. This involved the demolition of a part of the existing foundations and the execution of reinforced concrete curbs. Some inspections performed in 2015 ascertained the execution of the intervention with some modifications. Interventions on the damaged walls were carried out too. Several interventions were performed at the wooden roof over time (in the first, second, third, seventh, ninth decades of the XX century) and other interventions involved the bell tower, the roof and the windows of the domes and the perforated vaults. 2.2. San Erasmo and Agostino church in Governolo The church of San Erasmo and Agostino is located in Governolo, a small town in the province of Mantua in Lombardia region, about 15 km south-east of Mantua. The existence of an ancient church devoted to San Erasmo Martire and built probably during the XV century is reported in some historical documents dating back to the XVI-XVIII century. It is recorded that the pre-existing church pointed toward east and was built on the area currently occupied by the rectory and the San Giovanni oratory. Only the bell tower and some frescos on the refectory walls derive from the ancient church. Probably due to the small size of the church, between 1756 and 1804, a new church devoted to San Erasmo and Agostino was built perpendicularly to the oldest one. In the Teresian cadastre drafted at the end of the XVIII century both the ancient and the current churches are reported, indicating that the construction of the new building was carried out before the demolition of the oldest one, see Fig. 3. In the sources of the parish and diocesan Archives it is possible to trace neither the builders nor the designer of the new church. On the contrary, it is known that it was built thanks to the spontaneous offerings of the worshipper and, for this reason, the construction proceeded slowly. Among the inventories of the Parish, it is reported that at the beginning of the XX century the church was subjected to some interventions. In particular: in 1904 the façade was restored; in 1907 the Altare Maggiore was demolished to achieve the raising of the presbytery, the railing was erected and two windows were opened in the choir; the presbytery and the choir were painted in the same year by Martinenghi, who created the actual decoration of the whole church in 1910. 3. Geometric survey and description of the churches under study The geometrical survey was performed after the 2012 Emilia earthquake and it is the result of an integration between an accurate 3D TLS survey and a direct survey. 3.1. Sant'Antonio Abate church in Villa Pasquali The current church is oriented toward North and presents a three-apses cross plan. The nave (14.95 × 10.55 m) is covered by a barrel vault (+ 16.4 m at the level of the intrados crown) with lunettes in correspondence with the upper windows. It is marked by arches, which divide and strengthen the barrel vault, and external massive buttresses. These elements articulate the space in the aisles formed by two rectangular 4 × 3.7 m chapels at each side and separated from the central nave by round arches. The chapels are connected to each other by a rectangular space and are covered by domes surmounted by lanterns. The connecting rooms are covered by cloister vaults. The central square space is dominated by a singular dome (11 m diameter) supported by a high cylindrical drum 776

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(3 m) and closed by a lantern. This structure rests on round arches supported by large pillars (inscribed in a rectangular section of approximately 2.9 × 2.7 m); spherical pendentives connect the square basis with the cylindrical drum. The central space is flanked by a pseudo-transept formed by two large semicircular chapels covered by semi-domes. It is closed by a presbytery (6.80 × 10.15 m), covered by a barrel vault with lunettes in correspondence with the upper windows, and a semicircular apse, covered by a semi-dome. A sacristy on the east side of the presbytery and a chapel on the west side rise two floors above ground and have wooden Palladian trusses and timber beams. In addition, the roof structure of the church is made up of wooden Palladian trusses and timber beams. An important system of steel tie-rods has to be noted: a primary one is in correspondence with all the arches of the principal nave and presbytery and the four arches supporting the central dome; the secondary one connects the external walls of the two chapels of the pseudo-transept, passing through the drum. The exterior of the church is entirely in exposed brickwork. The main façade is characterized by a symmetrical composition: the central part, with a height equal to 20.15 m, is rearward and composed of both straight and curved portions; the lateral parts present two bell towers with a square plan of 5.25 m side at the ground level. Only the bell tower on the right was completely realized for a height equal to 38.2 m. The central nave has a height of 17.55 m at the eaves line and 20.6 m at the ridge line; the aisles present a height of 9 m at the eaves line and 11 m at the ridge line. The external volume of the central dome is enclosed in a tiburio with a height of 29.3 m at the eaves line. The church is entirely a masonry structure with lime mortar and clay bricks, with reference both to the vertical structures and the horizontal curved ones (arches, vaults and domes). The thickness of the bearing walls varies from 50 cm to 110 cm; the vaults are characterized by flat laid bricks (in foglio arrangement, with a thickness of 6.5 cm), while the arches have vertically laid bricks (thickness of 70 cm). The main feature of the church is the outstanding structure of the central dome. It is made up of a sort of double shell system, but the two structures are not connected and the lantern closes only the outer shell. The inner dome consists of eight masonry ribs with vertically laid bricks closed in a central loop and connected by thin masonry perforated sails with an in foglio arrangement of the bricks. The outer dome consists of a continuum masonry structure that rises over the bottom shell. Between the two shells, in correspondence with the ribs of the bottom one, eight windows open onto the tiburio and filter light in the interior space of the church through the perforated bottom dome. The described singular double shell system is recalled in the semi-domes of the main lateral chapels and apse: they are constituted by inner semi-domes (with six ribs converging in a half-ring and five perforated panels) and by outer masonry semi-domes (which, in correspondence with the lateral chapels, are cut to leave a passage around the drum at the under-roof level). The lighting is done by slits opened between the two shells, in correspondence with the ribs of the bottom semi-domes, at the two sides of the external pilaster strips. The upper half-shell has openings that filter light from small portholes placed slightly below the eaves line. Fig. 4 shows the plan, the elevation views and the sections of the church. Fig. 5 shows the main façade and two inner views. Fig. 6 shows the central dome and the semi-domes at the intrados and at the extrados. 3.2. San Erasmo and Agostino church in Governolo The current church is oriented toward North and presents a Greek cross plan, with extensions in the counter-façade and presbytery areas. The nave (28 × 12 m) is covered by a barrel vault (+18.25 m at the level of the intrados crown) with lunettes in correspondence with the upper windows. The nave vault is marked by arches that articulate the space in the aisles, which - at each side of the central nave - consist of three minor rectangular chapels and one major chapel in correspondence with the transept arms. The minor chapels are covered by elliptical vaults and the major chapels are covered by masonry barrel vaults. The central space presents a rectangular plan (8.5 × 11.9 m) and it is dominated by a masonry lowered vault with a height at the crown equal to 18.5 m. This structure rests on round arches supported by large pillars (inscribed in a rectangular section of approximately 1.8x1m); pendentives connect the dome with the rectangular basis. The presbytery (4.4 × 9.3 m) is covered by a barrel vault with lunettes in correspondence with the upper windows and it is closed by a mixtilinear apse, covered by a sort of semi-dome. The roof structure of the church is made up of wooden Palladian trusses and timber beams. The church presents a system of steel tie-rods arranged in the transversal direction in correspondence with all the arches of the principal nave and presbytery. The exterior of the church is in exposed brickwork, with the exception of the main façade that is plastered. It is composed of two orders of pilasters with curved shapes at the edge and at the top. Only one opening is present in correspondence with the main entrance and the total height is equal to 26 m. The central nave has a height of 20 m at the eaves line and 23.65 m at the ridge line; the lateral naves present a height of 11.4 m at the eaves line and 13.25 m at the ridge line. The church is entirely a masonry structure with lime mortar and clay bricks. The thickness of the bearing walls is approximately constant and equal to 75 cm; the vaults are characterized by flat laid bricks (in foglio arrangement, with a thickness of 6.5 cm), while the arches have vertically laid bricks (thickness of 70 cm). Fig. 7 shows the plan, the elevation views and the sections of the church; Fig. 8 shows the main façade and two inner views. 4. Diagnostic survey A diagnostic campaign was carried out on both Sant'Antonio Abate church and San Erasmo and Agostino church in order to assess the masonry characteristics. In what follows, some results of the tests are reported. 777

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Fig. 4. Sant'Antonio Abate church: (a) plan; (b) elevation views; (c) sections.

4.1. Sant'Antonio Abate church The experimental investigations on Sant'Antonio Abate church consisted of the following tests: sonic tests on some masonry elements, Schmidt hammer rebound tests on mortar joints, laboratory tests on some bricks, tests on some tie-rods.

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Fig. 5. Sant'Antonio Abate church: (a) main façade; (b) inner view of the central nave toward the entrance; (c) inner view of the church toward the apse.

4.1.1. Sonic tests on masonry Three different structural elements, subjected to high stress distributions or to particular external conditions that can affect the conservation of the element itself, were tested in order to assess the masonry quality: i) the wall of the main façade; ii) the wall between the presbytery and the sacristy; iii) one of the pillars supporting the central dome. The locations of the tests are reported in Fig. 9a.

Fig. 6. Sant'Antonio Abate church: (a) central dome; (b) semi-dome of the lateral chapel at the intrados and at the extrados.

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Fig. 7. San Erasmo and Agostino church: (a) plan; (b) elevation views; (c) sections.

The sonic tests on the masonry of the main façade and on the wall between the presbytery and the sacristy were aimed at detecting a possible degradation due to external environment exposure and at assessing the quality of a structure surely raised before the collapse of the dome, respectively. On the main façade, the region between the main entrance and the side one was selected for the test. A vertical grid of acquisition 5 × 5, with a constant pitch between the points equal to 15 cm, was used. On the wall between the presbytery and the sacristy, a vertical grid of acquisition 6 × 5 was used. As shown in Fig. 9b and c, in both cases, the average speed was 1250 m/s, with minimum values close to 1000 m/s and maximum values up to 1600–1700 m/s. This result confirms the fair quality of masonry and the general absence of voids. Some remarks can be drawn from the results of the sonic tests on the 780

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Fig. 8. San Erasmo and Agostino church: (a) main façade; (b) inner view of the central nave toward the entrance; (c) inner view of the church toward the apse.

constructive techniques used to realize masonry. Fig. 9b shows that the minimum values of the velocities are registered in the central part of the wall and the maximum values are observed in correspondence with the edges: this result shows a particular care in the execution of the perimeter areas, where the brickwork is supposed to be characterized by a higher toothing of the materials. In Fig. 9c, the presence of speed peaks in points 14, 16, 21 may indicate a particular care in the organization of the masonry texture, with the arrangement of some header elements, arranged at more or less regular intervals and aimed at increasing the toothing of the elements inside the masonry. As regards the pillar, a traditional sonic test was conducted on a vertical section. A vertical grid of acquisition 6 × 4, with a constant pitch between the points equal to 15 cm, was used. As shown in Fig. 9d, the recorded speed shows that masonry is almost homogeneous through the section and no voids or internal discontinuities emerge. The average value of speed is 1300 m/s, with minimum values close to 1100 m/s in two points (value probably due to a partial detachment of the surface plaster). In addition, to assess the masonry quality of the entire pillar, a sort of simplified horizontal sonic tomography was performed [33]. In particular, two different pillar levels were analyzed: the base (at + 40 cm), where elements of higher size and density were supposed to be used, and an upper level (at +116 cm). Fig. 10 shows the maps of speeds in the investigated sections, considering a grid of acquisition constituted by 10 trajectories in the North-South direction and 13 trajectories in the East-West direction with a constant pitch between the points equal to 30 cm. As it is possible to observe, the distribution of the velocities is generally uniform in the whole section. The obtained average speeds vary from 1350 m/s to 2400 m/s and from 1200 m/s to 1750 m/s at the levels + 40 cm and +116 cm, respectively. Internal discontinuities and voids were not detected. Due to the important sizes of the pillar considered (3–4 m), the results of the simplified tomography tests prove that masonry is in a fair conservation state in terms of both homogeneity and connection between the masonry materials. 4.1.2. Schmidt hammer rebound test on mortar joints By a visual inspection of the consistence and color of the mortar joints along the external façades and the spaces under the roof, the Sant'Antonio Abate church mortar has been classified as an air lime mortar, which is common to many historical buildings located in the northern part of Italy. The joint thickness is quite variable and it is equal to 1 cm on average. The quality of the mortar joints was tested by means of the type L Schmidt hammer rebound test, using a reduced energy hammer version, suitable for use on bricks and mortar. The obtained average rebound number is 24, which identifies a rather poor quality mortar. 4.1.3. Laboratory tests on bricks Tables 1 and 2 report the results of the physical and mechanical tests performed at the Laboratory of Politecnico di Milano on some 4 × 4 × 4 cm, 4 × 4 × 12 cm and 4 × 4 × 16 cm specimens obtained from three representative clay bricks; in Fig. 11 the results of the mechanical tests are shown. On the basis of the data in Table 2, the following observations can be summarized: (i) from splitting tests on 4 × 4 × 4 cm specimens a mean tensile strength of 1.0–1.7 MPa was found; (ii) from bending tests a mean rupture modulus of 3.2–6.1 MPa and 3.2–5.4 MPa for 4 × 4 × 12 cm and 4 × 4 × 16 cm specimens, respectively, was recorded; (iii) from 781

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Fig. 9. Locations of the sonic tests in Sant'Antonio Abate church (a) and sonic tests results: ST1 (b), ST2 (c), ST3 (d).

compressive tests on 4 × 4 × 4 cm specimens a mean compression strength ranging between 10.6 MPa and 18.5 MPa was detected. In addition, to evaluate the bricks Young's modulus, uniaxial compressive tests were conducted on three overlapped cube specimens (4 × 4 × 12 × m), providing the middle cubes with DD1 strain transducers on all sides, see Fig. 12a. For three bricks, two specimens were tested up about 80% of the mean compressive strength obtained on the corresponding brick and successively all the cubes were tested up to failure in order to correlate the compressive strength and the elastic modulus, computed between 30% and 60% of the compressive strength. The results are reported in Table 3. In Fig. 12b and c the stress-strain curves for the three bricks are shown and the correlation between the elastic modulus and the compressive strength is illustrated. As it is possible to note, laboratory mechanical tests on bricks showed a large scattering of the results on both specimens coming from different bricks and specimens coming from the same element. This result confirms what has been documented in the historical survey regarding the heterogeneity and different origin of the clay bricks used and the problems of not-uniform cooking that, according to the historical survey, can be related to the use of rudimentary furnaces built to accelerate the construction of the church.

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Fig. 10. Distribution of the velocities in the pillar: (a) at + 40 cm; (b) at +116 cm.

4.1.4. Tie-rods tests This section provides the results of available dynamic tests performed to measure the first natural frequency (in the horizontal and vertical directions) and assess the tension force in two rectangular cross-section steel tie-rods, denoted as T1 (the tie-rod between the presbytery and the apse) and T2 (the tie-rod between the presbytery and the central nave). A summary of the main results with some geometrical characteristics of the tie-rods is reported in Table 4, where A is the tie-rod cross-section, L is the tie-rod length, f0 is the tie-rod natural frequency and F is the tension force in each tie-rod: the results confirm the transmission of the thrusts on the tie-rods.

4.2. San Erasmo and Agostino church in Governolo The experimental investigations on San Erasmo and Agostino church consisted of the following tests: sonic tests on some masonry elements and tests on the tie-rods.

4.2.1. Sonic tests on masonry Two masonry portions of the transversal arms of the church, where some cracks were detected, were tested in order to assess the masonry quality and the effects due to the presence of discontinuities. The locations of the tests are shown in Fig. 13a. A vertical grid of acquisition 8 × 5 and 8 × 3 was used for the western and eastern arms, respectively, while, in both the cases, a constant pitch between the points equal to 20 cm was used. As shown in Fig. 13b and c, in both the cases, an average speed around 1900–2000 m/s was acquired, confirming the overall good quality of masonry. In the western arm, maximum values up to 4000 m/s were found and some minimum values close to 650 m/s were registered not only close to the crack: a significant scattering of the velocities was recorded, showing a rather inhomogeneous masonry. In the eastern arm, the maximum values of velocity reach 2800 m/s and minimum values smaller than 1000 m/s were detected only across the crack, clearly revealing the presence of a deep discontinuity. Table 1 Physical tests results. Specimen #

Dimensions [mm]

Mass after dry [g]

Gross volume [mm3]

Voids volume [mm3]

Voids percentage [%]

Gross dry density [kg/m3]

M01-09 M01-01 M01-07 Mean value M02-07 M02-01 M02-06 Mean value M03-17 M03-02 M03-18 Mean value

40.8 × 41.0 × 162.2 40.7 × 41.0 × 120.9 41.1 × 41.2 × 121.1

450.6 331.3 335.9

271,328 201,746 205,061

4568 4246 4371

41.0 × 41.7 × 161.4 39.9 × 41.8 × 120.8 39.8 × 40.6 × 120.8

442.4 322.1 312.8

273,723 201,473 195,198

4923 4413 3678

40.5 × 40.1 × 161.4 40.9 × 40.5 × 123.6 41.1 × 40.4 × 120.2

432 337 329

262,122 204,737 199,585

4132 3307 2595

1.68 2.10 2.13 1.97 1.80 2.19 1.88 1.96 1.58 1.62 1.30 1.50

1661 1642 1638 1647 1616 1596 1602 1606 1650 1646 1651 1649

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Table 2 Mechanical tests results. Specimen #

Tensile str. (ftb) [MPa]

Specimen #

Modulus of rupture (fxb) [MPa]

Specimen #

Compr. str. (fb) [MPa]

M01-03a M01-14a

2.0 1.3

M01-01b M01-07b M01-09c

4.4 3.6 4.5

M01-02a M01-05a M01-08a M01-10a M01-11a M01-12a M01-13a

Mean values Stand. dev. M02-08a M02-14a

1.6 0.5 1.3 0.7

M02-01b M02-06b M02-07c

4.0b 0.6b 3.2 3.2 3.2

Mean values Stand. dev. M03-01a M03-03a M03-04a M03-05a M03-06a M03-07a

1.0 0.4 1.1 1.2 2.0 2.0 2.3 1.7

M03-02b M03-18b M03-17c

3.2b 0.0b 6.5 5.7 5.4

Mean values Stand. dev.

1.7 0.5

16.5 15.3 15.2 15.8 16.6 14.7 14.8 15.6 0.8 10.8 10.6 9.5 10.4 10.6 10.6 10.9 11.6 10.1 10.6 0.6 15.4 18.5 21.8 21.1 20.9 20.4 16.2 18.0 20.8 18.3 20.3 20.0 16.7 15.4 15.5 17.4 18.5 2.2

a b c

M02-02a M02-03a M02-04a M02-05a M02-09a M02-10a M02-11a M02-12a M02-13a

M03-06a M03-09a M03-10a M03-11a M03-12a M03-13a M03-14a M03-15a M03-16a M03-19a M03-20a M03-21a M03-22a M03-23a M03-24a M03-25a

6.1b 0.6b

4 × 4 × 4 cm specimens. 4 × 4 × 12 cm specimens. 4 × 4 × 16 cm specimens.

4.2.2. Tie-rods tests This section provides the results of available dynamic tests performed to measure the first natural frequency (in the horizontal and vertical directions) and assess the tension force in the six rectangular cross-section steel tie-rods of the church. The main results and some geometrical characteristics of the tie-rods are reported in Table 5, where the tie-rods are numbered from the tie-rod closest to the façade. The values of the tension force confirm the transmission of the thrusts on the tie-rods. 5. Damage survey A damage survey was conducted on the two churches after the 2012 earthquake. The results were reported in detail and commented with photos and schematic drawings showing the main crack patterns. 5.1. Sant'Antonio Abate church in Villa Pasquali Sant'Antonio Abate church in Villa Pasquali was only partially damaged by the 2012 earthquake. The main damage involved the following parts of the church:

• Façade. Two small vertical cracks have been detected between the main door of the church and the upper central window, Fig. 15a (photos 01–02). • Central dome. An important crack at the base of the drum has been observed. In addition, cracks have been registered at the

keystone of all the arches around the main dome, Fig. 15b (photos 03–04), revealing the typical collapse mechanism of the arches. 784

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Fig. 11. (a) Splitting test; (b) bending test; (c) compressive strength test on Sant'Antonio Abate church bricks.

An inspection of the continuum vaults of the particular double shell system was not possible.

• Covering structures of the central nave and presbytery. Two different types of cracks can be distinguished: (i) cross cracks located

• • •

in the connection regions between the vaults and the arches, mainly visible at the under roof level in the nave covering; (ii) diffused through cracks in the vaults, Fig. 15c (photos 05–06). The first type of cracks reveals a detachment between different structures characterized by several thicknesses and geometries and without a good connection among them; the second type of cracks is due to the high vulnerability of the in foglio vaults. In particular, the cracks in the first span of the nave present a southwest - north-east direction that can be related to the asymmetric configuration of the main façade and, in particular, to the presence of the adjacent bell tower. Covering structures of the aisles. Some cracks have been detected in the masonry domes covering the first minor chapel on the right side and the second minor chapel on the left side of the church, Fig. 15d (photos 07–08). Semi-domes of the apse and transept. Significant and diffused crack patterns have been observed in the continuum vaults of the particular double shell system. They are localized mainly close to the corners of the openings, Fig. 15e (photos 09–10). Longitudinal walls of the hall and presbytery. Cracks are located mainly close to the openings and, in particular, in correspondence with the first chapel on the right side, probably due to the presence of the bell tower, Fig. 15f (photo 11), and the second chapel on the left side. The presence of the organ and the choir in the presbytery zone influences the development of an 785

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Fig. 12. Uniaxial compressive test for the definition of the elastic modulus on Sant'Antonio Abate church bricks: (a) set-up; (b) stress-strain curves for three bricks analyzed; (c) correlation between elastic modulus and compressive strength.

important crack pattern, Fig. 15f (photo 12).

• Walls of the apse. Some vertical cracks starting from the upper corners of the two windows have been observed, Fig. 15g (photos 13–14). • Walls of the transept. Extended vertical cracks characterize all the four connections between the main chapels of the pseudo•

transept and the central space with the dome, Fig. 15h (photos 15–18). These cracks can be related to a probable overturning mechanism of the lateral chapels due to the thrust of the central dome and supporting arches. External walls. Cracks have been reported on the western façade in correspondence with some discontinuity points, represented by the corners of the openings, the upper molding and the presence of elements arranged with a different brickwork (i.e. the arches in correspondence with the two chapels of the aisles), Fig. 15i (photos 19–20). Figs. 14 and 15 summarize the crack patterns observed in Sant'Antonio Abate church.

Table 3 Uniaxial compressive test for the definition of the elastic modulus. Specimen #

Compr. str. (fb) [MPa]

σ30% [MPa]

ε30% –

σ60% [MPa]

ε60% –

Eb (30–60%) [MPa]

M01-05 M01-08 Mean value M02-03 M02-11 Mean value M03-11 M03-15 Mean value

15.3 15.2

4.6 4.6

0.00130 0.00129

9.2 9.1

0.00234 0.00244

10.6 10.9

3.2 3.3

0.00111 0.00087

6.4 6.6

0.00252 0.00217

21.1 18.0

6.3 5.4

0.00108 0.00146

12.6 10.8

0.00254 0.00312

4410 3970 4190 2260 2530 2400 4330 3250 3790

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Table 4 Summary of the results on two tie-rods in Sant'Antonio Abate church. Tie-rod

A [mm2]

L [m]

f0 a [Hz]

T1

40 × 80

8.88

T2

36 × 70

9.73

3.50 4.65 6.35 7.00

a

F [kN] (H) (V) (H) (V)

95.56 168.68 302.84 368.01

“H” indicates the natural frequency measured in the horizontal direction; “V” indicates the natural frequency measured in the vertical direction.

5.2. San Erasmo and Agostino church in Governolo San Erasmo and Agostino church in Governolo was severely damaged by the 2012 earthquake and it was classified among the “yellow code churches” by the Mantua Diocese. The main damage involved the following parts of the church:

• Façade. Outside, some horizontal cracks with plaster detachment have been registered in the upper part of the main façade and • •

• •

the keys of the tie-rods connecting the roof with the façade are visible, Fig. 17a (photo 01). Inside, a crack between the counterfaçade and the arch of the covering has been detected, Fig. 17a (photo 02). These cracks are probably due to the longitudinal oscillations of the nave with the consequent thrusts of the wooden roof on the façade. Central vault. Despite the presence of the tie-rods in the transversal direction, cracks have been detected at the keystone of each arch supporting the central vaults, Fig. 17b (photos 03–04). Covering structures of the central nave and presbytery. The damage of the covering structures concerns: - vaults: three different types of cracks can be distinguished: (i) cross cracks in the connection regions between the vaults and the arches, Fig. 17c (photos 05–07); (ii) diagonal cracks located mainly close to the connections with the lunettes, Fig. 17c (photos 05–06); longitudinal cracks in the first barrel vaults, Fig. 17c (photo 07). The first cracks reveal a detachment between different structures characterized by several thicknesses and geometries and without a good connection among them; the second and third ones are due to the high vulnerability of the vaults made up of clay bricks in foglio; - arches: all the arches supporting the barrel vaults show cracks at the keystone and - in the triumphal arches between the presbytery and the central nave - also at the imposts locations, Fig. 17c (photo 08). Despite the presence of a steel tie-rods against the thrusts caused by the roof, the observed cracks threaten the collapse of the arches. Covering structures of the aisles. Some diagonal cracks have been detected in the vaults covering the second chapels of both the left and the right aisles, Fig. 17d (photos 09–10). Longitudinal walls of the hall. Cracks have been reported in the keystone of all the arches separating the lateral chapels from the central nave, Fig. 17e (photo 11). In correspondence with the second chapels of both the left and the right aisles a diffused crack

Fig. 13. Locations of the sonic tests in San Erasmo and Agostino church (a) and sonic tests results: ST1 (b), ST2 (c).

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Table 5 Summary of the results on the tie-rods in San Erasmo and Agostino church. Tie-rod

A [mm2]

L [m]

f0 a [Hz]

F [kN]

T1

37 × 67

10.90

T2

36 × 67

10.70

T3

35 × 65

10.80

T4

33 × 67

10.67

T5

18 × 47

7.88

T6

35 × 67

7.80

3.50 (H) 4.30 (V) 5.60 (H) 6.70 (V) 4.00 (H) 4.70 (V) 3.90 (H) 4.67 (V) 9.90 (H) 10.80 (V) 6.30 (H) 8.00 (V)

113.58 171.44 272.62b 390.24b 133.65 184.53 120.53 172.82 162.08 192.89 178.26 287.44

a b

• •

•

“H” indicates the natural frequency measured in the horizontal direction; “V” indicates the natural frequency measured in the vertical direction. The tie-rod was in contact with the scaffolding used for the strengthening works: the datum is not reliable.

pattern has been detected in the portion of the wall above the arches between the naves, Fig. 17e (photo 12). Walls of the apse. Vertical cracks have been observed in the left side of the apse, Fig. 17f (photos 13–14). Walls of the transept. In the longitudinal walls of the two transept arms, the damage concerns: - two through vertical cracks originating from the corners of the openings and related to the presence of the connection region between masonries built in different periods, Fig. 17g (photo 15). Externally, in the western façade the crack follows the direction of the courses of the clay bricks, Fig. 17g (photo 16); - a diffused crack pattern characterizing the upper portion of masonry, Fig. 17g (photos 17–18). The most significant cracks are in correspondence with the corners of the openings and in the connection regions between the masonry vaults and the walls, revealing the detachment between the two elements with a possible overturning mechanism of the wall. External walls. In addition to the through cracks already discussed, some minor cracks can be found in correspondence with the molding, Fig. 17h (photo 19). A significant vertical crack can be observed in the western façade in correspondence with the third minor left chapel: it starts from the upper corner of the opening and extends to the eaves, Fig. 17h (photo 20). Figs. 16 and 17 summarize the crack patterns observed in San Erasmo and Agostino church.

6. Finite element models Detailed three-dimensional FE models of the two churches were created using the data obtained through the geometric survey. Fig. 18 shows the geometric and FE models of both the churches. It is worth mentioning that only the masonry structures were modeled, while the wooden covering structures were considered neither as mechanical constraint nor as dead load, due to their negligible weight. The discretization of both the churches consists of four nodes tetrahedral elements having an average size ranging between 40 cm and 70 cm. As a result, the numerical models of Sant'Antonio Abate church and San Erasmo and Agostino church amount of about 400,000 and 350,000 elements, respectively. Figs. 19 and 20 show the location of the steel tie-rods in Sant'Antonio Abate church and in San Erasmo and Agostino church, respectively, in accordance with what has been described in Section 3. In particular, the tie-rods were modeled as axial springs using axial connector elements with negligible compression stiffness and tension stiffness assumed equal to EA/L, where A is the tie-rod cross-section, E is the steel Young's modulus and L is the tie-rod length. The non-linear behavior of masonry is modeled through the plastic-damage concrete model presented by [34] and then modified by [35]. The same model was already used to describe the behavior of ancient masonry structures, see, among the others, [36–38]. The model is implemented in Abaqus as Concrete Damaged Plasticity model and is based on the assumption of a scalar isotropic damage with distinct damage parameters in tension and in compression. It is particularly suitable for applications in which the material exhibits damage, especially under loading-unloading conditions, and therefore for seismic analyses. A different inelastic behavior in tension and compression is taken into account, Fig. 21. In compression, the response is linear up to the yield stress σco: the post-elastic compression phase is described by an inelastic part with hardening up to the peak stress σcu and softening behavior. In tension, the response is linear up to the peak stress σto; then, it is described by a brittle behavior with a softening curve. The degradation of the elastic stiffness is given by two dimensionless variables, dt (tensile) and dc (compressive), that are functions of plastic strains. The damage variables in tension dt and compression dc are defined through the following standard relationships:

σt = (1 − dt ) E0 (εt − εtpl ) σc = (1 − d c ) E0 (εc − εcpl )

(1)

where σt(σc) is the uniaxial tensile (compressive) stress, E0 is the initial elastic modulus, εt(εc) is the uniaxial total strain in tension 788

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Fig. 14. Sant'Antonio Abate church damage survey: crack pattern.

(compression), εtpl(εcpl) is the equivalent plastic strain in tension (compression). To describe the multi-dimensional behavior in the inelastic range, masonry is assumed to obey a Drucker-Prager strength criterion with non-associated flow rule. A parameter Kc, applied to the analytical expression of the Drucker–Prager surface in the principal stress space, allows distorting the surface, making it more similar to that of the Mohr–Coulomb criterion, Fig. 22. The main parameters of the Concrete Damaged Plasticity model [39] are the following: i) the dilation angle ψ: angle due to a 789

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Fig. 15. Sant'Antonio Abate church damage survey: photographic documentation.

variation in volume of the material following the application of a shear force; ii) the strength ratio fb0/fc0: ratio between the biaxial and uniaxial compression strength; iii); the eccentricity ε: distance between the points of intersection with the p-axis of the cone and the hyperbola in the p-q plane, where p is the hydrostatic pressure stress and q is the Mises equivalent stress; iv) the Kc parameter: ratio between the second stress invariant on the tensile meridian and the one on the compressive meridian; v) the viscosity parameter: numerical parameter which allows reaching convergence in softening without affecting the accuracy of the results. In this study, the assumption of the same masonry material for both the models of the churches is adopted because the churches under study were built in the same period and belong to the same territorial area. Moreover, experimental tests and diagnostic survey indicated that both the churches are made of solid masonry bricks and lime mortar, and proved the good quality of masonry. According to the Italian recommendations for existing buildings and built heritage [29–31], the following mechanical properties have been assumed for a masonry made of clay bricks and 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 790

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Fig. 16. San Erasmo and Agostino church damage survey: crack pattern.

σto = 0.1 MPa, obtaining a ratio between the tensile and compressive strength equal to about 0.04. The values of the main parameters adopted in the non-linear dynamic simulations for masonry with the Concrete Damage Plasticity model are the following: i) the dilation angle ψ is equal to 10°, which seems reasonable for masonry subjected to moderateto-low levels of vertical compression and is in agreement with experimental evidences available in the literature [40]; ii) the strength ratio fb0/fc0 is equal to 1.16, in agreement with experimental results reported in [41]; iii) the eccentricity ε is assumed equal to 0.1, as suggested by the user's Guide [39]; iv) the Kc parameter is set equal to 0.666 to well approximate the Mohr-Coulomb failure criterion, as suggested by the user's Guide [39]; v) the viscosity parameter is set equal to 0.002 to avoid convergence problems related to 791

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Fig. 17. San Erasmo and Agostino church damage survey: photographic documentation.

softening and stiffness degradation. The damage variables in tension dt is defined to be equal to 0.95 in correspondence with a plastic strain of 0.005.

7. Modal analysis The main dynamic properties of the two churches under study were obtained by performing a preliminary eigen-frequency analysis on the three-dimensional FE models. Figs. 23 and 24 show the modal deformed shapes of the main vibration modes characterized by a participating mass ratio larger than about 3.6% (Sant'Antonio Abate church) and 6% (San Erasmo and Agostino church), and the corresponding periods.

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Fig. 18. Geometric and FE models of the two churches. (a) Sant'Antonio Abate church; (b) San Erasmo and Agostino church.

7.1. Sant'Antonio Abate church in Villa Pasquali The first and second modes involve the bell tower: the first mode (T = 0.646 s) exhibits a participating mass ratio of about 8% in the longitudinal direction, the second mode (T = 0.485 s) presents a participating mass ratio of about 10% in the transversal direction. The third mode (T = 0.359 s) concerns the lateral walls of the nave with a participating mass ratio of about 38% in the 793

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Fig. 19. Sant'Antonio Abate church: (a) location of steel tie rods; (b) internal view.

transversal direction. The fifth mode (T = 0.286 s) mainly involves the transept and the nave with a participating mass ratio of about 39% in the longitudinal direction. The tenth mode (T = 0.224 s) concerns mainly the transept and the presbytery with a participating mass ratio of about 5% in the transversal direction. The other modes present a participating mass ratio smaller than 5%. The first two hundred modes correspond to a total participating mass ratio of 91% and 90% in the longitudinal and transversal direction, respectively. 7.2. San Erasmo and Agostino church in Governolo The first mode (T = 0.469 s) involves mainly the lateral walls of the central nave and of the aisles with a participating mass ratio of about 54% in the transversal direction. The second (T = 0.435 s), third (T = 0.393 s) and fifth (T = 0.307 s) modes involve the tympanum of the façade and the nave with a participating mass ratio of about 10%, 9% and 27%, respectively, in the longitudinal direction. The sixth, eighth and thirteenth modes concern the main body of the church in the transversal directions with a participating mass ratio ranging between 6 and 9%, while the seventh mode involves the tympanum and the nave in the longitudinal direction with a participating mass ratio of about 14%. The first two hundred modes correspond to a total participating mass ratio of 89% in the longitudinal direction and 91% in the transversal direction. Fig. 25 shows the distribution of the participating mass ratios of the first one hundred modes in the longitudinal and transversal directions as a function of the corresponding vibration periods for both the churches. It can be noted that the main vibration modes involving a significant percentage of participating mass ratio provided by the modal analysis exhibit a period range equal to about 0.21–0.65 s for Sant'Antonio Abate church and 0.17–0.47 s for San Erasmo and Agostino church. Therefore, considering these periods values associated with code response spectra, such structures may experience high amplifications of the peak ground acceleration. These features could partially justify the damage to the churches caused by the seismic sequence. Moreover, the possible macroblocks that could cause collapse during a seismic event have been roughly identified by such a preliminary dynamic analysis. As regards Sant'Antonio Abate church, the critical elements are the bell tower, the lateral walls of the nave and the transept with the

Fig. 20. San Erasmo and Agostino church: (a) location of steel tie rods; (b) internal view.

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Fig. 21. Representation of the masonry constitutive behavior in (a) tension and (b) compression.

dome. The lateral walls of the central nave, the walls of the aisles and the tympanum of the façade are the most vulnerable elements of San Erasmo and Agostino church. It can be noted that, if the presence of the bell tower of Sant'Antonio Abate church is neglected, both the churches exhibit the main first mode with high participating mass ratio involving the lateral walls and the nave in the transversal direction. 8. Non-linear dynamic analyses Non-linear dynamic bidirectional analyses were performed to study the seismic response of the two churches. Artificial accelerograms generated by means of the Simqke software [42] in order to match the Eurocode 8 response spectrum (soil type B) were adopted in the numerical simulations. The same accelerograms were used for the analyses of the two churches: they exhibit equal peak acceleration in the two orthogonal directions and present a duration of 10 s because of the high computational demand required by the analyses. Fig. 26 shows the two accelerograms, denoted as Acc1 and Acc2, and the corresponding acceleration response spectra. The tensile damage contour plots, obtained at the end of the numerical simulations with different peak ground accelerations, are reported for the two churches under study. The main aims of the numerical simulations are: (i) to evaluate the damage distribution and identify the most vulnerable elements of the churches; (ii) to assess the evolution of damage for different peak ground accelerations; (iii) to qualitatively compare the results with field observations. 8.1. Sant'Antonio Abate church in Villa Pasquali - The results of the non-linear dynamic bidirectional analyses under PGA = 0.08 g are reported in Fig. 27 for Sant'Antonio Abate church. As already pointed out in the previous sections, the church was only partially damaged by the earthquake and it is worth mentioning that not all the results derived from the numerical simulations find a direct connection with what actually emerged from the on-site survey. In any case, a satisfactory agreement between the numerical results and field observations proves the reliability of the numerical model to identify the critical elements of the churches and the most likely failure mechanisms that may trigger under the seismic action expected in that region. The analysis shows that the most vulnerable elements are the nave and presbytery vaults, and the central dome: this result is reflected in the main outcomes derived from the on-site survey. In particular, the transversal sections of the model in correspondence with the transept present a considerable damage between the base of the

Fig. 22. ABAQUS modified Drucker–Prager strength domain.

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Mode 1 T=0.646 s PMR long. dir.=8.31% PMR trans. dir.=0.21%

Mode 2 T=0.485 s PMR long. dir.=0.66% PMR trans. dir.=10.39%

Mode 3 T=0.359 s PMR long. dir.=0.03% PMR trans. dir.=38.02%

Mode 5 T=0.286 s PMR long. dir.=39.17% PMR trans. dir.=0.02%

Mode 7 T=0.242 s PMR long. dir.=3.66% PMR trans. dir.=0.47%

Mode 10 T=0.224 s PMR long. dir.=2.13% PMR trans. dir.=5.12%

Mode 11 T=0.220 s PMR long. dir.=3.83% PMR trans. dir.=1.45%

Mode 13 T=0.211 s PMR long. dir.=3.92% PMR trans. dir.=0.10%

Fig. 23. Sant'Antonio Abate church: deformed shapes of the main vibration modes, corresponding periods and participating mass ratios.

drum and the spherical pendentives: it is pretty similar to what has been described in Section 5. Vertical damage is registered in the connection region between the façade and the longitudinal walls: it can be noted that this result is not consistent with the onsite survey. A clear damage may be observed in the façade close to the central window, confirming the field survey. The bell tower presents a visible damage in both the belfry and the connection region with the façade and it does not correspond to the actual situation: however, the cracks observed in the first span of the nave may be related to the unfavourable presence of the bell tower. An evident vertical damage may be identified in correspondence with the connections between the main chapels of the pseudotransept and the central space of the dome, as observed from both the axonometric views and the cross-sections: it is consistent with what has been highlighted in the direct damage survey. The apse walls exhibit an onset of damage near the corners of the openings, in agreement with the on-site survey. A slight damage spreading from the top of the perimeter walls is also observed, even if it is not located in the same position shown in Section 5. The small damage observed during the field survey at the top of the perimeter walls is mainly related to the presence of the wooden roof beams, which has not been considered in the numerical model. On the other side, some other cracks detected in Fig. 14 are related to some localized masonry disconnections and/or insertions, which have not been taken into account in the model. The non-linear dynamic analyses show that the maximum normalized displacements (horizontal displacement/height) are registered for the dome in both the longitudinal and transversal directions. - Fig. 28 shows the damage contour plots at the end of the non-linear dynamic analyses for higher peak ground accelerations

Mode 1 T=0.469 s PMR long. dir.=0.02% PMR trans. dir.=53.95%

Mode 2 T=0.435 s PMR long. dir.=9.94% PMR trans. dir.=0.01%

Mode 3 T=0.393 s PMR long. dir.=9.16% PMR trans. dir.=0.01%

Mode 5 T=0.307 s PMR long. dir.=27.69% PMR trans. dir.=0.01%

Mode 6 T=0.264 s PMR long. dir.=0.01% PMR trans. dir.=6.37%

Mode 7 T=0.249 s PMR long. dir.=14.25% PMR trans. dir.=0.01%

Mode 8 T=0.222 s PMR long. dir.=0.1% PMR trans. dir.=9.06%

Mode 13 T=0.173 s PMR long. dir.=0.1% PMR trans. dir.=7.04%

Fig. 24. San Erasmo and Agostino church: deformed shapes of the main vibration modes, corresponding periods and participating mass ratios.

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Fig. 25. Distribution of the first one hundred modes in the longitudinal and transversal directions for the two churches: modal participating mass ratios as a function of the corresponding vibration periods.

(PGA = 0.12 g and PGA = 0.17 g). In this case only the damage state of the vertical elements is investigated without considering the vaults and the central dome, that were already extensively damaged in the previous analysis under smaller peak ground acceleration. As expected, a general increase of damage is registered. In particular, the analyses show a widespread distribution of vertical damage in the walls. The damage registered near the connection region between the bell tower and the façade results more severe and a considerable enlargement of damage is observed in the bell tower, especially near the openings of the belfry. The maximum values of the normalized displacements are computed for the façade in the longitudinal direction and for the bell tower in the transversal direction. 8.2. San Erasmo and Agostino church in Governolo - The tensile damage distribution at the end of the non-linear dynamic bidirectional analysis with PGA = 0.08 g is shown in Fig. 29 for San Erasmo and Agostino church. Significant damage is concentrated mainly in the light structures of the covering, especially in the vaults of the nave and in the central dome, with a distribution that is comparable with the crack pattern observed during the field survey. The numerical results show a widespread damage in the upper lunettes of the transept arch, which is consistent with the real damage. It should be noted that the tympanum of the façade presents an onset of damage at the lateral edges. In this case, damage is less evident than that observed during the on-site survey. - Fig. 30 presents the damage contour plots at the end of the non-linear dynamic analyses for higher peak ground accelerations (PGA = 0.12 g and PGA = 0.17 g). The analysis under PGA = 0.12 g shows a more extensive damage in the perimeter walls and in the façade. In the perimeter walls damage concentrates near the openings and the connection regions between orthogonal vertical elements. The vertical damage observed in the perimeter walls are in a good agreement with the surveyed damage. The façade presents extensive damage at the base of the tympanum, as confirmed by field survey. Moreover, a significant damage is registered near the interlocking between the façade and the lateral walls of the nave. The analysis under PGA = 0.17 g highlights the critical state of the façade, indicating a probable collapse of the tympanum. The oscillations of the nave in the longitudinal direction result in a more extensive horizontal damage in the façade. Moreover, it is possible to observe a widespread and severe vertical damage in the connection region between the façade and the load-bearing walls of the nave, which could cause the overturning of the façade. An increase of vertical damage can be found in the perimeter walls, especially close to the openings and the contact corners between orthogonal walls. In addition, a considerable vertical damage spreading from the openings of the walls is now visible in the apse. The non-linear dynamic analyses show that the maximum normalized displacements (horizontal displacement/height) are registered for the façade in the longitudinal direction and for the lateral chapels and the walls of the central nave in the transversal direction.

Fig. 26. Accelerograms used in the non-linear dynamic analyses and corresponding response spectra.

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Fig. 27. Sant'Antonio Abate church: tensile damage contour plot at the end of the non-linear dynamic analysis (PGA = 0.08 g).

Finally, it is worth mentioning that the numerical analyses carried out on the two churches were very time consuming and computationally demanding due to the complexity of both the FE models and the non-linear dynamic analyses performed. Moreover, it can be noted that the results of the numerical simulations are generally consistent with the on-site survey for both the churches. Damage concentrates mainly in the vaults of the nave and in the central dome, even for low peak ground accelerations. The coverings are the most vulnerable parts of the two churches due to their reduced thickness. The façade of San Erasmo and Agostino church presents significant damage in the upper part due to the oscillations of the nave in the longitudinal direction. Moreover, the analyses reveal the presence of severe damage in the connection region between the façade and the perimeter longitudinal walls, indicating a possible overturning mechanism of the façade. The façade of Sant'Antonio Abate church exhibits considerable damage near the bell tower, which represents an irregularity for the church. Extensive damage at the base of the dome is also detected in the transept. Considerable damage is registered in the perimeter walls, close to the openings and to the contact corner between orthogonal walls, for both the churches. 9. Conclusions In this paper an accurate knowledge of two masonry Baroque churches is obtained by means of an integrated approach in order to assess their structural safety under seismic actions. The work involved historical research, laser scanning survey, visual inspections and structural survey for damage identification, experimental tests on masonry structures and extensive structural analyses. The mutual interchange of information and data derived from the integrated activities allowed achieving an accurate and reliable diagnosis of the constructions, which can be the basis for future restoration design. - The historical research was supported by the examination of existing literature and historical maps with particular reference to the plan of the church. The results of the detailed literature research are used to recognize and understand the main transformations and the previous structural problems of the churches over the centuries. - The survey of the churches was performed by means of a laser scanner technique and traditional methods in order to acquire the exact geometry of both the structures. - An accurate field survey provided clear evidence of the location and extent of cracks. A comprehensive pictures collection of the

Fig. 28. Sant'Antonio Abate church: tensile damage contour plots at the end of the non-linear dynamic analyses for different peak ground accelerations (PGA = 0.12 g and PGA = 0.17 g).

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Fig. 29. San Erasmo and Agostino church: tensile damage contour plots at the end of the non-linear dynamic analysis (PGA = 0.08 g).

main damage observed on-site was provided along with schematic drawings of crack patterns. Moreover, visual inspections defined the conservation state of masonry and the construction techniques of the masonry walls. - Experimental tests carried out on site and in laboratory provided a wide range of information on the masonry structures of the churches, location of voids, defects and deteriorated areas, masonry bearing capacities, presence of water and moisture. The results of the experimental tests and visual inspections allowed affirming that the masonry walls seem to be in a good condition and no significant voids were recognized in the masonry structures. - Detailed FE models were first used to identify the main dynamic characteristics, providing a preliminary explanation of the weaknesses of the churches; then, non-linear dynamic analyses were carried out to simulate the seismic response of the two churches for different peak ground accelerations. The results of the numerical analyses allowed detecting the damage distribution in the churches and identifying the most vulnerable elements, then providing a valuable picture of possible damage for different peak ground accelerations. - The results of such an integrated approach, based on available information derived from historical evolution, field investigations, experimental campaign and structural analyses, allowed gaining a deep insight into the seismic assessment of the two churches, useful to define future proper strengthening interventions and reduce their seismic vulnerability. 800

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Fig. 30. San Erasmo and Agostino church: tensile damage contour plots at the end of the non-linear dynamic analyses for different peak ground accelerations (PGA = 0.12 g and PGA = 0.17 g).

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