The vulnerability assessment of historical constructions against seismic actions, which is the necessary pre-requisite for their continuous protection, is of strategic importance considering the richness of the European and Italian architectural heritage [1, 2].

Churches are usually characterised by a high seismic vulnerability due to their structural and geometric configurations, heterogeneous and deteriorated materials. These structures have very large and high external walls without internal orthogonal walls: the space thus created is often covered by some thin vaults or thrusting arches. Furthermore, the structural portions (i.e., macro-elements) present an autonomous dynamic behavior mainly caused by the lack of a rigid intermediate horizontal diaphragm and a lack of walls interlocking. For this reason, historic churches often show the absence of box-like behavior.

In the last century, the seismic events stroked the historic cultural heritage severely and in particular, 49% of the damaged structures were of the churches highlighting their intrinsic vulnerability [3-7]. The recent earthquakes that hit Italy in August and October 2016 confirmed the high vulnerability of this type of structures. Tuned with this issue, it becomes necessary to take a census of the flaws in these monuments through the structural identification procedures and the evaluation of the related ground motion characteristics [8, 9].

These particular monumental buildings cannot be reduced to any standard structural scheme, and this makes it difficult to evaluate their seismic reliability. To overcome this problem, the macro-element approach was proposed a few years ago and has been repeatedly used to recognize the collapsed mechanisms in the different macro-elements of the church. The typical collapsing configurations are shown in Italian Guidelines for the Cultural Heritage [10].

The formation of Italian historical centres is often the result of uncontrolled constructive evolution; in particular, this complex configuration of the centres leads the structures to strongly interact with one another when they are subjected to seismic action [11-15]. As a matter of fact, several historic churches are not isolated from the urban context, but, adjacent buildings, usually named annexes (convents, sacristy, tower, minor constructions, etc.) built at the same time of the church or subsequently added as shown in other case studies [16, 17].

To determine the construction phases of the church and of the annexes, the first operation to perform is the historical analysis of the building evolution, crucial is also the study of the documentations of the structural interventions [18]. There could be, for example, interventions that made a structure more stiffened with respect to the other.

In addition to the churches that belong to the aggregates in the historic centres [19], the cases of incorporated churches, present in all over the world, are typical of different types of monasteries [20]. As a matter of fact, these amazing complex structures are the clearest and spread example of churches affected by the presence of the annexes. These other buildings can affect the church (in width and height) partially or fully incorporate it.

This paper presents the case study of Santa Maria della Carità church, firstly hit by L’Aquila earthquake (on April 6, 2009) with a magnitude M_W=6.3. After this seismic event, the church was closed because several cracks appeared; in particular the main vault and the triumphal arch were the elements mainly damaged, and for this reason, retrofitting was done in 2010. The church was successively re-closed, as a precaution, in August 2016 due to the Marche-Umbria-Lazio-Abruzzo earthquakes, that presented an epicentre nearest to the church with respect to L’Aquila earthquake. Up to this moment, the earthquake of October 30^th, 2016, with a magnitude of 6.1 M_L and 6.5 M_W, was the strongest event of the sequence which began with the earthquake of August 24^th of M_W=6.0 and also counted a quake of magnitude M_W=5.9 on October 26^th. At the present time, the church presents only some damages on the stuccos and on the vault of the presbytery, but the question of how important annex had engraved on the dynamic-behavior during the earthquake arise from the observation of an unsymmetrical damage survey.

In this work, the influence of all parameters involved in the local and global structural response was evaluated, such as the annex, the floors stiffness (diaphragm effect), and the retrofitting works done in 2010. To this purpose, the use of advanced numerical tools to perform nonlinear three-dimensional (3D) analyses is necessary in order to investigate all the possible failure mechanisms, both local and global, of a masonry structure, when this is subjected to an earthquake. The complexity of this type of analysis is required to validate the implemented model accurately; differently, a sensitivity analysis is mandatory to reduce the variability of the structural response, or better to avoid unclear situations from a structural point of view as much as possible.

The estimation of the beneficial effects of the retrofitting actions is even more accurate, since such evaluation is based on the difference between the seismic vulnerability of the structure in the current state and in the restored one [21, 22], both of them analysed with the same Finite Element Model (FEM). For these reasons, in this work, eight different FEMs were studied in order to establish the significant deficiencies of the structure, and to capture the influence of all parameters involved in the structural seismic response. Moreover, the estimation of the beneficial effects of the proposed restoration actions is even more accurate and can be helpful to the designers in other case studies.

The church of Santa Maria della Carità in Ascoli Piceno has a significant historical and architectural value: it is one of the most prominent examples of the Barocco age in Marche Region and contains a lot of valuable paintings of local artists. Moreover, it has also a social value for the city of Ascoli Piceno (see Fig. 1), as it is the only one opened to the devotees all day and night long [23].

Fig. (1). Panoramic view of Santa Maria della Carità in Ascoli Piceno, Marche, Centre of Italy.

Fig. (2). Santa Maria della Carità (Ascoli Piceno, Marche, Centre of Italy) evolution through ages.

The period of its construction is unknown, but the first proof of the existence of a little church, dating back to 1306, can be found in a parchment. On the Northside of the Church, there is an annex that was built in 1196 and that hosted a hospital; this hospital, in particular, was managed by the same fraternity that took care of the church. The old church was very different from the actual one (2a-2b). Later, from the early years of the 16^th century up to 1583, the building was partially demolished and re-built in various phases and in the same place, with the modification of the facade by raising the tympanum and by opening the doors on the front facade Fig. (2c). Further to this intervention, the nave was covered with a masonry vault and connected to the apse through a triumphal arch. Therefore, iconographical documents attest the presence of a pre-existing bell-tower on the opposite side by comparison to the actual one Figs. (2d-2e). So the triumphal arch was built during the 16^th century, but the actual bell-tower was built only at the end of the 17^th century, after almost one hundred years (Fig. 2f) [24, 25].

Between 1930 and 1932 Fig. (3) the south allay of the church was closed after the edification of a building that features a concrete frame that is totally disconnected to the church. This very building now hosts a bank.

Fig. (3). The church and the annex.

The church has a unique nave of 12.93 m wide, 23.15 m long and has a maximum height of 16.5 m; it ends with a rectangular apse of 6.55 m wide, 8.30 m long and with a height of 11.95 m Fig. (4). The apse is inside the sacristy, that counts two floors and has a maximum height of 15.90 m. In the sacristy, there is also the bell-tower: it has a square shape with side of 4.31 m and a maximum height of 27.80 m. The thickness of the walls ranges between 2.21 m (the piers of the nave) and 0.91 m (the walls of the nave). The bearing structure is made of stone masonry; the main façade, characterized by three front doors, has ornaments with classical patterns (columns, tympanum, cornice) and the masonry layer is constituted by white travertine; the nave is covered by a brick elliptic vault (like the apse zone) with lunettes that create small ornamented niches that are joint to the internal columns. Also in Santa Maria della Carità, like many other Italian churches, the triumphal arch separates the nave area from the apse. The arch is inserted in a masonry panel, with an elliptically shaped opening that is about 1.2 m thick.

Fig. (4). Actual planning and section of the church.

The church walls present different masonry materials (i.e., brick, travertine, stone, etc.); in the walls of the nave there are two distinct types of masonry in the elevation: this can be explained by the different age of edification. At a height of 11.08 m there is travertine block, and up there is an irregular stone.

In the past, the annex (on the North side of the church, Fig. (3) was a hospital, while now it hosts shops and a private house. The annex has a rectangular plant of 13.10 m of maximum width, 36.80 m length and a height of 12.40 m, and it features an arcade that is visible thanks to the presence of cross vaults in the centre zone. The period of its construction is unclear. Nowadays a lot of shops and private houses are contained in this part of the aggregated buildings.

After L’Aquila earthquake in 2009, the church was closed due to several cracks on the triumphal arch (Fig. 5) and on the vault of the nave. Other damages were visible in the non-structural elements inside the church. Moreover, a possible activation of the overturning mechanism of the facade was observed; in fact, there were cracks on the connection with the vault.

In order to put the church back into service as fast as possible, interventions were designed and executed in 2010. Concerning this issue, it becomes necessary to investigate the weakness of this monument through the analysis of the possible local collapse of the macro-element, the material and damage survey, the structural identification procedures and the subsoil–structure interaction.

To perform a local analysis, it is common to subdivide the structure into macro-elements, that consist of sub-structures characterised by their own seismic behavior, almost independent from the rest of the structure (façade, apse, dome, bell tower, etc.). For each macro-element, one or more damage modes and the associated collapse mechanisms can be identified. Such approach is mainly based on the a priori-assumption of a set of failure mechanisms, identified through the experience of previous seismic events. They are reported for example in [10], and they represent the most diffused partial collapses occurring in real churches/monasteries which fell after recent earthquakes.

Fig. (5). Visible damage after L’Aquila earthquake (2009) in the triumphal arch area (a) in the façade area (b).

For the Santa Maria della Carità church, the linear kinematic procedure was implemented in order to analyse the possible activation chosen from the twenty-eight failure mechanisms contained in [10]. Actually, the following overturning mechanisms depicted in Fig. (6), can be activated:

Fig. (6). Main mechanisms analysed for Santa Maria della Carità church.

• Out-of-plane overturning mechanism of the facade;
• Out-of-plane overturning mechanism of the wall of the nave;
• In-plane damage mechanism of the vault of the nave.

The acceleration of the activation of the mechanism has been computed by following the Italian standards [26, 27]. To prevent the activation of these mechanisms, some interventions have been designed.

The masonry was not completely visible, and for this reason, a lot of surveys were performed (Fig. 7), in order to accurately recognize the masonry type and to confirm the wall thickness. To complete some missing data from in-situ tests, the Italian Codes for existing masonry buildings [26, 27] have been consulted.

Fig. (7). Material characterisation of the Santa Maria della Carità church.

The low level of knowledge obtained (KL1) for this case study has led to assume the highest confidence factor (FC) equal to 1.35, and so the compression strength was reduced by this factor. The masonry tensile strength was considered equal to 10% of the compressive strength [20]. The main mechanical characteristics used in the sequel, are shown in Table 1.

3.1. The 2010 Retrofitting Intervention

The extent and nature of the actions must then be balanced between the conflicting requirements of achieving a newly required safety level and regarding the original conception and historical value. However, it must be noticed that in some cases, the strict application of this approach may lead to erroneously accept higher risks to avoid or limit works that are recommended from a structural point of view, see e.g [28]. The philosophy followed in the restoration process tends to prefer measures that comply with the concepts of reversibility, recognisability, minimum impact and compatibility of the intervention with the existing structure, considering the possibility that in the future, a better intervention could be carried out, as a result of more accurate studies or the evolution of technologies.

The results of the limit analysis of the macro-elements showed that at that moment, the primary structural deficiencies were: (1) the lack of connection of the front façade to the rest of the structure and (2) the high-stress level of the upper part of the nave masonry walls subjected to the static load of the central vault. Therefore, the restoration actions should affect the entire structure of the church to restore a “box-like behavior”, that is able to transfer the horizontal actions to all the bearing walls and should consider the possibility of increasing the material resistance in the most stressed regions. However, to pursue this latter effect, it would be necessary to implement actions which are in contrast with the concept of reversibility of the intervention and therefore, care is needed at this stage.

Generally, a rigid diaphragm behavior can be achieved by operating both at the intrados (e.g., with metal rods, steel elements, and other reinforcement systems) or at the extrados by implementing a timber panel over and/or substituting the original one, inserting metal rods into the top light concrete layer or metal plates - to be fixed to the wood beams - or adding a new reinforced concrete thin slab securely connected to the walls. Interventions at the extrados present the advantage of being less invasive, since they are hidden in the floor and do not alter the architectural identity of the building. In order not to affect the view of the time, it was decided not to insert steel chains in the intrados.

Fig. (8). The reticular system for the retrofitting of Santa Maria della Carità: a 3D view.

Hence, it has been suggested that the roof slabs should be stiffened in their plane in order to be considered as rigid diaphragms and new timber beams, replacing the deteriorated existing ones, should be anchored to the bearing walls. The interventions consisted of making a reticular beam system on the plan of a pitched roof. The reticular beam system is composed of metal bands that act as strings, wood stands that serve as rafter, ridgepole, and framework curb, which serve respectively as (higher) tense and (lower) compressed truss (Fig. 8).

In its current state, the connections to the vertical structural elements rely exclusively on friction between them. Such connection improvement was achieved using a further reticular system (Fig. 8) fixed with bars to the top of the nave walls - in order to limit the out-of-plane movements and featuring anchored plates - of various types - directly anchored to the nave walls. Other connections should also be established between the beams and the façade; the beams have a support constraint so as to eliminate the horizontal force on the façade, force that acts only as a return to rollover. In a study [23], structural details and pictures of the realised retrofitting intervention are reported.

The retrofitting system is able to (i) contrast the out-of-plan collapse of façade, (ii) contrast out-of-plan collapse of the tympanum on the triumph arch, (iii) balance the thrust of the vault on the walls nave, (iv) stiffen the gabled roof. The post intervention is evaluated, again, with the linear kinematic analysis. This intervention permits to verify all the mechanisms. In order to limit the cracking on the nave vault, and on the triumph arch, carbon FRP strips were inserted to the extrados of these elements.

It is necessary, however, to consider that this approach presents the risk of exceeding the estimation of the collapsing horizontal acceleration. Furthermore, with this method it is impossible to quantify the effect of the retrofitting on the global response. For this reason, it is indispensable to contemplate additional methods of analysis, for example the 3D Finite Element Analysis procedure that has been recently applied to many churches, tower and monasteries in seismic areas [2, 29, 30].

Fig. (9). Cracking after the seismic events of 2016 in Santa Maria della Carità: stuccos on the triumphal arch (a), stuccos on the walls of the main naves (b), horizontal micro-cracking on the lunette (c), micro-cracking on the vault of the presbytery (d).

After the seismic event in October 30^th, only a few cracks have appeared on the stuccos of the triumphal arch and of the walls of the nave (Fig. 9a and 9b), confirming that the main mechanisms (as pointed out in chapter 3) did not activate as in the previous seismic event in 2009, consequently, this represents the first in-situ test of the intervention. The recurring observable damage (see Figs. 5b and 9c) between the two earthquakes is the horizontal cracking on the lunette near the façade. Differently, new micro-cracking appears on the vault of the presbytery near the triumphal arch (Fig. 9d).

However, to have a better perception of the influence of the retrofitting of the roof, a global analysis should be done with and without the annex, and at varying of the floor stiffness.

In this work, the nonlinear damage behavior of the masonry is considered within a continuum mechanics theory, based on a smeared crack approach [31, 32] where the cracks are not described one by one but are continuously spread within the body and affect (reduce) the medium stiffness instead.

The smeared crack concept itself offers a variety of possibilities, ranging from fixed single to fixed multi-directional and rotating crack approaches. Here, the distinction lies in the orientation of the crack, which is either kept constant, updated in a stepwise manner or updated continuously [33]. The smeared crack models are practice-oriented, due to the limited data required [34]. For example, in the context of macro-modelling, [35] adopted a smeared crack model for the simulation of brick masonry and adobe walls, and [36] used the isotropic rotating crack model to simulate panels with vertically perforated clay units and various types of head and bed joints.

The panels were modelled with solid tetrahedron elements with 4 nodes [37], and optimised regular mesh (see Fig. 10) was used for discretization. The nonlinear behavior of the masonry panels of the historical complex is represented by a Total Strain Crack Model based on fixed stress–strain law concepts available in Midas FEA^©. In this way, the cracks are fixed in the direction of the principal strain vectors that remain unchanged during the loading of the structure.

Fig. (10). Finite element model of the complex of Santa Maria della Carità church in Ascoli Piceno.

The compression behavior of the masonry was modelled by a constitutive law comprising a parabolic hardening rule and a parabolic softening branch after the peak of resistance Fig. (11a); the tension behavior was characterised by a linear hardening branch followed by a nonlinear softening branch Fig. (11b). The fracture energies in compression (G_c) and tension (G_f) are reported in Table 1, and h is the mean dimension of the mesh Fig. (10).

Fig. (11). Stress–strain constitutive relations used for the simulation: a) masonry uniaxial compression; b) masonry uniaxial tension.

The shear retention factor (β) gives the shear stiffness after cracking, which can be a constant (low) value between 0 and 1, or a value depending on the crack opening. Here, a constant value equal to 0.05 was adopted like requested in [31, 38].

4.1. Finite Element Model For the Global Response

Numerical Models (NMs) built to reproduce the geometry of the structures, focusing on the variations in the wall thickness, on geometrical and structural irregularities, and on wall connections [39]. The brick-vault has been connected to the walls nave by fixed constraints since it has been built at the same time. Finally, the major openings in the buildings have been reproduced. Two are the main models used: a model pre-intervention and post intervention model.

The construction of the undamaged FE model of the church and the annex (C+A) was fundamental to study the dynamic and seismic behavior. As previously said, the annex could have been built later than the church; this hypothesis is taken into consideration in an additional FE model (C) with the inclusion of a complete separation between the church and the annex. In fact, with a complete separation, it is possible to face one of the main problems of the historic masonry buildings, that is the materials deterioration - particularly of the mortars - that can affect the real partial interaction. The reason for the degradation of this part is often due to the low quality of the conservation and other exceptional events or new additional loads.

Furthermore, a proper assumption on the diaphragm stiffness may significantly affect the overall response [20]. In fact, in the limit case of “infinitely” flexible floors, there would be no load transfer from heavily damaged walls to still efficient structural elements. On the contrary, in the other limit case of floors assumed as “infinitely” stiff, this contribution could be overestimated. Although this represents a crucial feature to be considered, the floor behavior in 3D modelling is frequently assumed (with a rough approximation) as completely rigid. This hypothesis may be unrealistic in case of existing buildings (e.g. historical masonry structures), where various ancient constructive technologies (i.e. timber floors and roofs, structural brick or stone vaults) had been used for floor and roofing systems; moreover, this is also a major issue in new masonry buildings with wooden floors and roofs.

To analyse the effect of the diaphragm stiffness on the global capacity, two different situations were then considered: (i) all floors deformable (C+A+D) and (A+D), and (ii) all floors rigid in their plane (C+A+R) and (A+R). To have a complete characterisation of the case study, a full implement of the strengthening provision was done, finally obtaining:

Fig. (12). Numerical Models: a) the church and the annex with flexible floors in a pre-intervention phase; b) the church and the annex with rigid floors in a pre-intervention phase; c) only the church with flexible floor in a pre-intervention phase; d) only the church with rigid floor in a pre-intervention phase; e) church and annex with flexible floors in a post-intervention phase; f) church and annex with rigid floors in a post-intervention phase; g) only the church with flexible floor in a post-intervention phase; h) only the church with rigid floor in a pre-intervention phase.

• The Church and the Annex with Deformable floors Without Intervention (C+A+D+Wi) – Fig. (12a).
• The Church and the Annex with Rigid floors Without Intervention (C+A+R+Wi) – Fig. (12b).
• The Church with Deformable floors Without Intervention (C+D+Wi) – Fig. (12c).
• The Church with Rigid floors Without Intervention (C+R+Wi) – Fig. (12d).
• The Church and the Annex with Deformable floors Post-Intervention (C+A+D+P) – Fig. (12e)
• The Church and the Annex with Rigid floors Post-Intervention (C+A+R+P) – Fig. (12f)
• The Church with Deformable floors Post-Intervention (C+D+P) – Fig. (12g)
• The Church with Rigid floors Post-intervention (C+R+P) – Fig. (12h)

After meshing, the final 3D NMs are shown in Fig. (12) and the main characteristics of the mesh regarding nodes, the number of solid elements and the degrees of freedom (d.o.f.) are shown in Table 2.

Table 2. Key features of the meshed solids.

	Nodes	Solid elements	Degree of freedom
Model 1	21819	74623	62970
Model 2	21866	74623	60456
Model 3	16672	58698	48450
Model 4	16719	58698	47925
Model 5	22236	75557	64347
Model 6	22282	75557	61821
Model 7	17136	59632	49827
Model 8	17136	59632	49284

Nonlinear static analyses (i.e., pushover) are shown in the next sections and have been performed assuming a rigid ground foundation (fixed base model), and the following parameters have been adopted during the analyses:

• Maximum number of iterations of load increment: 200;
• Maximum analysis number of sub-steps: 1500;
• Minimum analysis number of sub-steps: 5;
• Initial load factor 0.01.

The nonlinear system of the equations has been solved by an incremental nonlinear static analysis with the Arc -length iteration procedure and the Initial Stiffness Method: an energy norm with a tolerance of 10^-2 was required. To simulate the hypothesis of rigid floors, rigid links have been inserted in correspondence of the floors.

To summarize the seismic performances of the complex, according to the NMs used in this work, the Seismic Risk Index I_R is used:

(1)

It might be worthy to remind that I_R≥1 corresponds to a safe structure, and I_R<1 corresponds to an unsafe building on the standard of the new constructions [44]. The T_R,C in Eq. (1) is the return time of the seismic action that produces, for the requested SLSD, the non-respect of the inequalities d*_max≤d*_u (d*_max is the demand, and d*_u is the capacity in the equivalent s.d.o.f. system [45] or 3<q*<6), while T_R,D is reported in Sect. 5.2. The use of the I_R gives the possibility to work, indifferently, with PGA (International country) or T_R (Italy). In fact, the exponent 0.41 in (1) is tuned to have the same scale of seismic vulnerability with I_R calculated in terms of PGA [46]. Fig. (30) shows how I_R differs at the varying of the control points. For all calculated I_R, the intrinsic ductility q* is <3.

Fig. (29). Pushover: uniform load -Y-Direction. Cracking patterns for (C+D+Wi), (C+R+Wi), (C+D+P) and (C+R+P) NMs.

Fig. (30). Seismic Risk Index for the eight MNs at varying of the control points.

From Fig. (30) the continuous line represents the ante-intervention condition while the dashed line the post-intervention one. The main difference consists in the fact that with the retrofitting of the roof, all the indexes are bigger than the previous condition. Furthermore, another consideration is related to the presence of rigid floors, which is not always associated with major I_R, as in this case. In fact, not spread rigid floors (see Fig. 12) do not permit the collaboration between the walls, and the damages accumulate in areas where this process is obviously minimum.

In order to consider the variability of the vulnerability with the annex, it is possible to say that for the model (C+A+D+Wi) I_R varies from a minimum of 0.32 to a maximum of 0.38, with an average value of 0.342 and a standard deviation of 0.027; for the Model (C+A+D+P) the index varies from a minimum of 0.32 to a maximum of 0.46, with an average value of 0.39 and a standard deviation of 0.058. This means that an increment of +13% in terms of seismic risk index is obtained with the retrofitting of the roof. This is due to the presence of a better “box-like behavior” than the diaphragm stiffness effect of the church roof, which gives a global better behaviour with respect to the perfect deformable floors.

Similarly, for the model (C+A+R+Wi) the I_R varies from a minimum of 0.21 and a maximum of 0.32, with an average value of 0.25 and standard deviation of 0.046; for the Model (C+A+R+P) the index varies from a minimum of 0.24 and a maximum of 0.38, with an average value of 0.296 and standard deviation 0.055. This allows to draw some considerations in presence of rigid floors and roof retrofitting noticing, in first place, that the I_R has an increment of about +16%, that is bigger than the previous case with deformable floors. Even if the percentage of improvement is greater in the presence of rigid floors, the situation of increased seismic security is given in the presence of deformable floors, where an increment of +24% comparing I_R of (C+A+D+P) and (C+A+R+P) is available. For this reason, it is important to stress out the fact that the behaviour is always nonlinear but, due to the low ductility of the material, the entire complex has a brittle-like behaviour in presence of rigid floors. Furthermore, in this case, the nonlinear analyses end as a very concentrated damage is reached in some parts of the complex, in particular on the main vault, and on the tower as in the case of (C+A+R+P) Figs. (28, 29).

Otherwise, considering the complete detachment of the annex, the different situation should be considered. In (C+D+Wi) the index varies from a minimum of 0.27 and a maximum of 0.36, with an average value of 0.32 and a standard deviation of 0.037; for Model (C+D+P) the index varies from a minimum of 0.33 and a maximum of 0.38, with an average value of 0.35 and standard deviation of 0.022. This means that in absence of rigid floors the retrofitting intervention gives to the structure an increment in terms of seismic resistance of about +10%. For the Model (C+R+Wi) the I_R varies from a minimum of 0.24 and a maximum of 0.34, with an average value of 0.28 and standard deviation of 0.042; for the model (C+R+P) the index varies from a minimum of 0.30 and a maximum of 0.34, with an average value of 0.32 and standard deviation 0.016. Again, the complex with rigid floors and retrofitting intervention has an increment of about +13% in terms of seismic resistance, major than the condition with deformable floors. As in the previous case with the annex, comparing the deformable and rigid cases, the I_R is less in the second case due to the presence of a concentrate cracking near the triumphal arch which gives unexpected numerical problems.

The variability of the obtained I_R at the varying of the control points suggests the importance of considering the appropriate control point. This highlights an inherent drawback of the pushover analysis for those structures where constant rigid floors are not present in all elevations.

As can be seen, the presence of the annex increases the I_R in the case of deformable floors, both with and without interventions. Differently, the presence of rigid floors and annex concentrates the damage in a little area, giving a worse seismic behavior.

The case study of “Santa Maria della Carità” church in Ascoli Piceno, hit by the L’Aquila earthquake in 2009, was useful to highlight the influence of the annexes in the structural global behaviour of churches. The observation of the damage scenario of the past (L’Aquila) and of the more actual (Marche-Abruzzo-Umbria-Lazio, 2016) earthquakes suggested this research which, with the support of a consciously restricted NMs, allows the presentation of some results about a very complex item.

The 3D nonlinear solid NMs have been used to evaluate the seismic capacity of the complex using a series of pushover analyses performed by varying the interactions among the church and the annex, by changing the stiffness of the floors and applying the effect of a past retrofitting intervention that were designed after L’Aquila earthquake. Eight different structural configurations have been considered, and their seismic risk indexes have been evaluated. These analyses provided important information on the influence of the aggregate on the seismic safety of the complex.

The influence – in terms of seismic risk index – of the choice of the control point has been analysed too, and it has been found that due to the extension of the complex, it affects the seismic response. The seismic analyses have been helpful to obtain a screening of the most vulnerable elements of the structural complex, which are the eccentric tower and the main vault. This information can be used to design local and global retrofitting works.

This paper also highlights that a good knowledge of the structure is essential to understand the seismic behaviour. Indeed, the lack of knowledge of certain parameters, such as adjacent buildings and the type of floors stiffness, can distort the response of the structure and therefore, requires more sophisticated procedures that go against the principle of minimum intervention.