free height of from the grand staircase in front of the church. By subdividing the church façade, by following the geometry of the openings, it is possible to identify ...
Assessment of seismic vulnerability of a Basilica: modeling and analysis of the façade macro-element Giovanni Castellazzi, Angelo Di Tommaso DICAM Department – University of Bologna. Viale Risorgimento 2, 40136 Bologna.
Keywords: monumental building, seismic vulnerability, dynamic analysis, limit analysis ABSTRACT This paper deals with a computational strategy based on Finite Element non-linear analysis and limit (kinematic) analysis applied to a monumental religious structure. The analyses are aimed at providing useful information to design adequate seismic structural improvements. When seismic, horizontal, loads are applied to a model of complex aggregates of masonry structural elements, the seismic response presents often some uncertainties.. Here the structural analysis is carried out for a church structure through the estimate of the collapse multipliers of each characteristic portion of the structure. Particular attention is posed into the study of façade of the church. The results herein obtained can provide useful indications on the seismic behavior and vulnerability of this important class of monumental buildings.
1
INTRODUCTION
Recent seismic events have demonstrated again how churches reach damage when undergoing earthquake motions. The high seismic vulnerability of historic churches is due basically to two main reasons: geometry proportions and building materials properties. In fact, designed to withstand vertical load, churches in general present slender walls, irregular stone texture and weak or non-existent connections among structural elements. These last issues is associated to the fact that often churches are considered just as a place of worship or monumental construction, focusing the attention on the artistic details of the church, such as: paintings, plasters conservation, stone or material appearance and so on. In this regards the only preservations action considered during conservation processes are addressed to only these last aspects often neglecting the structural needs in seismic prone areas. This is unfortunately supported by several case histories, as several are churches damaged or collapsed after earthquake events (sometimes also immediately after their renovations). Among all cases it is worthwhile to remember the partial
collapse of the Church of Santiago in Lorca, Spain in 2011; the collapse of the Catholic Cathedral of Port au Prince in Haiti in 2010 (right after its total restoration); the partial collapse of S. Pietro di Coppito in 2009 after consistent work of conservation. Addressing to this we can refer to such kind of restoration process calling those “cosmetic” restoration, since nothing is done but only preservation of the image of the building. A cosmetic conservation work (restoration) in general neglects the structural improving since often the strengthening of such kind of buildings cannot be done without changing or touching the original structure. In fact church structures in general possess some common weak points. Among these the lack of horizontal structures is the principal intrinsic weakness. These structural aspects added to poor material performance, especially in tensile stress mode, establish the reasons of most of the structural collapses when excited by seismic (horizontal) forces. Nevertheless this weakness allows to a better interpretation of the collapse mechanism since more evident are the effects of this actions by
cataloguing each collapse, damage and so mechanism, some standard behaviour can be traced for this wide class of buildings. For these reasons the prediction of the structural response of such monumental buildings must be considered peculiar as pointed out in (DIR.P.C.M. 2011). Dealing with masonry structures several are the approaches for structural predictions well established among practitioners: by using linear dynamic or non-linear dynamic analysis, by inspecting macro-elements or the interaction among macro-elements (intra-macro-elements analysis), by computing the maximum admissible displacement of some control points. Despite their efficiency, these approaches are often not all applicable to the wide scenario offered by monumental historical constructions. For instance the peculiarity of churches structures could not be completely understood by inspecting the results of linear dynamic analysis. In this case the lack of information can be completed by other complementary information derived from nonlinear dynamic analysis plus limit analysis (Castellazzi 2011), (De Luca 2004), (Mele 2003). Basically this approach aims at finding a reliable failure mechanism using a refined 3D structural model and then the limit (kinematic) analysis to validate this mechanism. This paper aims at providing a contribution to validation of this numerical procedure to church structures (basilica shape), applying it to a case of study, the church in S.Nicandro Garganico (south Italy) 1.1
Overview
The paper is organized as follows. In Section 1 the church structure is described, highlighting the conservation state through a detailed analysis of the cracking pattern. In Section 2 the case study is presented through the analysis of the conservation state. In Section 3 the analysis method adopted is briefly described. Section 4 presents a preliminary investigation of the structure through a linear dynamic analysis of the whole structure. In Section 5 a detailed investigation of the façade macro-element is presented. Some conclusive remarks end the paper. 2
Episcopal centre. The current layout is the result of several renovations. Among these the main one has been done around the year 1693 following the 1688’s earthquake, when lateral small buildings and chapels were probably added to the original project. Today the church presents a basilica layout, and measure about 30m, and 25m of length and width respectively. Lateral (party) walls are 11.0m height. The façade is 14.0m height. In general walls of monumental buildings such as churches are often of massive thickness with few and comparatively small openings: here the thickness, approximately, varies between 0.80 m along the main nave walls and 1.00 m at the apse, see Figure 1.
THE CASE STUDY: THE CHURCH OF SAN NICANDRO
The Chiesa Madre Santa Maria del Borgo, is located in San Nicandro Garganico (Foggia, Italy) and is the main church of the city. Built between 1573 and 1580 became quickly an important
Figure 1. Chiesa Madre Santa Maria del Borgo, San Nicandro (Italy): the plan layout is shown along with the illustration of the cracking pattern: H Horizontal crack (red line); V vertical crack (blue line).
These walls are made by local tuff stone (tufo) with different units aggregation schemes: opus incertum, opus mixtum and opus quadratum, with double leaves, filled with rubble of the same material. Two internal walls supported by five rectangular masonry columns each subdivide the three naves. Lateral naves are covered by cross vaults with impost at columns capital level and the principal nave is covered by a cylindrical stone vault. The roof structure of the church is timber made except for the Immaculate, C3, chapel roof structure that is realized by a masonry vault structure. Chapel C4, differently from other chapels, is the only one that has been recently
modified by the insertion of a ribbed-slab concrete floor, underneath the roof structure. The principal façade, rectangular shaped, is made by regular prismatic stone blocks. It is interesting to note that the church has been built on a privileged position: the church basement is higher than other buildings around the church. To use this privileged position the designer had to create an horizontal plane where settles the church’s basements since the natural terrain trends is sloped along the direction North West-South East. This last detail allowed designer to easily realize the crypt space by fitting the crypt beneath the intrados of the pavement. 2.1
Conservation status of the church
The survey of the conservation status of the Church can start from the visual detailed analysis of the cracking pattern. As anticipated this information can provide useful information in order to assess all the possible lack of effective connections among the structural elements. As shown by Figure 1, the St. Maria church exhibits a variegated cracking pattern, as registered after the Molise earthquake in 2002, magnitude 5.9 (San Nicandro is 50Km far from San Giuliano di Puglia, epicentre of the earthquake). This state does not allow a simple interpretation of a unique collapse mechanism, as there are cracks suggesting various failure modes. In particular the area near the crypt shows a severe damage/cracking pattern, see Figure 1 near the chapels C1, C2 and the nave N2. Among all possible reasons, two main causes could be responsible of this situation: (i) a localized subsiding of the walls located over the crypt due to a settlement of the foundation walls; (ii) a seismic interaction of the façade and the nave walls associated with an out of plane mechanism of the façade. For the sake of brevity only the second interpretation of the actual cracking pattern will be investigated in the present paper. 3
the particular applied load. Then it is very important to identify not only the interaction between the structural parts of the structure but also the more realistic load distribution. In the particular case of the church object of this study this means to detect whether or not all the different parts of the structure are cooperating all together during a seismic event.
STRUCTURAL ANALYSIS OF THE CHURCH
As sketched by several authors masonry limit state can be analysed under few simplistic hypotheses (Heyman 1966), (Como et al. 1985): no-tensile strength; infinite compression strength and absence of sliding at failure. In particular these simplified hypothesis lead to the definitions of the term “mechanism”. It is worth to highlight here that in general the same structure can collapse using different mechanism depending on
Figure 2. 3D model of the church: shell elements are employed to model the structure. Roof structure is here hidden to view.
As shown by Figure 1 and 2, small buildings and chapels surround the church. As emphasized recently by and addendum of the current Italian standard (CSLP 2009) the analysis of a structure belonging to an aggregation is different than the case of an isolated building due by the interactions with adjacent buildings. These reasons and the conservation state of the structure, highlighted in the previous section, suggest to organize the analysis procedure as follows: 1. a linear dynamic analysis of the whole structure to analyse the structural interaction among the singles macro-elements; 2. a non-linear analysis of main structural macro-elements, interacting with the macroelement façade, to identify the major structural potential effects. Results will be integrated with those provided by the limit analysis of each macro-elements. The comparison of the results provided by the above analysis are expected to estimate the seismic vulnerability of the structure and give a detailed indication of the type and location of the intervention needed to improve it. Static and dynamic analyses have been carried out on a 3D structural model of the church structural complex using the FE computer code ABAQUS (Karlsson et al. 1998).
(a) Mode shape Nr. 4: freq. = 3.656Hz
(b) Mode shape Nr. 5: freq. = 4.111Hz
(c) Mode shape Nr. 7: freq. = 5.334Hz
Transversal bending of nave walls, vault support in phase;
Transversal bending of nave walls, vaults support phase in opposition
Longitudinal bending of the façade and apse area;
Figure 3. Linear dynamic analysis: horizontal and vertical section of three eigen-modes. Vaults and roof structures are hidden in the horizontal section for clarity purpose.
4
LINEAR DYNAMIC ANALYSIS OF THE WHOLE STRUCTURE
The whole structure is here investigated in the linear range through a complete 3D model, in order to characterize the dynamic behaviour of the church. The masonry elements are modelled under the hypothesis of linear elastic behaviour and the masonry is modelled as an isotropic continuum. Values concerning the mechanical properties of masonry material have been established on statistical analysis of test data found in the literature for similar materials. In particular Young modulus is set to E = 1000MPa and the Poisson ratio to accounting for a poor property material. The 3D FEM model of the church is realized using shell elements to model the masonry walls, and using truss elements to model the timber roof structure of the nave and aisles. Shell elements are also employed to model the main vault of the nave, the vault of the apse, the vault of the C1 and C2 chapels and the vault roof structure of the C3 chapel. The model consists of 49781 shell elements and 30 one-dimensional elements for a total of 49674 nodes. The 3D model is provided with distributed mass, computed by assuming the weight per volume unit as ρ = 2000 Kg/m3 is employed.
The presence of the crypt space has been considered providing the model with different boundary conditions: horizontal support in both directions are set at the indoor pavement level except for the area near the crypt. Figure 3 collects three characteristic shape modes for the Church. Modes are listed along with the description of the mode behaviour. By inspecting the first 30 eigen-modes no global information can be derived from the linear dynamic analysis of the church. In fact the mass participation sum of the first 30 eigen-modes
Figure 4. Linear dynamic analysis: longitudinal section of the 7th shape mode, bending of the façade and apse area
result equal to 55.5% and 55.2% of the total mass in the transversal and longitudinal direction respectively. It has to be underlined here that this
proportion account for the belfry mass. Removing this mass from the previous sums, since all the belfry shape modes are characterized by lower frequency if compared with those related to the church structure, does not improve significantly the mass participation. In fact, in this latter case the mass participation sum of the first 30 eigenmodes result equal to 63.5% and 64.9% of the total mass in the transversal and longitudinal direction respectively. The modal analysis shows that the structure does not behave with monolithic behaviour: smaller surrounding sub-structure, with smaller dimension (S1, S2, S3, S4, C1, C2, C3, C4, T1), act each one with a different frequency. For this reasons the behaviour of the church will be investigated considering each single macroelement as church sub-structures, since no appreciable fundamental or global modes can be tracked back from this linear analysis. It is interesting to note that the longitudinal shape mode Nr.7, Figure 3(c), involves the façade and the nave walls. Detailed view of the longitudinal section of this mode shape is shown in Figure 4. Since this longitudinal mode shape is the only global mode shape found in the linear dynamic analysis, and since we are mainly interested into seismic vulnerability of the façade, this mode will be employed to suggest a failure mechanism of the façade complex. 5
particular attention is here posed in the second type of collapse. The interaction between the façade (transversal macro-element) and the longitudinal macro-elements, is studied by analysing and comparing the following cases: the simple out of plane failure mechanism of the façade; the failure mechanism due by the interaction of the façade
Figure 5. Out of plane mechanism of the single façade macro-element. Roof structure and surrounding chapels are hidden to view.
and the lateral walls; the failure mechanism due by the interaction of the façade, the lateral walls and nave walls. These mechanisms develop by the occurrence of a diagonal crack along the party walls (such as
FAÇADE MACRO-ELEMENT AND MACRO-ELEMENTS INTERACTION
If the structure has not undergone strengthening, it is assumed that the only means of restraint to overturning exerted by other elements onto the façade is governed by the quality of the connection between the façade itself and the party walls, and this will give rise to different types of failure mechanisms. In this section the seismic vulnerability of the church façade is investigated through the analysis of two principal mechanisms: (i) no connection is present at the edges of the wall, see Figure 5 (ii) total or partial connection between the façade and both party walls, see Figure 6. As reported by the recent survey developed after the L’Aquila earthquake (2009) the in-plane mechanism (M1) and the out-of-plane mechanism (M3) are the most frequent in historical buildings such as churches (Podestà et al. 2010). Since in the case study there is no evidence about the possible in-plane mechanism of the façade
Figure 6. Out of plane mechanism of the façade macroelement including the interlocking effect. Roof structure and surrounding chapels are hidden to view.
the one found near the chapel C1 and nave N2) and a horizontal hinge on the façade. 5.1
Equilibrium limit analysis
The limit analysis represents a simple and effective tool for deriving an estimate of ultimate strength capacity. The hypothesis summarized in Section 3 is at the base of the development of non-dissipative hinges which transform the structure in a mechanism. The more the positions of these hinges are correct the more accurate is
the estimation of the collapse multiplier of the structure when subjected to a distribution of horizontal load. This procedure is usually called kinematic procedure or the transformation of a macro element into a mechanism (unstable system) that aims at finding the mechanism (activation) collapse load multiplier . In this sense the damage limitation state may be defined as the incipient structural instability or the activation of such mechanism. The true mechanism corresponds to the one associated to the minimum value of the collapse multiplier, and could be found into the class of all the collapse multipliers that can be obtained by varying the position of each hinge. The kinematic procedure has been already adopted by the past Italian standard (OPCM 2003), (OPCM 2005) and the in force one (NTC 2008) and the collapse multiplier value is functional to obtain the corresponding seismic spectral acceleration that read as: (1) where is the effective mass and. are the weights of the activated blocks. These reference values of α0 does not take into account the presence of lateral walls as a restraining effect for the façade. This influence has been studied by various authors, see for example (D’Ayala et al. 2003) and (Lagomarsino 2009). In particular in (D’Ayala et al. 2003) the out-of-plane failure of wall assemblies is studied for several type of mechanism. By computing the collapse load multiplier 0 (for wall assemblies of multi-story buildings), the effect of party walls is carried out varying the restraining effect of these walls on the building façade. Similar study is presented in (Lagomarsino 2009) where collapse mechanism of wall assemblies has been studied for monumental buildings such as churches. By computing the collapse load multiplier (α01, α02) for wall assemblies similar to church façade the effect of party walls is carried out for two specific collapse mechanism: detachment between the façade and the transversal walls with (i) vertical crack opening near the corner (α01) and (ii) oblique crack opening (α02). All parameters 0, α01, and α02 measure the collapse load multiplier of the mechanism by including the masonry technological aspects, such as: texture of the lateral walls, brick dimensions, and frictional effects.
In particular the α01, α02 parameters are made depending by two coefficients (Lagomarsino 2009): (2) where B is the width of the façade and tp is the party wall thickness, µ is the frictional coefficient and b and h are the width and height of the brick respectively. In the following these parameters, 0, α01 and α02, will be compared with the results obtained by the FEM analysis and the limit analysis. In order to check if the hypothesized mechanism can be adopted as an admissible or true mechanism a 3D FEM model of each involved macro-element has been conducted using solid elements to model the masonry walls by employing the FE computer code ABAQUS (Karlsson et al. 1998). Here, to track the nonlinear behaviour of the masonry material, a smeared crack model is employed. As well known the weakness of smeared models lie in the calibration of the material parameters: joints are smeared out and the block-mortar composite is treated as a homogenous solid whose mechanical properties are averaged. The smeared crack model basically requires the definition of few parameters: the shape of the failure surface (by using the failure ratios option), and the postcracking tensile behaviour (by defining the tension stiffening option). The stress–strain curve in compression, has been extrapolated from experimental tests on tuff masonry panels. The selected values for the model parameters are: failure ratios fr=[1.12, 0.1, 1.33, 0.2] compression strength , and tensile strength . The non-linear FEM analysis provide the load capacity parameter , computed as the nondimensional ratio between the horizontal applied loads and the weight of the considered model when limit state is reached. 5.2
Mechanism 1: out of plane behaviour of the façade macro-element
Here a parametrical/preliminary analysis is carried out on the façade macro-element, see Figure 5. The simple out-of-plane mechanism of the façade is also used to investigate the influence of some parameters necessary to set up of the non-linear FEM model. The façade thickness measure and is wide and it has a
free height of from the grand staircase in front of the church. By subdividing the church façade, by following the geometry of the openings, it is possible to identify six different mechanism. Each mechanism is characterized by a different height of the overturning hypothetic cylindrical hinge. The centre of gravity of the whole façade is located at from the ground level. The equation of the principle of the virtual works yields to the collapse multiplier for the out of plane mechanism that read as . The remaining collapse multipliers for the other mechanisms posses higher values of this last one and in particular the collapse multiplier of the mechanism associated to the higher part of the facade is . For the sake of brevity these collapse mechanisms will not be listed in the following sections since we are mainly interested in global collapse mechanism of the façade macro-element. The comparison between the collapse load multiplier and the corresponding maximum load capacity obtained via FEM shows a good agreement of the results provided by the two procedures. 5.3
Mechanism 2: out-of-plane behaviour of the façade considering the interlocking effect
The nave colonnaded walls and the church lateral walls (party walls) are the only longitudinal macro-elements that interact directly with façade, see Figure 1, so the hypothetic mechanism due by this interaction is similar to the one shown in Figure 6. Since this interaction is not well defined a priori, different scenario will be used to compute a value of the collapse multiplier including the interlocking effect. In this section the colonnaded walls are not taken into account: due by its specific geometry the nave colonnaded walls macro-element are characterized by a remarkable deformation capacity (reduced restraining effect) if compared with the one associated with the party wall macro-elements. In Figure 7, the comparison of the deformed configuration of these two macroelements, with the vector representation of the minimum (compression) and maximum (tensile) principal stresses superimposed is reported. This representation helps to easily identify the critical zones where the hinges are likely to occur, in order to understand the collapse mechanism.
(a)
(b) Figure 7. Non-linear FE analysis: principal stresses with the locations of cracks opening for the colonnaded walls and right lateral wall: cyan and red area correspond to compression and traction area respectively.
Then the collapse multiplier has been computed, for each single macro-element using the limit analysis, as the minimum kinematic multiplier by varying the position of the hinges in these critical zones. The colonnaded walls collapse multiplier and load capacity parameter read as: and respectively. The normalized collapse displacement (obtained via FEM) of this macro-element is .
Figure 8. Non-linear FE analysis: smeared cracks opening running for the façade mechanism associated to the sole interlocking effect of two church lateral walls.
Assembling the façade and the party walls macro-elements we can investigate the behaviour of this assemblies of walls against horizontal loads. By using a non-linear FEM analysis we compute the load capacity parameter λ. By using the limit analysis we compute the collapse load multiplier associated to the mechanism provided by applying the hinges found in Figure 7(b) to the party walls. The comparison between the collapse multiplier and the maximum load capacity obtained via FEM confirms also for this hypothesis good agreement of the results obtained by these two methods.
Figure 9. Out-of-plane mechanism 2 of the façade macroelement including the lateral interlocking effect. Roof structure and surrounding chapels are here hidden to view.
Figure 11. Out of plane mechanism 3 of the façade macroelement including the lateral interlocking effect. Roof structure and surrounding chapels are here hidden to view.
Figure 8 shows the corresponding crack pattern found by using the smeared crack model. In particular the mechanism represented in Figure 9 would be the one associated to this particular condition: the restraining effect of party walls leads the façade to bend out of plane showing a cracked area on the top part of the façade. This scheme agrees with some experimental evidence occurred for this type of façade (without nave walls) when undergoing seismic actions.
Figure 10 shows the comparison between displacement obtained by using the non-linear FEM analysis for two control points at: (A) in the middle of the façade, and (B) on the corner top of the façade. The mechanism due by this configuration is characterized by a pronounced horizontal displacement at the centre of the façade, associated to a smeared crack pattern, see again Figure 10, very similar to the pattern that similar churches have experienced after earthquakes. By inspecting the results obtained by the smeared crack model we can obtain the hypothetic mechanism associated with this wall assemblies, as shown in Figure 11. 5.5
Figure 10. Non-linear FEM analysis of the out of plane collapse of the façade macro-element considering the contribution of lateral and nave walls: in the displacement parameter , is the displacement of the reference point of the mechanism. Smeared cracks due to tensile stresses are depicted in white.
5.4
Mechanism 3: façade overturning
By including the presence of also the nave colonnaded walls it is possible to proceed with the analysis of the further mechanism. Here due by the complexity of the mechanism we cannot proceeded with the calculation via limit analysis of the collapse load multiplier α0.
Comparison of the results
By comparing the three mechanisms previously introduced, it is possible to characterize the behaviour of the façade when pushed out of plane by a dominant longitudinal seismic action. In particular we can summarize these results by the comparison of the collapse multipliers as obtained by the different procedures. Here for the sake of brevity the α0 parameter, obtained by using the kinematic analysis is not reported since these results are in very good agreement with those obtained by nonlinear FEM analysis (indicated by λ). In Figure 12 the interlocking effect is represented as function of the parameter α0 vs. the two parameters β and ε and the height of the rotating portion of the façade. In particular the relationship between collapse load multiplier and the height H of the wall portion involved in
parameter plotted varying the effective length of the party walls that are restraining the facade. Here the comparison would be made only for values of L that spans from 0 to 4 meters, that is the range of lengths between the facade and the chapel C1, see Figure 1. In this range values of 0 (bold line in Figure 13) are comparable with those obtained by limit and FEM analysis that read as: 0.09 ≤ λ ≤ 0.17. 0.4
0 (L > 4) 0.3
0.22
1 2
0.25
3
0.2
0.15
01
0.2
collapse load multiplier 0
0 (L < 4)
0.35
collapse load multiplier
overturning. Here and , and consequently Considering and squared masonry block with h = b we obtain we obtain the plot represented in Figure 13(a) for the mechanism 1 and 2. In Figure 12(b) the relationship between activation seismic multiplier and the parameter is shown. For both Figures 12(a) and (b) red lines define the multipliers of the single façade, without restraining effect , the façade with restraining effect of lateral walls and the one related to the mechanism with restraining effect of lateral walls plus the effect of nave walls acting in the collapse mechanism . This values α01 and α02 obtained for H=11.7m and are in good agreement with those
02 0.18
0.1
1 0.05
2
0.16
0
1
2
3
4 L (m)
5
6
7
0.14 0.12 0.1 0.08
0
2
4
6 H (m)
8
10
0.22
Figure 13. Out of plane mechanism of the façade macroelement including the interlocking effect: collapse-load multiplier 0 vs. length of the party walls. Red lines define the load capacity parameter of the single façade , the façade with restraining effect of lateral walls and the load capacity parameters of the mechanism 3 that account also for the nave colonnaded walls ..
collapse load multiplier
0.2 0.18
6
0.16 0.14 0.12 0.1 0.08 0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
Figure 12. Interlocking effect: (a) relationship between activation seismic multiplier and the height H of the wall portion involved in overturning, in case of and : mechanism 1 and mechanism 2. (b) relationship between activation seismic multiplier and the parameter . Red lines define the load capacity parameter of the single façade , and the façade with restraining effect of lateral walls
computed by FEM non-linear analysis. As regard as the comparison with the collapseload multiplier 0 computed for a “mechanism B2” considering an equivalent one story building façade (D’Ayala 2003), Figure 13 shows the collapse-load multiplier and the load capacity
CONCLUSIONS
In this paper the assessment of seismic vulnerability of a basilica church structure has been presented. Due by the particular aggregation of the buildings surrounding the church, the linear dynamic analysis is not useful to study the whole seismic behaviour of the church but only to identify macro-elements and understand their interaction (intra-element interaction). We confirm the difficult applicability of linear dynamic analyses to such a class of structure. Otherwise 3D non-linear analysis of the structure, or its sub-structures (macro-elements), it is a valid tool to compute seismic parameters such as collapse load multiplier. Results obtained through the FEM non-linear (push-over) analysis seems reliable when compared with those obtained by applying limit analysis. This result confirm the possibility to use FEM non-linear
analysis to provide reliable simulation of the actual response of masonry elements if assisted by other numerical technique such as kinematic analysis. Results obtained within these analyses, for each macro-element, provide useful indications to design an effective restoration of the building, highlighting the seismic vulnerabilities of the structure against the out of plane collapse of the façade macro-element. Further ongoing analyses are studying the inplane behaviour of the façade macro-element, by including the effect of the colonnaded nave walls in the collapse mechanism. These longitudinal macro-element strongly interact with the façade when driven out of plane by horizontal actions, see for instance Figure 3(a) and (b). Is in authors opinion that, the results herein obtained for this specific case can be easily extended to other similar Basilica church structures. REFERENCES Castellazzi G., 2011. Seismic vulnerability of a basilica: numerical assessment of the static and dynamic behavior, International Journal of Architectural Heritage (submitted). Como M., Grimaldi A., 1985. An unilateral model for the limit analysis of masonry walls, in Unilateral Problems in Structural Analysis. 4th ed London: Springer. CSLP 2009. Istruzioni per l’applicazione delle ”Nuove norme tecniche per le costruzioni” di cui al decreto ministeriale 14 gennaio 2008. Circolare del 2/2/2009, n. 617 del Ministero delle Infrastrutture e dei Trasporti approvata dal Consiglio Superiore dei Lavori Pubblici, Suppl. ord. n. 27 alla G.U. del 26/02/2009 n. 47. D’Ayala D., Speranza E., (2003) Definition of Collapse Mechanisms and Seismic Vulnerability of Historic Masonry Buildings, Earthquake Spectra 19, 479-509. DIR.P.C.M. 2011, Direttiva del Presidente del Consiglio dei Ministri 9 febbraio 2011 recante "Valutazione e riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme tecniche per le costruzioni di cui al decreto del Ministero delle infrastrutture e dei trasporti del 14 gennaio 2008". Heyman, J., 1969. The safety of masonry arches. International Journal of Mechanical Sciences, 11 (4), 363–385. I. Heyman, J., 1966. The stone skeleton. International Journal of Solids and Structures, 2 (2), 249–256. Karlsson & Sorensen, Inc. Hibbitt, 1998. Abaqus Theory Manual. Lagomarsino S., Resemini S. (2009) The Assessment of Damage Limitation State in the Seismic
Analysis of Monumental Buildings Earthquake Spectra 25, 323-346. De Luca, A., Giordano, A., and Mele, E., 2004. A simplified procedure for assessing the seismic capacity of masonry arches. Engineering Structures, 26 (13), 1915–1929. Mele, E., De Luca, A., and Giordano, A., 2003. Modelling and analysis of a basilica under earthquake loading. Journal of Cultural Heritage, 4 (4), 355–367. NTC 2008 Decreto Ministeriale del Ministero delle Infrastrutture e dei Trasporti 14 Gennaio 2008, Nuove Norme Tecniche per le Costruzioni. Italy OPCM 2003, President of Ministry Council, OPCM, no. 3274, March 20, 2003. Official Bulletin no. 105, May 8, 2003 (in Italian). OPCM 2005, President of Ministry Council, OPCM, no. 3431, May 3, 2005. Official Bulletin no. 107, May 10, 2005 (in Italian). Podestà S., Brignola A., Curti E., Parodi S., Lemme A. 2010, Il rilievo del danno e la vulnerabilità sismica delle chiese: il terremoto dell’Abruzzo. Ingegneria Sismica, Anno XXVII – N.1 – Gennaio-Marzo 2010
