Valutazione della vulnerabilità sismica di edifici storici tramite l’analisi cinematica

Abstract

The current thesis deals with the seismic vulnerability assessment of historical masonry buildings towards out-of-plane failure mechanisms, also denoted as out-of-plane local collapse mechanisms, by means of linear and nonlinear kinematic analysis. Damage analyses usually carried out after earthquakes demonstrated that one of the main sources of vulnerability for existing masonry buildings is associated to local failures, mainly due to the activation of out-of-plane collapse mechanisms. The issue of the structural safety of existing structures, with regards to local out-of-plane failure mechanisms, is already known and studied since a long time by architects and engineers. However the interest to the problem of the seismic vulnerability assessment of existing masonry buildings has increased in time, especially after the recent and catastrophic earthquake that affected Italy in the last years. This interest is strictly tied to the need to interface with the problem of the safety level and at the same time, the need to preserve the artistic-historical value of existing buildings, especially with regards to historical buildings characterized by an important artistic-historical value. The damages caused by earthquakes highlighted the real necessity to plan improvements interventions in order to avoid similar situations and similar damages in future. As anticipated, within intervention planning the special attention to historical buildings is related to the artistic value of these type of buildings and, as a consequence, to the relation with the preservation and restoration criteria. In this context the first step deals with the definition of the seismic vulnerabilities and criticalities of historical buildings. As a matter of fact only by means of the identification and evaluation of the vulnerabilities of the buildings towards seismic actions, it is possible to propose interventions for the preservation of the building and the increase of its safety level. Hence the evaluation of the seismic vulnerability is the first fundamental step of the design process. Experience showed that seismic actions can involve small or larger portion of the building, and hence can activate local or global collapse mechanisms. As already anticipated and as well documented in literature, it has been demonstrated that one of the main sources of seismic vulnerability deals with the activation of out-of-plane local collapse mechanisms, that bring to the overturning of masonry walls or portion of them out of the plane of the masonry. In the current thesis the attention is paid to the evaluation of the seismic vulnerabilities towards out of-plane collapse mechanisms. The seismic vulnerability has been assessed for some historical buildings following the prescriptions of the Italian building code (D.M.2008, Circolare del 02 febbraio 2009). The Italian building code, with reference to the Direttiva del Presidente del Consiglio dei Ministri, 12 Ottobre 2007 for historical buildings, proposes a calculation method for the seismic vulnerability assessment of historical buildings towards local out-of-plane collapse mechanisms by means of the application of linear and nonlinear kinematic analysis. The thesis work has been subdivided in several parts, starting from a general introduction to the problem, a description of the theoretical background of the calculation method applied, to the discussion of the results obtained. In the first part of the thesis an historical overview on the theory and the construction techniques of masonry buildings, with particular attention to the basis theory of the calculation method adopted in the thesis, is presented. Then the seismic behavior of existing masonry buildings and the main criticalities of these buildings, detected and listed after recent earthquakes, are reported. The description is mainly addressed to the survey and cataloging aspects of the seismic damages, necessary for the identification of the main criticalities in the perspective of the seismic vulnerability assessment. After a first introductive description of the most common seismic damages detected after earthquakes, the main geometrical and morphological features of existing masonry buildings and their vulnerabilities towards seismic actions are described. As already anticipated the seismic vulnerability of existing buildings can be related to both the activation of global collapse mechanisms and local collapse mechanisms, that can be respectively studied and calculated by means of global or local analyses. Hence the main calculation aspects and the theory background of global and local analyses are described, with particular attention to local analyses, applied in the thesis for the seismic vulnerability assessment of historical buildings towards out-of-plane collapse mechanisms. Within local analyses the theoretical aspect of linear and nonlinear kinematic analyses according to the Italian building code framework are in detail described. As anticipated the seismic vulnerability assessment represents the first step towards the planning of interventions that aim to increase the seismic safety level of the building. Hence the possible type of intervention plans, according to the Italian building code prescriptions are briefly described. Within existing building a fundamental aspect that precedes the seismic vulnerability assessment is related to the building knowledge process. In order to identify the criticalities and vulnerabilities of the building, it is in fact of great importance to get a knowledge level of the building as much complete as possible. A complete and clear knowledge of the building allows first of all the analyst to know the history of the building, especially related to the previous restoration interventions done on the building or on the previous damages suffered by the building during previous earthquake. Furthermore the knowledge process has to bring important information on geometrical and structural features and most of all on the crack pattern detected during in-place surveys. The historical, geometrical and crack pattern surveys are then the basis instruments for the identification of the vulnerabilities that identify the collapse mechanisms active in the building or that could be activated due to the criticalities detected by the survey. The knowledge level of the building can affect the results of the seismic analysis carried out: the lower the knowledge of the building, the higher the uncertainties related to the building itself. Hence, as a consequence, the higher the uncertainties of the building, the higher safety coefficients must be applied to the results obtained in order to supply to such uncertainties. The knowledge level of the building results in fact in safety coefficients, denoted as confidence factors, that has to be applied to the capacity of the building. In the evaluation of the seismic vulnerability of existing masonry buildings by means of kinematic analyses according to the Italian building code the capacity of the structure has to be compared to the seismic demand, for the seismic verification. In particular the capacity of the structure is calculated towards a particular local collapse mechanism applying the kinematic analysis while the seismic demand is evaluated according to code prescriptions. It is straightforward to deduce that the seismic verification is satisfied if the capacity of the structure is higher that the demand request by the seismic action. As a matter of fact if the capacity of the structure is higher that the seismic demand, the building analyzed is not vulnerable towards the local collapse mechanism analyzed for that particular seismic demand, otherwise the collapse mechanism analyzed is critical for that building. The capacity of the structure depends on the geometrical features of the portion of building analyzed, subjected or potentially subjected to that local collapse mechanism, while the seismic demand depend on the site characteristic where the building stands and the limit state analyzed. According to linear kinematic analysis the capacity of the structure and the seismic demand are evaluated in terms of acceleration. By means of linear analysis the only acceleration activation of the mechanism, to be compared to the acceleration demand, can be evaluated. On the contrary according to nonlinear kinematic analysis capacity and demand are evaluated in terms of displacements. Nonlinear kinematic analysis represents a higher level of refinement respect to linear kinematic analysis. According to nonlinear kinematic analysis in fact, since the capacity of the structure is evaluated in terms of displacements, the whole evolution of the collapse mechanism can be investigated, starting from the activation point to the collapse of the portion of building analyzed. By means of nonlinear kinematic analysis in fact the capacity of the structure is represented by a capacity curve, and not only by a value. The ultimate capacity, to be compared to the seismic demand, is then evaluated according to the Italian building code prescriptions. Hence nonlinear kinematic analysis takes into account for hidden capacity of the structure and for a more realistic behavior of the structure itself. In the thesis the seismic verifications results, for both linear and nonlinear kinematic analysis, are expressed in terms of a seismic safety index, defined as the ratio between the capacity and the demand. Hence, if the seismic safety index is higher than one, the seismic verification is satisfied, otherwise, it can be stated that the portion of building analyzed is vulnerable with respect to the collapse mechanism calculated. If so, an intervention plan can be proposed in order to increase the seismic safety level of the building towards the local collapse mechanisms analyzed. As anticipated, since local collapse mechanisms are investigated, the same building can be subjected to several local collapse mechanisms, and hence several seismic safety indexes can be associated to that building. The seismic safety index can be considered as an immediate representation of the seismic vulnerability level. The last part of the thesis deals with the presentation and the discussion of the results obtained. The seismic vulnerability assessment has been evaluated according to different refinement levels, starting from relatively simple analysis to more complex and refined analysis, in particular applying first linear and then nonlinear kinematic analysis . The different refinement level is strictly related to the aim to be pursued or to the different project phases. A higher complexity and refinement of the analysis carried out implies of course a higher computational burden to be faced with. Within the refinement level issue and the aim of the study, it has to be distinguished, in this particular context, if the analyses to be carried out are in the framework of a territorial scale evaluation or of a local scale evaluation, in particular if several buildings have to be analyzed or if a relatively low number of buildings has to be analyzed towards out-plane collapse mechanisms. Part of the thesis work is associated to activities researches that fit into a research program between the University of Parma and the Superintendence of Cultural Heritage for the seismic vulnerability assessment of several historical buildings, in order to produce an intervention priority list of the buildings analyzed. The first part of the work provides preliminary analyses, relatively simple, for the identification of recurrent criticalities and common local collapse mechanisms that aim to quantify the vulnerabilities detected. In this framework the analyses carried out are relatively simple and refer to linear kinematic analysis. Some historical buildings have been chosen as cases studies for the application of linear kinematic analysis and for the discussion of the preliminary results. In particular four buildings placed in Emilia Romagna region have been investigated. The buildings analyzed in the thesis have been chosen on the basis on common local out-of-plane collapse mechanisms identified, associated to commonly findable geometrical and morphological features and criticalities . The process of the evaluation of the seismic vulnerability, in particular for the determination of the seismic safety index, followed the knowledge process previously described. For each building a detailed survey allowed to collect useful historical information, to determine the crack pattern and to identify some critical situations. This first knowledge step was the basis for the individuation of already active or potentially active out-of-plane collapse mechanisms that have been then calculated by means of linear kinematic analysis. It has been highlighted that a fundamental role in the definition of seismic vulnerability assessment towards out-of plane mechanisms is played by the connection level between orthogonal masonry walls and between the masonry wall with the floor. It is in fact well known that the connection level between structural parts of the building is one of the main aspects for the definition of the structural behavior. If all the masonry walls and the walls with the floor are well connected to each other, the building can assume a “box” behavior, that is the building behaves like a box and out-of-plane mechanisms are avoided, thanks to the good connection level. On the contrary if the structural parts are not well linked to each other, they behaves like independent elements, activating in the buildings local out-of-plane collapse mechanisms. Another fundamental aspect that leads to the activation of local out-of-plane collapse mechanisms is the effect of horizontal static force generated by arches and vaults not countered by tie rod. The lack of tie rod that counter horizontal forces in arches and vaults is in fact a common and dangerous criticality detected in existing masonry buildings. It is important to underline that most of the times simple and non invasive interventions, like steel tie rod placed in arches and vaults or linking of the floor to the masonry walls, can significantly increase the safety level of the structures. Especially for historical buildings with a certain artistic-architectonic value to be preserved, it is very important that the interventions plan increase the safety level of the building but at the same are not invasive for the building itself, following the restoration and sustainability concepts and respecting the “minimum intervention criterion”. For this reason the intervention plan has to be adequately calibrated and hence the preliminary phase of identification and evaluation of the seismic vulnerability appropriately calculated. A second part of the results deeps some aspects of the calculation process that proved to have significant influence on the preliminary results. Hence the second part of the results indirectly deals with the transition from the territorial scale to the local scale, focusing on some numerical aspects of the calculation process. This leads to increase the refinement level of the analysis. The second part of the results in fact mostly deals with calculation parameters strictly related to nonlinear kinematic analysis. In the second part of the results an analytical model for the evaluation of the structural capacity of historical buildings in the framework of kinematic analysis is presented. The analytical model has been implemented during the thesis work in Excel spreadsheets. This part of results is not directly related to a particular case study but aim to provide indications as much general as possible, with relation to the field of application investigated. The analytical model focuses on some parameters of high influence on the results obtained in the calculation of out-plane collapse mechanisms and aim to take into account, in a relatively simplified way, these parameters in the calculation process. In particular the analytical model has been validated through a parametric study in which the basis hypothesis related to the geometrical and mechanical parameters investigated have been combined and varied in order to cover a relatively wide range of cases. The parametric study starts from a “base case study”, that has been chosen as reference case study to which the variations have been applied for the parametric study. The base case study refer to the simple overturning of a masonry walls characterized by continuous masonry from the ground to the roof and wooden floor. The parameters mostly investigated in the case study refer to the friction developed at the floor-wall interface, to the internal masonry friction, to the position of the pole around which the masonry wall overturns, to the influence of transversal masonry walls participating to the mechanisms, to the influence of the floor warping and to the type of forces acting on the building. In particular, referring to the friction developed at the floor-wall interface, a friction model that takes into account the progressive decaying of the friction coefficient from a static to a dynamic value and the progressive extraction of the floor has been implemented. In the model it has been considered the possibility of floor extraction, that means that as the wall rotates, the floor loses support length on the walls and progressively slides on the wall, extracting from the wall itself. Regarding the internal masonry friction, both simple and composed mechanisms have been considered in the model. Simple mechanisms refer to simple overturning walls while composed mechanisms refer to masonry wedges, transversal to the main overturning wall, participating to the mechanism. Within composed mechanism it has been taken into account the internal friction developed between the overturning masonry wedge and the remaining stable part of the transversal wall. It must be reminded that, since according to kinematic analysis the overturning masonry walls are considered as rigid bodies, in simple overturning mechanisms the internal friction is not relevant. The internal masonry friction has been taken into account in the model by means of a fiber mode, according to which the transversal masonry wall is subdivided into vertical fibers that generate an internal friction at the interface between the overturning wedge and the remaining stable part. Even in case of internal friction it has been considered that the friction coefficient trend decreases from a static value to a dynamic value. Furthermore it has been considered that, as the wall overturns, the transversal masonry wedge participating to mechanism, detaches from the remaining stable part of the wedge, and hence it is subjected to both horizontal and vertical displacements. Hence, since as the wedge vertically detaches from the remaining stable part as the friction effect vanishes, it has been considered that the friction also reduces due to the uplift effect. This aspect has been considered in the model by reducing the friction forces through an uplift coefficient. Again related to composed mechanisms, different masonry texture quality have been taken into account. As a matter of fact bad texture quality leads to define a lower inclination angle of the transversal masonry wedge and hence a smaller transversal wedge portion, while good texture quality leads to define a higher inclination angle and hence a bigger transversal masonry wedge portion. For each composed mechanisms two inclination angle values have been considered in calculation. Regarding the position of the pole around which the wall overturns, it has been considered that, since for example due to cracks eventually plastered through time, it is not always easy to determine the exact position around which the wall rotates and the mechanism activates. Hence, for each combination of the parametric study the pole of the overturning wall has been placed at the basis of each floor. Finally particular attention has been paid to the type of forces acting on the overturning wall: constant forces or variable forces. Constant forces are forces that remain constant during the whole mechanism evolution while variable forces are forces that, for some reasons, stop to act at a certain step of the mechanism evolution. Referring to the case analyzed variable forces refer to the possibility of floor extraction. As a matter of fact, if the floor is not well connected to the overturning wall, it can extract from the wall: in this case, as soon as the floor loses its support on the wall, the floor weight and its related friction force immediately stop to act on the wall. This aspect is particularly important in the definition of the structural capacity. As a matter of fact, locally incompatible situations, like the extraction of the floor, affect the capacity of the wall itself. Hence particular attention has been paid to this aspect. As anticipated the proposed analytical model allows to determine the structural capacity of the analyzed portion of building subjected to out-of-plane collapse mechanism through linear and nonlinear kinematic analysis. The seismic safety verification are then carried out according to the Italian building code prescriptions. The model has been validated through a parametric study: each variation of the parametric study corresponds, in effect, to a single collapse mechanism associated to a seismic safety index. The analyses showed the great variability of the results obtained depending on the basis hypotheses adopted in the calculation, in particular on the calculation parameters effect previously described. These parameters are associated to uncertainties related to the effective knowledge of the building and hence to the knowledge level of the building itself. Hence the importance of the knowledge level of the building is again underlined by the variability of the results obtained in the parametric study. The aim of the study is also to underline how important is to improve the refinement level of the analysis in order to obtain reliable and at the same time safe results and to trust, as much as possible, the results obtained. This is an important step in the perspective of the planning, in a more targeted way, of the intervention for the increase of the safety level in the sustainability and minimum intervention criterion framework. The analytical model proposed hence well fits with both research and practical requirements. It is in fact of interest, from a research point of view, the deepening of numerical aspects and the of mechanical models that describe, in a rather simplified but efficient way, some physical aspects that proved to influence the structural response. From a practical point of view it is useful to face with a calculation instruments that help analysts in the seismic vulnerability assessment of existing masonry walls towards out-plane collapse mechanisms, according to codes prescriptions. Furthermore, although the great attention paid by researchers to the theme of the seismic vulnerability assessment of historical buildings, well documented by several works available in literature, the topic of the seismic vulnerability assessment towards out-of-plane collapse mechanisms has not yet been well addressed in European codes. The Italian building code is the only code that provides a relatively simple calculation method for the evaluation of the seismic vulnerability towards out-of-plane collapse mechanisms, by means of linear and nonlinear kinematic analysis. For this reason the Italian building code is in advanced with respect to other international standards. The research carried out can be considered as a starting point for future research developments. As a matter of fact it must be underlined some limitations of the research carried out to the application field, that can be extended in future researches. First of all, since the aim of the study was also to provide useful indications to be applied in the current design process, standard and conventional calculation methods have been applied to the cases study analyzed, mostly following the codes prescriptions. Remaining in the respect of standards prescriptions, it would be of interest deepening some aspects of the calculation procedure proposed by the standards, like for example the calibration of safety coefficients or the determinations of ultimate limit values, by means of more refined and addressed analyses. Furthermore the analytical model proposed only deals with limited cases of out-plane collapse mechanisms. As a matter of fact the study has been carried out on simply overturning masonry walls characterized by wooden floor. Future researches aim to extend the analytical model and the associated parametric study to further types of out-of-plane collapse mechanisms, like for example the out-of-plane bending of masonry walls, and to deal with the influence of further mechanical aspects related for example to the horizontal forces effect generated by arches and vaults. The aim is then to get a complete scenery of the main criticalities of historical buildings, implemented in an analytical model that allows to determine, in a rather refined but at the same time safe way, the structural capacity of portion of buildings subjected to out-of-plane collapse mechanisms, for the seismic safety verifications. This allows to have useful calculation instruments in the daily design process for the identification and the evaluation of the most common seismic vulnerabilities of existing masonry buildings.