Seismic fragility assessment of existing masonry buildings in aggregate

Highlights

• Procedure for derivation of fragility curves by NLDA accounting for both in-plane and out-of-plane mechanisms.

• The 3D equivalent frame model of the aggregate considers the interaction between buildings by proper joints.

• Rigid block NLDAs of the OOP response use time histories derived from the 3D model of the aggregate.

• For the corner building, damage limit state is governed by IP response while collapse by OOP mechanisms.

• The higher the connection between structural units, the higher the interaction of IP and OOP at collapse.

Abstract

The paper describes the derivation of fragility curves useful for the seismic risk analyses of existing unreinforced masonry buildings inserted in aggregate. The L-shaped examined aggregate consists of three adjacent structural units that may mutually interact during seismic events. The seismic assessment is focused on the corner unit. The effects of different connection types between the adjacent units on the structural response were investigated. The seismic vulnerability of the masonry aggregate was assessed through nonlinear dynamic analyses (NDA) performed according to the multi-stripes approach. Both the in-plane and out-of-plane mechanisms were analyzed. The in-plane response of the corner unit is assessed through a 3D equivalent frame model of the entire aggregate, while the evaluation of its out-of-plane response makes use of the rigid-block assumption. Although evaluated in a separate way, the NDAs performed on the latter are based on the time histories derived from the global 3D model. The results are then processed in order to derive fragility curves, firstly, of the single failure mechanisms and, then, of the overall combined behavior. To this aim, various performance conditions are examined. For the reference building, the damage limit state is mainly governed by the in-plane behavior, while the collapse limit state by out-of-plane mechanisms. Moreover, the higher the connection level between adjacent structural units, the higher the interaction between in-plane and out-of-plane mechanisms at the collapse limit state.

Introduction

Most of the existing unreinforced masonry buildings, especially in historical centers, are not isolated but aggregated in several adjacent structural units that are connected to each other by links more or less structurally effective. Indeed, most of masonry aggregates derive from the progressive transformation of structural units, i.e the addition of structural portions to existing ones (see Fig. 1a). In some cases, neighboring buildings share the same mid-walls. In other cases, the structural units were built separately but in contact with pre-existing ones. Hence, masonry aggregates are characterized by a wide structural variety because of their historical evolution, state of preservation, use of different materials and construction techniques. Moreover, they are often composed of structural units with different heights, number of stories, and inter-story heights.

Due to the features described above, the aggregates are particularly vulnerable to the activation of local mechanisms, as observed during recent seismic events [1], [2]. In particular, the out-of-plane (OOP) failure occurs especially for the overturning of the façade placed at the upper levels (see Fig. 1b). This is mainly due to the amplification phenomena of the seismic action, which is filtered, both in shape and magnitude, by the dynamic response of the structure and differ at each building floor, tending to increase for increasing building levels (e.g. [3], [4]). In addition, the upper levels are more frequently subjected to OOP failure mode because of the possible pushing action of the roof and/or the scarce interlocking of the façade with the internal walls (in particular when the unit is the result of subsequent transformations and additions as in Fig. 1b). It is worth noting that, the quality of masonry may significantly affect the OOP mechanism (e.g. [5]), with possible disintegration of external leaves in the case of poor masonry. However, in-plane (IP) failure mode is also frequently observed in masonry aggregate and is strongly influenced by the aggregate effect, which can positively or negatively affect the IP response. The latter can be also affected by the quality of the masonry. In particular, among the different masonry typologies, the irregular stone masonry is diffused largely therein historical buildings and is characterized by the highest vulnerability class – as defined by the European Macroseismic Scale EMS98 [6] – because it may be characterized by the total loss of cohesion between the stone elements, with a consequent quasi-brittle collapse that is also affected by the wall size [7].

Finally, during seismic action, one can observe local collapses also deriving from the unit interactions because of the high stresses caused by a continuous impacting or hammering imparted between adjacent buildings such as in [8] (see Figs. 1c).

For these reasons, seismic vulnerability of existing masonry aggregate may be different as compared to that of individual structural units which form the whole aggregate. The seismic safety assessment of aggregates should consider boundary conditions especially related to the interaction of such structural units. This interaction involves both the IP and OOP behavior of each structural unit and can be relevant especially if the units are characterized by various architectural features that lead to different dynamic properties, stiffness, and strength (e.g. [9]).

The identification of the quality of connections between walls of adjacent buildings plays a significant role in the seismic assessment of aggregates and is affected by the difficulties in both the definition of construction phases and the execution of exhaustive on-site structural tests. Hence, the seismic vulnerability of interacting masonry buildings of existing aggregates represents a difficult and open task that has not been largely investigated so far.

The definition of a reliable method for the evaluation of the seismic vulnerability of masonry aggregates is a challenging research topic. In general, advances in the development of analysis methods have been limited by the lack of experimental data on the seismic response of such aggregates that could constitute a useful benchmark to calibrate numerical/analytical models. In the literature, the experimental campaigns specifically addressed to this topic are very few and quite recent. In particular, an experimental study [10] in which unidirectional dynamic shake-table test, reproducing a low-intensity seismic event, was performed on a three-story prototype of a stone masonry aggregate consisted of two weakly connected structural units. Furthermore, it is noteworthy that the SERA - AIMS project (Seismic Testing of Adjacent Interacting Masonry Structures, http://sera-aims.com) was conducted in December 2020 by testing an aggregate composed of two buildings under two horizontal components of dynamic excitation by using shake table facilities; the results are not yet available to the whole scientific community.

Although experimental campaigns constitute a desirable reference point necessary for validation purposes, it is clear that the simplifications required for the execution of tests, also by using the shaking table, cannot represent all the variety and complexity of the existing buildings in terms of geometry, mass, mechanical properties, structural details, etc. Hence, it is essential to integrate the experimental investigation with numerical analysis.

Within this context, given the extensive amount of information required for the evaluation of the seismic vulnerability of aggregates, various simplified methods for structural evaluations at large scale are presented in the literature (e.g. [11], [12], [13], [14], [15], [16], [17]). Such methods allow classifying a high number of structures in a short time and identifying the buildings that require deep investigations [18]. However, the large-scale approach involves a reduction in the accuracy of the results.

Important details on the seismic capacity as well as the collapse mechanism of the interacting constructions cannot be achieved in that way. Also, current standard codes do not provide reliable methodologies and detailed procedures for the seismic assessment of such typology of structures.

Most practical-case analyses are usually referred to individual structural units within the building, as allowed by [19], or are based on the use of simplified mechanical-based approaches [20], [21] that disregard the accurate modeling of the entire aggregate although they attempt in including even in a practice-oriented way the possible interaction effects. A suitable method, based on the optimal portion of the aggregate to be considered in the modeling, was proposed in [22].

Passing to the application examples of numerical approaches aiming to study the seismic response of historical masonry aggregate, they vary for the adopted modeling approach (Finite Element-, Discrete Element- or frame-models), the type of the analysis (static or dynamic), and the type of collapse mechanisms (only in-plane, or both in-plane and out-of-plane). In general, the current literature studies are mainly applied to individual structural units and/or groups of buildings perfectly connected with each other.

The influence of group of buildings on the seismic behavior of the individual buildings that compose the block, the so-called “aggregate effect”, was analyzed in [23] through Non-linear Static Analyses (NSAs). Results showed that the individual buildings had lower safety factors than the compound and that, in general, the aggregate effect was beneficial for the buildings. Based on that result, the authors suggested that safety analysis of masonry aggregates can be carried out by considering isolated buildings, which reduces the effort and time to a great extent; only when the analysis on the isolated building indicates an unsafe condition, the analysis may be refined by considering the full compound.

The assessment of an entire aggregate and its individual structural units was determined by NSAs in [24]. In this case, the global seismic response was assumed to be governed only by the in-plane behavior. Results showed that a lower seismic performance of the structural unit is obtained when adjacent buildings have different heights or/and different floor levels.

Some recent studies proposed the implementation of simplified models for representing the boundary conditions of the structural unit to be examined. In particular, in [25] a “row housing”, consisting of a series of buildings aggregated in lines (very widespread in Italian historical centers), was numerically investigated through NSAs. A simplified procedure based on the calibration of elasto-plastic links both in terms of strength and stiffness (based on the main geometrical features) was proposed to study the global behavior of a single building extrapolated from an aggregate without modeling the whole building compound. An extension of the previous cited work can be found in [26].

The seismic response of two complex historical masonry aggregates belonging to the row housing typology was investigated in [27] by means of Non-linear Dynamic Analyses (NDAs) using one of the real accelerogram registered in the 2009 L’Aquila earthquake. By observing a damage distribution on the perimeter walls being subjected to the torsional effects induced by the seismic action, the authors highlighted that the structural response of an individual unit was strongly affected by the adjacent units.

The study performed in [28] focused attention on the vulnerability analysis of an existing aggregate by means, among others, mechanical non-linear macro-element analysis in order to compare the fragility curves of the whole aggregate and that of individual structural units.

NSAs on masonry aggregate, considered as isolated structures and within the construction compound, were also performed and discussed in [29]. Results showed that the aggregate effect reduced the seismic vulnerability of the individual structural units.

Another recent study discussed in [30] aimed of extending the results obtained for some identifiable typologies of single masonry buildings to more complex structural layout, highlighting a general decrease (of about 30%) in the seismic safety factors of the buildings within the aggregate, as compared to that of the isolated constructions. In that study, the structural units of the aggregate were perfectly connected to each other neglecting the interaction between contiguous walls, as well as the OOP masonry behavior.

Furthermore, a research [18] presented an automatic computational procedure for the seismic assessment of local failure mechanisms in historical masonry aggregate by adopting a sophisticated mesh adaptation scheme to assure the representation of the correct collapse mechanism by finding the real position of fracture lines.

Definitely, in most of the studies described above, some simplified assumptions were developed to study only individual structural units (by neglecting the modeling of adjacent constructions) or the overall aggregate modeled as an entire structure. In the latter case, the study of the whole aggregate (modeled as group of individual buildings perfectly connected to each other) may lead to unreliable results, as a shear redistribution among the structural units is assumed by neglecting the presence of discontinuities between the adjacent buildings that can modify the seismic response. Despite the aggregate effect is an important issue, the effect of the unit interactions has not been enough investigated in the actual literature. Furthermore, most of the conducted studies merely regard NSAs or NDAs with a limited number of seismic inputs. For the latter case, the OOP mechanisms were often not investigated, as well as the interaction between IP and OOP mechanisms.

A numerical analysis aiming at efficiently evaluating the seismic vulnerability of complex historical masonry aggregates needs to consider the main characteristics of masonry material, the actual condition of construction details, and realistic interaction behavior between structures.

The present research describes the derivation of fragility curves useful for the seismic risk analyses of existing unreinforced masonry buildings inserted in aggregate accounting for both the IP and OOP responses. In particular, the investigated aggregate consists of three adjacent structural units that form a L-shaped architectural plan (see details in Section 2). It is worth noting that the seismic assessment is focused on the corner unit. A 3D Equivalent Frame (EF) model implemented in the Tremuri software [31] was adopted to represent both the individual buildings and the entire aggregate (see Section 3.1). In the latter case, three connection typologies between walls of adjacent structures were assumed to consider the less or more interlocking contribution between adjacent structural units. This aimed to investigate qualitatively and quantitatively the consequences of the unit interaction on the structural response of the corner building inserted in the aggregate. While the IP response of the aggregate is based on the use of the equivalent frame model, the OOP response makes use of the rigid-block assumption through a newly three-linear analytical constitutive model, which is presented for the rocking of the façade located at the top floor (see Section 3.2).

The seismic risk analysis was assessed through NDAs performed according to the multi-stripes approach, by adopting twenty sets of accelerograms spectrum-compatible with ten increasing values of the return period of the examined structure (see Section 4). Pushover analyses were also performed on the 3D model to estimate thresholds of the structural capacity in terms of maximum inter-story drift of walls. The OOP response was evaluated in a separate way, as also carried out for example in [32] (see Section 6.2), but it was based on time histories derived from the NDAs performed on the 3D global model, thus aiming to implicitly consider the filtering effect at the upper level provided by the dynamic response of the structure. The NDA results were then processed in order to derive fragility curves representing the frequency of exceedance of two performance conditions, i.e. usability-prevention damage and collapse limit states (see Section 7). These curves considered the occurrence of both the IP and OOP failure mechanisms. First, the seismic response was evaluated separately for these mechanisms. Then, the fragility curves were computed for the overall behavior of combined mechanisms.