1. Introduction
At present, design standards prescribe few or no recommendations aimed at considering the contribution of masonry to the response of a structure. This is especially important in regard to structures that are located in areas of high seismic hazard. On the other hand, in Latin America and in other regions of the world with developing countries, reinforced concrete buildings are frequently built with informal construction practices given the low technological level required [
1,
2,
3]. Such buildings have a low ductility, which makes them vulnerable to damage [
4]. The difference between masonry infilled frames and confined masonry lies in the construction methodology, resulting in completely different load transfer mechanisms [
5].
Recent reports, produced after the inspection of areas affected by strong earthquakes, have concluded that informally constructed reinforced concrete buildings responded with a low level of damage or did not collapse due to the contribution of the masonry [
6]. Notably, it has been determined that the contribution of masonry is beneficial when the construction process is carried out with confined masonry structural systems, which present an acceptable performance even for modified Mercalli intensities between VIII and IX [
7]. This acceptable performance contrasts with the precarious performance of other informal construction typologies that include unreinforced masonry or adobe buildings, which have presented much more severe damage or even collapse [
8].
Following the Wenchuan earthquake [
9], various problems associated with the damage and even collapse of confined masonry buildings were detected, including floor diaphragm failure, excessive floor deformation failure, and local failure by debonding in beams and columns as a result of cyclical loads. The authors of this work have previously highlighted the adequate behavior of buildings designed in accordance with modern codes, without achieving a notable improvement in the global ductility. Similarly, based on observations of buildings damaged during the Jaya (Indonesia) earthquake, the following types of failures in confined masonry buildings were identified: loss of anchor, failure due to in-plane shear, failure due to out-of-plane action, and differential settlement [
10].
In another post-earthquake building survey campaign, this time in Sumatra, the team identified the causes of failure of confined masonry structures to be shear column failure, longitudinal reinforcement buckling, and premature masonry collapse [
11]. Likewise, the earthquake that affected Ludian Province in 2014 [
12] provided an opportunity for the authors to corroborate that the confined masonry buildings designed, according to current standards demonstrated adequate performance, especially those with a uniform distribution of masonry.
However, the beneficial effect of masonry on the seismic response of a reinforced concrete structure can produce a detrimental effect if the contribution of its stiffness and resistance is not taken into consideration [
6]. In the event that the distribution of the masonry in the structure does not follow the uniformity and symmetry criteria in both plan and elevation, it can produce an irregular structure, whose dynamic response is completely different from the dynamic response of the concrete structures analyzed alone, causing torsional effects that mainly affect the columns of the outer frames [
13]. Additionally, an inadequate distribution of masonry can produce harmful effects, such as changes in the dissipated energy and the generation of local failure mechanisms, such as the effects of a short column [
6].
This detrimental effect of masonry can be described by taking the Ecuador earthquake of 16 April 2016, as an example [
14]. In the city of Portoviejo, several buildings collapsed, among which it was possible to identify buildings with reinforced concrete frames in which the presence of masonry presumably caused an irregularity in the plan, producing a predominant torsional seismic response, and consequently the collapse of buildings located on corners. In previous work [
15], some of these corner buildings were observed to have undergone extensive damage or even collapse. Among the possible causes of extensive damage and collapse, the authors point out that the level of acceleration far exceeded the acceleration of normative design, the excessive flexibility of the structures, the construction of vertical extensions, the existence of ground floors with open plans (commercial space) and the effect of siege in some locations in the city. Notably, the capacity of buildings subjected to corrosive environments rapidly degrades [
15], a situation that may have affected damaged buildings but is not addressed in this research.
Figure 1 shows two buildings located on Chile Street in Portoviejo that are currently damaged; note the predominant structural typology based on columns and slabs with flat beams and open facades.
Figure 2 shows pre-earthquake and post-earthquake images of the Marinero building, which is also located on Chile Street in Portoviejo and had to be demolished because it collapsed under the effect of torsion.
This article studies the influence of masonry on the response of a model that attempts to reproduce the typology and the mechanical and geometric characteristics of the corner buildings of Portoviejo, obtaining the nonlinear response through incremental push (pushover) analysis and incremental dynamic analysis (IDA), with some records corresponding to the Ecuador earthquake of 16 April 2016.
2. Numerical Model for Confined Masonry Buildings
It is well documented that today, fewer tools are available for the analysis of confined masonry structures than there are for the analysis of reinforced concrete or steel structures. In the formulation of calculation programs for confined masonry structures, a compromise between the precision and the complexity of the model is necessary [
16].
The use of macroscale finite element models (macro-models) is common in the numerical study of structures based on confined masonry [
1,
5,
17,
18,
19,
20]. The authors developed a macro-model for simple masonry and confined masonry based on smeared-crack total strain, validated with experimental results [
21]. In the study of [
22], the dependence of the seismic behavior of the macro-models on the following parameters was described in detail:
The strength of the masonry;
The density of the masonry walls;
The level of axial compression of the masonry walls;
The characteristics of the confining elements.
It was detected in this work that the computational models reviewed to date could not be considered appropriate to carry out the conventional evaluation of the capacity of this type of structure, especially due to their numerical instability [
22]. In [
23], the aspects that influence the seismic response of masonry structures were studied and determined using pushover analysis, especially for cases that can be classified as exhibiting soft-floor behavior:
Among the models used for the analysis of masonry walls, whether simple, reinforced, or confined, the work of [
19] incorporated the size of the masonry units (bricks) as a variable. The joint model was obtained by considering a connection with two nonlinear springs, one longitudinal and the other transverse, connected in parallel, and a contact element connected in series with the other springs. The study of [
18] considered a constitutive model at the cohesion interface to simulate the behavior of cracks both in the concrete and in the masonry units and mortar joints, adopting an elastic-plastic model. During the numerical analysis of the cyclical response of masonry buildings, the influence of the following parameters has been determined: meshing, dilation angle, and boundary conditions [
1].
The consideration of window and door openings in masonry walls introduces a number of additional modeling complications [
5]. These openings have not been considered in this work. The presence of masonry has been included along only the perimeters of the studied building.
Most of the models used to numerically simulate the cyclical response of confined masonry buildings have been validated using laboratory tests in which the specimens were subjected to gravity loads and lateral loads in the masonry plane [
1,
24,
25,
26].
Inelastic Infill Panel Element
Among the finite element macro-models used to model inelastic infill masonry panels within frame structures, the one presented in the original work [
27] and implemented by other authors [
28], consisting of a four-node element, is highlighted here. In this macro-model, the structural elements of the frames act in association with the masonry infill panels, trying to reproduce what happens with these structural typologies when they are subjected to lateral displacements. In this macro-model, each masonry infill panel is represented by six struts that allows the interaction that occurs between the cracked masonry infill panels and the structural elements (beams and columns) that confine them to be captured (see
Figure 3a). Each diagonal direction is represented by two parallel struts that receive the axial forces along the entire length of these diagonals, and a third diagonal that supports the shear that is transmitted from the top to the bottom of the masonry panel. This last strut acts in only the direction of the strut that works in compression, depending on the activation of the deformations reached in the panel (
Figure 3c). The compression struts use a hysteretic strut model, and the shear strut uses a bilinear hysteretic model.
For the parallel struts, four internal nodes that allow the points of contact between the panel and the frame elements were set (
Figure 3b), considering the dimensions of the cross-section of the columns and the beams that confine the panel. In addition, four dummy nodes were used to take into consideration the contact length between the panel and the structural frame. All the internal forces were transferred to the four outer nodes, which are defined as the common nodes where the beams and columns of the frame meet. By defining the internal nodes and the dummy nodes, the area of the compression or tension strut shown in
Figure 3b was obtained. This area represents the cracking condition of the masonry infill panels, which reduces the contact between the panels and the frame elements that confine them.
The thickness of the masonry infill panels is defined from the width of the masonry units arranged in the analyzed structure, ignoring the contribution of the mortar used to bond the units. Finally, in this model, it is important to define the interstory drift that indicates the failure of the panel under the action of out-of-plane forces. This leads to the panels of the model being deactivated when this interstory drift is reached, so that the panels are unable to provide stiffness and resistance to the structure anymore, although the masonry continues to add weight to the structure.
3. Damage in Structures with Masonry Infill Panels
It is important to characterize the failure of masonry infill panels. To do so, the results of post-earthquake surveys were consulted, where it was determined that global plasticization in confined masonry buildings occurs with drifts of approximately 0.5% and 0.9% [
9]. In a numerical study [
4], the authors reported the following drifts for confined masonry buildings: for formal buildings, drifts of 0.4% and 0.8% correspond to the maximum response and collapse, respectively, while for informal buildings, these drifts are 0.25% and 0.5%, respectively. On the other hand, the sudden loss of stiffness that affects the overall stiffness of buildings is achieved at very low floor drifts. The authors [
15] have indicated that for a drift of 0.1%, 50% of the stiffness of the walls is lost, while for a drift of 0.5%, up to 84% of the stiffness of the walls is lost.
The type of failure of confined masonry buildings designed according to industry standards shows adequate resistance to strong seismic actions, as was demonstrated in [
16], in which a value of up to 0.8 g was reached in shaking table tests, producing global collapse through the weak ground floor mechanism. In terms of damage to confined masonry buildings, two main types must be distinguished: out-of-plane stress failures and in-plane stress failures. For this last type of failure, numerous researchers have proposed certain displacements or drifts associated with certain behavioral states [
6].
On the other hand, in [
29], it was proposed that for interstory drifts between 0.4% and 1.5%, the masonry is expected to fail, while in [
30], it was considered that cracking occurs in masonry walls at lower drifts of approximately 0.25%. An extreme state of damage in masonry walls has been reported in [
5], indicating that the experimental results show that the bricks undergo crushing when an interstory drift of 1.4% occurs. This value is very close to that indicated in [
6], where a value of 1.5% is set for the limit at which the masonry collapses. The improvement in the behavior of masonry walls can be achieved by increasing the presence of confining elements (especially columns) and placing steel meshes in the seat of the masonry walls [
15]. Finally, in [
9], the maximum lateral resistance of confined masonry structures subjected to the action of earthquakes was reached at values between 0.5% and 0.9%.
The following section provides a concise and precise description of the numerical results, their interpretation, and the conclusions that were drawn.
6. Discussion of the Results
Nonlinear static analysis provides a good characterization of the seismic response of regular structures. In the present research, this analysis is used, considering its limitations, to capture the torsional behavior of a complete structure and to use the results as a basis for characterization before applying IDA. The results of this analysis show that the structure presents a low displacement ductility, calculated from the capacity curves determined by applying conventional and adaptive procedures. On the other hand, it is possible to observe the influence of the stiffness and resistance of the masonry infill panels on the lateral deformations of the structure. Upon reaching a global drift of the center of gravity at the roof of approximately 1%, the masonry infill panels cease to provide stiffness, and there is a sudden loss in the overall stiffness of the structure, which affects the sharp reduction in rotation as the lateral loading increases, since the structure loses much of its eccentricity. In addition, upon reaching the maximum rotation of the roof’s center of gravity, additional lateral displacements are imposed on the columns farthest from it, which implies an increase in the global drift of approximately 0.3%. This increase reflects a higher concentration of rotations in the frames than in the columns (perimeter frames) and is introduced due to the displacements with a component normal to the plane, which especially affects the masonry infill panels.
The IDA applied using accelerograms recorded during the Ecuador earthquake of 16 April 2016, results in curves that are not very dispersed, with very well defined points of collapse for the sections in which at least 20% of the initial stiffness has been lost.
Regarding the fragility curve obtained for this type of building, it is evident that, for moderate accelerations, for example, 0.2 g, the building would reach a high probability of exceeding the collapse limit state (approximately 60%). However, if the probability of exceedance is calculated for the basic acceleration of the current design for the coastal zone of Ecuador [
48], which contains the city of Portoviejo (0.5 g), the probability of exceedance of the collapse limit state is approximately 90%. If the accelerations achieved in the response spectra of the two components of the record obtained in Portoviejo are taken into account, exceedance probabilities very close to 100% are obtained.
Based on the floor rotations obtained from the IDA, it can be clearly seen that, for both the negative and positive maximum rotations, the floors show an increase up to a certain value of spectral acceleration slightly higher than 0.10 g. At this threshold, the seismic action causes the collapse of the masonry infill panels, and without that contribution to the stiffness of the extreme frames, this change drastically reduces the torsional behavior of the building; all the rotations reduce to a minimum value corresponding to a spectral acceleration of approximately 0.17 g. After this, an increase in rotations is again experienced due to the increase in lateral displacements induced by the application of accelerograms with ordinates of greater amplitude and the presence of the weight of the masonry, which remains, although it no longer contributes to the lateral stiffness of the building. This behavior is similar to that experienced by the rotations of the centers of gravity when applying the different types of pushover analyses reported in
Figure 8a,b.
On the other hand, the relative rotation of the centers of gravity between successive floors is considered applicable to measure the damage concentrated in a specific floor, considering a kind of local concentration of rotations similar to that observed when determining the interstory drifts based on the relative displacements. However, the curves shown in
Figure 15b do not exhibit a clear trend in the evolution of these relative rotations, for which it is recommended to use the relative rotation of the center of gravity with respect to the foundation level as a damage measure (see
Figure 15b), providing new possibilities for the study of the dynamic behavior of buildings that, due to their irregularity, are prone to a response dominated by torsion instead of translation.
7. Concluding Remarks
First, the need to incorporate the contribution of masonry infill panels to the strength and stiffness of the structure in design is evident, since at present, seismic codes take into account the contribution of only the seismic weight of buildings. The results presented above show how the response of the structure in the case study was altered by the presence of the masonry infill panels.
The model used here captured the failure mode of the corner buildings that failed in Portoviejo as a consequence of the earthquake that shook the Ecuadorian coast in 2016. The behavior of these buildings was clearly torsional due to the effect of the eccentricity introduced by the resistance and stiffness contributions of the masonry infill panels located on the boundaries of the buildings.
Although nonlinear static analysis (pushover) is not the most effective method of obtaining the nonlinear response of irregular structures, it provided certain indications that allow cataloging the seismic behavior of the case studied. On the one hand, it provided global ductility values lower than 2, which are characteristic of fragile buildings, and on the other hand, it provided evidence of the occurrence of the loss of lateral stiffness of corner buildings. Adaptive nonlinear static analysis was shown to be more suitable for capturing the masonry panel failure threshold than conventional analysis.
The incremental dynamic analysis of the model revealed the inadequate resistance of this type of building, which may result in an inadequate performance under dynamic action. The fragility curve obtained by applying a set of records obtained from the seismic event that triggered the failure of the Portoviejo buildings indicated a high probability that the limit state of collapse of this type of building was exceeded when considering the basic acceleration indicated by the Ecuadorian Construction Code for the site area or the values of the spectral acceleration corresponding to the response spectra of the components of the Ecuador earthquake of 16 April 2016, recorded in Portoviejo.
The results of the incremental dynamic analysis using the relative rotation of the centers of gravity with respect to the floor level as a damage measure show that the floor rotations, instead of the interstory drifts or the global drift, can provide useful indicators of the threshold at which significant changes in stiffness occur in buildings that are irregular in plan due to the presence of masonry infill panels. Further studies are required on different configurations of irregular buildings to validate the use of floor rotation as a damage measure. Based on the results obtained, it is suggested that studies are carried out on the effect of uniformly distributed masonry panels on the response of buildings.