Infill masonry panels are used worldwide for reinforced concrete buildings. This heterogeneous material is used for internal and external separations, which provide thermal and acoustic insulation. During earthquakes, infill panels are subjected to in-plane lateral forces received from the frame-infill connections. These forces imply different failure modes to a masonry infill. According to the experimental investigation conducted by Mehrabi et al. (1996), five different failure modes are observed. At lower displacement, diagonal/sliding cracks are started to develop along the infills. This failure is recorded in all specimens tested. During the increase of the displacement, the first mode is followed by a slip failure along with beam-infill connection for specimens with a strong frame and then followed by shear cracks developed in the columns when strong infills are used. On the other hand, a slip along the bed joints is developed instead of column shear cracks for specimens with weak infills. At higher displacement amplitudes, corner crushing appears to all tested specimens. More recent classification is made by Asteris P. G. et al. (2011) based on the experimental investigation conducted by Kakaletsis and Karayannis (2007). The masonry in-plane damages are classified to five different failure modes: sliding shear (SS), diagonal cracking (DK), diagonal compression (DC), corner crushing (CC), and frame failure (FF). In addition to in-plane loading, the infill masonry can be subjected to out-of-plane loads. This type of loads is applied in the perpendicular direction of the frame which can cause collapse of the infill out of the plane of the frame.

During the last few decades, important attention is given to the effect of masonry infill walls on responses of steel and reinforced concrete (R/C) frames. Experimental studies demonstrated that the existence of masonry infills affects the global response of structures by increasing the strength and the stiffness. The effect of masonry infills is directly affected by several parameters such as the existence of openings, the frame-infill connection, type of units (solid or hollow), and type of mortar (weak or strong). Zarnic and Tomazevic’s (1988) experimental study showed that the effect of masonry infills is related to the masonry units’ type and the presence of openings. A similar investigation conducted by Kakaletsis and Karayannis (2007) indicates that the presence of an opening in the infill masonry panel reduces the strength and the stiffness of the infilled frames whereas the reduction rate is related to the size, position, and type of the opening. Moreover, the frame-infill connection has an important role in the force transferring between the two elements. Based on an experimental study, Pires and Carvalho (1992) concluded that a strong frame-infill connection leads to higher strength and stiffness of the infilled frames rather than a poor connection. Besides, the study also showed that the mechanical characteristics of masonry affect both the behavior and the failure mode mechanisms. In addition, Mehrabi et al. (1996) concluded that the aspect ratio of infills and the distribution of the vertical loads affect the global behavior of infilled frames.

Furthermore, numerical studies are introduced to investigate the in-plane and out-of-plane behaviors of masonry infills using different modeling techniques. Nicola et al. (2015) and Petracca et al. (2017) classified three main strategies, namely, micro-modeling, meso-modeling, and macro-modeling. In the first technique, the masonry infill is divided into numerous elements (Crisafulli et al. (2000)). Two strategies can be distinguished, detailed micro-modeling, where the units, mortar, and unit–mortar interfaces are modeled separately. This method is used by Riddington and Naom (1994) to predict the compressive strength of masonry. On the other hand, the complexity is reduced by replacing the mortar joints with zero-thickness elements [Lourenço Paulo and Rots. (1997)]. This method is classified as the simplified micro-model, as mentioned by Nicola et al. (2015). Mehrabi and Benson Shing (1997) developed a cohesive dilatant interface model to represent the behavior of mortar joints using finite element code FEAP. A similar approach is used by Al-Chaar et al. (2008) to simulate the behavior of infilled reinforced concrete (R/C) frames using the commercial finite element software DIANA. More recently, Mohyeddin et al. (2013) suggested adding an elastic mortar band in the center of each brick element in order to eliminate the penetration and the complete loss of contact elements during the analysis.

The previous method takes into account all masonry infill details by modeling each component as a separate element. This approach makes the modeling process more complex and difficult to realize. Alternatively, the meso-modeling approach treats the masonry infills as one single element. The masonry infill components are smeared out as one equivalent element using the homogenization technique. This technique is based on selecting a periodic unit cell that includes all component types. The periodic unit cell should be selected in a way where its repetition generates the entire masonry panel [Quinteros et al. (2012)]. This technique was used by several researchers. Based on numerical simulation, (Ma et al. (2001) applied the homogenization concept on a representative volume element, equivalent to a periodic unit cell, to determine the equivalent properties of masonry infills with various boundary conditions. The authors report that the homogenized properties can be employed to simulate large masonry panels by using a small unit cell concept and when the stress and strain field does not vary intensively. Quinteros et al. (2012) used the homogenization technique proposed by Lopez et al. (1999), which is based on the periodic unit cell, to study the behavior of masonry walls subjected to a combination of in-plane and out-of-plane loads. The authors conclude that the homogenization procedure can be developed to include the effect of compressive strength and the tensile failure of bricks and can be used to study the out-of-plane behavior of masonry panels. For masonry panels subjected to in-plane loads, Houda et al. (2017) applied the homogenization method to estimate the strength of masonry panels constructed with a periodic concrete hollow block. The previous homogenization is applied for masonry walls with periodic patterns. In the case of non-periodic masonry walls, masonry walls without regular distribution of brick units, and mortar joints, such as old buildings, the homogenization technique can be applied using the concept of test-window [Tiberti and Milani (2020a)]. Tiberti and Milani (2020b) applied this technique to investigate the out-of-plane collapse behavior of old European structures with multi-leaf masonry walls.

The macro-modeling strategy adopts different modeling techniques. A simplification comprises the use of a single strut or multi-diagonal struts. The first appearance of this technique is established based on the observation made by Polyakove (1957) [as reported by Furtado et al. (2015)] who observed during a series of experimental tests on infilled steel frames that the infills behave as a compression element in a diagonal direction when the surrounding frame is subjected to lateral in-plane forces. Later, the studies conducted by Holmes (1961) and by Mainstone and Weeks (1970) confirmed the diagonal behaving action of masonry infills. Recently, different macro models are proposed in the literature. Holmes (1961), Mainstone RJ. (1974), Liauw and Kwan (1984), Decanini and Fantin (1986), and Turgay et al. (2014) suggested that the representation of masonry infills with a single diagonal strut is appropriate to capture the global behavior of infilled frames. On the contrary, El-Dakhakhni et al. (2003), Crisafulli and Carr, (2007), and Yekrangnia and Mohammadi (2017) suggested that multi-diagonal struts are more accurate to capture the internal effects of infills on R/C or a steel frame. Considering the out-of-plane behavior, Pantò et al. (2018) developed a three-dimension macro-model to represent the out-of-plane behavior of infilled frame structures. Other researchers developed macro-models to account both the in-plane and the out-of-plane. Among them, Kadysiewski and Mosalam (2009) proposed a model to describe the combined behaviors with single strut models. Meanwhile, Pradhan and Cavaleri (2020) used the multi-strut model proposed by Rodrigues et al. (2010) to account the in-plane and out-of-plane behaviors of infilled masonry.

The first main contribution proposed in this study is the use of the meso-modeling approach to investigate the accuracy of several width models proposed in the literature. To this aim, the masonry infills are modeled as an equivalent homogenized diagonal element. The width in meso-modeling is calculated according to several models selected for macro-modeling. The equivalent properties are defined from the experimental behaviors of masonry infills.

In addition, this study contains a comparison between the accuracy of micro-, meso-, and macro-modeling techniques. In micro-modeling, the infills are modeled with the simplified approach where the units are extended to the half-thick of joints in each direction. In macro-modeling, the diagonal strut is modeled with a 3D spar element that works only in compression and has no tension or bending resistance. The numerical simulation is carried out using the finite element software ANSYS. Two specimens experimented by Mehrabi et al. (1996) subjected to monotonic increasing loads are selected to validate the numerical simulations. Thus, the comparisons are performed by comparing the numerical and the experimental results in terms of maximum force, initial stiffness, and stiffness at the peak force, followed by comparing the behavior of the force–displacement curves after reaching the maximum force. In addition, the deformation shape obtained from the micro-modeling is compared to that of the experimental.

From the literature, three different modeling techniques can be classified to model masonry infills, known as micro-, meso-, and macro-modeling. These techniques are different in terms of complexity, computational time, and accuracy. The micro-modeling technique is more accurate among the two other methods. The consideration of details in the modeling process makes this method more useful for research purposes which can capture the local phenomena and the failure modes of the interaction between the different components. The complexity and the computational time make micro-modeling inappropriate in large structures. The meso-modeling approach is less complicated than micro-modeling. These modeling techniques are based on modeling the masonry infill as one homogenized element. This simplification is useful to study the frame-infill contacts. A more practical method is known as macro-modeling. The simplicity makes this method more appropriate for large structures.

Twelve experimental tests on one-story, one-bay, 1/2 scale R/C frames infilled with concrete masonry units are tested by Mehrabi et al. (1996) to investigate the effect of four different parameters: the masonry unit type, aspect ratio, lateral load type, and distribution of vertical force on the behavior of the infilled frames. Two infilled frames with the same geometric characteristics, namely, specimens 8 and 9 are selected from the experimental test to calibrate the numerical simulation. The specimens have an aspect ratio of 0.67 and are subjected to in-plane monotonic lateral loads and vertical loads distributed on beams and columns. The frames are designed according to Institute American Concrete (1989) to resist lateral wind loads. The masonry infills are constructed with (92 × 92 × 194) mm³ hollow and solid units in specimens 8 and 9, respectively. A type S mortar is used to connect the brick units. The joint’s thickness is 10 mm. According to Mehrabi et al. (1996), the compression stress of the solid units is higher than that of hollow units by 1.5 times. For the concrete, the compressive strength and the elastic modulus are 26.8 and 17225 MPa, respectively. For masonry infills, the compression strengths are 9.5 and 14.2 MPa and the elastic modulus are 5089.6 and 8233.6 MPa for specimens 8 and 9, respectively. The geometry of the infilled frame and the details of the frame elements are illustrated in Figures 4A–C.

Figure 4D illustrates the force–displacement curves obtained from the experimental test for specimens 8 and 9. Figure 4E, F illustrates the failure modes at the end of each test, where the solid line and areas represent the cracks and the crushes, respectively. Before reaching the maximum loads, minor diagonal and sliding cracks start to develop along with the infill panel. In the case of specimen 8, the former failure modes were followed by sliding in the bed joints, and at high displacement amplitudes, crushing failure at the masonry panel occurred (Figure 4E). In the case of specimen 9, the diagonal cracks were followed by shear cracks that appeared in the columns. These cracks are extended until the end of the test (Figure 4F).

The results obtained from this analytical study are presented and discussed in this section. The dissection is split into two phases: 1) before reaching the maximum lateral load and 2) after reaching the maximum lateral load. Before the peak load, the results are compared in terms of maximum force ( F max ), initial stiffness ( K in ), and stiffness at the peak load ( K peak ), where the initial stiffness is defined at 45% of the maximum load. The second comparison is based on the behavior of each model after the force reaches its maximum value.

This work contains a numerical investigation on the accuracy of width strut models using meso-modeling. The homogenized concept is used to model the masonry infill as a diagonal element. In addition, the work contains a comparison between micro-, meso-, and macro-modeling techniques of infills surrounded by reinforced concrete frames using the finite element software ANSYS. Two experimental specimens with weak and strong infill panels subjected to monotonic increasing lateral loading are selected to calibrate the numerical study.

First, seven width models are selected. The variation of the strut width equation according to the relative stiffness indicates that the selected equations can be classified according to the relative stiffness to dependent and independent equations. The dependent equations show constant width values during the variation of the relative stiffness. Otherwise, the independent equations show a reduction of width values during the increase of the relative stiffness.

Next, the masonry is modeled using a simplified micro-model. The global responses of the infilled frames of the experimental test are well predicted using the simplified micro-modeling approach (in terms of strength and stiffness). The deformation shapes of the numerical models can capture the shear sliding in specimen 8. While in specimen 9, the numerical model can capture the diagonal and sliding cracks. In macro-modeling, the masonry infills are modeled using a 3D spar, known as LINK180. In meso-modeling, the masonry infills are modeled as an equivalent homogenized diagonal element using SOLID65. The width is calculated according to the models used in macro-models.

In general, the macro-modeling with a single-strut model indicates the capability of the single strut to capture the global behavior of the infill frames. The force-deformation curves obtained from different macro-modeling show the same curve. Using meso-modeling, the single-strut models are more predictable to the global response by using Mainstone R. J. (1974) and Turgay et al. (2014)’s models in specimens 8 and 9. The model of Holmes (1961) gives the approximate behavior in specimen 9 compared to other models. Moreover, the models of Liauw and Kwan (1984), Decanini and Fantin (1986), and Moghaddam and Dowling (1988) show acceptable results. In the case of the multi-strut model, the models of Chrysostomou et al. (2002) and Yekrangnia and Mohammadi (2017) show approximate behavior using meso- and macro-modeling techniques. The models underestimate the lateral behavior of infill masonry in both modeling techniques, except for the model of Yekrangnia and Mohammadi (2017) where the behavior is overestimated in specimen 8 using meso- and macro-modeling. Finally, the modeling of the diagonal strut (s) with the meso-modeling technique presents an acceptable tool to study the diagonal behaving infill masonry. Further works are needed to investigate the application of the meso-modeling technique on infilled frames subjected to cyclic loading.