Experimental Testing and Numerical Modeling of Robust Unreinforced and Reinforced Clay Masonry Infill Walls, With and Without Openings

This paper presents an overview of the experimental results obtained by combined in-plane/out-of-plane (IP/OOP) tests carried out on robust clay masonry infill walls. The combined tests were carried out on eight full-scale one-bay, one-story infilled reinforced concrete (RC) frames, plus one reference RC bare frame. In four cases, the masonry walls fully fill the RC frame: two walls are made of unreinforced masonry (URM), whereas the other two are made of reinforced masonry (RM), with both vertical and horizontal reinforcement. Each pair of specimens was tested up to different levels of IP drift before carrying out the OOP tests. Four other specimens, still made of URM and RM walls, are characterized by the presence of a central opening, and in one case, the effect of a lintel is analyzed. On the basis of the tests carried out, an analytical model was developed for the analysis of the OOP behavior. It was used to calibrate IP damage degradation models based on the experimental results to define limits for the applicability of well-known flexural and arching mechanism models for the evaluation of the OOP capacity of the infill walls and to evaluate the efficiency of vertical reinforcement. In this work, the experimental campaign is presented, and the results of both experimental tests and numerical analyses are discussed.


INTRODUCTION
The use of clay masonry infill walls in reinforced concrete (RC) frames is a common construction practice worldwide, and experimental studies on their in-plane (IP) behavior were conducted since the 1950's (e.g., Thomas, 1952, Polyakov, 1960, with particular attention to failure modes and infillframe interaction. As an example, some recent works are those of Anil and Altin (2007), Blackard et al. (2009), Kakaletsis et al. (2011), Cavaleri and Di Trapani (2014), Bergami and Nuti (2015), and Gazic and Sigmund (2016).
However, these infill walls are often overlooked in the design procedures, being classified substantially as non-structural elements, and represent a critical element for the seismic vulnerability of the entire building. Indeed due to their fragile behavior, they are easily damaged as a result of seismic events, even for medium-intensity earthquakes, and are therefore responsible for both the loss of functionality of the building (Dolce and Goretti, 2015) and the significant economic losses (Chiozzi and Miranda, 2017;De Martino et al., 2017;Di Ludovico et al., 2017a,b).
Only a few experimental studies focused instead on the IP/OOP interaction behavior of these infill walls (such as Angel et al., 1994;Flanagan and Bennett, 1999;Calvi and Bolognini, 2001;Furtado et al., 2016;Ricci et al., 2018), showing that the OOP strength of the panel reduces significantly as the IP displacement demand increases. In addition, in order to increase the IP/OOP seismic performance of thin walls, scientific interest has recently been focused on TRM-based strengthening solutions, such as fiber-reinforced or textile-reinforced mortars (e.g., da Porto et al., 2015;Ismail et al., 2018;Sagar et al., 2019;Minotto et al., 2020).
It is worth noting that, with the aim of reducing the IP/OOP seismic vulnerability of masonry infill systems, numerous studies oriented toward innovative solutions have recently been initiated (refer to da . A group of solutions is based on decoupling techniques between masonry infill and frame so that the deformations of the latter do not generate stress on the panel (e.g., Nasiri and Liu, 2016;Tsantilis and Triantafillou, 2018;Marinković and Butenweg, 2019). Another approach consists in reducing the infill-frame interaction through the use of sliding or deformable joints, which concentrate the IP deformation and damage in selected planes, keeping the infill panel undamaged even if in contact with the surrounding frame (Mohammadi et al., 2011;Preti et al., 2015;Verlato et al., 2016;Vintzileou et al., 2016;Morandi et al., 2018b). However, a general consensus has not yet been reached on any of these innovative solutions, presenting all some pros and cons in terms of seismic, thermal, and acoustic performances, as well as durability and cost. In addition, they mainly represent research products and have not yet been used for real applications in a widespread way.
Furthermore, nowadays, masonry infill walls with strong or thick perforated clay units (i.e., with thickness > 25-30 cm) are adopted with increasing frequency in Europe, even in highly seismic areas, due to their good thermal and acoustic performances necessary for the fulfillment of the recent European regulations regarding both energy efficiency of buildings and environmental sustainability. These infill walls are less sensitive to the IP/OOP interaction effects and, in general, allow better seismic performance; moreover, the vulnerability of these systems can be further reduced by means of vertical and/or horizontal reinforcement (da Porto et al., 2013;Vintzileou et al., 2017).
Despite this, the experimental studies available in the literature on robust clay masonry walls are rather limited. In particular, the first systematic characterization of the IP/OOP behavior of these walls, including reinforcement solutions, was carried out by da Porto et al. (2013). Further experimental studies on strong infill walls, both in full and partial configuration, were subsequently carried out at the University of Pavia, investigating the IP behavior  and the reduction of OOP performance upon reaching certain IP damages . All these studies allowed a first evaluation of the infill limit states, as well as the definition of the associated IP limit drifts. The latter experimental work, with regard to IP tests, was further deepened in a recent publication (Morandi et al., 2018a), where the performances of strong (thick) and weak (thin) infill walls are also compared, with the ultimate goal of providing useful indications for the design and verification of these non-structural elements in seismic areas. Finally, more recently, Butenweg et al. (2019) performed quasi-static cyclic tests on strong masonry infills by means of separate, sequential, and combined IP and OOP loading, thus assessing the effects of the loading conditions.

Research Significance
In summary, the framework in which this research has been developed, over the last few years, was characterized by the awareness that traditional thin clay masonry infill walls are very vulnerable to earthquakes; robust clay masonry infill walls behave better, but experimental studies on their seismic performance are rather limited; and, lastly, the behavior of both masonry systems is significantly worsened due to the interaction with the RC frame and the effects of simultaneous IP and OOP actions.
In this context, the present research aimed at filling this gap by means of a systematic experimental characterization of the combined IP/OOP behavior of robust clay masonry infills. The detailed aims of the research encompassed the following: (i) assessing the reliability of robust clay masonry walls in sustaining seismic actions, (ii) comparing the effectiveness of unreinforced (URM) and reinforced (RM) masonry solutions, (iii) assessing the effect of openings in the behavior of robust clay infill masonry walls, taking into account solutions with or without lintels, and (iv) calibrating IP damage degradation models and OOP capacity models for the infill walls.
The paper presents the results of these tests, carried out on full scale, one-bay and one-story infilled RC frames with a quasistatic procedure, under cyclic IP displacements of increasing amplitude and, after certain IP drift levels, under a monotonic incremental OOP force until the infill collapsed. This allowed obtaining the experimental OOP strength degradation laws of the infills due to their IP damage. Given the type of panels tested, this is a new result that expands the relevant experimental literature, providing relevant information for an increasingly reliable calibration of analytical degradation laws. In addition, the paper presents a novel and fairly refined analytical model for predicting the OOP behavior of infill walls based on the well-known arching mechanism, where almost all simplifying hypotheses are removed; this model, validated and calibrated on the experimental results, proved to be effective in predicting the OOP response of the infills, even when degraded in strength and stiffness due to IP damage.

CONSTRUCTION SYSTEM
The specially developed construction system makes use of clay units with vertical holes, percentage of holes of 50%, and special recesses for the insertion of vertical reinforcing bars. The unit dimensions are 195 × 240 × 300 mm in height, length, and thickness, respectively. Two webs of the units can be removed, forming an open-shaped "C" pocket, so that the units can be easily laid after the vertical reinforcement has been placed in position (Figure 1). The units are laid with a M10 general purpose mortar on 10-mm-thick bed joints. The units have tongue and groove on their lateral faces; hence, the head joints are left unfilled and rely on these indentations only.
In the RM infill walls, four vertical reinforcement bars, with spacing varying between 1,000 and 1,500 mm and with a diameter of 8 mm, were used. In the initial system development, the vertical bars were anchored to both the base and the top beam of the RC frame, whereas in the final configuration reached after the initial tests, anchoring is provided only to the base beam. The horizontal reinforcement (stirrups) was made of two bars with a diameter of 6 mm, placed every three joints and with no connection to the RC frame columns. The stirrups were placed starting from the second mortar bed joint in the full infill walls and starting from the third mortar bed joint in the partial infill walls, for a total of four or three stirrups, respectively (Figure 3).

EXPERIMENTAL PROGRAM
The experimental program has been defined in order to investigate the combined IP/OOP behavior of robust clay masonry infill wall construction systems. In particular, the specimens were IP tested, imposing different levels of maximum displacements of the frame top beam. Only after the occurrence of IP damage, differentiated according to the IP drift attained by the frame, were the specimens tested OOP until collapse.
The other objectives of the experimental campaign, as already mentioned in the introduction, were as follows: comparing the effectiveness of unreinforced and reinforced masonry solutions, evaluating the behavior of infill walls that fully fill the frame and of partial infill walls having some openings, and, in the latter case, verifying the effect of lintels.

Material Properties
Mechanical characterization of materials and masonry subassemblages preceded tests on frame specimens. Standard tests on units, mortar, and reinforcement bars, compression tests on URM walls, and flexural tests on RM walls were carried out.
The clay units were tested in compression in the directions parallel to the holes and orthogonal to the holes in the plane of the wall, according to EN  Figure 2]. Four specimens (URM_V) were tested in the vertical direction, i.e., loading in the direction orthogonal to the bed joints, and other four specimens (URM_H) were tested in the horizontal direction, i.e., loading in the direction parallel to the bed joints. Table 1 shows the average values of stress at first cracking (σ 1 ), maximum compressive strength (σ max ), modulus of elasticity (E), Poisson's ratio (ν), and shear modulus (G) in between 10 and 40% of peak strength.
Flexural tests were carried out on six RM specimens having a dimension of about 1.0 × 2.5 m, according to EN 1052-2 [CEN (European Committee for Standardization), 2001b, see Figure 2]. Three specimens (RM_V) were tested in flexure with the failure line parallel to the bed joints (vertical masonry strips), and three other specimens (RM_H) were tested in flexure with the failure line orthogonal to the bed joints (horizontal masonry strips). Table 2 shows the average values of the bending moment at first cracking (M 1 ) and yielding (M y ), of the maximum moment (M max ), of the corresponding mid-span deflections (δ 1 , δ y , and δ max ), and of the ultimate deflection at 20% strength decrease (δ u ).

Combined In-Plane/Out-of-Plane Test Program
The combined IP-OOP tests were conducted on full-scale, onebay and one-story, RC frames, infilled with the URM and RM infill wall systems described above. The choice to adopt full-scale specimens was made to avoid any scaling effect related to the relative stiffness ratio between the RC frame and the infill wall. The specimens were designed following the criteria described in   et al. (2013), and their main characteristics are briefly reported below. The infill wall dimensions were 4.15 × 2.65 m (length × height), and the RC frame was designed as part of the groundlevel frame of a regular and typical three-story Italian residential building (class of use II), with columns spaced 4.5 m × 4.5 m and stories 3.0 m high. The frame was seismically designed in a high-ductility class [class "A" according to MIT (Italian Ministry of Infrastructure Transport), 2008], considering a peak ground acceleration of 0.25 g, thus ensuring the hierarchy of strength of the RC cross-sections.
To evaluate the reciprocal influence between the masonry infill wall and the RC frame, a bare frame (i.e., without any infill wall, specimen 1-RCF) was built, and tested IP was up to 3.4% drift. Table 3 is a list of the specimens of the above-described test program and Figure 3 shows some of them. Besides these eight specimens, whose results will be thoroughly described in the following, three other specimens were tested. Specimen 7-PRIU was similar to specimen 8-PRIU, i.e., partial RM infill with a full height opening, with the difference that the anchorage of the vertical reinforcement is realized both in the bottom RC beam (as for 8-PRIU) and in the top RC beam. Specimen 9-PRIU also had a partial infill with a full height opening, with the particularity that one of the two partial walls only had vertical reinforcement (three bars of 8-mm diameter at about 550-mm spacing), whereas the other only had horizontal reinforcement (four stirrups of 6-mm diameter at about 600-mm spacing). Lastly, specimen 10-P still had a partial infill with a full height opening, but one partial wall was made of URM (similarly to 6-PIU) and the other of RM (similarly to 8-PRIU). These last two walls were simply tested OOP to get information on the OOP capacity of the walls not previously damaged.
The results of these additional specimens will not be presented in detail, but some specific aspects of their behavior will be described, where relevant.

Test Setup, Instrumentation, and Procedure
The experimental setup (Figure 4) consisted of two servocontrolled hydraulic actuators placed over the beam-column nodes for applying vertical loads. The load is transferred to the columns through a self-locking device, hinged to a reaction steel beam at the top of the actuator, and connected by ball-and-socket joints to the RC frame bottom beam. An axial load of 400 kN on each column was kept constant during the IP and OOP tests. One servo-controlled hydraulic actuator is placed at the height of the top beam for applying horizontal IP cyclic displacements. Lastly, the loading system for the OOP test is made of commercial steel profiles connected to another hydraulic jack. The system allows applying four punctual forces of equal intensity at every third of the infill wall length and height, in the case of full infill walls, and two linear forces of equal intensity at every third of the infill wall height, in the case of infill walls with openings. Two linear guides on the lateral face of the top beam constrain the frame displacements in the OOP direction.
In the first phase of the test, the frame columns are preloaded to simulate the presence of upper stories. Then, horizontal cyclic displacements are applied to the upper beam with a quasi-static procedure (maximum stroke speed of < 0.5 mm/s). The displacement history consists of cyclic displacements of increasing amplitude that are repeated three times for each amplitude ( Figure 5); the target displacements were defined based on the following inter-story drifts:

Specimen
Masonry type Vertical reinforcement

Horizontal reinforcement
Opening Test type  Frontiers in Built Environment | www.frontiersin.org FIGURE 5 | In-plane test protocol adopted for infilled frames (up to 1.2% drift) and bare frame.
At the end of the IP test, the specimens were brought back to null horizontal displacement, and then the OOP test was performed by applying a monotonic incremental force until the collapse of the infill.
The in-plane test on the bare frame continued up to the maximum actuator stroke, to study its elastic and plastic behavior; hence, the following top displacement cycles were added: ± 1.6, ± 2.0, ± 2.4, ± 3.2, and ± 3.4%. The three main target inter-story drifts, at which the IP tests were stopped to start the OOP tests, were identified as 0.5, 1.0, and 1.2% based on the following considerations: ; -1.0% drift has been assumed, on the basis of the experimental observations of damage propagation, as a life safety limit state for the partial infill walls; and -1.2% drift has been assumed, on the basis of the experimental observations of damage propagation, as a life safety limit state for the full infill walls.
The instrumentation setup was designed to measure the global and local deformation of the RC frames, the global IP deformation of infill walls and the local strain on masonry due to the infill wall-RC frame interaction, the global OOP deflection shape of infill walls, and the strain of some horizontal and vertical reinforcement bars used in the RM walls. For this purpose, 35 linear potentiometers, 15 draw wire potentiometers, and 12 strain gauges (on the reinforcement bars) were used, as shown in Figure 6. Figure 7 shows the crack patterns of the specimens with masonry infill walls at the end of the IP tests. The data acquired during the tests were used to obtain the hysteresis loops shown in Figure 8. The hysteresis loops were not completely symmetrical due to a non-symmetrical damage on the reverse loading cycles and, in two cases (3-IU and 11-PRIU), due to a sudden sliding of the bottom RC beam on the laboratory floor, which was immediately corrected during the test. However, in general, it can be seen that the test phases give comparable results, demonstrating the reliability of the tests. The infill force-displacement envelope curves associated with the third IP loading cycle are shown in Figure 9A, and the associated stiffness degradation curves are shown in Figure 9B. In Figure 9A, the envelope curve obtained from the test of the bare frame (1-RCF) ( Figure 10A) was subtracted from the envelope curves obtained by testing the infilled frames ( Figure 10B), allowing to derive the IP behavior of the infill wall as the difference between the force-displacement envelope curve of the infilled frame and that of the bare frame [according to the procedure described in Minotto et al. (2020)]. The masonry infill wall contribution and limit states are thus derived with reference to these "subtracted" curves. Conversely, energy dissipation capacity and equivalent viscous damping ratio (Figure 11) are directly given with reference to the global specimen behavior, as in this case the direct comparison with the 1-RCF specimen highlights the differences of the infilled and bare frame specimen responses.

EXPERIMENTAL RESULTS
Lastly, Table 4 is a list, with reference to the infill contribution only, of the initial stiffness values K init (in-between 0 and 0.1% drift) and the load and drift values measured at characteristic limit states, corresponding to maximum strength (F max , θ max ) and ultimate displacement possibly attained during the IP test (F u , θ u ).
The data processing and presentation of OOP tests is relatively simpler. Figure 12 shows some details of the failure mechanisms, whereas Figure 13 shows the OOP force-displacement curves of all specimens. Table 5 is a list of load and deflection values measured at maximum strength (F max , d max ) and at ultimate deflection, conventionally set at 20% degradation of the OOP strength (F du , d u ). The presented values of deflection are those corresponding to the midspan control point, i.e., the maximum values for each tested specimen.

In-Plane Cyclic Tests
During the IP tests, all infilled specimens presented the first non-linearity starting from 0.1% drift, as can be seen also by the change of stiffness in the envelope curves ( Figure 9B). First cracks develop at the infill masonry wall/RC frame interface. The full masonry infill walls start cracking in between 0.2 and 0.4% drift levels. Then, stepped cracks along the head and bed joints develop from the masonry corner to the wall center (Figure 7). In between 0.4 and 0.6% drift, these infill wall systems reach their maximum strength (F max ). At this point also, the RC frame nodes start cracking (minor cracks started already at 0.2% drift). The RM infill wall system reaches an average IP maximum strength (5-RIU, 401 kN at 0.6% drift) that is 26% higher than that of the URM system (3-IU, 319 kN at 0.4% drift). In RM walls, diagonal cracks cross both the masonry joints and the units, but they have a smaller dimension and a slightly higher diffusion on the masonry surface (Figure 7).
Regarding the partial masonry infill walls (infills with openings), all three tested specimens have smaller and more variable initial stiffness than the fully filled specimens, with the highest values shown by 8-PRIU, at least up to 0.3% drift. At this point, this RM specimen (8-PRIU) reaches a maximum strength of 168 kN, whereas the URM specimen (6-PIU) reaches, at 0.4% drift, a maximum strength of 171 kN (Figure 9A). The RM specimen with the lintel (11-PRIU) reaches its maximum strength at 0.6% drift with load values that, related to the effective load-bearing area of the wall, are comparable to those of fully filled infill masonry walls (243 kN). Regarding the crack pattern, the URM specimen (6-PIU) is characterized by the sudden formation of sharp diagonal cracks along the compressed struts, starting from the RC frame nodes to the RC base beam (Figure 7). The crack pattern of the RM specimen (8-PRIU) develops more gradually, involving mainly the compressed toes close to the RC frame nodes and base beam, and leaves almost intact the central part of the walls (Figure 7). The RM specimen with lintel presents a more moderate and uniform damage pattern. At the ultimate drift, there are light diagonal cracks developing in both loading directions, but definitely smaller than those of 6-PIU, and a limited toe crushing close to the masonry corner (Figure 7).
The energy dissipation capacity of all tested specimens is greater than that of the bare RC frame, with values that, starting from 0.5% drift, are in between 40 and 50%, compared to 20% of the bare frame ( Figure 11A). The equivalent viscous damping ratio as well is higher in infilled specimens than in bare RC frame, with values (starting from 0.5% drift) in between 6 and 8%, compared to 4% of the bare frame. 8-PRIU only deviates from these values, reaching higher values ( Figure 11B). This might be due to the higher rotations of the two masonry panels observed during the test, with subsequent development of friction along the RC frame beam and progressive crushing of the corner units.

Results of Out-of-Plane Tests
After the cyclic in-plane test, the masonry infill walls were subjected to monotonic out-of-plane loads until collapse. All tested walls developed an arching mechanism, mainly in the vertical direction. The stiffness degradation (Figure 13) during the OOP test is mainly due to the progressive crushing of the units caused by the compressed struts developed in the arching mechanism. In the case of the full infill walls, the particular load application procedure (four-point loads) caused some local failures in the final test phases, after the attainment of the maximum OOP strength. Tests on RM specimens showed that the insertion of vertical and horizontal reinforcement bars allowed containing the OOP expulsion of masonry portions in reinforced specimens, at least until the attainment of the ultimate deflection (at 80% of maximum strength) and after (Figure 12). The OOP strength of full RM masonry infill walls was higher than that of URM infills, particularly for higher levels of previous IP drift (F max of 5-RIU is 32% higher than that of 3-IU; F max of 4-RID is 14% higher than that of 2-ID). The strength decrease due to previous IP damage was smaller in RM walls (−6% going from 0.5 to 1.2% drift) than in URM walls (−20% going from 0.5 to 1.2% drift). Similar observations can be drawn for OOP stiffness (see Figure 13).
Partial RM infill masonry wall (8-PRIU) presented similar values of OOP strength compared to URM wall (6-PIU), although with different values of initial stiffness and ultimate deflections (see Figure 13). The URM wall (6-PIU), despite the very significant cracking during IP tests, presented a surprisingly high value of OOP strength, due to the indentation of the masonry portions separated by the crack and the  subsequent activation of the arching mechanisms in this case, too. However, this most likely happened because of the specific (quasi-static) loading condition; during a real dynamic excitation, it is reasonable that the two damaged and unstable portions of masonry would collapse without developing any resisting mechanism. Partial RM infill masonry wall with lintel (11-PRIU) presented a completely different OOP behavior, reaching values of initial stiffness and maximum strength definitely higher than those of the RM specimen without lintel (8-PRIU) (see Figure 13). The presence of the lintel, due to its coupling effect, reduces the relative rotation of the two masonry panels during the IP cyclic displacements, and this, in turn, reduces the unit damage at the toe (close to the masonry corner, at the top and bottom beams), thus also increasing the OOP capacity.
In addition to these tests, a further test (10-P) was carried out on a specimen without carrying out a previous IP test.
The objective was to experimentally evaluate the maximum OOP capacity due to the activation of the arching mechanism within the masonry thickness. The OOP force-displacement curves associated with the URM and RM walls of this specimen (respectively, 10-PI and 10-PRI in Figure 13B) show values of initial stiffness, maximum strength, and ultimate deflection, which are clearly higher than those of the partial specimens previously tested IP, with and without lintel.

Effect of Reinforcement
Although the behavior of full URM masonry infill walls is already adequate due to the unit robustness and the overall masonry thickness, the positive effect of the reinforcement in the full RM masonry infill walls is evident. In particular, the IP behavior is characterized by a drift level at the attainment of the peak strength (conventionally taken as damage limit state for the masonry infill) that changes from 0.4 to 0.6% in URM and RM specimens. The RM strength is 26% higher than that of the URM specimen. The damage in RM walls is more diffused but locally less intense than in URM walls. This, in turn, improves the OOP behavior of the RM walls, for which the OOP strength is higher than that of URM infills, and particularly for higher levels of previous IP drift, as the strength degradation due to previous IP damage is smaller in RM than URM walls.
In the case of partial infills (walls with openings), omitting the case of the wall with lintel, the situation is more complex. Indeed looking at the load-displacement envelop curves, the RM specimen appears more fragile, with peak strength (hence damage limit state) reached at 0.3% drift (compared to 0.4% of the URM specimen), similar maximum strength (168 kN), and smaller ultimate displacement (0.4% drift compared to 0.65% of the URM specimen). However, this might be due also to the higher initial stiffness of the RM wall, and indeed besides the different initial stiffness, the overall shape of the IP load-drift curve in the two cases is quite similar. In the case of partial infills, in any case, the beneficial effect of the reinforcement can be seen in a definitely less critical crack pattern and less fragile crack propagation, a very high energy dissipation capacity, and better control of the OOP expulsion of the masonry walls.
Lastly, in both cases, full and partial infill walls, the presence of the reinforcement bars makes the final crack pattern less severe, still positively increasing the energy dissipation capacity and equivalent viscous damping ratio of the specimens.
As mentioned above, two other specimens (7-PRIU and 8-PRIU) with partial infill walls and a full height opening, whose results were not discussed before, were tested during the experimental campaign. The first case, 7-PRIU, had the two walls made as in 8-PRIU, except for the fact that the vertical reinforcement was anchored on both the bottom and the top RC beams. Probably due to the rigid connection to the top beam and therefore to a more intense stress transfer at the top beampanel interface, a much more pronounced crushing of the entire upper course of the masonry panels was observed compared to that in 8-PRIU, starting from a relatively low drift level. This even caused, at 0.8% drift, the failure of one of the vertical reinforcement bars close to the RC frame node (Figure 14A). This type of damage at the top course prevents the infill wall  from fully exploiting its IP capacity and, above all, does not allow developing a proper resisting mechanism when the infill wall is loaded OOP. Hence, the OOP failure occurs with an almost rigid outwards rotation of the infill panels ( Figure 14B). Based on this evidence, in the prosecution of the research, top beam-infill wall connections were avoided. This was also justified by the fact that, to prevent the OOP collapse of this type of walls, it is very important to preserve the top masonry course integrity, allowing an arching mechanism to develop within the (considerable) masonry thickness. The second case, 9-PRIU, had two different panels, one made with vertical reinforcement only (three bars of 8mm diameter at about 550-mm spacing) and the other with horizontal reinforcement only (four stirrups of 6-mm diameter at about 600-mm spacing). The main aim for testing this specimen was understanding whether a partial reinforcement configuration, based on vertical or horizontal reinforcement only, was also effective. This test was characterized by the premature failure of the panel with vertical reinforcement only that, at 0.4% drift, formed a sharp diagonal crack along the compressed strut, starting from the RC frame node to the RC base beam. This very fragile crack subdivided the masonry panel into two unstable triangular portions (Figures 15A,B), similarly to what happened in 6-PIU. The very asymmetrical behavior that the specimen presented starting from this moment onwards does not allow one to make a clear assessment of the behavior of the second masonry panel, with horizontal reinforcement only. In any case, partly because of the modified frame behavior, the second panel reduced the IP rotation effect observed in the previous 6-PIU and 8-PRIU specimens, and this reduced the damage level close to the masonry corners (close to the RC frame node and to the base beam), limiting the overall crack pattern ( Figure 15C) and improving the general behavior of the panel with horizontal reinforcement only.

Effect of Openings
As reported in "Section In-plane cyclic tests" and "Section Results of out-of-plane tests, " when there is an opening in the wall, the behavior of the infill is worse than in the case of the full infill walls. In this case, in general, the behavior under IP loading is more fragile, with a trend to have less diffused, but sharper, diagonal cracks and sometimes intense toe crushing. This crack pattern is more intense and fragile in the case of URM walls (6-PIU). The stiffness of partial walls is obviously smaller than that of full infills, but the strength values of the partial walls, related to the effective load-bearing area of the panel, are less than proportional compared to those of fully filled infill walls. These drawbacks are only partly mitigated by the presence of reinforcement in the RM specimen (8-PRIU).
The OOP behavior of partial infill walls is strongly affected by the specific IP behavior. Indeed the significant damage state at 1.0% drift implies a stronger strength degradation for the masonry properties, thus the OOP capacity of 6-PIU and 8-PRIU is less than half that of a partial wall without any previous IP damage (10-P), and this strong reduction is probably higher than the corresponding reduction that could be inferred in full infill walls, from the comparison of data that we have at 0.5 and 1.2% drift. Besides that, partial masonry infill walls are less constrained than full infills; hence, it is more difficult that a plate or a horizontal arching mechanism gives a contribution to the overall OOP strength.
The coupling effect given by the presence of masonry lintels completely change the behavior of masonry infill walls with openings; this effect induces a change of crack pattern, avoiding the very fragile and strong damage undergone by the URM wall with opening but also allows less damage than the RM wall with opening. The high values of IP capacity reached by the specimen 11-PRIU, due to the simultaneous activation of both masonry panels separated by the opening (as demonstrated by the diagonal cracks oriented in both directions in each masonry panel), make it more similar to full infill walls. Following the enhancement of the IP behavior, the OOP capacity of the partial infill wall with lintel is also definitely improved.

State of the Art and Development of a New Analytical Model
The OOP capacity of infill walls is generally expressed in terms of the maximum uniform lateral pressure q lat which causes their collapse. The first analytical solutions for the prediction of q lat were based on the flexural response of the infill panel, modeled with homogeneous isotropic material with linear elastic behavior, relying on its tensile strength (Timoshenko and Woinowsh-Krieger, 1959) or flexural strength (Haseltine et al., 1977). However, subsequent experimental studies highlighted the limits of these solutions, demonstrating that the OOP response of infill panels, in particular after their cracking, is governed by the arching mechanism, which can be modeled considering the infill panel divided into two rigid blocks that rotate about their supported ends, as shown in Figure 16A. According to this approach, the OOP capacity of the panel depends on the compressive strength of the masonry, except for possible phenomena of "snap-through" instability in the case of high OOP displacements (e.g., for infill walls with significant slenderness). The first study in this regard is that of McDowell et al. (1956) under the hypothesis of one-way behavior of a masonry strip having rigid supports at the ends. Subsequently, other researchers included in their evaluations the two-way action of the panel and the deformability of the supports (Dawe and Seah, 1989b) and also investigated the effects of degradation due to previous IP damage (Angel et al., 1994;Abrams et al., 1996). An indepth literature review on these analytical solutions, developed for the prediction of the OOP response of infilled frames, is presented in Asteris et al. (2017), together with a discussion on the effectiveness of recent integrated IP/OOP numerical models to be used in structural analysis (which is outside the scope of this study). Furthermore, an extension of the arching mechanism solution was proposed by Hak et al. (2013) to take into account the contribution of a possible external reinforcement of the panel. Among the first experimental and analytical studies on the OOP infill capacity, that of Angel et al. (1994) is one of the most comprehensive, and its results converged, with some simplification, in the following expression proposed in FEMA-306 [FEMA (Federal Emergency Management Agency), 1998]: where λ is a slenderness parameter dependent on the h w /t w ratio and defined in Tables 8-5 of the FEMA-306, and R 1 and R 2 are OOP strength reduction factors that take into account, respectively, the existing IP damage and the confining frame flexibility [for further details, please refer to FEMA (Federal Emergency Management Agency), 1998]. For the verification of the OOP capacity of infill walls, EN 1996-1-1 [CEN (European Committee for Standardization), 2005] also provides a simplified formula based on the arching mechanism, although without indications about the IP/OOP interaction, whereas the current EN 1998-1 [CEN (European Committee for Standardization), 2004] is silent in this regard, and the Italian building code [MIT (Italian Ministry of Infrastructure Transport), 2018] generically refers to flexural mechanism for the verification of load-bearing masonry walls. However, the bending mechanism is inadequate to evaluate the OOP capacity of infill walls, as they are generally characterized by the absence of vertical load (besides their self-weight) and by a negligible tensile strength (especially if previously damaged); therefore, this mechanism fails to explain the significant OOP infill strengths observed in the experimental tests (as abovementioned). In addition, the compression level in the infill wall, necessary to apply a flexural model, varies significantly with the OOP deflection of the panel. On the other hand, verification formulas based on the flexural mechanism could be adequate in the case of thin, externally reinforced/strengthened infill walls; indeed Minotto et al. (2020)   developed during the OOP response of the panel, although in a simplified way.
Therefore, given the shortcomings of the standards in this regard and the lack of widely accepted solutions, a new analytical model, based on the arching mechanism, was developed in this study in order to further investigate the OOP behavior of clay masonry infill walls, both unreinforced and reinforced. This model, which includes the non-linear behavior of masonry, the possible presence of reinforcements, and the deformability of the supports, can effectively reproduce the entire OOP capacity curve of the infill wall, predicting its experimental OOP response not only in terms of strength but also of stiffness. This represents a novelty, as the few similar analytical models available in the literature, such as those of Tumialan et al. (2003b) and Varela-Rivera et al. (2012), are based on linear modeling of the infill panel and allow predicting the ultimate OOP capacity only.
In our proposal, the infill wall is idealized as a vertical strip of unitary depth placed within linear elastic supports in vertical direction and subjected to OOP loads applied to the thirds of the infill height, consistently with the test setup ( Figure 16A). To avoid overestimation of the infill capacity due to the generally adopted simplifying assumptions (such as the infinite stiffness of the RC confining elements), the proposed model takes into account the beam vertical deformation, the ratio between infill wall length and frame span, and the position of the infill wall within the frame. In particular, the average vertical stiffness K v,avg of the upper beam used in the model was calculated as the ratio between the integral of its bending stiffness, K v (x), over the total length of the beam, and the beam length l, as shown in Equation (2). For the calculation of K v (x), the rotational elastic stiffness of the end supports of the beam was calibrated in order to obtain the best fit with the experimental results.
The compressive behavior of masonry was modeled by an elastoplastic stress-strain law, which also includes a softening branch ( Figure 16B), whereas the tensile strength of masonry was assumed to be zero. The rigid rotation of the two wall segments implies reaction forces and section deformations, which modify the initial geometrical configuration of the system. The OOP strength of the infill walls can therefore be calculated using an iterative procedure, imposing the balance of the masonry sections that are subjected to both the reaction forces of the frame and the OOP loads. According to this approach, the collapse of the infill wall can be due to either masonry crushing or loss of balance, allowing a reliable evaluation of the actual behavior.

Model Calibration
The experimental OOP tests were performed on masonry walls previously subjected to different levels of IP drift, hence damage. To take into account the degradation of mechanical properties of masonry due to IP damage, two independent reduction factors for the compressive strength (f m ) and the elastic modulus (E m ), respectively, α and β, were introduced in Equations (3) and (4). Both coefficients depend on the type of masonry (URM and RM) and on the attained drift level, according to Equations (5) and (6).  Table 6 gives the coefficients a, b, c, and d in Equations (5) and (6), obtained through regression analysis based on experimental data. Figure 17 shows the comparison between the  load-deflection curves obtained with the analytical model (in red) and the experimental curves (in gray). Black squares and black dots highlight the achievement of the masonry elastic limit (at cross-section level) and the peak strength, respectively. In the case of RM, black triangles highlight the yielding of vertical bars. As can be seen, the calibrated analytical model allows one to reproduce almost perfectly the OOP load-deflection curves of the tested masonry infill walls. Figure 18A shows the trend of the reduction factors α and β, which apply to the model input parameters (f m and E m ) as a function of the infill IP drift. These analytical laws provide the degradation of the mechanical characteristics of the masonry due to IP damage. However, for design and verification purposes, the evaluation of the performance reduction of the infill wall by applying an overall reduction coefficient R directly to its OOP strength is more effective. In this regard, Figure 18B shows the OOP strength reductions for both URM and RM masonry infill walls tested in this experimental campaign as well as the associated analytical degradation laws obtained by calibration and based on Equation (7) and the coefficients of Table 7.
Quite recently, some researchers have proposed similar degradation laws, calibrated on not only mainly experimental Ricci et al., 2018;Minotto et al., 2020) but also numerical (Cavaleri et al., 2020) results. For comparison purposes, Figure 19 shows the various OOP strength reduction laws provided by previous authors for URM infill walls, including the one proposed in FEMA-306 [FEMA (Federal Emergency Management Agency), 1998, i.e., the R 1 factor in Equation (1)]. In particular, since the slenderness of the infill wall (h/t) significantly influences its OOP behavior, these laws are presented grouped in two graphs: Figure 19A refers to slender panels (h/t ≈ 20), whereas Figure 19B refers to squat panels (h/t ≈ 9). It is worth noting that the degradation laws given by Ricci et al. (2018) and FEMA-306 are also a function of wall slenderness; therefore, they are shown in both graphs of Figure 19 with different h/t values; in addition, the law of Cavaleri et al. (2020) is calibrated on the average of numerical results referred to various slenderness values, so it was equally reported in both graphs. Clearly, due to the different type of infills, the two graphs in Figure 19 cover a different range of IP drift values (up to a representative value for the ultimate limit state of the panel). As can be seen from these comparisons: the FEMA formulation does not seem conservative enough; the robust infill walls analyzed in this study show a much lower degradation than the slender ones; in general, the various laws proposed to date for the evaluation of the infill OOP strength reduction, although quite similar in trends, show evident differences which require further investigations and experimental validations.

Parametric Analyses and Results
Some parametric analyses, to investigate the most influential parameters on the OOP capacity of masonry infill walls, were carried out on the basis of the developed model. First, the top beam stiffness has a significant influence on the OOP strength of the infill wall. Figure 20A shows the variation of the infill OOP maximum strength when changing the ratio between the considered stiffness (R f ) and the experimental one (R f,exp ) for a wall that has undergone a 1.2% IP drift. For low stiffness values, the OOP strength rapidly goes to zero, whereas for higher stiffness values, the OOP strength asymptotically tends to higher values. This is consistent with the smaller rotation of the masonry portion in the case of stiff constraints, which increases the lever arm of internal forces and hence the stabilizing moment, allowing better exploitation of the available masonry compressive strength.
Another very significant parameter is, of course, the thickness of the masonry infill wall. Figure 20B shows the maximum OOP strength varying the masonry slenderness (i.e., height-tothickness ratio, blue curve). The red curve represents the flexural strength of masonry evaluated according to MIT (Italian Ministry of Infrastructure Transport) (2018). The dotted lines highlight, for a height of the wall corresponding to that of the experimental specimens, the behavior of walls having thickness of 100, 200, and 300 mm. It can be seen that, for high slenderness, the OOP strength tends to very small values, which correspond to the flexural capacity of the wall. Clearly, for very high slenderness, the collapse might be due to local phenomena related to fragile failure of the units or shear failure; hence, the model reliability decreases as far as we try to extrapolate results related to values of slenderness very distant from the experimental ones.
Lastly, the depth of the vertical reinforcing bars within the masonry thickness was evaluated. Figure 20C shows the maximum OOP strength varying the position of the vertical bar.
In this case, all the other aspects of the model coincide with the geometrical configuration of the experimental specimens, and the masonry is assumed undamaged. It must be underlined that the main aim to use a RM system for the infill walls is not increasing the masonry strength but, rather, limiting damage and avoiding OOP masonry expulsion in the case of a seismic event. Consistently with these objectives, low reinforcement percentage has been used in the experimental specimens, and vertical bars have been placed at the masonry center line. This position is the least effective under the mechanical point of view, but it is also the least expensive, as it does not require the insertion of reinforcement on both masonry sides. Figure 20C obviously confirms that the center line position is the least effective for the vertical bars; however, it also shows that, due to the very low percentage of reinforcement in the specific case, the increase in strength achievable by placing the bars outwards in the wall is very limited (about 5%).

CONCLUSIONS
From the experimental tests and numerical analyses carried out on robust clay masonry infill walls in this research, it can be drawn that: -Considering the results in terms of general IP behavior (crack pattern, stiffness, and strength) and resulting OOP behavior and capacity after reaching various levels of previous IP damage, the overall performance of robust clay masonry infill wall systems is adequate. -The presence of a system of vertical and horizontal reinforcement, in full masonry infill walls, slightly reduces the IP damage and increases the IP strength. This, in turn, allows obtaining higher values of OOP capacity for RM walls and smaller impact of previous IP damage on the OOP behavior (smaller degradation of the mechanical properties).
In addition, the reinforcement system, both in full and partial infill walls, increases the energy dissipation capacity and the viscous damping ratio of the infills and is very effective to avoid the OOP expulsion of masonry portions, which, on the contrary, is not hindered in the case of URM infills.
-The effect of some reinforcement details, such as anchoring the vertical reinforcement to the top beam, dramatically worsen the behavior of the infill masonry system. At least in this case, where the thickness of the wall itself is already enough to provide good restraint against the OOP overturning, this type of connection is not recommended. In this research, no connection of horizontal bars to the RC frame columns was provided. The tests carried out also evidenced a bad performance of walls reinforced with vertical bars only. -Partial masonry infill walls (infill with opening) presented a worse behavior than full infill walls. Some specific aspects resulted critical when compared to the corresponding full infills-in particular, the very fragile crack pattern of URM infills and, in general, the anticipation of the limit states. The beneficial effect of reinforcement was also reduced, although it was still evident in some respects, such as controlling the OOP collapse or improving the parameters of the cyclic behavior. -The coupling effect given by masonry lintels to infills significantly improved the behavior in case of walls with openings, both in the IP and OOP loading conditions, at least in this case of robust masonry systems. -Considering the results in terms of energy dissipation and equivalent viscous damping, the contribution of robust masonry infill walls to the dissipative behavior of an RC frame is very significant. Therefore, even if the ductility of the RC frame may not be fully exploited, due to the increase in stiffness caused by the presence of robust masonry infill walls, the greater dissipation capacity offered by the masonry system can be advantageous. -An analytical model was developed based on the arching mechanism, taking into account, although in a simplified way, the RC frame deformability and the degradation of the mechanical properties of the masonry due to IP drift. This model allows estimating the actual OOP load-deflection curves very well. -From the experimental and model results, it was possible to derive simplified degradation laws of the infill OOP strength due to IP drift to be used for design purposes. These degradation laws were compared with other proposals in the literature, highlighting the high variability between them and, consequently, the need for further investigations. -In addition, from the parametric analyses carried out, it was possible to estimate, with reference to the infill OOP strength, the influence of the frame stiffness, the values of masonry thickness for which the arching mechanism becomes less effective in favor of a flexural resisting mechanism (slenderness >30), and the small effect of the position of the vertical reinforcement bar in this specific masonry system.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, upon reasonable request.

AUTHOR CONTRIBUTIONS
FdP: conceptualization, methodology, writing-original draft, and supervision. MD: methodology, validation, data curation, writing-review, and editing. NV: investigation, formal analysis, data curation, and software. GG: methodology, investigation, formal analysis, and data curation. All authors contributed to the article and approved the submitted version.

FUNDING
The authors declare that this study received funding from Cisedil s.r.l.. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article or the decision to submit it for publication.