Shear response of partially-grouted reinforced masonry walls with a central opening: Testing and detailed micro-modelling

Accepted Manuscript Shear response of partially-grouted reinforced masonry walls with a central opening: Testing and detailed micro-modelling

Sebastián Calderón, Cristián Sandoval, Oriol Arnau PII: DOI: Reference:

S0264-1275(17)30019-9 doi: 10.1016/j.matdes.2017.01.019 JMADE 2660

To appear in:

Materials & Design

Received date: Revised date: Accepted date:

11 October 2016 6 January 2017 9 January 2017

Please cite this article as: Sebastián Calderón, Cristián Sandoval, Oriol Arnau , Shear response of partially-grouted reinforced masonry walls with a central opening: Testing and detailed micro-modelling. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Jmade(2017), doi: 10.1016/ j.matdes.2017.01.019

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ACCEPTED MANUSCRIPT Shear response of partially-grouted reinforced masonry walls with a central opening: Testing and detailed micro-modelling Sebastián Calderóna, Cristián Sandovala,b,*, Oriol Arnauc a

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Department of Structural and Geotechnical Engineering. Pontificia Universidad Católica de Chile. Casilla 306, Correo 22. Santiago, Chile. b School of Architecture. Pontificia Universidad Católica de Chile. Casilla 306, Correo 22. Santiago, Chile. c Department of Structural Engineering. Instituto de Ingeniería. Universidad Nacional Autónoma de México. ABSTRACT

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Openings can have a significant effect on the seismic response of partially grouted reinforced masonry (PG-RM) walls. Despite this, very few investigations have been carried out to study their influence. Accordingly, this paper presents the results of an experimental and numerical research project aimed at increasing the knowledge of the shear response of PG-RM walls with openings. The experimental program includes test results of three full-scale walls (one solid wall and two perforated walls with a central window) tested under cyclic lateral loading up to failure. In addition, a complete characterization of the constituent materials and their interfaces is reported, with an emphasis on the experimental data needed for implementing advanced numerical models. The results obtained are used to validate a numerical model based on the detailed micro-modelling approach. Once validated, the models are used to conduct a sensitivity analysis that considers opening size variation and the horizontal reinforcement ratio at piers. The results show that a rise in the pier horizontal reinforcement ratio leads to an increase in shear strength and displacement ductility of the entire wall, while an increase in the pier aspect ratio decreases the shear strength and increases the displacement ductility in the entire wall.

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Keywords: Reinforced masonry; detailed micro-modelling; shear strength; partially grouted; perforated wall. ________ * Corresponding author: Tel.: +56 2 23544210

E-mail addresses: [email protected] (S. Calderón); [email protected] (C. Sandoval), [email protected] (O. Arnau);

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1. INTRODUCTION The seismic response of partially grouted reinforced masonry (PG-RM) walls is receiving increasing attention due to their wide presence as a seismic-resistant system in countries such as the U.S., Canada and New Zealand. In Chile, PG-RM typology is rather common in buildings up to four stories high (Moroni et al. 2004). This type of construction has displayed an acceptable seismic performance for the recent major earthquakes that have struck Chile (Maule 2010 (Mw 8.8), Iquique 2014 (Mw 8.1), Illapel 2015 (Mw 8.3)). However, some post-earthquake observations (Astroza et al. 2012, Valdebenito et al. 2015) noted that several constructions made of multi-perforated clay brick masonry suffered moderate-to-severe structural damage. In general, damaged structures commonly exhibited a shear failure mode characterized by x-shaped diagonal cracks. This type of failure was observed mainly in walls with low aspect ratio located at the bottom floors due to their limited displacement capacity, and in the piers formed at the sides of an opening due to their less resistant area. As it is known, PG-RM walls are characterized by the exclusive grouting of those cells containing vertical reinforcing steel bars. In addition, and depending on the construction technique used, horizontal reinforcement can be concentrated in bond beams or placed in horizontal mortar joints, as shown in Fig. 1. On the other hand, existing literature shows that the seismic response of PG-RM walls depends mainly on the following design parameters: wall geometry (aspect ratio), axial load level, vertical and horizontal reinforcement (amount and spacing), and mechanical properties of the constituent materials and their interfaces. Due to the multiple and heterogeneous configurations that can arise from the combination of these design parameters, predicting the PG-RM walls’ seismic response continues to be a complex task.

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In recent years, significant efforts have been devoted to investigating the seismic response of PG-RM walls. However, experimental research available has offered limited data for constructing fragility functions (Murcia-Delso & Shing 2012) or validating new design formulas (Aguilar et al. 2016, Bolhassani et al. 2016). In spite of this, some relevant experimental information has been obtained. In general, an increase in applied axial compressive load on a wall has a positive effect in their shear strength, but it can cause a more brittle behavior once the maximum lateral load has been reached (Ghanem et al. 1993, Voon & Ingham 2006, Haach et al. 2011, Bolhassani et al. 2015, Ramírez et al. 2016). An increase in axial load has also been observed to lead to a greater energy dissipation capacity (Minaie et al. 2010), although this greater capacity would be more noticeable in walls with low aspect ratio (Ramírez et al. 2016). In walls governed by shear, enlarging the axial load level increases the frictional resistance along the diagonal cracks and mortar bed joints. This is especially significant in walls constructed with multi-perforated clay bricks, where the presence of hardened mortar spikes into the brick cavities can produce a mechanical interlock between both components, conditioning the seismic response of PG-RM walls (Zepeda et al. 2000, Gabor et al. 2006; Abdou et al. 2006; Fouchal et al. 2009, Sandoval & Arnau 2017). For this reason, any realistic numerical analysis aimed at producing accurate predictions should adequately consider the blocking mechanisms that takes place at the brick-mortar interface, and the unit cracking it promotes (Sandoval & Arnau 2017). Increased horizontal reinforcement ratio has been demonstrated to often lead to an increased shear strength in walls (Schultz et al. 1998, Sepúlveda 2003, Voon & Ingham 2006), although a greater effect has been reported for slender walls (Ramírez et al. 2016). It has been also noted that walls with a greater horizontal

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reinforcement ratio show a higher number of cracks and are more widely distributed (Haach et al. 2011, Ramírez et al. 2016), although their contribution seems to begin only once the diagonal cracking has occurred (Sepúlveda 2003, Haach et al. 2011). On the other hand, the amount of vertical reinforcement seems to have no influence on shear strength (Meli et al. 1968). In fact, their main contribution would be a greater resistance to sliding failure mode and, depending on their horizontal spacing, to more effectively controlling the cracking process (Dhanasekar & Haider 2011). Very few studies have systematically investigated the influence of aspect ratio. According to Ramírez et al. (2016), aspect ratio has a strong influence on the majority of seismic performance parameters (i.e. stiffness degradation, shear strength, displacement ductility, and drift level). In particular, the results show that as the aspect ratio increases, shear strength decreases (Matsumura 1988, Voon & Ingham 2006). Additionally, walls with lower aspect ratios exhibit greater initial stiffness, as well as greater stiffness degradation during the cyclic response. It has been also observed that greater drifts are achieved when aspect ratio increases (Ramírez et al. 2016). Several other experimental works have investigated the seismic response of PG-RM walls with openings (also called “perforated walls”). Some tests conducted in New Zealand on PG-RM walls with openings were summarized in Ingham et al. (2001). It was concluded that masonry piers on either side of an opening could be treated as individual cantilever walls. However, some effects could be neglected such as frame action or rocking on short piers. On the other hand, Elshafie et al. (2002) carried out an experimental campaign using 1/3-scale concrete masonry walls. In this research, walls were tested in a cantilever-type support condition under monotonic lateral in-plane loading. This research concluded that, for walls with similar overall dimensions and flexural reinforcement arrangement, the reduction in stiffness is proportional to the reduction in shear strength, regardless of the opening size and location. Meanwhile, Voon (2007) tested eight PG-RM walls that were subjected to cyclic lateral loading. The results obtained in this research show that the opening size and trimming reinforcement length significantly affects the lateral capacity of perforated walls. It should be noted that, in all experimental works mentioned above, the horizontal reinforcement of tested walls was embedded in the so-called bond beams. These are masonry unit courses with special units that are designed to receive horizontal reinforcement and grout. This constructive detail, commonly used in countries such as the U.S., Canada and New Zealand, differs from that used in other quake-prone countries, such as Chile, where this reinforcement is embedded inside the horizontal mortar bed joints (as shown in Fig. 1). Despite the efforts made so far in this research area, further experimental research on the seismic behavior of PG-RM walls with openings is required. In order to complement and extend the available worldwide experimental evidence database, this research contributes new experimental data related to shear response in perforated walls with bed-joint reinforcement and constructed with multi-perforated clay bricks. In addition, and as noted by Nolph & ElGawady (2012), the development of proper numerical models, allowing for investigation into the way parameters affect seismic response, is also urgently needed. In this context, the combination of experimental evidence, always limited and costly to obtain, with sufficiently validated simulation models, offers interesting possibilities for enlarging the existing database. With this in mind, a numerical strategy able to realistically consider all mechanical phenomena involved in the structural response of PG-RM walls has been recently proposed by authors. The strategy, based on a detailed micromodelling approach, has been successfully validated through a comparison with experimental results from small samples (Sandoval & Arnau 2017) as well as from solid walls (Arnau et al. 2015), thus emerging as a powerful and reliable tool for studying in depth all the aspects and variables that influence the seismic behavior of PG-RM walls with openings. The main objective of this paper is to investigate the influence of a window opening on the in-plane shear response of PG-RM walls, both experimentally and numerically. For this purpose, three full scale PG-RM walls built with multi-perforated clay units were tested under cyclic lateral loading up to failure. One of them is solid and the other two have a central opening with different aspect ratios. The experimental results obtained from a complete material characterization are used to numerically reproduce the behavior of tested walls. The micro-modelling scheme proposed by authors in previous works (Arnau et al. 2015, Sandoval & Arnau 2017) has been adopted in this research project. Firstly, numerical results are contrasted with the experimental wall response, with special attention being paid to accuracy, in terms of correct reproduction

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ACCEPTED MANUSCRIPT of failure modes, lateral resistance and ductility. Once validated, a brief parametric study is carried out in order to study the influence of the window opening aspect ratio, and of the horizontal reinforcement ratio at piers, on the lateral response of PG-RM walls. These aspects are particularly important in the field of structural and earthquake engineering.

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2. MATERIAL TESTING The implementation of the numerical approach adopted in this research requires, as input parameters, several elastic and inelastic properties of the constituent materials and their interfaces. A detailed characterization of materials used in the construction of full-scale walls was performed for this purpose. It is worth noting that materials and construction details typically used in the Chilean PG-RM constructions were employed in this research. A detailed description of the specimens and tests methods used in the experimental program are given in this section.

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2.1. Multi-perforated clay brick, mortar, grout and masonry composite. A multi-perforated clay brick, with external dimensions of 290x140x110 mm3, was used in this experimental program. Average dimensions of the internal geometry of the bricks are shown in Fig. 2, which were determined experimentally. The percentage of voids (ratio between area of perforations and gross area of brick) was obtained by means of three tests according to NCh167.Of2001 (INN, 2001), resulting in an average value of 53.3% with a coefficient of variation (CV) of 0.8%. The compressive properties were calculated according to NCh167.Of2001 (INN, 2001), obtaining an average compressive strength (𝑓𝑐𝑏 ) of 15.3 MPa (CV=7.4%) and an average Young’s modulus (𝐸𝑏 ) of 6787.6 MPa (CV=28.6%). In addition, an average flexural tensile strength of brick (𝑓𝑥𝑏 ) equal to 1.69 MPa (CV=7%) was obtained from three point bending tests. Therefore, a tensile strength (𝑓𝑡𝑏 ) of 1.04 MPa was indirectly determined using Eq. (1), provided by the Model Code 90 (CEB, 1993), where ℎ is the specimen height and 𝑓𝑥 is its flexural tensile strength.

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Fig. 2 – Geometry of multi-perforated clay brick used in this research (average sizes) The compressive properties for mortar and grout used in the research were obtained according to NCh1037.Of1977 (INN, 1977). Three cylinders of 150 mm diameter and 300 mm height were tested in compression for each material, obtaining average values for compressive strength of 6.83 MPa (CV=1.0%) and 8.64 MPa (CV=2.6%) for mortar (𝑓𝑐𝑚 ) and grout (𝑓𝑐𝑔 ), respectively. Additionally, average Young’s modulus values of 8295 MPa (CV=37.2%) for mortar (𝐸𝑚 ) and 14392 MPa (CV=18.1%) for grout (𝐸𝑔 ) were obtained. An average mortar flexural tensile strength (𝑓𝑥𝑚 ) of 3.7 MPa (CV=14.3%) was obtained

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ACCEPTED MANUSCRIPT from three point bending tests carried out according to NCh158.Of1967 (INN, 1967), resulting in a mortar tensile strength (𝑓𝑡𝑚 ) equal to 1.63 MPa by using Eq. (1). It should be noted that the low dispersion shown by some experimental results could be due to the use of premixed commercial products for mortar and grout which are commonly used in the Chilean masonry construction. The masonry used in the experimental program was characterized by an average compressive strength based on gross area of 𝑓𝑘 =7.77 MPa (CV=10.5%) and an average elastic modulus of 𝐸𝑘 =8830 MPa (CV=38.6%). Both properties were obtained from three masonry prisms constructed and tested according to NCh1928.Of.1993 Mod.2009 (INN 2009).

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2.2. Steel reinforcement Prefabricated ladder-type bed-joint reinforcement with 4.2 mm diameter cold-drawn wire was used as horizontal reinforcement in the construction of full-scale walls. Tensile properties of these reinforcing bars were determined by means of three tensile tests performed according to NCh200.Of1972 (INN, 1972). An average yielding stress (𝑓𝑦ℎ ) of 578 MPa (CV=2.4%) was obtained, while an average value of Young’s modulus (𝐸𝑠ℎ ) of 205 GPa (CV=1.3%) was determined as the secant modulus up to 40% of the yielding stress. Low CV values for mechanical properties of steel reinforcements have been also reported by Nolph & ElGawady (2012). Also, the small number of tests performed could lead to low CV values. For the vertical reinforcement, A630-420H steel was specified for 22 mm diameter and 25 mm diameter bars. Due to laboratory limitations, only one 22 mm diameter steel reinforcement was tested up to its nominal yielding stress 𝑓𝑦𝑣 (420 MPa), presenting a Young’s modulus (𝐸𝑠𝑣 ) of 233 GPa.

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2.3. Interfaces According to Lourenço (1996), the unit-mortar interfaces can fail under tension (mode I) or shear (mode II). A Morh–Coulomb friction model has been adopted by several researchers (Rahman & Ueda 2014, Drougkas 2015, Sandoval & Arnau 2017) to include both failure modes in numerical models. In this research, bed joint mortar–unit interfaces were characterized by direct shear tests and direct tension tests following the Sandoval & Arnau’s procedures (2017).

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2.3.1. Joint shear test Direct shear tests were carried out according to NCh167.Of2001 (INN, 2001), as shown in Fig. 3(a). Specimens were formed by three units and two 10 mm thick mortar joints with the central unit displaced 10 mm along testing direction. Three different axial pre-compression levels were considered, given average stress values (𝜎𝑛 ) of 0.1, 0.6 and 1.2 MPa based on net contact area. Three specimens were tested at each compression level. A bed joint specimen failed prematurely in maturing process, so only two tests were carried out, with a pre-compression of 0.6 MPa. Axial pre-compression (𝑃 in Fig. 3) was applied by means of a 50 kN hydraulic jack and measured by a 50 kN load cell. Lateral displacement was applied by a 100 kN hydraulic jack and measured by a LVDT, whilst shear load (𝑉 in Fig. 3) was measured by a 100 kN load cell. Relative displacement between external and central bricks was measured by two LVDTs (𝛿𝑉1 and 𝛿𝑉2 in Fig. 3(a)), one at each joint, in a measurement length of 110 mm. Also, absolute displacement of the central brick was measured by a LVDT (𝛿𝑉3 in Fig. 3(a)). Horizontal displacement between central brick and an end brick (𝛿𝐻1 in Fig. 3(b)), and between the end bricks (𝛿𝐻2 in Fig. 3(b)) were also measured. The absence of any specimen rotation was ensured, as the displacements recorded by LVDT H1 and LVDT H2 had the same direction Several researchers (Haach 2009, Tomazevic 2008, Zimmermann et al. 2011, Rahman & Ueda 2014, among others) have adopted this test configuration to study the shear bond properties of mortar joints. The Mohr–Coulomb internal cohesion stress (𝑐) and internal friction angle (tan𝜙) were calculated by linear regression of axial stress - shear bond strength diagram, as shown in Fig. 3(c). 𝑐𝑏−𝑚ℎ =0.96 MPa and tan(𝜙𝑏−𝑚ℎ )=0.535 values were obtained. The goodness of fit of this lineal regression is satisfactory, reaching a coefficient of determination 𝑅 2 of 0.74. As was also noted by Abdou et al. (2006) and Sandoval & Arnau (2017), a shear key effect in bed joint tests was observed, produced by the mortar that penetrates

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ACCEPTED MANUSCRIPT into the holes of the bricks. As a result, web crushing and face spalling proportional to pre-compression stress were observed, as shown in Fig. 3(d).

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2.3.2. Joint tensile test Tensile specimens were composed of two bricks connected by one mortar joint, as can be seen in Fig. 4. The employed mortar was the same described in section 2.1. Upper and lower faces of specimens were glued to a 50 mm thick steel plates with SIKADUR® 31. The tests were carried out under displacement control at an approximate rate of 0.5 μm/s (Almeida et al. 2002). Displacement was applied to the upper steel plate with a 50 kN hydraulic jack and the load was measured with a 50 kN load cell. A similar configuration has been adopted in several previous experimental works (Van der Pluijm 1997, Rots 1997, Almeida et al. 2002, Sandoval et al. 2011, Sandoval & Arnau 2017). During the tests, the failure occurred suddenly by separation of one of the contact faces between mortar and one of bricks. This was observed in both testing directions, as can be seen in Fig. 4. According to this, bond tensile strength was calculated by means of three tests in each testing direction, obtaining an average bond strength of 0.06 MPa (CV=70%) for bed joint interface and 0.07 MPa (CV=83%) for head joint interface, both referred to contact net area. In the typical failure mode for bed joint interface, mortar spikes can be seen to be present on the small brick’s hollows (named as T1, T2, T3 and T4 on Fig. 2), as it is shown in Fig. 4(a). The height of mortar spikes was measured obtaining an average value of 7.1 mm. As it was expected, mortar roughness was not observed in typical head joint interface failure mode, as is shown in Fig. 4(b).

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3. IN-PLANE CYCLIC TESTS ON FULL-SCALE WALLS 3.1. Tests description Three full-scale PG-RM walls, built with the materials characterized in section 2, were tested under inplane cyclic lateral loading. Their geometry and reinforcing schemas are shown in Fig. 5. They were designed according to the Chilean RM design code provisions (NCh1928 Of.2003 Mod.2009 (INN, 2009)) for ensuring shear failure mode. Openings were designed to represent the centered windows openings typically encountered in Chilean masonry constructions. The wall dimensions were 2180 mm length, 2230 mm height and 140 mm thick. Wall S1 did not have an opening and therefore is considered as a “control wall”, whilst walls O1 and O2 had a centered opening of 655 mm length by 798 mm height (aspect ratio of 1.24) and 655 mm length by 1318 mm height (aspect ratio of 2.06), respectively. Consequently, piers for walls O1 and O2 had an aspect ratio of 1.05 and 1.73, respectively. It should be noted that these openings represent an area of 10.7% and 17.8% of the solid wall (wall S1). Two 4.2 mm steel rods were horizontally placed every two mortar rows, resulting in a horizontal reinforcement ratio equal to 0.71‰. The same ratio was provided in the three walls. Meanwhile, vertical reinforcement consisted of two 25 mm diameter steel rods (one at each end of the wall) and two 22 mm diameter steel rods (one at each side of the opening). Notice that high vertical reinforcement ratio was provided in all walls to avoid a flexural or sliding failure mode during the tests. The bottom head beams were inverted T-shaped RC beams, whose wing was 700 mm thick and 300 mm height, and a web 140 mm thick and 200 mm height. The upper RC head beams were 140 mm thick and 500 mm height (Fig. 5). As observed in Fig. 6, walls were connected to a 1000 mm thick reaction slab with 36 mm diameter steel bolts spaced at 500 mm. Tests were performed on a displacement control at a mean rate of 3 mm/min. Cyclic in-plane lateral displacement was applied at the center of the top head beam by a 300 kN hydraulic jack, performing two cycles at each deformation level. The load protocol was the same used in previous Chilean investigations in terms of drift (normalized by wall’s height) (Alcaino & Santa Maria 2008, Ramirez et al. 2016). Lateral load was measured by a 300 kN load cell, whilst lateral displacement of each pier was measured relative to the bottom head beam by LVDTs. Walls were tested without external axial load. Note that out-of-plane displacements were prevented at head beam level by two steel lateral hinged rods spaced at 1500 mm, which were connected to a reaction wall parallel to the plane of tested wall, as is shown by the lateral view in Fig 6.

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3.2. Observed behavior and test results Fig. 7 shows the cracking pattern observed for each the walls at the end of the tests. In wall S1, small horizontal flexural cracks could be observed at early testing stages, which progressively turned into shear stepped cracks along units-mortar interfaces (Fig. 8(a)). Subsequently, cracks spread over the whole diagonal of wall in both loading directions, forming an x-shaped crack pattern, as can be seen in Fig. 7(a). In wall O1, pre-test cracking was detected below row number six (counting from the bottom head beam), which was caused by anchor bolt tensioning. After testing, the right pier concentrated the damage, exhibiting an x-shaped crack pattern (Fig. 8(b)), but the cracks in the left pier were more spread and less

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wide, as can be seen in Fig. 7(b). Despite this, its hysteresis curve was symmetrical in both loading directions. In wall O2 flexural cracks were observed at the first layer of both piers, but the length and width of these cracks did not increase during the test. At the end of test, distributed diagonal cracks were observed in both piers, as can be observed in Fig. 7(c). Bricks face spalling (Fig. 8(d)) and crack penetration into head beams (Fig. 8(c)) were also observed at wall corners during the final stages of the three tests. Also, some fractured bed joint reinforcements were observed (Fig. 8(e)). Few cracks grew outside of wall O1 and O2 piers. Wall S1 and right pier of wall O1 had a similar failure mode, despite the O1 pier did not have the internal grouted cores of wall S1. The similar behavior of both walls could be attributed to their similar aspect ratio (approximately 1.0). Meanwhile wall O2 exhibited a behavior with a higher flexural component than wall S1 and O1, caused by the higher aspect ratio of wall O2 piers than of wall S1 and wall O1 piers. The different behavior of wall O2 can be identified by the observed initial flexural cracks and by the diagonal cracks further distributed along the pier height.

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(e) (d) Fig. 8 - Damage observed during the tests: (a) stair–stepped crack, (b) x-shaped diagonal cracks at piers, (c) crack penetration into head beams, (d) brick’s face spalling, (e) fracture of horizontal steel bars.

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Fig. 9 illustrates the hysteretic curves and their envelopes obtained for specimens in the cyclic tests, and Table 1 summarizes the parameters characterizing the response for the tested walls. It is important to state that the maximum shear strength (𝜈𝑚𝑎𝑥 ) was obtained for the net horizontal wall area. This area was calculated by taking into account the gross area affected by the void percentage of units, and including the grouted cells. In all cases, maximum lateral load occurred approximately 10% higher in the first cycle than in the inverse cycle, as has also been reported for concrete block walls (Ingham et al. 2001). In addition, the maximum lateral loads for walls S1 and O1 were achieved at lower deformation in the inverse cycles than in first cycles. On the contrary, wall O2 inverse cycle maximum load (-118.1 kN at a deformation of -10.45 mm) was very close to the load achieved in the previous inverse cycle (-117.7 kN at a deformation of -8.42 mm); thus, if -8.42 mm is considered as the deformation corresponding to the maximum load of the inverse cycle, wall O2 behaved the same way as walls S1 and O1. Accordingly, the damage produced in the first loading direction reduces the maximum load achieved in the inverse loading direction, and its associated lateral deformation.

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-18 -15 -12

-9

-6

-3

0

3

6

9

12

15

18

Lateral displacement (mm)

Fig. 9 – Load-displacement curves: (a) wall S1, (b) wall O1, (c) wall O2, (d) envelopes.

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As can be observed, wall S1 presented higher shear strength than perforated walls, while walls O1 and O2 achieved a similar value. Therefore, it can be said that the presence of an opening significantly reduces the shear strength of a PG-RM wall. On the other hand, walls O1 and O2 had similar shear strength but their piers had different aspect ratios, so the aspect ratio seems to have no influence on shear strength. However, as commented above, wall O1 had pre-test cracking and its piers behaved asymmetrically, so the shear strength of the wall O1 could be higher if it had not been damaged before the test. Thus, further tests are necessary to make conclusions about the influence of the pier aspect ratio and the opening aspect ratio on the shear strength of a PG-RM wall. Displacement ductility of walls (𝜇𝑑 ) was calculated by a bilinear idealization following the methodology proposed by Lüders & Hidalgo (1987) and recently used by Ramírez et al. (2016). The idealized bilinear envelope diagram is shown in Fig. 10. In this diagram, the initial secant stiffness (𝐾𝐸 ) is determined by the point (𝛿𝑆𝐿 , 𝑉𝑆𝐿 ) where a significant variation of the envelope tangential stiffness is produced. On the other hand, the point (𝛿𝐸 , 𝑉𝐸 ) is determined by comparing the amount of energy under the experimental envelope with the energy under the bilinear envelope up to the maximum lateral resistance (𝛿𝑀𝑅 , 𝑉𝑀𝑅 ). In this way, the displacement ductility is calculated as the ratio between the displacement of the maximum resistance and the displacement of the elastic limit (𝜇𝑑 = 𝛿𝑀𝑅 𝛿𝐸 ). Obtained values are presented in Table 1. Note that all walls presented higher displacement ductility in the first loading direction than in the inverse, thus the damage produced in the first loading direction reduces the wall’s deformation capacity in the inverse loading direction. The solid wall had higher displacement ductility than perforated walls, so the presence of an opening can be understood to reduce displacement ductility, probably because wall S1 had higher crosssectional area than walls O1 and O2. Wall O2 had higher displacement ductility than wall O1, hence the displacement ductility seems to increase in proportion to the piers’ aspect ratio, as was reported in Shing et al. (1989) for RM-PG solid walls.

Idealized elastic limit

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Table 1: Parameters of idealized bilinear curves Maximum Resistance

𝜈𝑚𝑎𝑥 (𝑀𝑃𝑎)

𝜇𝑑 𝜇𝑑 ̅̅̅ 𝛿𝐸 𝑉𝐸 Δ𝑀𝑅 𝑉𝑀𝑅 𝛿𝑀𝑅 (mm) (mm) (𝑘 ) (𝑘 ) (%) First 2.35 113.35 12.46 0.56 210.3 1.4 5.4 S1 4.8 2.60 120.46 Inverse -10.77 -0.48 -191.4 1.2 4.2 2.15 87.79 First 8.59 0.39 131.1 1.2 4.3 O1 3.8 2.15 81.03 Inverse -6.85 -0.31 -111.4 1.0 3.2 2.12 90.50 First 9.72 0.44 133.5 1.2 4.6 O2 4.4 2.50 87.5 Inverse -10.45 -0.47 -118.1 1.1 4.2 Note: 𝛿𝐸 =displacement associated with elastic limit of bilinear idealization; 𝑉𝑒 =horizontal force associated to elastic limit of bilinear idealization; 𝛿=measured displacement associated with maximum load; ∆=measured drift associated with maximum load; 𝑉=maximum lateral load; 𝑣𝑚𝑎𝑥 =maximum shear strength considering horizontal net area; 𝜇𝑑 =displacement ductility; ̅̅̅=average 𝜇𝑑 displacement ductility.

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Wall Cycle

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Horizontal Force (V)

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𝐾𝑅

(𝛿𝐸 , 𝑉𝐸 )

(𝛿𝑀𝑅 , 𝑉𝑀𝑅 )

𝜇𝑑 =

(𝛿𝑆𝐿 , 𝑉𝑆𝐿 ) 𝐾𝐸

𝛿𝑀𝑅 𝛿𝐸

Experimental envelope Bilinear idealization

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Lateral displacement (δ)

Fig.10 – Displacement ductility calculation

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4. DETAILED MICRO-MODELLING 4.1. General scheme The 2D plane stress models implemented in this study for reproducing the shear response of tested walls are based on the micro-modeling strategy for partially grouted masonry proposed by the authors in past works (Arnau et al. 2015, Sandoval & Arnau 2017). Therefore, the modeling scheme employed in this study follows a similar configuration to the one previously used in terms of mesh size, element types and material models. The full definition of the wall micro-models for the purpose of the numerical simulation requires the use of continuum elements, interface elements and reinforcement elements. Interface elements (e.g. mortar-concrete interface), which have two sides, connect two adjacent and different continuum materials (in this case mortar and concrete) by sharing nodes with only one continuum material per side. The detailed geometry and material models adopted for continuum elements, and the presence of interface elements with non-linear behavior, allows to implicitly include the masonry anisotropy. Reinforcement elements were assumed to be embedded and perfectly bonded to their surrounding continuum materials (mortar for horizontal reinforcement and grout for vertical reinforcement), thus reinforcement elements share nodes with their adjacent continuum elements. Fig. 11 shows the configuration and meshing used in the micromodels generated. As can be observed, this strategy allows the detailed consideration of all structural elements in the composite material and their interfaces, thus representing the most natural and realistic way to simulate PG-RM structures. It is important to note that the Diana software (TNO Diana 2015) was used to develop the models and to perform the analyses. Lateral displacement was applied as deformation-controled static pushover, by displacing the middleheight nodes of the upper head beam. Bottom nodes of bottom head beam were laterally and vertically fixed, thus defining a cantilever configuration. Self-weight was considered distributed in the whole wall. A 0.05 mm load step and BFGS iteration method with linear tangent stiffness at each initial iteration and a convergence criteria of 0.025% energy tolerance were employed in all simulations. It is important to state that most input parameters used in the micro-models correspond to the average experimental data described in section 2.

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Reinforcement Continuum elements elements

ACCEPTED MANUSCRIPT Concrete Grout Mortar Brick unit Vertical reinforcement Horizontal reinforcement

Interface elements

Horizontal brick-mortar

Mortar-concrete Mortar-grout Brick-grout

Element edge Node

US

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T

Vertical brick-mortar

Fig. 11 – Detailed micro-model of wall O1

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CE

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4.2. Material models 4.2.1. Bricks, mortar and grout. Multi-perforated clay masonry units (CMU), mortar, grout and RC were modelled through eight node quadrilateral plane stress elements, named CQ16M in DIANA 9.6 (TNO Diana 2015). The fragile CMU, mortar and grout response was considered through the total strain rotating smeared crack model, adopting an exponential softening law in tension and a parabolic constituent law in compression. Linear elastic behavior was assumed for RC head beams due to the insignificant damage observed in the tests. Brick compressive fracture energy (𝐺𝑐𝑏 ) was determined with the clay paste compressive fracture energy (𝐺𝑓𝑐,𝑐𝑙𝑎𝑦 =29 Nmm/mm3) reported by Lourenco et al. (2010), and the average percentage of voids in the units (Table 2). Tensile fracture energy of units (𝐺𝑡𝑏 ) was calibrated from a numerical model of the three point bending test performed, following the methodology presented in Arnau et al. (2015). Best fit was achieved with a value of 0.045 Nmm/mm3, which is within the range of values of tensile fracture energy reported by Lourenço et al. (2005). Note that input parameters of units were obtained with respect to the gross area. Grout tensile strength (𝑓𝑡𝑔 ) was calculated by rule of three between its average compressive strength and the values of tensile strength and compressive strength values for grout reported by Arnau et al. (2015). Tensile fracture energy for mortar (𝐺𝑡𝑚 ) and grout (𝐺𝑡𝑔 ) was assumed from the equation proposed in Model Code 90 (CEB, 1993) considering an 8mm maximum aggregate size. As proposed by Drougkas et al. (2013), the compressive fracture energy of mortar (𝐺𝑐𝑚 ) and grout (𝐺𝑐𝑔 ) were determined through Eq. 2, assuming a ductility index (𝑑) of 1mm, where 𝑓𝑐,𝑅𝐼𝐿𝐸𝑀 is the prismatic compressive strength determined 𝑅𝐼𝐿𝐸𝑀 from RILEM test. Grout’s RILEM compressive strength (𝑓𝑐𝑔 ) was calculated by rule of three between grout compressive strength, mortar compressive strength and mortar RILEM compressive strength. On the other hand, Poisson’s ratio value for brick (𝜈𝑏 ), mortar (𝜈𝑚 ) and grout (𝜈𝑔 ) were assumed from (Sandoval & Arnau 2017) since similar materials were used. 𝑑 = 𝐺𝑐 𝑓𝑐,𝑅𝐼𝐿𝐸𝑀

(2)

4.2.2. Reinforcements Steel bars were modelled with two nodes Bernoulli beam elements, named L7BEN in DIANA 9.6 (TNO Diana 2015). Stress–strain response of horizontal reinforcement was calibrated from experimental tests

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ACCEPTED MANUSCRIPT results, whilst elastoplastic behavior was assumed for 22 mm and 25 mm diameter bars. Von Misses isotropic plasticity with hardening was assumed for their appropriate simulation. A Poisson’s ratio (𝜈𝑠 ) equal to 0.3 was assumed for all reinforcements (Arnau et al. 2015).

1.8

0.9

1.6

Shear stress (

0.6 0.5 0.4 0.3 0.2

(a)

0.1

1.2

1 0.8 0.6

Experimentalsig 𝜎 ==0.1 0.1N/mm2 2 Experimental Experimentalsig 𝜎= 0. N/mm2 2 Experimental = 0.6 Experimentalsig 𝜎= 1. N/mm2 2 Experimental = 1.2

Model Modelsig 𝜎 ==0.1 0.1N/mm2 2 Modelsig 𝜎 ==0.6 0. N/mm2 2 Model

M

Cohesion (

0.7

1.4

AN

0.8

US

1.0

)

)

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4.2.3. Interfaces CMU-mortar, CMU-grout, mortar-grout and mortar-concrete interfaces were introduced in the models through six node interface elements, named CL12I in DIANA 9.6 (TNO Diana 2015). As it is proposed by Sandoval & Arnau (2017), axial stiffness (𝑘𝑛𝑛 ) and tangential stiffness (𝑘𝑡𝑡 ) of interfaces were determined by reproducing a slice of 0.5 mm thickness of the stiffer material (Table 2). Values obtained with these assumptions are high enough to avoid linear deformations of interfaces, as recommended by Drougkas (2015), but not excessively high so as to avoid numerical instabilities. CMU–bed joint interfaces were modelled with a Mohr–Coulomb friction model (Sandoval & Arnau 2017). The shear key effect of the mortar spikes observed in the tests (as commented in section 2) was introduced in the numerical models via the cohesion hardening option available in DIANA 9.6 (TNO Diana 2015), as it is reported by Sandoval & Arnau (2017). The CMU-bed joint mortar cohesion hardening diagram, which is shown in Fig. 12(a), was calibrated by inverse analysis of detailed micro modelling of direct shear tests, following the methodology exposed in Sandoval & Arnau (2017). The response of the model and the experimental results for the three tested axial compression levels are shown in Fig. 12(b).

0.4

Modelsig 𝜎 ==1.2 1. N/mm2 2 Model

(b)

0.2

0

0

1

2

3

4

5

6

7

Joint displacement (mm)

8

ED

0.0 9

10

0

1

2

3

4

5

6

7

8

9

10

Lateral displacement (mm)

PT

Fig. 12 - Bed joint interface simulation: (a) cohesion hardening diagram, (b) model response.

AC

CE

Gapping appears on the interface once the introduced tensile stress is exceeded. Despite that, mortar spikes could not be completely out of brick hollows and, consequently, the interface can still present some shear response. In order to take this phenomenon into account, a post tensile opening shear stiffness is assigned to 𝑜𝑝 CMU- bed joint mortar interfaces (𝑘𝑡𝑡,𝑏−𝑚ℎ ). It was calculated with Eq. 3, where 𝐺𝑚 is the mortar shear modulus, ℎ𝑚 is the mortar spikes height that it is considered to be demanded in shear (adopted as an average crack opening of 1mm), 𝐴𝑠𝑚𝑎𝑙𝑙 ℎ𝑜𝑙𝑙𝑜𝑤𝑠 is the total area of small hollows of bricks (named as T1, T2, T3 and T4 on Fig. 2) and 𝐴𝑛 is the net area of units. When bed joint interface fails in tension, equivalent thickness of bed joint interface needs to be changed from net area of units to the area of the mortar spikes, but the thickness of an interface is a geometrical input that cannot be changed during a model run. Therefore, the 𝐴𝑠𝑚𝑎𝑙𝑙 ℎ𝑜𝑙𝑙𝑜𝑤𝑠 𝐴𝑛 ratio is introduced in Eq. 3 to solve this limitation. For the other interfaces without shear key effect, traditional Morh–Coulomb friction model without post opening shear retention was assumed. Same values of CMU-vertical mortar joint interface’s internal friction angle (𝜙𝑏−𝑚𝑣 ) and tensile strength (𝑓𝑡,𝑏−𝑚𝑣 ) were assumed for CMU-grout interface (Table 2). Also, the same values of CMU-vertical mortar joint interface’s cohesion (𝑐𝑏−𝑚𝑣 ) and internal friction angle (𝜙𝑏−𝑚𝑣 ) were assumed for mortar-grout interface and mortar-concrete interface. The dilatancy angle (Ψ) was set to 0° for all interfaces, as in several similar investigations (Arnau et al. 2015, Sandoval & Arnau 2017, Lourenço 1996, Rots 1997, among others) . This assumption is equivalent to not considering the influence of rough surfaces in interface slipping.

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ACCEPTED MANUSCRIPT 𝑜𝑝

𝑘𝑡𝑡,𝑏−𝑚ℎ =

𝐴𝑠

𝑎𝑙𝑙 ℎ𝑜𝑙𝑙𝑜𝑤𝑠

𝐴𝑛

⋅

𝐺 ℎ

(3)

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4.3. Input parameters This section summarizes the input parameters used to reproduce the mechanical response for walls tested using the detailed micro-modelling approach. Table 2 shows the assumed values for the different elements that comprise the micro-models. Again, it is important to remark that the majority of input parameters used in the numerical models corresponds to average experimental data described in section 2.

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ACCEPTED MANUSCRIPT Table 2: Adopted values for detailed micro-modeling material mechanical parameters. Values obtained from literature or inverse analysis are presented in brackets. Property

Nomenclature

3

Value

Source/details (Sandoval & Arnau 2017)

kg m %

{1800}

Index of voids

𝜌𝑏 -

Young's modulus

𝐸𝑏

a

6787.6

Poisson's ratio

𝜈𝑏

Compressive strength Compressive fracture energy Tensile strength

𝑓𝑐𝑏 𝐺𝑐𝑏

Tensile fracture energy

𝐺𝑡𝑏

Nmm mm3

{0.045}

𝜌𝑚

kg mm3 a

{2000}

a Nmm mm3 a

𝜈𝑚

𝐸𝑔

𝑓𝑡𝑔 𝐺𝑡𝑔

(Arnau et al. 2015)

6.83

Nmm mm3 a

3

Nmm mm 3

kg m

{14.09} 1.64 {0.0191} {2000}

a

(Drougkas et al. 2013)

(CEB 1993) (Sandoval & Arnau 2017)

14392.05 {0.2}

a

(Sandoval & Arnau 2017)

8.64

Nmm mm3 a 3

Nmm mm 3

{17.82}

(Drougkas et al. 2013)

{2.07}

(Arnau et al. 2015)

{0.0226}

(CEB 1993)

𝜌𝑅𝐶

kg m

{2500}

(CEB 1993)

Young's modulus

𝐸𝑅𝐶

a

{25000}

(CEB 1993)

CE

PT

Tensile fracture energy

𝐺𝑐𝑔

(Sandoval & Arnau 2017)

8295.25

𝜈𝑔

𝑓𝑐𝑔

(Lourenco et al. 2005)

1.04

a

AN

𝐺𝑡𝑚 𝜌𝑔

ED

Compressive strength Compressive fracture energy

𝑓𝑡𝑚

M

Tensile fracture energy Grout Density (Referred to net Young's modulus area) Poisson's ratio

𝐺𝑐𝑚

{13.55}

{0.15}

𝑓𝑐𝑚

(Sandoval & Arnau 2017)

15.28

CR IP

𝐸𝑚

Compressive strength Compressive fracture energy Tensile strength

Tensile strength

{0.15}

𝑓𝑡𝑏

Mortar Density (Referred to net Young's modulus area) Poisson's ratio

53.3

T

Density

Poisson's ratio

𝜈𝑅𝐶

{0.2}

(CEB 1993)

Axial stiffness

𝑘𝑛𝑛,𝑏−𝑚ℎ

N mm3

𝑘𝑡𝑡,𝑏−𝑚ℎ

3

Density

Tangential stiffness

AC

Reinforced concrete ( Referred to net area) Brick - bed joint interface (Referred to net contact area)

Unit

US

Elements Brick (Referred to gross area)

Cohesion Internal friction angle Tensile strength Residual tangential stiffness Axial stiffness

Brick-head joint interface Tangential stiffness (Referred to net Cohesion contact area) Internal friction angle Tensile strength

𝑐𝑏−𝑚ℎ tan(Φ𝑏−𝑚ℎ ) 𝑓𝑡,𝑏−𝑚ℎ 𝑜𝑝

N mm a

{16590.50}

(Arnau et al. 2015)

{7213.26}

(Arnau et al. 2015)

0.96 0.54

a

0.06

𝑘𝑡𝑡,𝑏−𝑚ℎ

N mm3

{306.20}

𝑘𝑛𝑛,𝑏−𝑚𝑣

N mm3

{16590.50}

(Arnau et al. 2015)

𝑘𝑡𝑡,𝑏−𝑚𝑣

3

{7213.26}

(Arnau et al. 2015)

𝑐𝑏−𝑚𝑣

N mm a

tan(Φ𝑏−𝑚𝑣 ) 𝑓𝑡,𝑏−𝑚𝑣

a

{0.6}

(Sandoval & Arnau 2017)

{0.767}

(Sandoval & Arnau 2017)

0.07

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Tensile strength Mortar - grout Axial stiffness interface Tangential stiffness (Referred to net Cohesion contact area) Internal friction angle

𝑘𝑛𝑛,𝑏−𝑔

N mm3

{28784.10}

(Arnau et al. 2015)

𝑘𝑡𝑡,𝑏−𝑔

3

{11993.38}

(Arnau et al. 2015)

𝑐𝑏−𝑔

a

tan(Φ𝑏−𝑚𝑣 ) 𝑓𝑡,𝑏−𝑔

a N mm

{16590.50}

(Arnau et al. 2015)

𝑘𝑡𝑡,𝑚−𝑔

N mm3

{7213.26}

(Arnau et al. 2015)

𝑐𝑚−𝑔

a

CR IP

𝑘𝑛𝑛,𝑚−𝑅𝐶

N mm3

𝑘𝑡𝑡,𝑚−𝑅𝐶

3

4.2 mm diameter steel

Density

𝜌𝑠ℎ

Young's modulus

𝐸𝑠ℎ

Poisson's ratio

𝜈𝑠ℎ 𝑓𝑦ℎ

N mm

Young's modulus

{20833.33}

(Arnau et al. 2015)

0.29

US

a

kg m3 G a

𝑐𝑚−𝑅𝐶 tan(Φ𝑚−𝑅𝐶 ) {7850} (CEB, 1993) 205 {0.3}

a

578.43 3

𝜌𝑠𝑣

kg m

{7850}

G a

233

𝜈𝑠𝑣 𝑓𝑦𝑣

{0.3} a

(Arnau et al. 2015) (CEB, 1993) (Arnau et al. 2015)

{420}

PT

ED

Poisson's ratio

(Arnau et al. 2015)

𝐸𝑠𝑣

M

Density

{50000.0}

0.82

AN

Yielding stress

Yielding stress

a

tan(Φ𝑚−𝑅𝐶 ) 𝑓𝑡,𝑚−𝑅𝐶

Tensile strength

0.822 𝑐𝑚−𝑔 tan(Φ𝑚−𝑔 )

a

𝑐𝑚−𝑅𝐶

Internal friction angle

0.29

tan(Φ𝑚−𝑔 )

Axial stiffness Cohesion

0.07 3

𝑘𝑛𝑛,𝑚−𝑔

Mortar reinforced concrete interface (Referred to net contact area)

Tangential stiffness

0.56 0.82

𝑓𝑡,𝑚−𝑔

Tensile strength

22 - 25 mm diameter steel

N mm

T

Brick-grout Axial stiffness interface Tangential stiffness (Referred to net Cohesion contact area) Internal friction angle

CE

5. COMPARISON OF EXPERIMENTAL AND NUMERICAL RESULTS 5.1. Load-displacement envelopes

AC

Fig. 13 shows the lateral force–lateral displacement diagrams obtained by proposed numerical models in combination with their corresponding experimental envelopes. As can be appreciated, excellent fitting was achieved for all walls in terms of maximum resistance and ultimate displacement. Also, micro-models can be observed to successfully capture the significant stiffness degradation occurred at a lateral displacement of about 3-4 mm, which physically corresponds to the development of the first major diagonal crack in the experiments. The maximum lateral force obtained by micro-modelling of walls S1, O1 and O2 (217.20 kN, 142.64 kN and 124.88 kN, respectively) presented a difference of 3.27%, 8.84% and -6.45% for their corresponding experimental values. Displacement associated with maximum lateral force obtained by means of micromodels of walls S1, O1 and O2 (12.96 mm, 9.29 mm y 12.33 mm, respectively) presented a difference of 4.01%, 8.15% and 26.85% for their corresponding experimental values. These differences between numerical and testing results are within the ranges of experimental variability reported by several authors for masonry structures (Sandoval & Arnau 2017, Arnau et al. 2015, Haach 2009, and Almeida et al. 2002,

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250

250 225

(a) Wall S1 Horizontal Force (kN)

200 175 150 125

75

Experimental - First Experimental - Inverse Numerical

50 25

(b) Wall O1

200 175 150 125

100 75

US

100

CR IP

225

Horizontal Force (kN)

T

among others). Main differences are obtained for the model S1 around a lateral displacement of 4mm, where numerical results slightly overestimate the horizontal force. Small differences are also observed between the initial lateral stiffness of simulated walls up to 0.5 mm displacement, which are consistent with theoretical expressions because the higher the aspect ratio of the resistant section, the smaller is its lateral stiffness. Although experimental results did not show this trend, it could be due to the inherent variability of masonry and the lack of more experimental specimens. Nevertheless, and considering the complexity and variability of the masonry itself, the possible differences between tests, and the fact that real loading was cyclic instead of monotonic, numerical models is considered to provide an excellent agreement with the actual lateral response of the tested walls.

Experimental - First Experimental - Inverse Numerical

50 25

0

0

2

4

6

8

10

12

14

16

Lateral displacement (mm) 250

175 150 125 100

75

PT

50

0

2

4

6

8

10

12

14

16

18

Lateral displacement (mm)

M

(c) Wall O2

200

ED

Horizontal Force (kN)

225

18

AN

0

Experimental - First Experimental - Inverse Numerical

25 0

CE

0

2

4

6

8

10

12

14

16

18

Lateral displacement (mm)

Fig. 13 – Experimental and numerical shear response of the walls: (a) S1, (b) O1, (c) O2.

AC

5.2 Failure modes Principal tensile strain of micro-models can be interpreted as an indicator of the numerical cracking pattern. As can be observed in Fig. 14, all walls failed in diagonal tension. A diagonal cracking band can be seen in the wall S1 model. Models of walls O1 and O2 adequately reproduce the diagonal cracks observed at the right pier, and likewise in tests, cracks in wall O2 are more widely distributed than in wall O1 (see Fig. 7). On the contrary, diagonal cracking appearing on the left pier is not fully developed on the numerical model, despite some damage starting at the grout column position. Diagonal cracking under the left piers and under the opening fits the model O2 very well, whilst a slight damage overestimation is obtained for model O1. Despite that, and considering the complexity and variability of the problem under study, experimental crack patterns are considered to have been reproduced with accuracy and reliability by the proposed detailed micro-modelling.

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CR IP

T

5.3 Ductility The displacement ductilities obtained from the micro–modelling results were similarly determined for experimental data, obtaining values of 5.1, 3.5 and 3.78 for walls S1, O1 and O2, respectively, and that represents a difference from experimental results of 6.3%, 7.1% and 14.9%, respectively. Numerical displacement ductility of wall S1 is higher than for walls with an opening, while wall O2 presents a higher value than wall O1, following the trend observed in the test results. Numerical models show an excellent agreement in the ductility prediction for walls S1and O1, whilst a satisfactory value is obtained for wall O2. Part of these differences could be attributed to the inexactitude of the calculation method, specifically in the determination of the cracking point (𝛿𝑆𝐿 , 𝑉𝑆𝐿 ).

AN

(a) Wall S1 (c) Wall O2 (b) Wall O1 (mm/mm) Fig. 14 – Micro-modelling principal total strain E1 (mm/mm): (a) S1 (b) O1 (c) O2.

ED

M

6. WALL OPENING INFLUENCE The effect of the opening size and the pier horizontal reinforcement ratio on the lateral response of PG-RM walls were numerically investigated through the modelling strategy validated in the previous section. Seven additional walls were simulated for this purpose, and their behavior is described in terms of their maximum shear strength (calculated on net area) and displacement ductility.

AC

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6.1. Influence of the opening size In order to obtain different opening sizes, the opening in walls O1 and O2 was widened by half a unit at each opening side, obtaining a wall with an opening of 970 mm wide and 800 mm height (named O1M) and a wall with an opening of 970 mm wide and 1320 mm height (named as O2M). These walls had the same horizontal reinforcement scheme described for tested walls, with the particular characteristic that the position of the 22 mm diameter vertical reinforcements was displaced horizontally by half unit from the position in the original walls. Consequently, a modified solid wall (named as S1M) with this modified reinforcement scheme was also simulated to perform an appropriated comparison. Load–displacement diagrams obtained for the simulated walls are presented in Fig. 15. As can be observed, both solid walls S1 and S1M present almost same response, presenting a slight difference in the ultimate deformation. This could be explained by the fact that the maximum spacing between vertical reinforcement in wall S1 is smaller than in wall S1M, so cracks have less distance in which they could grow freely. This was also reported by Dhanasekar & Haider (2011) for PG-RM walls constructed with concrete units.

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Fig. 15 - Load–displacement diagrams for different opening’s size.

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The influence of the opening size is analyzed in terms of pier aspect ratio, opening aspect ratio and opening area to solid wall area ratio. With the aim of performing an adequate comparison and using the different cross section areas for perforated walls, the results for walls O1 and O2 were normalized by the value of wall S1 and results of walls O1M and O2M by the value of wall S1M. As can be observed in Fig. 16, all opening size indicators denotes that an increase in the size opening produces a decrease in the shear strength. Consequently, a reduction in the shear strength by 10% is achieved if the pier’s aspect ratio is increased by 57%, the opening’s aspect ratio by 107%, or the opening area to solid wall area ratio by 48.4%. The same conclusion was also reported by Voon (2007) for PG-RM walls of concrete brick. The displacement ductility of walls S1M, O1M and O2M are 4.87, 3.43 and 3.89, respectively. From Fig. 17, the general trend shows that displacement ductility of a perforate wall increases if the opening size increases. As can be seen, the results obtained for perforated walls do not reach 80% of the solid wall displacement ductility, so a perforated wall would present a lower displacement ductility than a solid wall in any case. Shear strength and displacement ductility variations present a better correlation with pier aspect ratio than with any other of the two analyzed variables. Therefore, the shear strength and the displacement ductility of perforated walls could be determined in terms of the shear strength of the wall without perforation and the pier’s aspect ratio. 1.00

WO1M

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Fig. 16 – Opening’s size parameters influence on maximum lateral force: (a) pier aspect ratio, (b) opening aspect ratio, (c) opening area to solid wall area ratio 0.90

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Fig. 17 – Opening size parameters influence on displacement ductility: (a) pier aspect ratio, (b) opening aspect ratio, (c) opening area to solid wall area ratio. 6.2. Influence of pier’s horizontal reinforcement ratio Two new pier’s horizontal reinforcement amounts were analyzed in this section: under-reinforced (UR) (2𝜙 . mm every 3 rows) and over-reinforced (OR) (2𝜙 . mm every row). Tested walls with openings represent the base configuration (O1-BR and O2-BR) with a pier horizontal reinforcement ratio of 0.74‰ (2𝜙 . mm every two rows). A total of four modified configurations were simulated: O1-UR (𝜌ℎ = 0. ‰), O1-OR (𝜌ℎ = 1. ‰), O2-UR (𝜌ℎ = 0. ‰) and O2-OR (𝜌ℎ = 1. ‰). Load – displacement diagrams of simulated variations for walls O1 and O2 are presented in Fig. 18(a) and Fig. 18(b), respectively. As can be clearly seen, the increase in horizontal reinforcement produces an increase in the walls’ lateral resistance their corresponding lateral displacement. Notice that, as expected,

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initial behavior of walls is not influenced by the horizontal reinforcement ratio, since diagonal cracking has not been produced. Shear strength increases proportionally to the pier’s horizontal reinforcement ratio, as can be appreciated in Fig. 19(a). For wall O1 numerical results indicate that an increase of 66.6% in the pier’s horizontal reinforcement ratio would imply an increment in the shear strength of 8.1%, which is significantly lower than the 66.6% predicted by some design codes (NCh1928.Of1993 Mod.2009 (INN, 2009) or CSA S304-14 (CSA, 2014)). Displacement ductility of walls O1-UR, O2-UR, O1-OR and O2-OR is 3.19, 3.52, 3.97 and 4.10, respectively, and increases with the pier’s horizontal reinforcement ratio (Fig. 19(b)), as it is also reported in Shing et al. (1989) and Zepeda et al. (2000). Notice that the increase in displacement ductility produced by the increment in horizontal reinforcement in wall O1 is higher than in wall O2, denoting an interaction between the horizontal reinforcement ratio and the pier aspect ratio. An explanation for this interaction could be found in the fact that failure of wall O1 piers is influenced more by shear mode than the failure mode of wall O2 piers, which should present a higher contribution of a flexural failure mode. Nevertheless, further research is required to comprehend and clarify this phenomenon.

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Fig. 19 - Influence of horizontal reinforcement ratio: (a) shear strength, (b) displacement ductility 7. CONCLUSIONS In this paper, the results of an experimental and numerical research project for evaluating the seismic response of partially grouted reinforced masonry (PG-RM) walls with a central opening were presented and discussed. The following comments and conclusions can be summarized: - Three full-scale partially-grouted reinforced masonry (PG-RM) walls were tested under in-plane cyclic lateral loading: one wall was solid and two other walls presented a centered opening with aspect ratios of 1.22 and 2.01. All tested walls had same the overall dimensions, as well as horizontal and vertical reinforcement ratios. As expected, a shear failure mode occurred in all walls, due to the high vertical

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reinforcement ratio provided. From tests, the presence of an opening is concluded to reduce the shear strength and the displacement ductility. Also, a more distributed crack pattern was observed with the increase of the pier aspect ratio. A comprehensive mechanical characterization was carried out on main constitutive materials and their interfaces, to enlarge the current database on masonry materials and obtain the parameters required for a proper numerical simulation of the tested walls. It should be noted that most mechanical parameters used in the detailed micro-models were applied without arbitrary corrections. Detailed micro-models of tested walls were constructed and validated by comparing numerical and experimental results. Obtained results presented a good agreement in terms of maximum lateral force, displacement ductility and failure mode. On the other hand, it is important to note that, due to intrinsic complexities of the mechanical phenomena involved, an appropriate selection of material models, along with many input parameters, is required for the correct implementation of detailed micro-models. Additionally, their creation and analysis is a time-consuming activity that requires highly specialized professionals, and convergence difficulties can arise due to the complex materials and interfaces responses implemented. The influence of the opening size on the lateral behavior of PG-RM walls was numerically studied with the validated strategy by comparing six simulated walls. Obtained results showed that the increase in the opening size produces a decrease in the shear strength of the resisting piers, while its displacement ductility increases. The pier’s aspect ratio is the studied parameter that presents a better correlation with the results. The influence of the pier’s horizontal reinforcement ratio on the lateral behavior of PG-RM walls was numerically investigated with the validated strategy by comparing six simulated walls. It is concluded that an increment in the pier’s horizontal reinforcement ratio increases the perforated wall’s shear strength and displacement ductility. An apparent interaction between the influence of the horizontal reinforcement ratio and pier aspect ratio was reported.

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Although only a limited number of specimens were tested, the previously validated methodological approach has allowed for investigation into the influence of main structural response parameters for perforated PG-RM walls subjected to lateral loading. Overall, the numerical strategy presented in this research could reproduce the complex behavior of PG-RM walls with openings and, therefore, can be regarded as a reliable numerical tool for carrying out broader studies. The systematic use of this numerical approach could result, in the long term, in new design methodologies and/or modifications to the current masonry design codes. However, additional experimental results are still required to confirm some of the results reported in this paper.

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ACKNOWLEDGEMENTS This research has received financial support from the Fondo Nacional de Ciencia y Tecnología de Chile, FONDECYT (Fondecyt de Iniciación) through Grant No 11121161. The first author wants to acknowledge the resources provided by CONICYT-Chile through the program CONICYT-PCHA/Magister Nacional/2015-22150715. The third author also wants to acknowledge the resources provided by the Institute of Engineering of UNAM through the Emilio Rosenblueth fellowship. Finally, the authors would like to thank the technician Camilo Guzmán for his support during the tests. REFERENCES 1) Instituto Nacional de Normalización de Chile (INN) (1967). NCh158 Of.1967: Cementos - Ensayo de flexión y compresión de morteros de cemento. Instituto Nacional de Normalización. 2) Instituto Nacional de Normalización de Chile (INN) (1972). NCh200 Of.1972: Productos metálicos - Ensayo de tracción. Instituto Nacional de Normalización. 3) Instituto Nacional de Normalización de Chile (INN) (2001). NCh167 Of.2001: Construcción Ladrillos cerámicos - Ensayos. Instituto Nacional de Normalización.

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4) Instituto Nacional de Normalización de Chile (INN) (2009). NCh1928 Of.19933 Mod. 2009: Requisitos para el diseño y cálculo. Instituto Nacional de Normalización. 5) Instituto Nacional de Normalización de Chile (INN) (1977). NCh1037 Of.1977: Hormigón - Ensayo de compresión de probetas cúbicas cilíndricas. 6) Abdou, L., Saada, R.A., Meftah, F., & Mebarki, A. (2006). Experimental investigations of the jointmortar behaviour. Mechanics Research Communications, 33(3), 370–384. 7) Aguilar, V., Sandoval, C., Adam, J. M., Garzón-Roca, J., & Valdebenito, G. (2016). Prediction of the shear strength of reinforced masonry walls using a large experimental database and artificial neural networks. Structure and Infrastructure Engineering, 1-14. 8) Alcaino, P. & Santa María, H. (2008). Experimental response of externally retrofitted masonry walls subjected to shear loading. Journal of Composites for Construction, 12(5), 489-498. 9) Almeida, J.C., Lourenço, P.B., & Barros, J. (2002). Characterization of brick and brick – mortar interface under uniaxial tension. VII International Seminar on Structural Masonry for Developping Countries, Belo Horizonte, Brazil. 10) Arnau, O., Sandoval, C., & Murià-Vila, D. (2015). Determination and validation of input parameters for detailed micro-modelling of partially grouted reinforced masonry walls. In: 10th Pacific conference on earthquake engineering, 6–8 November, Sydney. 11) Astroza, M., Moroni, O., Brzev, S., & Tanner, J. (2012). Seismic performance of engineered masonry buildings in the 2010 Maule earthquake. Earthquake Spectra, 28(1), 385–406. 12) Bolhassani, M., Hamid, A.A., Johnson, C., & Schultz, A.E. (2016). Shear strength expression for partially grouted masonry walls. Engineering Structures, 127, 475-494. 13) Comite Euro-International du Beton (CEB) (1993). CEB - FIP Model Code 1990. London, UK: Thomas Telford Services Ltd. Thomas Telford House. 14) Canadian Standard Association (CSA) (2014). CSA S301-04 - Design of masonry structures. CSA. 15) Dhanasekar, M., & Haider, W. (2011). Effect of Spacing of Reinforcement on the Behaviour of Partially Grouted Masonry Shear Walls. Advances in Structural Engineering, 14(2), 281–294. 16) Drougkas, A. (2015). Derivation of the Properties of Masonry through Micro-Modeling Techniques. PhD Dissertation, Universitat Politècnica de Catalunya, Barcelona. 17) Drougkas, A., Roca, P., & Molins, C. (2013). Micro-Modeling of Stack Bond Masonry in Compression Using a Plasticity Law. XII International Conference on Computational Plasticity, 919–928. 18) El-Dakhakhni, W.W., Banting, B.R., & Miller, S.C. (2013). Seismic Performance Parameter Quantification of Shear-Critical Reinforced Concrete Masonry Squat Walls. Journal of Structural Engineering, 139, 957–973. 19) Elshafie, H., Hamid, A., & Nasr, E. (2002). Strength and Stiffness of Masonry Shear Walls with Openings. The Masonry Society Journal, 20(1), 49–60. 20) Fouchal F, Lebon F, Titeux I. (2009) Contribution to the modelling of interfaces in masonry construction. Construction and Building Materials, 23(6), 2428-2441. 21) Gabor A, Ferrier E, Jacquelin E, Hamelin P. (2006) Analysis and modelling of the in-plane shear behaviour of hollow brick masonry panels. Construction and building materials, 20(5), 308-321. 22) Ghanem, G.M., Salama, A.E., Elmagd, S.A., and Hamid, A.A. (1993). Effect of axial compression on the behavior of partially-grouted reinforced masonry shear walls. Proceedings of the 6th North American Masonry Conference, Philadelphia, PA. 23) Haach, V.G. (2009). Development of a design method for reinforced masonry subjected to in-plane loading based on experimental and numerical analysis. PhD. Dissertation, University of Minho, Guimaraes. 24) Haach, V.G., Vasconcelos, G., & Lourenço, P.B. (2009). Experimental analysis of reinforced concrete block masonry walls subjected to in-plane cyclic loading. Journal of Structural Engineering, 136(4), 452-462.

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25) Haach, V.G., Vasconcelos, G., & Lourenço, P.B. (2011). Parametrical study of masonry walls subjected to in-plane loading through numerical modeling. Engineering Structures, 33(4), 13771389. 26) Ingham, J.M., Davidson, B.J., Brammer, D.R., & Voon, K.C. (2001). Testing and codification of partially grout-filled nominally-reinforced concrete masonry subjected to in-plane cyclic loads. The Masonry Society Journal, 19(1), 83-96. 27) Lourenço, P.B. (1996). Computational strategies for masonry structures. PhD Dissertation, Delft University of Technology. Delft. 28) Lourenço, P.B., Almeida, J., & Barros, J. (2005). Experimental investigation of bricks under uniaxial tensile testing. Journal of the British Society Masonry International, (1), 11-20. 29) Lourenço, P.B., Vasconcelos, G., Medeiros, P., & Gouveia, J. (2010). Vertically perforated clay brick masonry for loadbearing and non-loadbearing masonry walls. Construction and Building Materials, 24(11), 2317–2330. 30) Lüders, C., & Hidalgo, P. (1987). Ductilidad y Degradación de Rigidez de Muros de Albañilería Armada. Paper presented at the XXIV Jornadas Sudamericanas de Ingeniería Estructural. Porto Alegre, Brasil. 31) Matsumura, A. (1988). Shear strength of reinforced masonry walls. Proceedings of 9th World Conference on Earthquake Engineering. Tokyo/Kyoto, Japan. 32) Minaie, E., Mota, M., Moon, F.L., & Hamid, A.A. (2010). In-plane behavior of partially grouted reinforced concrete masonry shear walls. Journal of Structural Engineering, 136(9), 1089-1097. 33) Meli, R., Wolf, A.Z., and Esteva, L. (1968). Comportamiento de muros de mampostería hueca ante carga lateral alternada. Revista Ingeniera, 38(3), 371–390. 34) Moroni, M.O., Astroza, M., & Acevedo, C. (2004). Performance and seismic vulnerability of masonry housing types used in Chile. Journal of Performance of Constructed Facilities, 18(3), 173– 179. 35) Murcia-Delso, J., & Shing, P.B. (2012). Fragility analysis of reinforced masonry shear walls. Earthquake Spectra, 28(4), 1523-1547. 36) Nolph, S.M., & ElGawady, M.A. (2012). Static cyclic response of partially grouted masonry shear walls. Journal of Structural Engineering, 138(7), 864–879. 37) Rahman, A., & Ueda, T. (2014). Experimental investigation and numerical modeling of peak shear stress of brick masonry mortar joint under compression. Journal of Materials in Civil Engineering, 26(9), 04014061. 38) Ramírez, P., Sandoval, C., & Almazán, J.L. (2016). Experimental study on in-plane cyclic response of partially grouted reinforced concrete masonry shear walls. Engineering Structures, 126, 598–617. 39) Rots. (1997). Structural Masonry: An Experimental/ Numerical Basis for Practical Design Rules (CUR Report 171). CRC Press. 40) Sandoval, C., & Arnau, O. (2017). Experimental characterization and detailed micro-modeling of multi-perforated clay brick masonry structural response. Materials and Structures, 50(1), 34. 41) Sandoval, C., Roca, P., Bernat, E., & Gil, L. (2011). Testing and numerical modelling of buckling failure of masonry walls. Construction and Building Materials, 25(12), 4394–4402. 42) Schultz, A.E., Hutchinson, R.S., and Cheok, G.C. (1998). Seismic performance of masonry walls with bed joint reinforcement. Structural Engineers World Congress Proceedings, T119-4. San Francisco. 43) Sepúlveda, M. (2003) Influencia del refuerzo horizontal en el comportamiento sísmico de muros de albañilería. Memoria de Ingeniero Civil, Pontificia Universidad Católica de Chile, Santiago, Chile. 44) Shing, P., Schuller, M., & Hoskere, V. (1989). Inelastic behavior o f concrete masonry shear walls. Journal of Structural Engineering, 115(9), 2204-2225. 45) TNO DIANA. (2015). DIANA finite element analysis. TNO Diana, Delft. 46) Tomaževič, M. (2008). Shear resistance of masonry walls and Eurocode 6: shear versus tensile strength of masonry. Materials and Structures, 42(7), 889–907.

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47) Valdebenito, G., Alvarado, D., Sandoval, C., & Aguilar, V. (2014). Terremoto de Iquique Mw=8.2 01 Abril 2014: Daños observados y efectos de sitio en estructuras de albañilería. In XI Congreso Chileno de Sismología e Ingeniería Sísmica. 18-20 March, Santiago, Chile. 48) Van der Pluijm, R. (1997). Non-linear behaviour of masonry under tension. HERON Journal, 42(1). 49) Voon, K.C., & Ingham, J.M. (2006). Experimental in-plane shear strength investigation of reinforced concrete masonry walls. Journal of Structural Engineering, 132(3), 400-408. 50) Voon, K.C. (2007). In-plane Seismic Design of Concrete Masonry Structures. PhD Thesis. University of Auckland, Auckland. 51) Zepeda, J., Alcocer, S., & Flores, L. (2000). Earthquake-resistant construction with multi-perforated clay brick walls. In: 12th World Conference on Earthquake Engineering, pp. 1541–1548. 52) Zimmermann, T., Strauss, A., & Bergmeister, K. (2011). Structural behavior of low- and normalstrength interface mortar of masonry. Materials and Structures, 45(6), 829–839.

Graphical abstract

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Research Highlights - The proposed micro-modelling approach can capture well the response of partially grouted reinforced masonry walls with openings. - Shear strength and displacement ductility of a perforated wall could be determined from the shear strength of wall without opening and the aspect ratio of their piers.

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- Shear strength increases proportionally with horizontal reinforcement ratio of pier, regardless of its aspect ratio

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- Displacement ductility would be dependent on an interaction between both aspect ratio and horizontal reinforcement ratio of pier.

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