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Flexural capacity of long-span transversely loaded hollow block masonry walls
Construction and Building Materials 220 (2019) 489–502
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Flexural capacity of long-span transversely loaded hollow block masonry walls Raffaele Ardito, Alberto Taliercio ⇑ Department of Civil and Environmental Engineering, Politecnico di Milano, 20133 Milano, Italy
h i g h l i g h t s Four-point bending tests on long-span unreinforced and reinforced masonry walls, using traditional and innovative stirrups, were carried out. Eurocode 6 underestimates the flexural capacity of low-rise unreinforced walls. In reinforced tall walls, traditional stirrups perform better than innovative stirrups. Limit analysis underestimates the flexural capacity if only the reinforced cores are taken into account. A finite element model is developed to predict the flexural capacity.
a r t i c l e
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Article history: Received 29 January 2019 Received in revised form 31 May 2019 Accepted 4 June 2019 Available online 24 June 2019 Keywords: Testing Long-span walls Hollow concrete blocks Transverse loads Unreinforced masonry Reinforced masonry Four-point bending
a b s t r a c t An experimental programme was carried out on long-span masonry walls made of hollow concrete blocks. Both low-rise unreinforced walls and tall reinforced walls were subjected to four-point bending tests. The tests aim at obtaining indications on the flexural capacity of partially grouted, long-span masonry walls, which basically consist of unreinforced walls laterally supported by reinforced columns, and are mainly subjected to transverse loads. The tests on reinforced walls were also intended to compare the effectiveness of two types of reinforcement (a traditional one and an innovative one in which stirrups are replaced by metal strips welded to the longitudinal rebars) on the flexural capacity. Eurocode 6 is found to strongly underestimate the experimental flexural strength of the unreinforced walls. The traditional reinforcement was found to be more effective than the innovative one. Eventually, a finite element model of the reinforced walls was developed to try and capture their failure modes. Upon a careful calibration, the numerical model is able to match the experimental ultimate load, although the real transverse displacements cannot be correctly captured. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction In the last decades, the demand for ever-taller and wider buildings in the industrial and service sectors has increased the span of roofing elements, the height of the walls, and the spacing between supporting columns. Accordingly, ‘long-span masonry walls’ have become increasingly common: indicatively, this term refers to walls higher than 3.5 m and wider than 8 m. The slenderness of prefabricated long-span walls is much higher than that of ordinary walls: the height-to-thickness ratio is of the order of 35–50, and the width-to-thickness ratio ranges between 50 and 100. Whereas vertical loads are the main actions that ordinary walls have to withstand, the mechanical response of long-span masonry walls ⇑ Corresponding author. E-mail addresses: [email protected] (R. Ardito), [email protected] (A. Taliercio). https://doi.org/10.1016/j.conbuildmat.2019.06.042 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
is mainly affected by transverse loads (e.g. wind pressure or seismic actions). Accordingly, these walls behave more as plates or slabs than as ordinary walls. In this paper, the results of an experimental and numerical research programme regarding the mechanical behaviour of unreinforced and reinforced masonry walls, made of concrete hollow blocks, will be illustrated. The aim of the research is to get reliable information on the flexural capacity of long-span walls under transverse loads, when no significant vertical compression can be relied on. These walls consist of vibro-compacted hollow concrete blocks, in which vertical rebars are inserted at regular intervals in the superposed cores of the blocks. Upon grouting, reinforced columns supporting the interposed long-span walls are obtained. The cost of the walls can be reduced by decreasing the number of reinforced columns: this goal can be achieved if the flexural capacity of the different parts forming the walls can be predicted with fair approximation.
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Literature on hollow block masonry walls is rather scanty, not to mention literature on long-span walls, which is virtually nonexistent. A bibliographic survey on the out-of-plane strength of masonry walls, although not updated, is available in the paper by Omote et al. [1]. Three-point bending tests on unreinforced concrete hollow block walls were carried out as early as the 50’s of last century by Cox and Ennega [2]. The blocks employed in that research were not too different from those referred to hereafter (200 200 400 mm3); the height of the walls was about 0.6– 1.5 m, but the length was only 2.5 m. Accordingly, the results do not apply to long-span walls. Later on, Yokel et al. [3] tested hollow concrete and solid brick masonry walls under vertical compression and uniform transverse pressure, for different values of the vertical load. Air-bags were used to apply increasing transverse loads to failure. Significant vertical loads are usually lacking in real longspan walls: unlike the tests described by Yokel et al. [3], those presented in this paper do not include vertical loads. The possibility of replacing traditional steel bars by GFRP rods in concrete cavity walls, either partially- or fully-grouted, subjected to transverse loads was investigated by Galal and Sasanian [4]. Despite the reduced ductility of the GFRP-reinforced walls with respect to steel-reinforced walls, the use of GFRP rods was found to provide sufficient deformability. The tests, however, refer to walls with a span much shorter than those considered here. More recently, Buch and Bhat [5] investigated the bearing capacity and the failure modes of hollow block masonry walls under in-plane lateral loads and vertical compression, but transverse loads were not dealt with. Hollow brick masonry panels were also subjected to diagonal compression by Gabor et al. [6]; a successful numerical modeling of the experimental tests is also presented. Whereas these test are useful when the in-plane behaviour of hollow block masonry is dealt with, they are not particularly helpful in predicting the behaviour of long-span walls in which transverse loads are predominant. Some attention has recently been paid to the performances of cavity walls consisting of one or more wythes of concrete masonry units (CMUs) under blast actions. This is mainly due to the concern about the possibility of attacks to public and residential buildings. Single-wythe and veneer CMU walls were subjected to static and dynamic transverse loads by Browning et al. [7]. The tests mainly aimed at assessing the contribution of a nonstructural veneer to the blast resistance of cavity walls. The walls were fully grouted and reinforced, but cannot be classified as long-span walls. Hoemann et al. [8,9] subjected partially grouted CMU walls, similar to those considered in the present paper, to transverse static loads and blast loads to assess the effectiveness of different types of reinforcement on the flexural capacity. The span of these walls is half that considered in the present research. Eamon et al. [10] focus on the development of a finite element model capable of replicating the behaviour of CMU walls under blast actions of different intensity. The walls considered by these authors are either ungrouted or fully grouted and reinforced, but their slenderness is again half that of the walls considered hereafter. The numerical model was partially successful in predicting the collapse modes of the walls.
The present paper aims to fill the gap in the existing literature regarding the behaviour of real long-span hollow block masonry walls subjected to transverse loads. 2. Materials and methods 2.1. Specimens The experimental tests presented in this paper were carried out on single-wythe walls consisting of hollow concrete blocks 500 mm wide and 200 mm high. The block thickness was either 200 or 240 mm: Fig. 1 shows the geometry of typical 200 and 240 mm-thick blocks. Twelve low-rise walls, consisting of five courses of 16 unreinforced and ungrouted blocks, were subjected to four-point bending tests to assess their flexural strength when the plane of failure is perpendicular to the bed joints. These tests are meant to be representative of long-span walls delimited by columns. The walls are 8 m long and 1 m high. Six walls, labeled A1 . . .A6 from here onwards, were 200 mm-thick; other six were 240 mm-thick, and will be labeled A7 . . .A12 throughout the paper. Fig. 2 shows the geometry of a typical, 200 mm-thick unreinforced wall. Additionally, reinforced and partially grouted walls, 6 m high and 1 m wide, were subjected to four-point bending tests to assess their flexural strength when the plane of failure is parallel to the bed joints: these tests are meant to reproduce the behaviour of the columns supporting long-span walls and experiencing transverse loads. The tested walls consist of thirty courses, as shown in Fig. 3 in the case of 200 mm-thick blocks. Courses consisting of two adjacent blocks are alternated with courses consisting of a central block and two outer half-blocks. The outer cores are empty, whereas the two inner cores are filled by grout, with mechanical properties poorer than those of the concrete used to manufacture the blocks. Four 12 mm-diameter longitudinal rebars are embedded within each core. In six 200 mm-thick walls (labeled C1 . . .C6 from here onwards) and six 240 mm-thick walls (labeled C7 . . .C12) a classical stirrup system was used, consisting of 8mm diameter rods externally welded to the longitudinal rebars and spaced every 200 mm (Fig. 4(a)). In other six 200 mm-thick walls, labeled B1 . . .B6 in the following paragraphs, stirrups were replaced by metal 2 mm-thick clamps, which were internally welded to the longitudinal rebars with a spacing of 500 mm. This innovative reinforcement layout is shown in Fig. 4(b). The distance between longitudinal rebars is 8.1 mm in the C-labeled specimens, and 9.2 mm in the B-labeled specimens. The innovative stirrups were designed with a twofold goal. One is the ease in construction: metal clamps can be achieved by automatically cutting square tubes; the longitudinal reinforcements can be welded to the clamps in a controlled environment (rather than in the yard) and the whole cage can be easily cast in place. Moreover, the innovative stirrups allow the distance between the rebars to be increased, which is expected to increase the flexural strength. The experimental campaign was useful to assess the validity of this technique. In all types of walls, bed and head mortar joints were approximately 5 mm thick.
Fig. 1. Geometry of the hollow blocks (dimensions are mm): (a) 200 mm-thick blocks; (b) 240 mm-thick blocks.
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Fig. 2. Geometry of the unreinforced, ungrouted, low-rise walls (dimensions are mm); the location of the supports is also shown.
ties of these materials, as reported in data sheet provided by the producers, are summarized in Table 1. The material data are in excellent agreement with routine tests carried out on a large number of specimens. The unreinforced, low-rise walls are made with the same concrete and mortar as the tall walls.
2.3. Testing procedures
Fig. 3. Geometry of the tall, reinforced, partially grouted walls (dimensions are mm); the locations of the supports and the LVDTs are also shown.
2.2. Materials and concrete mixes The tested tall walls are composed of four materials: vibrocompacted concrete for blocks (cylindrical compressive strength 28 MPa, cement dosage 320 kg/m3, water/cement ratio 0.45), grout to fill the hollow blocks (cylindrical compressive strength 25 MPa, cement dosage 370 kg/m3, water/cement ratio 0.65), mortar for joints, and steel for rebars. The characteristic mechanical proper-
2.3.1. Unreinforced walls Four-point bending tests on low-rise, unreinforced walls were carried out according to the EN 1052-2 Standards [11]. Steel buttresses were placed at both ends of the walls to prevent horizontal displacements. Load was exerted by two hydraulic jacks, bolted on another couple of steel buttresses. All the buttresses were fixed to the floor of the testing area by chemical anchors or self-tapping screws. Each one of the inner buttresses was placed at a distance of 2 m from the nearmost side buttress. Steel bars were used to distribute the load exerted by the jacks over the entire height of the walls. Fig. 5(a) shows the layout of a test on a typical low-rise wall. Fig. 5(b) shows the location of the points at which displacements were measured by LVDTs. In one of the tests (on specimen A6), the location of the LVTDs is different from the remaining ones (Fig. 5(c)). The jack pressure was manually driven. Before the walls were monotonically tested to failure, a few loading-unloading cycles of increasing amplitude were carried out to settle the test equipment and overcome base friction. Under the 200 mm-thick walls, a single polyethylene sheet was laid to reduce friction. According to the load-displacement diagrams (see Section 3), the effect of friction was actually quantified in about 1 kN: as the weight of each wall is about 17 kN, this corresponds to a very low angle of friction (3 approximately). In tests on 240 mm-thick walls, friction was further reduced by using two polyethylene sheets, with lubricant interposed between the sheets. It was experimentally observed that friction at the base was virtually nullified.
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Fig. 4. Layout of the traditional (a) and the innovative (b) reinforcements.
Table 1 Mechanical properties of the constituent materials (⁄ yield stress).
Density (kg/m3) Elastic modulus (MPa) Poisson’s ratio Compressive strength, f ck (MPa) Tensile strength (MPa)
Concrete
Grout
Mortar
Steel
2300 33000 0.2 28 2.03
2300 – – 25 1.80
1800 – – 13 –
7600 210000 0.35 – 450
2.3.2. Reinforced walls The reinforced walls were restrained to the floor of the testing shed by four L-shaped 14 mm-diameter steel anchors, embedded within the walls for 1.5 m. The anchors protrude from the lower base of the walls with a bend of 90 , and extend for additional 100 mm within the floor. The walls underwent four-point bending tests, according to the EN 1052-2 standards [11], with the aim of evaluating their bending strength when the failure planes are parallel to the bed joints. Note, however, that the boundary conditions at the lower base of the wall does not exactly match those prescribed in the standards, where both ends are assumed to be simply supported. The standards were actually conceived for unreinforced, shorter walls. A steel frame, nearly as high as the walls, was designed to constrain the end bases of any wall and provide support to the hydraulic jacks. The frame is shown in Fig. 6(a), together with a typical tall wall. Details on the geometry of the frame are given in Figs. 6(b, c). The outer supports prescribed by the standards were obtained by two fixed beams, which were bolted at the ends of the frame. The inner supports, on which the thrust of the jacks is exerted, are obtained by two additional movable beams. The distance of each inner support from the adjacent outer support is 1.5 m approximately. Rubber layers were interposed between each beam and the wall. The centerline of the fixed beam at the bottom (respectively, at the top) of the wall is at 110 mm (resp., at
400 mm) from the nearmost base. The centerline of the lower (respectively, of the upper) movable beam is at 1640 mm from the top (resp., at 1360 mm from the bottom) of the wall; thus, the distance between the beams acted upon by the jack thrust is approximately of 3 m. The geometry of the walls and the location of the supports are shown in Fig. 3. Before the testing programme started, a 200 mm-thick concrete floor, embedding two welded meshes, was poured over the preexisting floor to ensure stability of the loading frame. Four anchors were fit in the reinforced floor at each of the lower supports of the frame, to allow the frame to be fastened to the floor at the beginning of each test. At the end of the test, the end supports were unbolted, the frame was moved to another wall, the frame base was fastened at the new location, and the end supports were bolted again. The loads were exerted by two hydraulic jacks, with a stroke of 240 mm. The jacks were hand operated by a pump, with a maximum operating pressure of 700 bar. Each test started with a few loading-unloading cycles of increasing amplitude, basically with the aim of adjusting the frame-wall system. After the third unloading, the load was monotonically increased until either the wall was significantly damaged by visual inspection, or the deformation experienced by the wall was excessive. During the tests, the jack pressure was recorded, together with the transverse displacements measured by LVDT’s at three locations along the loaded side of the walls (see Fig. 6). The three LVDT’s are located at 4100, 3100 and 1700 mm from the lower base of the wall, and will be labeled LVDT1, LVDT2, and LVDT3, respectively, from here onwards. LVDT2 is placed near the midspan of the walls. LVDT1 and LVDT3 are nearly located at the same distance from the nearest support. The location of the corresponding points where displacements were measured is shown in Fig. 3. In all the graphs shown in the next Sections, the load values refer to a single jack, and are equal to half the total applied load accordingly.
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Fig. 5. Tests on low-rise walls: (a) typical instrumented and constrained wall; (b) points where displacements were measured in walls A1 to A5; (c) points where displacements were measured in wall A6 (dimensions are mm).
3. Experimental results for unreinforced walls Fig. 7 shows the load-displacement graphs recorded during the tests on each one of the 200 mm-thick, low, unreinforced walls at the three measurement points; the graphs recorded by the transducer placed at the mid-section of the walls are summarized in Fig. 8. Figs. 9 and 10 have the same meaning as Figs. 7 and 8, respectively, but refer to 240 mm-thick walls. All graphs exhibit a first, clear change in slope at the presumed first cracking of the head joints. Failure, corresponding at the peak of the graphs, invariably occurred when also a few concrete blocks cracked, at a section close to one of the inner buttresses. Fig. 11 shows a typical crack pattern at failure. Table 2 summarizes the values of the failure loads for the low, unreinforced walls. The flexural strength of the specimens when the plane of failure is perpendicular to the bed joints, f xi (i ¼ 1 . . . 6), is also reported. f xi is computed as [11]
f xi ¼
3F i;max ðl1 l2 Þ 2
bhu
;
ð1Þ
where F i;max is the failure load of the i-th specimen (in N), l1 is the distance between the end supports (=7900 mm), l2 is the distance between the central supports (=4000 mm), b is the height of the
walls (=1000 mm), and hu is the wall thickness (=200 or 240 mm). The mean strength values, f xm are reported in Table 2. The average load rates are reported as well: the values comply with the prescription of the EN 1052-2 standard. All the load values pertinent to 200 mm-thick walls (Figs. 7, 8 and Table 2) are the recorded values minus 1 kN, to discard the effect of base friction (see Section 2.3.1). The experimental failure loads allowed the characteristic flexural strength when the plane of failure is perpendicular to the bed joints, f xk2 , to be computed according to the EN 1052-2 Standards [11]. A statistical data processing was possible as 6 experimental values were available for each set of specimens. Let yi ¼ logf xi ; P6 yi compute the average of the logarithmic values, ym ¼ 6i¼1 , and their standard deviation, s: the values of ym and s for both sets of specimens are reported in Table 2. Also, let yk ¼ ym ks, with k ¼ 2:18 for a batch of 6 specimens. With the values in Table 2, yk ¼ 0:0511 for 200 mm-thick walls and yk ¼ 0:0798 for 240 mm-thick walls. Eventually, the characteristic strength of the walls is given by f xk2 ¼ antilogðyk Þ, and is reported in the last line of Table 2. The values obtained for both types of walls are definitely higher than those suggested by Eurocode 6 [12], which range between 0.2 and 0.4 N/mm2 depending on the type of units and the strength and thickness of the joints.
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Fig. 6. Loading frame for 4-point bending tests on tall walls: (a) 3D view; (b) side view; (c) front view (dimensions are mm).
Fig. 7. Load-displacement graphs for 200 mm-thick A-type walls.
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Fig. 8. 200 mm-thick A-type walls: midpoint deflection.
4. Experimental results for reinforced walls 4.1. Load-displacement curves Fig. 12 shows the load-displacement curves obtained for 200 mm-thick B-type walls (reinforced by an innovative stirrup system), according to the measurements of the three LVDT’s placed along the height of the wall. The asymmetry induced by the boundary conditions at the ends of the wall is apparent, as transducers LVDT1 and LVDT3 are supposed to record similar displacements in case of symmetric end restraints.
495
Fig. 10. 240 mm-thick A-type walls: midpoint deflection.
In Fig. 13 the displacements recorded for the six B-type walls by transducer LVDT2, located near the midspan, are compared. Except for wall B2, the remaining load-displacement curves are in good agreement with each other, meaning that the tests have a fairly good repeatability. The slope of the curves decreases as the load increases, consistently with the visually observed progressive cracking in the bed joints. The tests stopped at different load values, according to the estimated damage state. In most cases, also the final unloading branch was monitored. Note, however, that no curve exhibits a negligible slope at the maximum attained load: accordingly, this load underestimates the real collapse loads,
Fig. 9. Load-displacement graphs for 240 mm-thick A-type walls.
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Fig. 13. B-type walls: midpoint deflection.
Fig. 11. Typical crack pattern for a low-rise wall.
Table 2 Average load rate, maximum load attained and bending strength in tests on low, unreinforced walls. Specimen label
Average load rate (N/mm2 /min)
Failure load (kN)
Bending strength (N/mm2 )
Specimen label (N/mm2 /min)
Average load rate (kN)
Failure load (N/mm2 )
Bending strength
A1 A2 A3 A4 A5 A6
0.28 0.21 0.10 0.29 0.06 0.55
5.41 4.47 4.25 4.66 4.98 5.58
1.58 1.31 1.24 1.36 1.46 1.63
A7 A8 A9 A10 A11 A12
0.30 0.33 0.42 0.19 0.22 0.61
5.25 4.84 4.76 5.97 4.52 5.26
1.07 0.98 0.97 1.21 0.92 1.07
f xm ym s f xk2
1.43 0.1536 0.0470 1.12
f xm ym s f xk2
1.04 0.0135 0.0428 0.83
Fig. 12. Load-displacement graphs for B-type walls.
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which could not be attained because of the excessive deformation experienced by the walls (see Fig. 14). Figs. 15 and 17 show the load-displacement curves obtained for C-type walls (reinforced by traditional stirrups): Fig. 15 refers to 200 mm-thick walls, whereas Fig. 17 to 240 mm-thick walls. Figs. 16 and 18 summarize the test results relevant to 200 mmthick and 240 mm-thick walls, respectively, in terms of displacement recorded by the central transducer. Comparing these curves with those related to unreinforced walls (Section 3), the increase in strength and ductility due to the presence of rebars is apparent. The curves exhibit a progressive decrease in slope, corresponding to the growth of cracks in the bed joints as visually observed. Similarly to tests on B-type walls, several tests had to be stopped because of excessive deformation of the specimens. Figs. 16 and 18 also show that the repeatability of the tests is good. Accordingly, it is reasonable to assume that in many cases the real collapse load was underestimated by the maximum load attained in the test, as the corresponding experimental load-displacement curve might continue similarly to those of other specimens that were found to be stronger. Finally, Fig. 19 shows the typical failure modes observed in the tests on tall walls, namely tilting of the base (a) and cracking of one or more bed joints in the central part (b). In some tests, crushing of blocks in the central part was also noticed.
497
4.2. Flexural capacity Table 3 summarizes the maximum load attained in the tests on 200 mm-thick reinforced walls with innovative stirrups (specimens B1 to B6), on 200 mm-thick walls with traditional stirrups (specimens C1 to C6), and on 240 mm-thick walls with traditional stirrups (specimens C7 to C12). For each type of wall, the average loading rate is reported: as the load is manually operated, it was not possible to ensure that the loading rate was constant during each test and in all tests. Nevertheless, the variation is small enough to state that the tests on similar specimens were carried out in homogeneous conditions. The mean collapse load (in kN) is also reported, for each type of specimens. A statistical data processing of the maximum load values, similar to that proposed by the EN 1052-2 Standards [11] and used in Section 3 for low-rise walls, was done. Denote by F i the failure load of the i-th specimen P6 Yi and let Y i ¼ logF i . Compute Y m ¼ i¼1 and Y k ¼ Y m ks, with 6 k ¼ 2:18, being s the standard deviation of the logarithmic values Y i (see Table 3). The characteristic strength of the walls in terms of failure load, F k , can be estimated as F k ¼ antilogðY k Þ. The values or F k are reported in the last line of Table 3. Table 3 shows that 200 mm-thick walls with traditional stirrups have a strength higher that those with innovative stirrups, despite the smaller distance between rebars in the traditional system (8.1 mm) with respect to the innovative system (9.2 mm). This might be explained by the reduced confinement provided by the innovative stirrups, which are welded internally to the longitudinal rebars unlike the traditional stirrups. Also, the spacing of the innovative stirrups (500 mm) is higher than that of the traditional stirrups (200 mm). Thicker walls are obviously stronger. As discussed in Section 4.1, it is worth emphasizing that the values reported in Table 3 are likely to underestimate the real flexural capacity of the walls. It is instructive to compare the test results with a hand calculation of the flexural capacity. Assume the walls to behave as beams fixed at the lower end and simply supported at the upper end, subjected to point loads as shown in Fig. 3. The resisting moment M rk is given by the inner, reinforced cores; the outer hollow cores are neglected. Rebars have a yield strength of 450 MPa; the cylindrical strength of grout is supposed to be 25 MPa. For a 200 mm-thick wall, the resisting moment is computed at two critical sections, where plastic hinges are likely to occur: the section where the upper load is applied (M rk1 ¼ 34:89 kNm), and the lower base (M rk2 ¼ 26:08 kNm). At both sections, failure occurs with rebars yielding at the compressed side, so that ductile failure can be assumed and limit analysis can be applied to compute the characteristic value of the collapse load:
F k;num ¼
M rk1 5:5 m þ Mrk2 1:25 m ¼ 32:65 kN 5:5 1:25 m2
ð2Þ
As F k;num is definitely lower than the characteristic collapse loads reported in Table 3 for 200 mm-thick walls, it can be concluded that the actual flexural capacity of the walls is higher than that predicted by limit analysis. Similar conclusions can be drawn for 240 mm-thick walls. More refined numerical models, such as that shown hereafter, have to be developed to correctly capture the failure mode and the flexural capacity of the reinforced walls. 5. Numerical simulations
Fig. 14. Typical deformed tall wall at the end of the test.
As experimental tests on large-size specimens are expensive and time-consuming, it would be advisable to have reliable numerical models to predict the mechanical behaviour of long-span masonry walls of different geometry and type of reinforcement. As a simple model based on limit analysis was shown to underes-
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Fig. 15. Load-displacement graphs for 200 mm-thick C-type walls.
Fig. 16. 200 mm-thick C-type walls: midpoint deflection.
timate the experimentally measured collapse loads, a finite element model was developed to simulate the response of reinforced hollow block masonry walls. For the sake of illustration, attention is focused here on walls 200 mm-thick and a distance between longitudinal rebars of 8.1 mm (specimens C1 to C6). Stirrups are not included in the numerical model. Only half of the wall was modeled because of symmetry (Fig. 20(a)). A detail of the Finite Element (FE) model is shown in Fig. 20(b). The entire model consists of more than 417,000 8-node, 3D solid hexaedral elements to discretize blocks, joints and grout, whereas 4800 2-node truss elements were used to discretize rebars. The commercial FE program used (AbaqusTM) allows perfect bonding between rebars
and grout to be modeled by prescribing truss elements to be ‘embedded regions’ within grout. Concrete blocks were assumed to be linear elastic, as no significant crushing or cracking of the blocks was recorded until the very end of the tests. Mortar joints, in which most inelastic phenomena are confined, were assumed to behave like elastic-plastic materials with softening in compression, and like elastic-brittle materials in tension. In order to reduce the computational cost, and avoid problems in defining the interaction with rebars, grout was assumed to behave elastically, except for the layers crossing the mortar joints, where tensile failure was found to occur in the experiments: a constitutive law similar to that of mortar was used for these layers. Steel is assumed to be elastic-perfectly plastic, the nonlinear behaviour being completely defined by the yield stress, f y . The mechanical properties of the materials used in computations are listed in Table 4. The properties that are not listed in Table 1 were deduced from a parametric study, in order to match the experimental load-displacement diagrams as closely as possible. E and m denote the Young’s modulus and the Poisson’s ratio of the materials. Except for concrete, the mean strength in uniaxial compression (f cm ) and tension (f ctm ) are reported (f y ¼ f cm ¼ f ctm for steel), together with the displacement at zero stress in tension (u0 ) for mortar and grout. AbaqusTM allows the behaviour of quasi-brittle materials to be described by the so-called ‘concrete smeared cracking’ model. If any principal stress is tensile, no macrocrack develops, but cracking is rather spread over any FE. As deformation increases, the material tensile strength progressively decreases to zero: to avoid mesh-dependency, the constitutive law in tension is defined in
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Fig. 17. Load-displacement graphs for 240 mm-thick C-type walls.
Fig. 18. 240 mm-thick C-type walls: midpoint deflection.
terms of fracture energy, that is, a stress-displacement law is prescribed. Assuming a linear decrease in tensile strength, only the uniaxial strength, f ctm , and the displacement at zero stress, u0 , have to be assigned. Whereas the top of the wall is assumed to be simply supported, in the FE analysis the base was considered to be either fixed or supported. This is because moderate rotations were observed at the base of the walls during the tests. As discussed hereafter, a better prediction of the experimental collapse load is obtained if the base is assumed to be fixed. The comparisons between numerical and experimental load-displacement curves presented in the next sections refer to
the displacement at the center of the mid-section of the walls, where LVDT2 is located. A preliminary analysis was carried out to validate the numerical model in the initial phase of the tests, just after the occurrence of the first cracks, and to identify the unknown mechanical properties of mortar by a parametric investigation. By adopting the parameters listed in Table 4, the load-displacement curve shown in Fig. 21 is obtained. The numerical curve is compared with the experimental diagram relative to the first part of the test on wall B1: an excellent match is observed. In Fig. 22 the load-displacement diagram obtained by the numerical model with fixed base is reported and compared with the average experimental collapse load of B-type walls (47.92 kN). The numerical collapse occurs at 52.4 kN, and overestimates the experimental collapse load by 9%. The difference between the two values can be motivated in light of the following observations: debonding of rebars, even if limited, might decrease the collapse load with respect to the numerical analyses, where perfect bonding is assumed; except for walls B2 and B3, the ultimate loads attained in tests on B-type walls are extremely close to each other (see Table 3): it is likely that the ultimate loads of walls B2 and B3 have been underestimated. Assuming these values to be outliers, an average collapse load of 50.23 kN is obtained: the discrepancy with the numerical collapse load decreases to 4%. The load-displacement curve contains some interesting information. Up to a load of about 6.5 kN, the entire wall is in the linear
500
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Fig. 19. Typical failure mode of tall walls: (a) base tilt; (b) cracking of bed joints and crushing of blocks.
Table 3 Average load rate and maximum load attained in tests on high, reinforced walls. Specimen label
Average load rate (kN/min)
Max. load (kN)
Specimen label
Average load rate (kN/min)
Max. load (kN)
Specimen label (kN/min)
Average load rate (kN)
max. load
B1 B2 B3 B4 B5 B6
14.2 10.2 12.0 13.0 11.4 6.87
50.39 43.73 42.82 50.86 50.20 49.50
C1 C2 C3 C4 C5 C6
7.0 10.1 11.2 12.6 14.3 13.1
45.34 48.83 48.50 54.23 53.23 57.05
C7 C8 C9 C10 C11 C12
8.40 6.82 5.51 5.69 5.27 4.46
49.10 54.13 54.75 58.39 50.55 57.36
Fm Ym s Fk
47.92 1.6794 0.0338 40.34
Fm Ym s Fk
51.20 1.7079 0.0371 42.37
Fm Ym s Fk
54.05 1.7319 0.0297 46.48
elastic field. Afterwards, the mortar joint at the base of the wall progressively cracks, and plastic strains occur at the compressed side. Rebars entirely carry tensile stresses, until complete yielding and formation of a plastic hinge at the base of the wall at about P ¼ 34 kN. At the same time, mortar joints at the center of the wall progressively crack. Above 34 kN, the wall behaves as a simplysupported beam, as the rebars at the base cannot carry any increase in bending moment. The moment in the central zone of the wall is nearly uniform: rebars yield at the cracks that occur between the loaded sections, an additional plastic hinge is formed, and collapse occurs at a load of about 52 kN. The numerical model is able to capture correctly the loaddisplacement curve in the elastic field and in the early postelastic phase; moreover, the ultimate load is computed with sufficient accuracy: this confirms the validity of the proposed model as a predictive tool for the flexural capacity of the considered walls. Although the ultimate force is correctly evaluated, the agreement between numerical and experimental displacements is far from
being satisfactory. The maximum deflection computed by the model heavily underestimates the experimental values. An explanation might be the assumed perfect bonding between rebars and grout, which does not significantly affect the prediction of the collapse load, but excessively stiffens the numerical model. A first attempt in this direction has already been made, by adding inelastic springs at the grout-rebar interface to simulate the possible bond-slip: this expedient gave good results in preliminary numerical tests on small samples, but caused convergence problems in the analyses of full-scale walls performed so far.
6. Concluding remarks. Future perspectives The experimental programme carried out on concrete hollow block masonry walls can give useful indications in the design of long-span walls for industrial and commercial buildings. Very limited investigations have been carried out on this important topic so
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Fig. 20. Finite element model of a typical tall wall: (a) geometrical model of half the wall; (b) detail of the finite element mesh.
Table 4 Material properties used in the FE model. Material
E
m
f cm (N/mm2 )
f ctm (N/mm2 )
u0 (mm)
0.2 0.2 0.1 0.3
– 10 13 450
– 1.5 1 450
– 0.05 0.04
(N/mm2 ) Concrete Grout Mortar Steel
33000 7000 2000 210,000
Fig. 22. Numerical load-displacement diagram for walls with fixed base; the average experimental failure load is also shown (dashed line).
Fig. 21. Wall B1: comparison between numerical and experimental load-displacement diagrams up to the first cracking.
far. Low-rise, unreinforced walls subjected to four-point bending tests exhibited a flexural strength much higher than that suggested by the Eurocode 6. Accordingly, a design of long-span walls based on EC6 entails an unnecessarily high number of reinforced columns. Similar tests carried out on tall, reinforced walls showed that failure is preceded by large displacements, and that all the wall components participate in the failure mechanism (joint crack-
ing, block crushing, rebar yielding). According to limit analysis, the flexural strength of the tall walls is underestimated by that of the single reinforced cores, indicating that the outer, empty cores contribute to the flexural capacity of the walls. Finally, traditional stirrups were found to be more effective than metal strips welded to the rebars in terms of flexural strength of the walls. As far as the numerical modeling of the tests on reinforced walls is concerned, good results were obtained in terms of ultimate load. Boundary conditions were shown to play an important role in predicting the flexural strength of the reinforced walls, which is captured definitely better if the base is assumed to be fixed rather than supported: in the former case, the ultimate load is overestimated by 9%, whereas in the latter case it is underestimated by 50%. Strictly speaking, the tests on tall walls are not exactly fourpoint bending tests, but the base constraints are likely to match those found in real buildings.
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The numerical results obtained so far can be a first step for future developments aimed at modeling the entire loaddisplacement experimental curves with sufficient precision. The difficulties in achieving this goal are mainly related to the correct description of the mechanical behaviour and the mutual interactions of the four materials that partially grouted, reinforced walls are made of. An extension of the experimental programme to walls made with blocks reinforced by vegetable fibers, similar to those tested by Soto Izquierdo et al. [13], might give useful guidelines for the design of sustainable buildings. Declaration of Competing Interest None. Acknowledgments The financial support of Senini SpA, which also provided the specimens to be tested and the site where tests were carried out, is gratefully acknowledged. The authors are also indebted to Dr. Nicola Sacco for developing the numerical analyses. References [1] Y. Omote, R.L. Mayes, S.-W.J. Chen, R.W. Clough, A Literature Survey – Transverse Strength of Masonry Walls, Report no. UCB/EERC-77/07, Earthquake Engineering Research Center, University of California, Berkeley (CA), 1977.
[2] F.W. Cox, J.L. Ennega, Transverse strength of concrete block walls, ACI J. 29 (11) (1958) 951–960. [3] F.Y. Yokel, R.G. Mathey, R.D. Dikkers, Strength of masonry walls under compressive and transverse loads, U.S. Dept. of Commerce, Nat. Bur. Stand. Bldg. Sci. Ser. 34 (1971). [4] K. Galal, N. Sasanian, Out-of-Plane flexural performance of GFRP-reinforced masonry walls, J. Compos. Constr. 14 (2010) 162–174. [5] S.H. Buch, D.M. Bhat, Performance of hollow concrete block masonry under lateral loads, in: V. Matsagar (Ed.), Advances in Structural Engineering, Springer, India, 2015, pp. 2435–2444. [6] A. Gabor, E. Ferrier, E. Jacquelin, P. Hamelin, Analysis and modeling of the inplane shear behaviour of hollow brick masonry panels, Constr. Build. Mater. 20 (2006) 308–321. [7] R.S. Browning, R.J. Dinan, J.S. Davidson, Blast-resistance of fully-grouted reinforced concrete masonry veneer walls, ASCE J. Perform. Constr. Facil. 28 (2014) 228–241. [8] J.M. Hoemann, J.S. Shull, H.H. Salim, B.T. Bewick, J.S. Davidson, Performance of partially grouted, minimally reinforced CMU cavity walls against blast demands. I: Large deflection static resistance under uniform pressure, ASCE, J. Perform. Constr. Facil. 29 (2015) 04014113. [9] J.M. Hoemann, J.S. Shull, H.H. Salim, B.T. Bewick, J.S. Davidson, Performance of partially grouted, minimally reinforced CMU cavity walls against blast demands. II: Performance under impulse loads, ASCE, J. Perform. Constr. Facil. 29 (2015) 04014114. [10] C.D. Eamon, J.T. Baylot, J.L. O’Daniel, Modeling concrete masonry walls subjected to explosive loads, ASCE J. Eng. Mech. 130 (2004) 1098–1106. [11] EN 1052-2, Methods of test for masonry – determination of flexural strength (1999).. [12] Eurocode 6: design of masonry structures – Part 1. 1: general rules for reinforced and unreinforced masonry structures – clause 3.6.3: characteristic flexural strength of masonry (2005).. [13] I. Soto Izquierdo, O. Soto Izquierdo, M.A. Ramalho, A. Taliercio, The use of Sisal fibers in hollow concrete blocks for structural applications: testing and modeling, Constr. Build. Mater. 151 (2017) 98–112.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Flexural capacity of long-span transversely loaded hollow block masonry walls Raffaele Ardito, Alberto Taliercio ⇑ Department of Civil and Environmental Engineering, Politecnico di Milano, 20133 Milano, Italy
h i g h l i g h t s Four-point bending tests on long-span unreinforced and reinforced masonry walls, using traditional and innovative stirrups, were carried out. Eurocode 6 underestimates the flexural capacity of low-rise unreinforced walls. In reinforced tall walls, traditional stirrups perform better than innovative stirrups. Limit analysis underestimates the flexural capacity if only the reinforced cores are taken into account. A finite element model is developed to predict the flexural capacity.
a r t i c l e
i n f o
Article history: Received 29 January 2019 Received in revised form 31 May 2019 Accepted 4 June 2019 Available online 24 June 2019 Keywords: Testing Long-span walls Hollow concrete blocks Transverse loads Unreinforced masonry Reinforced masonry Four-point bending
a b s t r a c t An experimental programme was carried out on long-span masonry walls made of hollow concrete blocks. Both low-rise unreinforced walls and tall reinforced walls were subjected to four-point bending tests. The tests aim at obtaining indications on the flexural capacity of partially grouted, long-span masonry walls, which basically consist of unreinforced walls laterally supported by reinforced columns, and are mainly subjected to transverse loads. The tests on reinforced walls were also intended to compare the effectiveness of two types of reinforcement (a traditional one and an innovative one in which stirrups are replaced by metal strips welded to the longitudinal rebars) on the flexural capacity. Eurocode 6 is found to strongly underestimate the experimental flexural strength of the unreinforced walls. The traditional reinforcement was found to be more effective than the innovative one. Eventually, a finite element model of the reinforced walls was developed to try and capture their failure modes. Upon a careful calibration, the numerical model is able to match the experimental ultimate load, although the real transverse displacements cannot be correctly captured. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction In the last decades, the demand for ever-taller and wider buildings in the industrial and service sectors has increased the span of roofing elements, the height of the walls, and the spacing between supporting columns. Accordingly, ‘long-span masonry walls’ have become increasingly common: indicatively, this term refers to walls higher than 3.5 m and wider than 8 m. The slenderness of prefabricated long-span walls is much higher than that of ordinary walls: the height-to-thickness ratio is of the order of 35–50, and the width-to-thickness ratio ranges between 50 and 100. Whereas vertical loads are the main actions that ordinary walls have to withstand, the mechanical response of long-span masonry walls ⇑ Corresponding author. E-mail addresses: [email protected] (R. Ardito), [email protected] (A. Taliercio). https://doi.org/10.1016/j.conbuildmat.2019.06.042 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
is mainly affected by transverse loads (e.g. wind pressure or seismic actions). Accordingly, these walls behave more as plates or slabs than as ordinary walls. In this paper, the results of an experimental and numerical research programme regarding the mechanical behaviour of unreinforced and reinforced masonry walls, made of concrete hollow blocks, will be illustrated. The aim of the research is to get reliable information on the flexural capacity of long-span walls under transverse loads, when no significant vertical compression can be relied on. These walls consist of vibro-compacted hollow concrete blocks, in which vertical rebars are inserted at regular intervals in the superposed cores of the blocks. Upon grouting, reinforced columns supporting the interposed long-span walls are obtained. The cost of the walls can be reduced by decreasing the number of reinforced columns: this goal can be achieved if the flexural capacity of the different parts forming the walls can be predicted with fair approximation.
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Literature on hollow block masonry walls is rather scanty, not to mention literature on long-span walls, which is virtually nonexistent. A bibliographic survey on the out-of-plane strength of masonry walls, although not updated, is available in the paper by Omote et al. [1]. Three-point bending tests on unreinforced concrete hollow block walls were carried out as early as the 50’s of last century by Cox and Ennega [2]. The blocks employed in that research were not too different from those referred to hereafter (200 200 400 mm3); the height of the walls was about 0.6– 1.5 m, but the length was only 2.5 m. Accordingly, the results do not apply to long-span walls. Later on, Yokel et al. [3] tested hollow concrete and solid brick masonry walls under vertical compression and uniform transverse pressure, for different values of the vertical load. Air-bags were used to apply increasing transverse loads to failure. Significant vertical loads are usually lacking in real longspan walls: unlike the tests described by Yokel et al. [3], those presented in this paper do not include vertical loads. The possibility of replacing traditional steel bars by GFRP rods in concrete cavity walls, either partially- or fully-grouted, subjected to transverse loads was investigated by Galal and Sasanian [4]. Despite the reduced ductility of the GFRP-reinforced walls with respect to steel-reinforced walls, the use of GFRP rods was found to provide sufficient deformability. The tests, however, refer to walls with a span much shorter than those considered here. More recently, Buch and Bhat [5] investigated the bearing capacity and the failure modes of hollow block masonry walls under in-plane lateral loads and vertical compression, but transverse loads were not dealt with. Hollow brick masonry panels were also subjected to diagonal compression by Gabor et al. [6]; a successful numerical modeling of the experimental tests is also presented. Whereas these test are useful when the in-plane behaviour of hollow block masonry is dealt with, they are not particularly helpful in predicting the behaviour of long-span walls in which transverse loads are predominant. Some attention has recently been paid to the performances of cavity walls consisting of one or more wythes of concrete masonry units (CMUs) under blast actions. This is mainly due to the concern about the possibility of attacks to public and residential buildings. Single-wythe and veneer CMU walls were subjected to static and dynamic transverse loads by Browning et al. [7]. The tests mainly aimed at assessing the contribution of a nonstructural veneer to the blast resistance of cavity walls. The walls were fully grouted and reinforced, but cannot be classified as long-span walls. Hoemann et al. [8,9] subjected partially grouted CMU walls, similar to those considered in the present paper, to transverse static loads and blast loads to assess the effectiveness of different types of reinforcement on the flexural capacity. The span of these walls is half that considered in the present research. Eamon et al. [10] focus on the development of a finite element model capable of replicating the behaviour of CMU walls under blast actions of different intensity. The walls considered by these authors are either ungrouted or fully grouted and reinforced, but their slenderness is again half that of the walls considered hereafter. The numerical model was partially successful in predicting the collapse modes of the walls.
The present paper aims to fill the gap in the existing literature regarding the behaviour of real long-span hollow block masonry walls subjected to transverse loads. 2. Materials and methods 2.1. Specimens The experimental tests presented in this paper were carried out on single-wythe walls consisting of hollow concrete blocks 500 mm wide and 200 mm high. The block thickness was either 200 or 240 mm: Fig. 1 shows the geometry of typical 200 and 240 mm-thick blocks. Twelve low-rise walls, consisting of five courses of 16 unreinforced and ungrouted blocks, were subjected to four-point bending tests to assess their flexural strength when the plane of failure is perpendicular to the bed joints. These tests are meant to be representative of long-span walls delimited by columns. The walls are 8 m long and 1 m high. Six walls, labeled A1 . . .A6 from here onwards, were 200 mm-thick; other six were 240 mm-thick, and will be labeled A7 . . .A12 throughout the paper. Fig. 2 shows the geometry of a typical, 200 mm-thick unreinforced wall. Additionally, reinforced and partially grouted walls, 6 m high and 1 m wide, were subjected to four-point bending tests to assess their flexural strength when the plane of failure is parallel to the bed joints: these tests are meant to reproduce the behaviour of the columns supporting long-span walls and experiencing transverse loads. The tested walls consist of thirty courses, as shown in Fig. 3 in the case of 200 mm-thick blocks. Courses consisting of two adjacent blocks are alternated with courses consisting of a central block and two outer half-blocks. The outer cores are empty, whereas the two inner cores are filled by grout, with mechanical properties poorer than those of the concrete used to manufacture the blocks. Four 12 mm-diameter longitudinal rebars are embedded within each core. In six 200 mm-thick walls (labeled C1 . . .C6 from here onwards) and six 240 mm-thick walls (labeled C7 . . .C12) a classical stirrup system was used, consisting of 8mm diameter rods externally welded to the longitudinal rebars and spaced every 200 mm (Fig. 4(a)). In other six 200 mm-thick walls, labeled B1 . . .B6 in the following paragraphs, stirrups were replaced by metal 2 mm-thick clamps, which were internally welded to the longitudinal rebars with a spacing of 500 mm. This innovative reinforcement layout is shown in Fig. 4(b). The distance between longitudinal rebars is 8.1 mm in the C-labeled specimens, and 9.2 mm in the B-labeled specimens. The innovative stirrups were designed with a twofold goal. One is the ease in construction: metal clamps can be achieved by automatically cutting square tubes; the longitudinal reinforcements can be welded to the clamps in a controlled environment (rather than in the yard) and the whole cage can be easily cast in place. Moreover, the innovative stirrups allow the distance between the rebars to be increased, which is expected to increase the flexural strength. The experimental campaign was useful to assess the validity of this technique. In all types of walls, bed and head mortar joints were approximately 5 mm thick.
Fig. 1. Geometry of the hollow blocks (dimensions are mm): (a) 200 mm-thick blocks; (b) 240 mm-thick blocks.
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Fig. 2. Geometry of the unreinforced, ungrouted, low-rise walls (dimensions are mm); the location of the supports is also shown.
ties of these materials, as reported in data sheet provided by the producers, are summarized in Table 1. The material data are in excellent agreement with routine tests carried out on a large number of specimens. The unreinforced, low-rise walls are made with the same concrete and mortar as the tall walls.
2.3. Testing procedures
Fig. 3. Geometry of the tall, reinforced, partially grouted walls (dimensions are mm); the locations of the supports and the LVDTs are also shown.
2.2. Materials and concrete mixes The tested tall walls are composed of four materials: vibrocompacted concrete for blocks (cylindrical compressive strength 28 MPa, cement dosage 320 kg/m3, water/cement ratio 0.45), grout to fill the hollow blocks (cylindrical compressive strength 25 MPa, cement dosage 370 kg/m3, water/cement ratio 0.65), mortar for joints, and steel for rebars. The characteristic mechanical proper-
2.3.1. Unreinforced walls Four-point bending tests on low-rise, unreinforced walls were carried out according to the EN 1052-2 Standards [11]. Steel buttresses were placed at both ends of the walls to prevent horizontal displacements. Load was exerted by two hydraulic jacks, bolted on another couple of steel buttresses. All the buttresses were fixed to the floor of the testing area by chemical anchors or self-tapping screws. Each one of the inner buttresses was placed at a distance of 2 m from the nearmost side buttress. Steel bars were used to distribute the load exerted by the jacks over the entire height of the walls. Fig. 5(a) shows the layout of a test on a typical low-rise wall. Fig. 5(b) shows the location of the points at which displacements were measured by LVDTs. In one of the tests (on specimen A6), the location of the LVTDs is different from the remaining ones (Fig. 5(c)). The jack pressure was manually driven. Before the walls were monotonically tested to failure, a few loading-unloading cycles of increasing amplitude were carried out to settle the test equipment and overcome base friction. Under the 200 mm-thick walls, a single polyethylene sheet was laid to reduce friction. According to the load-displacement diagrams (see Section 3), the effect of friction was actually quantified in about 1 kN: as the weight of each wall is about 17 kN, this corresponds to a very low angle of friction (3 approximately). In tests on 240 mm-thick walls, friction was further reduced by using two polyethylene sheets, with lubricant interposed between the sheets. It was experimentally observed that friction at the base was virtually nullified.
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Fig. 4. Layout of the traditional (a) and the innovative (b) reinforcements.
Table 1 Mechanical properties of the constituent materials (⁄ yield stress).
Density (kg/m3) Elastic modulus (MPa) Poisson’s ratio Compressive strength, f ck (MPa) Tensile strength (MPa)
Concrete
Grout
Mortar
Steel
2300 33000 0.2 28 2.03
2300 – – 25 1.80
1800 – – 13 –
7600 210000 0.35 – 450
2.3.2. Reinforced walls The reinforced walls were restrained to the floor of the testing shed by four L-shaped 14 mm-diameter steel anchors, embedded within the walls for 1.5 m. The anchors protrude from the lower base of the walls with a bend of 90 , and extend for additional 100 mm within the floor. The walls underwent four-point bending tests, according to the EN 1052-2 standards [11], with the aim of evaluating their bending strength when the failure planes are parallel to the bed joints. Note, however, that the boundary conditions at the lower base of the wall does not exactly match those prescribed in the standards, where both ends are assumed to be simply supported. The standards were actually conceived for unreinforced, shorter walls. A steel frame, nearly as high as the walls, was designed to constrain the end bases of any wall and provide support to the hydraulic jacks. The frame is shown in Fig. 6(a), together with a typical tall wall. Details on the geometry of the frame are given in Figs. 6(b, c). The outer supports prescribed by the standards were obtained by two fixed beams, which were bolted at the ends of the frame. The inner supports, on which the thrust of the jacks is exerted, are obtained by two additional movable beams. The distance of each inner support from the adjacent outer support is 1.5 m approximately. Rubber layers were interposed between each beam and the wall. The centerline of the fixed beam at the bottom (respectively, at the top) of the wall is at 110 mm (resp., at
400 mm) from the nearmost base. The centerline of the lower (respectively, of the upper) movable beam is at 1640 mm from the top (resp., at 1360 mm from the bottom) of the wall; thus, the distance between the beams acted upon by the jack thrust is approximately of 3 m. The geometry of the walls and the location of the supports are shown in Fig. 3. Before the testing programme started, a 200 mm-thick concrete floor, embedding two welded meshes, was poured over the preexisting floor to ensure stability of the loading frame. Four anchors were fit in the reinforced floor at each of the lower supports of the frame, to allow the frame to be fastened to the floor at the beginning of each test. At the end of the test, the end supports were unbolted, the frame was moved to another wall, the frame base was fastened at the new location, and the end supports were bolted again. The loads were exerted by two hydraulic jacks, with a stroke of 240 mm. The jacks were hand operated by a pump, with a maximum operating pressure of 700 bar. Each test started with a few loading-unloading cycles of increasing amplitude, basically with the aim of adjusting the frame-wall system. After the third unloading, the load was monotonically increased until either the wall was significantly damaged by visual inspection, or the deformation experienced by the wall was excessive. During the tests, the jack pressure was recorded, together with the transverse displacements measured by LVDT’s at three locations along the loaded side of the walls (see Fig. 6). The three LVDT’s are located at 4100, 3100 and 1700 mm from the lower base of the wall, and will be labeled LVDT1, LVDT2, and LVDT3, respectively, from here onwards. LVDT2 is placed near the midspan of the walls. LVDT1 and LVDT3 are nearly located at the same distance from the nearest support. The location of the corresponding points where displacements were measured is shown in Fig. 3. In all the graphs shown in the next Sections, the load values refer to a single jack, and are equal to half the total applied load accordingly.
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Fig. 5. Tests on low-rise walls: (a) typical instrumented and constrained wall; (b) points where displacements were measured in walls A1 to A5; (c) points where displacements were measured in wall A6 (dimensions are mm).
3. Experimental results for unreinforced walls Fig. 7 shows the load-displacement graphs recorded during the tests on each one of the 200 mm-thick, low, unreinforced walls at the three measurement points; the graphs recorded by the transducer placed at the mid-section of the walls are summarized in Fig. 8. Figs. 9 and 10 have the same meaning as Figs. 7 and 8, respectively, but refer to 240 mm-thick walls. All graphs exhibit a first, clear change in slope at the presumed first cracking of the head joints. Failure, corresponding at the peak of the graphs, invariably occurred when also a few concrete blocks cracked, at a section close to one of the inner buttresses. Fig. 11 shows a typical crack pattern at failure. Table 2 summarizes the values of the failure loads for the low, unreinforced walls. The flexural strength of the specimens when the plane of failure is perpendicular to the bed joints, f xi (i ¼ 1 . . . 6), is also reported. f xi is computed as [11]
f xi ¼
3F i;max ðl1 l2 Þ 2
bhu
;
ð1Þ
where F i;max is the failure load of the i-th specimen (in N), l1 is the distance between the end supports (=7900 mm), l2 is the distance between the central supports (=4000 mm), b is the height of the
walls (=1000 mm), and hu is the wall thickness (=200 or 240 mm). The mean strength values, f xm are reported in Table 2. The average load rates are reported as well: the values comply with the prescription of the EN 1052-2 standard. All the load values pertinent to 200 mm-thick walls (Figs. 7, 8 and Table 2) are the recorded values minus 1 kN, to discard the effect of base friction (see Section 2.3.1). The experimental failure loads allowed the characteristic flexural strength when the plane of failure is perpendicular to the bed joints, f xk2 , to be computed according to the EN 1052-2 Standards [11]. A statistical data processing was possible as 6 experimental values were available for each set of specimens. Let yi ¼ logf xi ; P6 yi compute the average of the logarithmic values, ym ¼ 6i¼1 , and their standard deviation, s: the values of ym and s for both sets of specimens are reported in Table 2. Also, let yk ¼ ym ks, with k ¼ 2:18 for a batch of 6 specimens. With the values in Table 2, yk ¼ 0:0511 for 200 mm-thick walls and yk ¼ 0:0798 for 240 mm-thick walls. Eventually, the characteristic strength of the walls is given by f xk2 ¼ antilogðyk Þ, and is reported in the last line of Table 2. The values obtained for both types of walls are definitely higher than those suggested by Eurocode 6 [12], which range between 0.2 and 0.4 N/mm2 depending on the type of units and the strength and thickness of the joints.
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Fig. 6. Loading frame for 4-point bending tests on tall walls: (a) 3D view; (b) side view; (c) front view (dimensions are mm).
Fig. 7. Load-displacement graphs for 200 mm-thick A-type walls.
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Fig. 8. 200 mm-thick A-type walls: midpoint deflection.
4. Experimental results for reinforced walls 4.1. Load-displacement curves Fig. 12 shows the load-displacement curves obtained for 200 mm-thick B-type walls (reinforced by an innovative stirrup system), according to the measurements of the three LVDT’s placed along the height of the wall. The asymmetry induced by the boundary conditions at the ends of the wall is apparent, as transducers LVDT1 and LVDT3 are supposed to record similar displacements in case of symmetric end restraints.
495
Fig. 10. 240 mm-thick A-type walls: midpoint deflection.
In Fig. 13 the displacements recorded for the six B-type walls by transducer LVDT2, located near the midspan, are compared. Except for wall B2, the remaining load-displacement curves are in good agreement with each other, meaning that the tests have a fairly good repeatability. The slope of the curves decreases as the load increases, consistently with the visually observed progressive cracking in the bed joints. The tests stopped at different load values, according to the estimated damage state. In most cases, also the final unloading branch was monitored. Note, however, that no curve exhibits a negligible slope at the maximum attained load: accordingly, this load underestimates the real collapse loads,
Fig. 9. Load-displacement graphs for 240 mm-thick A-type walls.
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Fig. 13. B-type walls: midpoint deflection.
Fig. 11. Typical crack pattern for a low-rise wall.
Table 2 Average load rate, maximum load attained and bending strength in tests on low, unreinforced walls. Specimen label
Average load rate (N/mm2 /min)
Failure load (kN)
Bending strength (N/mm2 )
Specimen label (N/mm2 /min)
Average load rate (kN)
Failure load (N/mm2 )
Bending strength
A1 A2 A3 A4 A5 A6
0.28 0.21 0.10 0.29 0.06 0.55
5.41 4.47 4.25 4.66 4.98 5.58
1.58 1.31 1.24 1.36 1.46 1.63
A7 A8 A9 A10 A11 A12
0.30 0.33 0.42 0.19 0.22 0.61
5.25 4.84 4.76 5.97 4.52 5.26
1.07 0.98 0.97 1.21 0.92 1.07
f xm ym s f xk2
1.43 0.1536 0.0470 1.12
f xm ym s f xk2
1.04 0.0135 0.0428 0.83
Fig. 12. Load-displacement graphs for B-type walls.
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which could not be attained because of the excessive deformation experienced by the walls (see Fig. 14). Figs. 15 and 17 show the load-displacement curves obtained for C-type walls (reinforced by traditional stirrups): Fig. 15 refers to 200 mm-thick walls, whereas Fig. 17 to 240 mm-thick walls. Figs. 16 and 18 summarize the test results relevant to 200 mmthick and 240 mm-thick walls, respectively, in terms of displacement recorded by the central transducer. Comparing these curves with those related to unreinforced walls (Section 3), the increase in strength and ductility due to the presence of rebars is apparent. The curves exhibit a progressive decrease in slope, corresponding to the growth of cracks in the bed joints as visually observed. Similarly to tests on B-type walls, several tests had to be stopped because of excessive deformation of the specimens. Figs. 16 and 18 also show that the repeatability of the tests is good. Accordingly, it is reasonable to assume that in many cases the real collapse load was underestimated by the maximum load attained in the test, as the corresponding experimental load-displacement curve might continue similarly to those of other specimens that were found to be stronger. Finally, Fig. 19 shows the typical failure modes observed in the tests on tall walls, namely tilting of the base (a) and cracking of one or more bed joints in the central part (b). In some tests, crushing of blocks in the central part was also noticed.
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4.2. Flexural capacity Table 3 summarizes the maximum load attained in the tests on 200 mm-thick reinforced walls with innovative stirrups (specimens B1 to B6), on 200 mm-thick walls with traditional stirrups (specimens C1 to C6), and on 240 mm-thick walls with traditional stirrups (specimens C7 to C12). For each type of wall, the average loading rate is reported: as the load is manually operated, it was not possible to ensure that the loading rate was constant during each test and in all tests. Nevertheless, the variation is small enough to state that the tests on similar specimens were carried out in homogeneous conditions. The mean collapse load (in kN) is also reported, for each type of specimens. A statistical data processing of the maximum load values, similar to that proposed by the EN 1052-2 Standards [11] and used in Section 3 for low-rise walls, was done. Denote by F i the failure load of the i-th specimen P6 Yi and let Y i ¼ logF i . Compute Y m ¼ i¼1 and Y k ¼ Y m ks, with 6 k ¼ 2:18, being s the standard deviation of the logarithmic values Y i (see Table 3). The characteristic strength of the walls in terms of failure load, F k , can be estimated as F k ¼ antilogðY k Þ. The values or F k are reported in the last line of Table 3. Table 3 shows that 200 mm-thick walls with traditional stirrups have a strength higher that those with innovative stirrups, despite the smaller distance between rebars in the traditional system (8.1 mm) with respect to the innovative system (9.2 mm). This might be explained by the reduced confinement provided by the innovative stirrups, which are welded internally to the longitudinal rebars unlike the traditional stirrups. Also, the spacing of the innovative stirrups (500 mm) is higher than that of the traditional stirrups (200 mm). Thicker walls are obviously stronger. As discussed in Section 4.1, it is worth emphasizing that the values reported in Table 3 are likely to underestimate the real flexural capacity of the walls. It is instructive to compare the test results with a hand calculation of the flexural capacity. Assume the walls to behave as beams fixed at the lower end and simply supported at the upper end, subjected to point loads as shown in Fig. 3. The resisting moment M rk is given by the inner, reinforced cores; the outer hollow cores are neglected. Rebars have a yield strength of 450 MPa; the cylindrical strength of grout is supposed to be 25 MPa. For a 200 mm-thick wall, the resisting moment is computed at two critical sections, where plastic hinges are likely to occur: the section where the upper load is applied (M rk1 ¼ 34:89 kNm), and the lower base (M rk2 ¼ 26:08 kNm). At both sections, failure occurs with rebars yielding at the compressed side, so that ductile failure can be assumed and limit analysis can be applied to compute the characteristic value of the collapse load:
F k;num ¼
M rk1 5:5 m þ Mrk2 1:25 m ¼ 32:65 kN 5:5 1:25 m2
ð2Þ
As F k;num is definitely lower than the characteristic collapse loads reported in Table 3 for 200 mm-thick walls, it can be concluded that the actual flexural capacity of the walls is higher than that predicted by limit analysis. Similar conclusions can be drawn for 240 mm-thick walls. More refined numerical models, such as that shown hereafter, have to be developed to correctly capture the failure mode and the flexural capacity of the reinforced walls. 5. Numerical simulations
Fig. 14. Typical deformed tall wall at the end of the test.
As experimental tests on large-size specimens are expensive and time-consuming, it would be advisable to have reliable numerical models to predict the mechanical behaviour of long-span masonry walls of different geometry and type of reinforcement. As a simple model based on limit analysis was shown to underes-
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Fig. 15. Load-displacement graphs for 200 mm-thick C-type walls.
Fig. 16. 200 mm-thick C-type walls: midpoint deflection.
timate the experimentally measured collapse loads, a finite element model was developed to simulate the response of reinforced hollow block masonry walls. For the sake of illustration, attention is focused here on walls 200 mm-thick and a distance between longitudinal rebars of 8.1 mm (specimens C1 to C6). Stirrups are not included in the numerical model. Only half of the wall was modeled because of symmetry (Fig. 20(a)). A detail of the Finite Element (FE) model is shown in Fig. 20(b). The entire model consists of more than 417,000 8-node, 3D solid hexaedral elements to discretize blocks, joints and grout, whereas 4800 2-node truss elements were used to discretize rebars. The commercial FE program used (AbaqusTM) allows perfect bonding between rebars
and grout to be modeled by prescribing truss elements to be ‘embedded regions’ within grout. Concrete blocks were assumed to be linear elastic, as no significant crushing or cracking of the blocks was recorded until the very end of the tests. Mortar joints, in which most inelastic phenomena are confined, were assumed to behave like elastic-plastic materials with softening in compression, and like elastic-brittle materials in tension. In order to reduce the computational cost, and avoid problems in defining the interaction with rebars, grout was assumed to behave elastically, except for the layers crossing the mortar joints, where tensile failure was found to occur in the experiments: a constitutive law similar to that of mortar was used for these layers. Steel is assumed to be elastic-perfectly plastic, the nonlinear behaviour being completely defined by the yield stress, f y . The mechanical properties of the materials used in computations are listed in Table 4. The properties that are not listed in Table 1 were deduced from a parametric study, in order to match the experimental load-displacement diagrams as closely as possible. E and m denote the Young’s modulus and the Poisson’s ratio of the materials. Except for concrete, the mean strength in uniaxial compression (f cm ) and tension (f ctm ) are reported (f y ¼ f cm ¼ f ctm for steel), together with the displacement at zero stress in tension (u0 ) for mortar and grout. AbaqusTM allows the behaviour of quasi-brittle materials to be described by the so-called ‘concrete smeared cracking’ model. If any principal stress is tensile, no macrocrack develops, but cracking is rather spread over any FE. As deformation increases, the material tensile strength progressively decreases to zero: to avoid mesh-dependency, the constitutive law in tension is defined in
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Fig. 17. Load-displacement graphs for 240 mm-thick C-type walls.
Fig. 18. 240 mm-thick C-type walls: midpoint deflection.
terms of fracture energy, that is, a stress-displacement law is prescribed. Assuming a linear decrease in tensile strength, only the uniaxial strength, f ctm , and the displacement at zero stress, u0 , have to be assigned. Whereas the top of the wall is assumed to be simply supported, in the FE analysis the base was considered to be either fixed or supported. This is because moderate rotations were observed at the base of the walls during the tests. As discussed hereafter, a better prediction of the experimental collapse load is obtained if the base is assumed to be fixed. The comparisons between numerical and experimental load-displacement curves presented in the next sections refer to
the displacement at the center of the mid-section of the walls, where LVDT2 is located. A preliminary analysis was carried out to validate the numerical model in the initial phase of the tests, just after the occurrence of the first cracks, and to identify the unknown mechanical properties of mortar by a parametric investigation. By adopting the parameters listed in Table 4, the load-displacement curve shown in Fig. 21 is obtained. The numerical curve is compared with the experimental diagram relative to the first part of the test on wall B1: an excellent match is observed. In Fig. 22 the load-displacement diagram obtained by the numerical model with fixed base is reported and compared with the average experimental collapse load of B-type walls (47.92 kN). The numerical collapse occurs at 52.4 kN, and overestimates the experimental collapse load by 9%. The difference between the two values can be motivated in light of the following observations: debonding of rebars, even if limited, might decrease the collapse load with respect to the numerical analyses, where perfect bonding is assumed; except for walls B2 and B3, the ultimate loads attained in tests on B-type walls are extremely close to each other (see Table 3): it is likely that the ultimate loads of walls B2 and B3 have been underestimated. Assuming these values to be outliers, an average collapse load of 50.23 kN is obtained: the discrepancy with the numerical collapse load decreases to 4%. The load-displacement curve contains some interesting information. Up to a load of about 6.5 kN, the entire wall is in the linear
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Fig. 19. Typical failure mode of tall walls: (a) base tilt; (b) cracking of bed joints and crushing of blocks.
Table 3 Average load rate and maximum load attained in tests on high, reinforced walls. Specimen label
Average load rate (kN/min)
Max. load (kN)
Specimen label
Average load rate (kN/min)
Max. load (kN)
Specimen label (kN/min)
Average load rate (kN)
max. load
B1 B2 B3 B4 B5 B6
14.2 10.2 12.0 13.0 11.4 6.87
50.39 43.73 42.82 50.86 50.20 49.50
C1 C2 C3 C4 C5 C6
7.0 10.1 11.2 12.6 14.3 13.1
45.34 48.83 48.50 54.23 53.23 57.05
C7 C8 C9 C10 C11 C12
8.40 6.82 5.51 5.69 5.27 4.46
49.10 54.13 54.75 58.39 50.55 57.36
Fm Ym s Fk
47.92 1.6794 0.0338 40.34
Fm Ym s Fk
51.20 1.7079 0.0371 42.37
Fm Ym s Fk
54.05 1.7319 0.0297 46.48
elastic field. Afterwards, the mortar joint at the base of the wall progressively cracks, and plastic strains occur at the compressed side. Rebars entirely carry tensile stresses, until complete yielding and formation of a plastic hinge at the base of the wall at about P ¼ 34 kN. At the same time, mortar joints at the center of the wall progressively crack. Above 34 kN, the wall behaves as a simplysupported beam, as the rebars at the base cannot carry any increase in bending moment. The moment in the central zone of the wall is nearly uniform: rebars yield at the cracks that occur between the loaded sections, an additional plastic hinge is formed, and collapse occurs at a load of about 52 kN. The numerical model is able to capture correctly the loaddisplacement curve in the elastic field and in the early postelastic phase; moreover, the ultimate load is computed with sufficient accuracy: this confirms the validity of the proposed model as a predictive tool for the flexural capacity of the considered walls. Although the ultimate force is correctly evaluated, the agreement between numerical and experimental displacements is far from
being satisfactory. The maximum deflection computed by the model heavily underestimates the experimental values. An explanation might be the assumed perfect bonding between rebars and grout, which does not significantly affect the prediction of the collapse load, but excessively stiffens the numerical model. A first attempt in this direction has already been made, by adding inelastic springs at the grout-rebar interface to simulate the possible bond-slip: this expedient gave good results in preliminary numerical tests on small samples, but caused convergence problems in the analyses of full-scale walls performed so far.
6. Concluding remarks. Future perspectives The experimental programme carried out on concrete hollow block masonry walls can give useful indications in the design of long-span walls for industrial and commercial buildings. Very limited investigations have been carried out on this important topic so
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Fig. 20. Finite element model of a typical tall wall: (a) geometrical model of half the wall; (b) detail of the finite element mesh.
Table 4 Material properties used in the FE model. Material
E
m
f cm (N/mm2 )
f ctm (N/mm2 )
u0 (mm)
0.2 0.2 0.1 0.3
– 10 13 450
– 1.5 1 450
– 0.05 0.04
(N/mm2 ) Concrete Grout Mortar Steel
33000 7000 2000 210,000
Fig. 22. Numerical load-displacement diagram for walls with fixed base; the average experimental failure load is also shown (dashed line).
Fig. 21. Wall B1: comparison between numerical and experimental load-displacement diagrams up to the first cracking.
far. Low-rise, unreinforced walls subjected to four-point bending tests exhibited a flexural strength much higher than that suggested by the Eurocode 6. Accordingly, a design of long-span walls based on EC6 entails an unnecessarily high number of reinforced columns. Similar tests carried out on tall, reinforced walls showed that failure is preceded by large displacements, and that all the wall components participate in the failure mechanism (joint crack-
ing, block crushing, rebar yielding). According to limit analysis, the flexural strength of the tall walls is underestimated by that of the single reinforced cores, indicating that the outer, empty cores contribute to the flexural capacity of the walls. Finally, traditional stirrups were found to be more effective than metal strips welded to the rebars in terms of flexural strength of the walls. As far as the numerical modeling of the tests on reinforced walls is concerned, good results were obtained in terms of ultimate load. Boundary conditions were shown to play an important role in predicting the flexural strength of the reinforced walls, which is captured definitely better if the base is assumed to be fixed rather than supported: in the former case, the ultimate load is overestimated by 9%, whereas in the latter case it is underestimated by 50%. Strictly speaking, the tests on tall walls are not exactly fourpoint bending tests, but the base constraints are likely to match those found in real buildings.
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The numerical results obtained so far can be a first step for future developments aimed at modeling the entire loaddisplacement experimental curves with sufficient precision. The difficulties in achieving this goal are mainly related to the correct description of the mechanical behaviour and the mutual interactions of the four materials that partially grouted, reinforced walls are made of. An extension of the experimental programme to walls made with blocks reinforced by vegetable fibers, similar to those tested by Soto Izquierdo et al. [13], might give useful guidelines for the design of sustainable buildings. Declaration of Competing Interest None. Acknowledgments The financial support of Senini SpA, which also provided the specimens to be tested and the site where tests were carried out, is gratefully acknowledged. The authors are also indebted to Dr. Nicola Sacco for developing the numerical analyses. References [1] Y. Omote, R.L. Mayes, S.-W.J. Chen, R.W. Clough, A Literature Survey – Transverse Strength of Masonry Walls, Report no. UCB/EERC-77/07, Earthquake Engineering Research Center, University of California, Berkeley (CA), 1977.
[2] F.W. Cox, J.L. Ennega, Transverse strength of concrete block walls, ACI J. 29 (11) (1958) 951–960. [3] F.Y. Yokel, R.G. Mathey, R.D. Dikkers, Strength of masonry walls under compressive and transverse loads, U.S. Dept. of Commerce, Nat. Bur. Stand. Bldg. Sci. Ser. 34 (1971). [4] K. Galal, N. Sasanian, Out-of-Plane flexural performance of GFRP-reinforced masonry walls, J. Compos. Constr. 14 (2010) 162–174. [5] S.H. Buch, D.M. Bhat, Performance of hollow concrete block masonry under lateral loads, in: V. Matsagar (Ed.), Advances in Structural Engineering, Springer, India, 2015, pp. 2435–2444. [6] A. Gabor, E. Ferrier, E. Jacquelin, P. Hamelin, Analysis and modeling of the inplane shear behaviour of hollow brick masonry panels, Constr. Build. Mater. 20 (2006) 308–321. [7] R.S. Browning, R.J. Dinan, J.S. Davidson, Blast-resistance of fully-grouted reinforced concrete masonry veneer walls, ASCE J. Perform. Constr. Facil. 28 (2014) 228–241. [8] J.M. Hoemann, J.S. Shull, H.H. Salim, B.T. Bewick, J.S. Davidson, Performance of partially grouted, minimally reinforced CMU cavity walls against blast demands. I: Large deflection static resistance under uniform pressure, ASCE, J. Perform. Constr. Facil. 29 (2015) 04014113. [9] J.M. Hoemann, J.S. Shull, H.H. Salim, B.T. Bewick, J.S. Davidson, Performance of partially grouted, minimally reinforced CMU cavity walls against blast demands. II: Performance under impulse loads, ASCE, J. Perform. Constr. Facil. 29 (2015) 04014114. [10] C.D. Eamon, J.T. Baylot, J.L. O’Daniel, Modeling concrete masonry walls subjected to explosive loads, ASCE J. Eng. Mech. 130 (2004) 1098–1106. [11] EN 1052-2, Methods of test for masonry – determination of flexural strength (1999).. [12] Eurocode 6: design of masonry structures – Part 1. 1: general rules for reinforced and unreinforced masonry structures – clause 3.6.3: characteristic flexural strength of masonry (2005).. [13] I. Soto Izquierdo, O. Soto Izquierdo, M.A. Ramalho, A. Taliercio, The use of Sisal fibers in hollow concrete blocks for structural applications: testing and modeling, Constr. Build. Mater. 151 (2017) 98–112.