Bar buckling in ductile RC walls with different boundary zone detailing: Experimental investigation

Engineering Structures 198 (2019) 109544

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Bar buckling in ductile RC walls with different boundary zone detailing: Experimental investigation

T

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Mayank Tripathia, , Rajesh P. Dhakala, Farhad Dashtib a b

Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, New Zealand UC Quake Centre, Christchurch, New Zealand

A R T I C LE I N FO

A B S T R A C T

Keywords: Structural walls Boundary zone detailing Bar buckling Cyclic tests Bar fracture

The performance of reinforced concrete (RC) structural walls during the past earthquakes in New Zealand (2010–11) and Chile (2010) have highlighted the susceptibility of these critical structural components to several undesirable modes of failure. One such failure mode is premature buckling of the longitudinal reinforcing bars, which has also been observed in experimental tests of flexurally-dominant structural walls. This paper presents the results of an experimental program investigating the effects of transverse reinforcement detailing on buckling resistance of longitudinal reinforcement located in the boundary regions of RC structural walls. Three large-scale rectangular walls with different boundary zone transverse reinforcement detailing were tested under in-plane cyclic loading. The effects of these three types of detailing are reported in terms of drift capacity, buckling length of the longitudinal bars and cumulative energy dissipation capacity of the specimens. The test results confirm that bar buckling modes depend on transverse reinforcement detailing, which consequently also influences the ultimate flexural deformation capacity of ductile walls. By comparing the responses of the tested wall specimens, the inadequacy of code-compliant transverse reinforcement to restrain bar buckling is discussed and the effect of improved transverse reinforcement detailing (designed using a mechanics-based approach) on deformation capacity of slender walls is scrutinised.

1. Introduction Reinforced concrete (RC) walls or simply shear walls are widely used as the primary lateral load-resisting systems in RC buildings located in regions of medium to high seismicity. The performance of RC shear walls in past seismic events [1–3], along with evidence from experimental tests on RC structural walls, has demonstrated the vulnerability of RC walls designed according to the current design methodologies [4,5] to compression-controlled failure modes. During the Chile (2010) and Christchurch (2010–11) earthquakes, a considerable number of RC walls were reported to have failed due to reinforcement buckling, reinforcement fracture, concrete crushing and out-of-plane instability. In current design methodology for ductile RC wall buildings [4–6], slender RC walls are designed to respond predominately in flexure with formation of plastic hinges at the critical region of the wall. In such walls, ultimate failure is expected to be characterised by ductile tension-dominated response rather than brittle compression-dominated response. Most of the slender RC walls experimentally tested in the laboratory have reportedly experienced failure due to loss in compression capacity [7–14], which shows that even though slender RC

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walls are designed to undergo a tension-dominated response, they are vulnerable to premature compression failure. Reinforcement buckling is considered as an important limit state that restricts the seismic performance of RC structural members and has been the subject of numerous investigations [15–19]. However, researchers have generally focussed on investigating the buckling behaviour of bare reinforcing bars under different loading histories (monotonic, cyclic and random) and recommended that the compressive stress degradation in reinforcing bars can be avoided by limiting the slenderness ratio of bars (i.e. the ratio of unsupported length to bar diameter) to 6 or less [20–35]. However, although the reduction in compressive stress capacity of a bar is dependent on its slenderness ratio, the issue of bar buckling in RC structures is mainly associated with the inadequacy of transverse reinforcement to restrict bar buckling to single tie spacing, therefore resulting in larger slenderness ratios of bars (as buckling can span multiple tie spacings). Fig. 1 shows the schematic layout of typical buckling modes. Herein, the buckling mode is defined as the number of tie spacings within which the longitudinal bars buckle. As can be seen in Fig. 1, the first buckling mode is the desired mode of failure where all ties/stirrups are successful in

Corresponding author. E-mail addresses: [email protected] (M. Tripathi), [email protected] (R.P. Dhakal), [email protected] (F. Dashti).

https://doi.org/10.1016/j.engstruct.2019.109544 Received 1 April 2019; Received in revised form 11 August 2019; Accepted 11 August 2019 Available online 20 August 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

Engineering Structures 198 (2019) 109544

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Buckling mode 1

that RC walls designed according to NZS3101:2006 [4] are susceptible to premature buckling and the current anti-buckling requirements have no significant effect on delaying buckling of reinforcing bars [41]. To achieve a ductile wall response until the design drift demand is reached, design codes [4–6] recommend that boundary regions of the wall susceptible to compression yielding should be detailed with adequate confinement reinforcement. However, even though the design guidelines are provided to ensure adequate deformability in compression, the outcomes of recent tests carried out on rectangular RC prisms designed according to modern standards have shown that they are prone to premature compression failure [38,42,43]. This difference in the responses (expected versus actual) is mainly due to inconsistencies between the transverse reinforcement detailing used in the experimental program that formed the basis for the development of these design guidelines (the studies carried out to investigate the confinement properties of concrete [44,45]) and the transverse reinforcement detailing used in recent experimental programs. In tests carried out by Mander et al. [44] to investigate the confinement properties of concrete, significantly large transverse reinforcement ratios ranging from 3 to 6% (as compared to a practical range of 0.5–2%) were used [40], which was adequate to limit any bar buckling to single tie spacing. Therefore, the reduction in compressive stress capacity due to bar buckling was avoided and hence a large ductility in compression was observed. In addition to this, in these confinement studies the effect of tensile loading on the compression response of prisms was also not investigated. Although it has been acknowledged in the literature that reinforcement buckling is a commonly observed failure mode that results in deterioration of seismic performance of RC walls, its consideration in design codes is limited. To restrict reinforcement buckling in RC walls, design codes (e.g. NZS3101:2006 [4], ACI318-14 [5] and Eurocode-8 [6]) recommend providing closely-spaced stirrups/ties in regions of the wall that are susceptible to compression yielding, where the maximum tie/stirrup spacing is limited to 6db (where db is the diameter of longitudinal reinforcing bars). In addition to restricting spacing of transverse reinforcement in plastic hinge regions, NZS3101:2006 [4] also provides a simple expression to calculate the minimum area of each tie leg required to restrict buckling, whereas no such requirement is provided in ACI318-14 [5] and Eurocode-8 [6]. Most design codes [5,6] provide an expression to evaluate the area of transverse reinforcement required to ensure adequate strength and ductility (hence confinement) in the probable plastic hinge regions and inherently assume that the amount of confinement reinforcement is adequate to restrain buckling in RC structures. However, the performance of RC structures subject to lateral load has exposed the inability of the current code provisions to control reinforcement buckling in RC walls. Even though NZS3101:2006 [4] provides an expression to estimate the area of antibuckling reinforcement, the provision contradicts the findings of research reported in the literature on buckling of reinforcing bars inside RC structural members [46]. NZS3101:2006 [4] suggests that the area of transverse reinforcement required to restrict buckling to single tie spacing (referred to as anti-buckling reinforcement) can be reduced as the spacing is reduced. However, Dhakal and Maekawa [46], based on extensive numerical and analytical investigation of reinforcing bars, concluded that the effective stiffness of transverse reinforcement defines the buckling resistance of longitudinal reinforcing bars in RC structures. Reducing the spacing of transverse reinforcement can improve the confinement properties of the concrete; however, it results in increased buckling-induced axial demands on the transverse reinforcement, thereby deteriorating their anti-buckling performance. This can explain why Thomsen and Wallace [7] found that closelyspaced stirrups deteriorated the buckling of reinforcing bars. Despite research being carried out in literature to evaluate the buckling behaviour of reinforcing bars, reinforcement buckling inside RC structures still remains an unresolved topic. With a significant number of RC structures undergoing failure due to reinforcement

Buckling mode 3

Fig. 1. Schematic layout of the buckling modes.

counteracting the buckling tendency of longitudinal bars. However, if the transverse reinforcement is inadequate to restrain bar buckling to single tie spacing, the tie legs elongate in the direction of potential buckling. This results in an increase in bar buckling length and consequently, the slenderness ratio of the longitudinal reinforcing bar. An illustration of bar buckling with buckling mode 3 is shown in Fig. 1. Owing to this increased slenderness ratio, the compressive stress capacity of the bars reduces, which subsequently leads to reduction in the flexural capacity of the RC member. To avoid this buckling-induced compressive stress degradation in bars during an earthquake, most design codes [4–6] limit the spacing of transverse reinforcement in probable plastic hinge regions to less than or equal to six times the diameter of the longitudinal bar being restrained. However, observations from past earthquakes and experimental tests were buckling has spanned multiple tie spacings highlight the inadequacy of transverse reinforcement designed according to these guidelines. In the last decade, numerous experimental investigations have been carried out to evaluate the performance of RC walls under lateral loading. However, limited research has been reported in the literature aiming to limit reinforcement buckling in RC structural walls. Most of the reported works have focused on evaluating the effect of transverse reinforcement spacing on the hysteretic response of RC structural walls. Thomsen and Wallace [36] conducted tests on slender RC walls with different transverse reinforcement spacing and concluded that providing closely spaced stirrups improves the deformation capacity of walls (due to improved concrete confinement) but results in deteriorated reinforcement buckling performance (reduction in spacing of transverse reinforcement resulted in an increment of the buckling length) due to the increased buckling-induced axial demand on the tie legs. Oh et al. [37] conducted tests on RC walls to investigate the effect of boundary zone details on deformation capacity of walls and concluded that increasing the volumetric transverse reinforcement ratio can improve the deformation capacity of walls (due to increased confinement), but buckling of the reinforcing bars was not addressed. Further tests were carried out on confined end regions of walls, i.e. boundary zone prisms, to investigate the effect of transverse reinforcement detailing on the response of RC walls. Hilson [38] conducted tests on rectangular RC prisms representing the confined end region of walls to investigate the effect of transverse reinforcement spacing required by ACI318-11 [39] and concluded that confined end regions of walls are susceptible to failure due to reinforcement buckling and out-of-plane instability. Welt et al. [40] conducted tests on rectangular prisms to evaluate the efficacy of ACI318-14 [5] transverse reinforcement requirements for special and ordinary boundary elements and concluded that current transverse reinforcement detailing requirements cannot achieve the required axial deformation capacity. Also, tests on structural walls with distributed reinforcement concluded 2

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SWD-2 consisted of a set of 2-R6 stirrups (identical to wall SWD-1 in terms of the arrangement) with centre-to-centre spacing of the transverse reinforcement increased to 72 mm (corresponding to s = 6db; i.e. the maximum transverse reinforcement spacing allowed by New Zealand and American concrete standards for ductile RC walls). Specimen SWD-3 had an improved transverse reinforcement detailing chosen to restrain the buckling of longitudinal reinforcing bars within single tie spacing. For this purpose, the transverse reinforcement size and arrangement were chosen to provide the axial stiffness required to limit the buckling length of longitudinal bars to single tie spacing using the approach proposed by Dhakal and Maekawa [46] and Dhakal and Su [48]. As stated earlier, the ability of a transverse reinforcement to restrict bar buckling (i.e. restraining buckling to single tie spacing) is dependent upon the axial stiffness of the transverse reinforcement. In this study, an iterative procedure to design the transverse reinforcement was adopted. For a given boundary zone longitudinal reinforcement detailing, different possible configurations of transverse reinforcement (arrangement and diameter) were derived and the expected buckling mode for each configuration was evaluated using the stability model proposed by Dhakal and Maekawa [46]. The configuration resulting in a buckling mode of 1 was selected for wall SWD-3. As the axial stiffness of a tie leg is inversely proportional to its length, an increase in the axial stiffness of ties was achieved by reducing the effective length of the tie leg, keeping the area constant. Therefore, smaller size stirrups were provided in specimen SWD-3 compared to SWD-1 and SWD-2. In addition to increasing the tie stiffness, the middle rebar (which was exempted from being restrained according to the New Zealand Standards) was restrained against buckling using a small triangular stirrup. Therefore, specimen SWD-3 exhibited a set of 3-R6 stirrups spaced at 55 mm centre-to-centre (Fig. 2). Herein, it should be noted that the middle rebar could also be restrained using a cross tie (with an increased area) designed to ensure that the tie legs have adequate stiffness to restrain bar buckling to single tie spacing. However, due to the vulnerability of cross tie hooks to opening during a seismic event (subsequently making them inadequate to restrain bar buckling) [40,49], a 6 mm triangular stirrup was used to restrain the middle bar in wall SWD-3. Table 1 summarises the general characteristics of the tested wall specimens. Table 2 summarises the anti-buckling provisions of the design codes (NZS3101:2006 [4], ACI318-14 [5]). In the table, Ate is the area of one tie leg in the direction of buckling, ∑Ab is the sum of the area of longitudinal bar reliant on the tie leg, s is the spacing of the transverse reinforcement, db is the diameter of the longitudinal bar being restrained and fy and fyt is the yield strength of longitudinal and transverse reinforcement, respectively. Table 2 also presents a comparison between the provided transverse reinforcement detailing and the required detailing based on the design recommendations of NZS3101:2006 [4] and ACI318-14 [5]. Table 3 provides the mechanical properties of the reinforcing bars used in the specimens obtained from uniaxial tension tests.

buckling [15–19,38,40], there is a strong need to investigate the measures necessary to control reinforcement buckling in RC structures. In addition to this, most existing works focus only on the overall compression response of members rather than considering buckling as a limit state, which, together with the other compression failure modes (e.g. crushing), results in premature failure of RC structures. Therefore, this paper aims to investigate measures for controlling reinforcement buckling inside RC walls such that the bar buckling is restricted to single tie spacing. Based on the literature review and understanding of the problem, parameters influencing buckling of reinforcing bars inside RC walls are identified and evaluated using experimental tests on RC walls. The objectives of the paper are: (i) to evaluate the efficacy of anti-buckling requirements of NZS3101:2006 [4]; (ii) to evaluate the efficacy of an improved transverse reinforcement detailing designed to restrict buckling of reinforcing bars within single tie spacing; and (iii) to compare seismic performance of RC walls with different transverse reinforcement detailing. 2. Experimental investigation on RC structural walls 2.1. Details of the RC wall specimens The experimental program comprised of testing three slender rectangular RC wall specimens under quasi-static reversed cyclic loading. To be compatible with the size and ability of the facility, the test specimens were decided to be half-scale models, representing the first story of a multi-storey wall. The unsupported height of the specimen was 2000 mm, thereby representing a storey height of 4000 mm. The prototype wall was part of a multi-storey prototype building located in New Zealand and had a length, storey height and thickness of 4000 mm, 4000 mm and 300 mm, respectively. To ensure that the specimens were flexurally-dominated, a shear span ratio of 3 was selected and the longitudinal reinforcement for the prototype wall was designed such that the over-strength moment capacity of the wall did not exceed the wall shear strength in order to avoid shear failure. Further, while the overall dimensions (length, storey height and thickness) of the wall specimens were scaled, the longitudinal reinforcement ratio in different regions (boundary zones and wall web) of the prototype wall and the corresponding scaled specimens were kept the same. The three test specimens (labelled as SWD-1, SWD-2 and SWD-3) had a height, length and thickness of 2000 mm, 2000 mm and 150 mm, respectively. A wall thickness of 150 mm was identified to limit the outof-plane deformations that were observed during previous tests carried out on similar RC wall specimens with a thickness of 125 mm [11,47]. In addition to the dimensions, the longitudinal (i.e. vertical) and shear (i.e. horizontal) reinforcement amount and arrangement were also kept identical in all specimens. In an RC structure, buckling performance of reinforcing bars inside concrete primarily depends on the effectiveness of transverse reinforcement in restraining reinforcement buckling [46]. Contrary to this, the current design codes emphasise only on the spacing of ties as an important parameter to restrain buckling of reinforcing bars. Therefore, the major parameter considered in this study was the transverse reinforcement detailing that includes both the spacing and arrangement of stirrups/ties in the boundary zones. Fig. 2 shows the geometry and reinforcement layout of the three tested specimens. Specimen SWD-1 was the benchmark specimen, with transverse reinforcement designed and detailed according to NZS3101:2006 [4]. It should be noted that the provided detailing also satisfied the antibuckling provision of ACI318-14 [5] (as the spacing of transverse reinforcement was kept well under 6db). The transverse reinforcement in the boundary zones consisted of a set of 2-R6 stirrups provided at a centre-to-centre spacing of 55 mm (corresponding to s = 4.5db) to ensure that the selected s/db ratio followed a practical range. Specimens SWD-2 and SWD-3 had identical longitudinal and shear reinforcement layout as SWD-1 but featured different transverse reinforcement detailing in the boundary zones. Transverse reinforcement for specimen

2.2. Test setup and loading protocol Schematic layouts of the test setup, along with a specimen and positioning of the hydraulic actuators are shown in Fig. 3 and an image of the test setup used for carrying out the tests is shown in Fig. 4. All three tested walls were cast monolithically with a foundation block and a cap beam. The specimens were connected to the strong floor using fourteen high-strength threaded rods that passed through the ducts provided in the foundation block. To avoid lateral movement of the foundation during the test, shear keys were provided all around the foundation block. The test setup was designed to enable application of the complex loading pattern that bottom storey walls of multi-storey buildings are subjected to during a seismic excitation. Therefore, in addition to the axial load, bending moment arising from the upper 3

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2000 mm 627 mm

112

292

112

112

SWD-1

112

2000 mm

292

112

112

SWD-2 202

830 mm

112

112

112

112

112

SWD-3

Reinforcement layout

Typical cross-section of the tested RC specimens Fig. 2. Cross-sectional details of the tested RC walls.

potentiometers were provided on the wall surface to measure the axial deformation of the walls. These potentiometers were provided on both faces of the wall (along the height and length) to measure the local flexural and shear deformations. Fig. 6 shows the instrumentation provided on the wall faces (east and west) to measure the vertical deformation of the specimens. In addition to this, draw-wire potentiometers were also provided to measure the elongation and out-of-plane deformation of the wall. The axial load was applied before applying the displacement history, beginning with a positive loading (i.e. the wall pushed in the north direction).

stories was also applied (Fig. 5). The specimens were tested under a constant axial compression with the axial load ratio fixed at 5.5% of the axial capacity. Lateral displacements were applied at the top of the wall through a horizontal actuator (connected to the cap beam using a stiff steel loading beam), whereas the combination of axial load and bending moment resulting from upper stories was applied using two vertical actuators (as shown in Figs. 3 and 4). The walls were tested under inplane quasi-static reversed cyclic loading applied at the top of the specimen (2000 mm from base of the wall) with gradually increasing drift cycles repeated three times per drift level [11]. The storey level restraint in the out-of-plane direction was provided by restricting the movement of the cap beam using the two out-of-plane actuators as shown in Figs. 3 and 4. To avoid arching of RC walls due to in-plane loading and consequent movement of the wall in the out-of-plane direction, small displacements were also applied simultaneously in the out-of-plane direction. Fig. 5 shows the idealised loading pattern and the applied displacement history in both in-plane and out-of-plane directions. In the loading history, positive and negative displacements correspond to the wall being pushed in north and south directions, respectively. To capture the global and local behaviour of the tested specimens, extensive instrumentation was provided on all specimens. To avoid any potential imperfection that would be induced by mounting instrumentation on the longitudinal bars, only linear

3. Hysteresis behaviour and failure modes The hysteretic response of the tested specimens along with the key milestones are shown in Fig. 7. Fig. 7d shows the comparison of loaddisplacement envelopes of the three tested wall specimens. The drifts corresponding to the key milestones observed during the tests are summarised in Table 4. Failure drift for the tested wall specimens was defined when the applied shear force dropped by 15% of the maximum shear achieved during the test. All the tested specimens exhibited flexure-dominated response, with development of flexure-shear cracks distributed along the entire wall height and predominant cracks concentrated in the bottom half. Fig. 8 shows the crack pattern distributed

Table 1 Summary of the tested RC wall specimens. Specimen

SWD-1 SWD-2 SWD-3

Length (Lw), mm

2000 2000 2000

Thickness (t), mm

150 150 150

Shear span ratio

3 3 3

Concrete strength (fc′), MPa

35.94 37.71 41.31

Axial load ratio, N/(Agfc′)

0.055 0.055 0.055

4

Longitudinal reinforcement ratio, ρ = As/Ac Boundary zone (ρb)

Web (ρw)

0.0228 0.0228 0.0228

0.0055 0.0055 0.0055

Volumetric transverse reinforcement ratio (ρv)

0.0102 0.0077 0.0110

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Table 2 Summary of the anti-buckling requirements in NZS3101:2006 and ACI318-14 for ductile walls. Provision

NZS3101:2006

Spacing of anti-buckling reinforcement Area of anti-buckling reinforcement

Spacing(s) ≤ 6db

Ate =

∑ Abf y s 96f yt db

ACI318-14

Spacing(s) ≤ 6db No specific requirement

D12

D10

R6

fy (MPa) fu (MPa) E (MPa) εy εsh εu

307.5 422.15 212,170 0.0015 0.025 0.227

258.2 425.34 204,710 0.0015 N/A 0.224

376.6 481.53 209,232 0.0018 0.0167 0.167

Provided/Required (ACI318-14)

SWD-1

SWD-2

SWD-3

SWD-1

SWD-2

SWD-3

0.76 5.23

1 4.0

0.76 5.23

0.76 N/A

1 N/A

0.76 N/A

and 3 in the south boundary zone (Fig. 9b). Buckling of the longitudinal reinforcing bars continued during the subsequent drift cycles and resulted in the fracture of some bars. Fracture of buckled reinforcing bars, which occurred due to the accumulation of low-cycle fatigue damage in reinforcing bars (Fig. 9c), led to a noticeable drop in the lateral loadcarrying capacity of the wall (Fig. 7a). Specimen SWD-1 experienced a 15% drop in its lateral load-carrying capacity during the first 2.5% drift cycle. At this stage, a considerable shift was observed in the neutral axis position, resulting in buckling of unrestrained web reinforcing bars. This buckling of web reinforcing bars forced the horizontal shear reinforcement to bend, thereby further compromising the global response of the specimen (Fig. 9d). The final failure of specimen SWD-1 (marked with a significant drop in lateral load-carrying capacity) was due to the development of localised out-of-plane instability in the end regions (i.e. boundary zones) at the base of the wall due to a significant loss in the compression capacity of the wall because of reinforcement buckling, fracture and concrete crushing. SWD-2: The boundary zone ties were spaced 72 mm apart in Specimen SWD-2, which is different from the transverse reinforcement spacing of 55 mm in specimens SWD-1 and SWD-3. This is the maximum spacing for confinement and anti-buckling reinforcement allowed by the seismic design codes (New Zealand and American concrete standards) for ductile RC structures. In the initial stages, the behaviour of SWD-2 was similar to SWD-1, with the development of flexural cracks along the wall height at 0.15% drift followed by development of flexure-shear cracks during subsequent cycles. Tension and compression yielding of the longitudinal reinforcing bars occurred at 0.375% drift. Vertical cracks developed in the compression toes at 1.0% drift (indicating the initiation of bar buckling inside) and the buckled reinforcing bars were exposed during the third cycle of 1.0% drift. At this stage, buckling of reinforcing bars was restricted within single tie spacing in the south boundary zone (Fig. 10a), whereas no physical buckling was observed in the north boundary due to the presence of cover concrete. However, even though cover concrete had not fallen off, it could be inferred from the size of vertical cracks that buckling had been initiated within. The first sign of physical buckling in the north

Table 3 Mechanical properties of reinforcing bars. Reinforcement

Provided/Required (NZS3101:2006)

in the bottom half of the tested specimens at failure. Reinforcement buckling was the primary mode of failure in all three specimens, though the buckling mode varied between the different specimens. As mentioned previously, the RC wall specimens were scrupulously designed to avoid out-of-plane deformations; however, minor localised out-of-plane displacement accompanied reinforcement buckling at the base of the wall. The ultimate failure of all specimens was due to the development of localised out-of-plane instability in the end regions of walls, mainly attributed to loss of compressive stress capacity of the walls due to bar buckling and concrete crushing in the plastic hinge regions [11,50]. SWD-1: Specimen SWD-1 was the benchmark specimen with transverse reinforcement satisfying the confinement and anti-buckling provisions of NZS3101:2006 [4]. SWD-1 responded predominately in flexural mode, with initiation of flexural cracks along the wall height during the 0.15% drift cycle followed by tension and compression yielding of reinforcing bars at 0.375% drift. After yielding of the edge reinforcing bars at 0.375% drift, flexural cracks extended diagonally to develop flexure-shear cracks distributed over the entire height of the specimen, with the predominant cracks starting to concentrate in the bottom half of the specimen. Signs of buckling initiation in the form of vertical cracks in the compression boundary zones were observed during the first 1.5% drift cycle and physical buckling of reinforcing bars was observed during the second cycle of 1.5% drift. At this stage, buckling of reinforcing bars spanned multiple tie spacing with the buckling mode ranging between 2 and 4 in the north boundary zone (Fig. 9a) followed by reinforcement buckling with buckling modes of 2 Loading beam

Horizontal actuator

2700

Strong wall

Strong wall

Vertical actuator

2000

2000

500

150

700 830

Vertical actuator

627

Out-of-plane actuator

Strong floor

Strong floor

In-plane test setup

Out-of-plane restraint

Fig. 3. Schematic layout of the test setup in in-plane and out-of-plane directions. 5

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(a) Test setup in in-plane direction

(b) Out-of-plane restraint

Fig. 4. Test-setup: In-plane and out-of-plane directions.

F4

P4

P

V

F2

P2

F1

P1

M

4 3 2 1 0 -1 -2 -3 -4

V P

ǻV1

ǻV2

P/2

P/2

V P

M

0.06

North

0.05

Drift (%)

P3

Drift (%)

F3

V

M*

0.04 0.03 0.02 0.01

South

0.00

In-plane loading history

Out-of-plane loading history

Fig. 5. Idealised loading pattern and loading protocol in in-plane and out-of-plane directions.

south boundary buckled with buckling mode of 1 during the first cycle of −2.0% drift (Fig. 11b). As the loading progressed, buckling of these reinforcing bars was restricted to within a single tie spacing until one of the buckled reinforcing bars in the north boundary zone fractured at −1.6% during the second cycle of −2.0% drift. When the load was reversed, the fractured bar in the north boundary zone deteriorated the buckling performance of adjacent longitudinal reinforcing bars (due to redistributed compressive stresses in the north boundary zone), resulting in an increment in the buckling mode of the adjacent bars from 1 to 2 (Fig. 11c). At 2.5% drift, all the three extreme bars in the south boundary underwent buckling with buckling mode 1, out of which one bar underwent double bending (but still restricted the buckling mode of each bend to 1), as shown in Fig. 11e. During further loading cycles, reinforcing bars fractured in the north boundary at −1.65% and −2.2% drift levels. In addition to buckling of boundary zone reinforcing bars, buckling of web reinforcing bars was observed during the last cycle of +2.5% drift. Significant loss in load-carrying capacity was observed during the third cycle of ± 2.5% due to development of localised out-of-plane instability, mainly attributed to the loss in compression capacity of the wall. Overall, all the tested specimens with different transverse reinforcement detailing achieved similar lateral load carrying capacity, but had different deformation capacities. The comparison of load-displacement envelopes shows that the global response of the tested

boundary was observed during the second cycle of 1.5% drift, with buckling modes of 1 and 2 (Fig. 10b). During subsequent loading cycles, the buckling mode of the buckled reinforcing bars increased from 1 to 3 in both boundary zones (Figs. 10c and d). Fracture of a reinforcing bar (which had buckled in the previous cycles) was observed at 1.9% drift during the first 2.0% drift cycle and resulted in a sudden drop in the load-carrying capacity (marked by a kink in the hysteresis loop). Specimen SWD-2 exhibited a drop in load-carrying capacity by 15% during the first cycle of 2.0% drift and exhibited failure due to the development of localised out-of-plane instability in both north and south boundary zones. SWD-3: Out of all the tested wall specimens, specimen SWD-3 was the only specimen that featured an improved transverse reinforcement detailing to restrain buckling of longitudinal bars to within a single tie spacing (i.e. buckling mode 1). Note that this specimen differed with the base specimen (i.e. SWD-1) only in terms of arrangement of the stirrups/ties, while the diameter and spacing remained similar to SWD1. Similar to the other two specimens, in this specimen too flexural cracks were first observed at 0.15% drift, followed by tension-compression yielding of reinforcing bars at 0.375% drift. At subsequent drift cycles, the flexural cracks developed in previous cycles widened and extended to form flexure-shear cracks. One of the corner reinforcing bars underwent buckling during the third cycle of +1.5% drift, with the buckling mode constrained to 1 (Fig. 11a). Another corner rebar in the 6

g3

a2

a7

g7

g2

210

o4

c3

c8

o8

o3

c2

c7

o7

o2

c1

c6

o6

o1

g15 a6

a10 365

240

a14 250

g11

g10

240

g6 365

g1 210

210

(a) West face

250

a1

o9

250

300

a15

700

g8

c9

300

a8

c4

330

300

a3

700

g4

330

g9

300

a9

o5

c5

330

700 330

a4

330

g5

a5

330

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210

(b) East face

Fig. 6. Instrumentation for measuring the flexural deformation of the wall specimens.

specimens was similar until initiation of individual failure modes. Change in the boundary zone transverse reinforcement detailing resulted in alteration of the local response of RC walls, causing acceleration or delay of different compression failure modes. Out of all three tested wall specimens, specimen SWD-3 showed promising performance both in terms of local response (restraining buckling of reinforcing bars to single tie spacing) and global behaviour compared to specimens SWD-1 and SWD-2; specimen SWD-2 showed the worst seismic performance. Buckling of reinforcing bars was observed in all the tested specimens, but the extent of buckling (in terms of buckling mode) depended on the transverse reinforcement detailing of the specimen. Even though specimen SWD-3 had the same size and spacing of transverse reinforcement as SWD-1, it showed better performance by restraining buckling to within single tie spacing.

Additionally, these failure modes combined with the presence of wide cracks and strain gradient across the wall thickness during inelastic cyclic loading make the walls vulnerable to the development of localised out-of-plane instability [50]. On the contrary, in the walls in which bar buckling was restricted to single tie spacing, the loss of concrete confinement and damage to reinforcing bars due to fatigue was limited, and therefore any fracture of reinforcing bars and development of out-of-plane deformations were delayed; thereby resulting in better deformation capacity. Further details on the effect of transverse reinforcement detailing on the development of bar buckling, strain distribution and the hysteretic response of the tested wall specimens are presented in the subsequent sections.

4. Analysis and discussion of the test results

As discussed earlier, buckling of longitudinal reinforcing bars was the primary mode of failure for all three tested specimens. Even though reinforcement buckling did not influence the lateral load-carrying capacity of the tested wall specimens until failure (i.e. buckling did not result in an immediate drop of lateral load-carrying capacity), it did alter their deformation capacity/ductility due to the change in local compression response of the wall associated with the modified transverse reinforcement detailing. Therefore, in this section, the different mechanisms of reinforcement buckling observed during the tests are discussed in detail. The compression behaviour of an RC member (wall and columns) is a complex phenomenon that primarily depends on two interdependent compression failure modes (reinforcement buckling and concrete crushing) both of which depend on the efficacy of the transverse reinforcement provided in the member. The interdependence of these two compression modes of failure on the performance of transverse reinforcement results in an alteration of one failure mode due to modification in the performance of the other. For instance, increasing the spacing of transverse reinforcement results in reduction of bucklinginduced inelastic strain demand on transverse reinforcement but results in higher inelastic axial strain demands on transverse reinforcement due to the core expansion (as the core concrete has to undergo large

4.1. Reinforcement buckling in RC structural walls

As stated in the earlier sections, loss of lateral-load carrying capacity of all three specimens was caused due to the combined effect of bar buckling, concrete crushing, bar fracture (due to low cycle fatigue) and localised out-of-plane instability. However, the drift capacity of the tested wall specimens was significantly influenced by the boundary zone transverse reinforcement detailing. Different boundary zone detailing resulted in different buckling behaviour of longitudinal reinforcing bars, which affected the development of secondary failure modes (i.e. concrete crushing, bar fracture and out-of-plane instability) and consequently influenced the lateral drift-capacity of the tested wall specimens. The initiation of bar buckling spanning multiple tie spacings accelerated the reduction of the bar’s compressive stress capacity, and deteriorated the effective confinement of concrete. Bar buckling with higher buckling modes extends the tie legs beyond elastic limit; thereby making them ineffective to confine the concrete core, which causes premature crushing of the core concrete resulting in a rapid loss of lateral load-carrying capacity. In addition to this, bar buckling accelerates the accumulation of fatigue damage in reinforcing bars [51], causing the reinforcing bars to prematurely fracture in cyclic loading, and gradually lose the lateral load-carrying capacity of the walls. 7

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Drift (%) -1

0

Drift (%) 1

2

3

Bar buckling Bar fracture Instability

0

0

-20

0

20

40

-2

-200

-300

-300

-300 -60

-40

-20

0

20

Top displacement (mm)

(b) SWD-2

0

2

-3

3

0

200

200

100

100

0

40

0

1

2

3 300

SWD-1 SWD-2 SWD-3

200

100

0

0

-200

-200

-200

-300

-300

-200

20

-1

-100

-100

-300

-2

-100

-100

0

60

300

Lateral load (kN)

100

-20

40

Drift (%) 1

Lateral load (kN)

Lateral load (kN)

0

(a) SWD-1

Bar buckling Bar fracture Instability

-40

100

-200

300

-60

200

0

60

300

200

300

Top displacement (mm)

-1

3

100

Drift (%) -3

2

-200

-200

-40

1

-100

-100

-60

0

-100

-100

-300

Lateral load (kN)

100

100

-1

Bar buckling Bar fracture Instability

200

200

Lateral load (kN)

200

-2

300

300

300

Lateral load (kN)

-3

Lateral load (kN)

-2

-300 -60

60

Lateral load (kN)

-3

-40

-20

0

20

40

Top displacment (mm)

Top displacement (mm)

(c) SWD-3

(d) Load-displacement envelope

60

Fig. 7. Hysteresis response of the tested RC wall specimens.

SWD-2 resulted in a reduction of inelastic strain demands on transverse reinforcement associated with buckling; however, it also increased the strain demands on the stirrups due to core expansion. This increase in inelastic strain demands on transverse reinforcement due to core expansion deteriorated the effectiveness of transverse reinforcement to restrain buckling, thereby worsening the buckling performance of the longitudinal reinforcing bars (buckling mode changed from 1 to 3 in subsequent loading due to loss in axial stiffness of ties). This correlation

axial compressive strains to balance the same amount of tensile force), thereby degrading the effectiveness of the ties to resist buckling of longitudinal reinforcing bars. This trade-off between reinforcement buckling and concrete crushing was observed during these tests, where improved buckling performance (i.e. change in the buckling mode of reinforcing bars) was observed during the initial stages in specimen SWD-2 compared to SWD-1. The increase of transverse reinforcement spacing in specimen

Table 4 Key milestones observed during the tests. Specimen

Direction

Cracking (%)*

Yielding (%)

Reinforcement buckling (%)

Reinforcement fracture (%)

Failure (%)

SWD-1

+ – + – + –

+0.151 −0.151 +0.151 −0.151 +0.151 −0.151

+0.3751 −0.3751 +0.3751 −0.3751 +0.3751 −0.3751

+1.53 −1.52 +1.52 −1.03 +1.52 −2.01

+2.03 −2.03 +2.01 N/A N/A −2.02

+2.51

SWD-2 SWD-3

* Superscript denotes the cycle number. 8

+2.01 −2.52

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(a) SWD-1

(b) SWD-2

(c) SWD-3

Fig. 8. Crack distribution in the bottom half of the tested wall specimens at failure.

times the yield strain of reinforcing bars in specimens SWD-1, SWD-2 and SWD-3, respectively, whereas the residual strain at zero displacement was always in excess of the yield strain. This accumulation of residual tensile strain in reinforcing bars (i.e. residual crack width in concrete) in the base of the wall forced their compression yielding, thereby initiating premature buckling of reinforcing bars prior to the development of compressive strains in the bars. The point of initiation of buckling depended on the maximum tensile strain experienced by the reinforcement at reversals, whereas the strain corresponding to initiation of compressive stress degradation due to buckling depended on the buckling length of the reinforcing bar, which is a function of the transverse reinforcement detailing. In addition to buckling, the fracture of buckled rebars was also observed in all the tested specimens. According to AS/NZS4671-2001 [53], the structures designed to resist seismic forces are required to have either Grade 300E or Grade 500E reinforcing bars with minimum uniform elongation capacities of 15% and 10%, respectively. This means that the reinforcing bars can sustain large tensile strains (with an ultimate strain being at least 3.5 times the maximum average tensile strain measured during the tests) before undergoing fracture. Also, the tests on reinforcing bars reaffirm that New Zealand reinforcing bars can sustain large uniform elongation before undergoing fracture (Table 3). This clearly implies that the fracture of reinforcing bars inside the wall specimens was a result of the accumulation of low-cycle fatigue damage in reinforcing bars that was accelerated due to the presence of inelastic buckling [51,54–56]. The authors [51,55,56] conducted low-cycle fatigue tests on a series of Grade 300E and 500E bars and confirmed that buckling has detrimental effects on low-cycle fatigue life of reinforcing bars. Overall, reinforcement buckling in RC walls subjected to cyclic lateral loading is imminent and the drift corresponding to the initiation of buckling depends on the maximum tensile and compressive strains

between compression failure modes has also been observed in RC circular bridge piers [17]. In addition to this, premature buckling of the longitudinal reinforcing bars in RC members results in permanent deformation of stirrups/ties, thereby further deteriorating their effectiveness in restraining buckling and confining the core concrete. During the tests on specimens SWD-1 and SWD-2, buckling of the unrestrained middle bars at the two edges resulted in permanent deformation of the stirrups. Based on interpretation of the progression of damage in the tested wall specimens and the literature review, it is clear that buckling of reinforcing bars in RC structural members is a continuous and recursive phenomenon that initiates when the compressive stresses in reinforcing bars exceed their compressive yield stress capacity while unloading from large tensile strains. This phenomenon of reinforcement buckling during the reversal from large tensile strain has also been reported in the literature [52]. At reversals from inelastic drift cycles, the presence of residual cracks concentrated at the base of the wall results in premature compressive yielding of reinforcing bars prior to crack closure, thereby making them susceptible to buckling. At this stage, depending on the effectiveness of transverse reinforcement detailing, buckling may initiate with or without a loss in compression capacity of the bars. To investigate the strain state in reinforcing bars, the average axial strains measured at the base of the boundary zones of the tested walls are calculated using the measurement of linear potentiometers, as shown in Fig. 6. Table 5 summarises the maximum tensile strain and residual strain the reinforcing bars were subjected to before undergoing buckling. The table also presents the buckling mode and the corresponding maximum compressive strain experienced by the reinforcing bars at peak displacement. Herein, it should be noted that buckling initiation and the corresponding buckling mode were identified based on visual observation. The average maximum tensile strains attained in reinforcing bars prior to buckling were approximately 24, 14 and 22

Fig. 9. Reinforcement buckling and fracture observed in wall SWD-1. 9

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Fig. 10. Reinforcement buckling and fracture observed in wall SWD-2.

300 mm of the tested wall specimens are evaluated and compared. Herein, the average axial strain at the wall base was obtained through the potentiometers attached to the wall surface (Fig. 6a). Fig. 12 shows the distribution of the strains along the wall length observed during the three tests. As can be observed in Fig. 12, the strain profile along the wall length (i.e. strain gradient) is linear until the maximum tensile strain reaches the yield strain capacity of the reinforcing bars. After yielding of reinforcing bars the strain gradient became non-linear with a steep increase in tensile strain demands on boundary zone reinforcing bars. This implies that the assumption of plane section remains plane does not hold well in the post-yielding range [57]. However, it should be noted that even after yielding of reinforcing bars (in tension and compression), the strain gradient in compression was linear until the compression limit state due to bar buckling and crushing was reached, after which the strain gradient in compression became nonlinear (Fig. 12). Furthermore, after the yielding of reinforcing bars the depth of the compression region (i.e. neutral axis depth) became almost constant; there were slight variations as the loading progressed, but no considerable shift of neutral axis occurred. However, neutral axis position shifted once bar bucking influenced the local deformation of the wall specimen and resulted in redistribution of strains along the wall length. This redistribution of strains along the length of the wall is mainly attributed to the loss in compression capacity of the buckled reinforcing bars forcing the neutral axis to shift as more concrete needs to be engaged in compression to balance the corresponding tensile force. This resulted in increased curvature demands on the wall crosssection, thereby further increasing the tensile and compressive strain demands on the wall boundary elements. This increase in tensile strain demands, along with the detrimental effect of buckling, accelerated the accumulation of fatigue damage in reinforcing bars, which ultimately resulted in fracture of edge-reinforcing bars within a few cycles after the first visible bar buckling. Further progression of bar buckling and bar fracture in the boundary regions resulted in development of larger compressive strains and dramatic shift in neutral axis depth (Fig. 12).

attained in reinforcing bars at load reversals. The maximum tensile and compressive strain attained by reinforcing bars during loading depends on the characteristics of the wall (dimensions and reinforcement ratio) in addition to the loading history. Although buckling of reinforcing bars depends on the tensile strain at reversal, the stress degradation associated with buckling can be avoided until the design drift demand is reached by providing transverse reinforcement with sufficient axial stiffness to restrain bar buckling to within a single tie spacing (provided that the ratio of the transverse reinforcement spacing to diameter of longitudinal reinforcing bar is less than 6). This objective (i.e. restricting the reinforcement buckling to single tie spacing) was achieved in specimen SWD-3 by restraining all three extreme longitudinal bars against buckling, with transverse reinforcement arranged optimally to provide the required anti-buckling resistance. During subsequent loading, the efficacy of the transverse reinforcement arrangement was proved by its capability to restrain the buckling within a single tie spacing until one of the boundary zone reinforcing bars fractured. The bar fracture resulted in redistribution of stresses in the compression boundary and deteriorated the buckling performance of adjacent reinforcing bars thereafter. However, the bar buckling was restricted to single tie spacing in the other boundary zone until the failure drift was reached. Note that even though specimen SWD-3 had slightly improved confinement (the volumetric transverse reinforcement ratio in wall SWD-3 was increased by 8% compared to SWD-1) due to additional transverse reinforcement, the amount of transverse reinforcement (in terms of the area of each tie leg) was identical in all three tested specimens. 4.2. Strain gradient along the wall length The inelastic buckling of reinforcing bars is known to affect their compressive stress capacity resulting in redistribution of strain demands in wall boundaries. Therefore, in this section the increase in inelastic strain demands (tension and compression) due to buckling of boundary zone reinforcing bars is investigated and discussed. The average axial strains distributed along the wall length in the bottom

Fig. 11. Reinforcement buckling and fracture observed in wall SWD-3. 10

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Table 5 Average strains and the buckling mode of reinforcing bars.

North South North South North South

SWD-3

0.15% 0.38% 0.50% 0.75% 1.00% 1.50% 2.00% 2.50%

50 40 30 20 10

Residual strain at zero displacement

Maximum compressive strain

3 3 2 1 1 1

0.03683 0.03490 0.02408 0.01807 0.02774 0.03723

0.00402 0.00870 0.00021 0.00317 0.00218 0.00361

−0.00766 −0.00741 −0.01209 −0.00652 −0.00875 −0.00915

60

SWD-1

0 -10

Drift

-20 -30

60

0.15% 0.38% 0.50% 0.75% 1.00% 1.50% 2.00%

50 40 30 20

SWD-2

10 0 -10 -20 -30

0

400

800

1200

1600

2000

400

Length of the wall (mm)

800

1600

30 20 10 0 Drift

-30 400

800

1200

1600

Length of the wall (mm)

2000

SWD-3

10 0 -10 -20 0

400

40 30 20

0.15% 0.38% 0.50% 0.75% 1.00% 1.50% 2.00%

10 0 -10 -20

1200

1600

2000

(c)

SWD-2

50

800

Length of the wall (mm)

-30 0

20

2000

Drift

40

Normalised average strain

Normalised average strain

1200

60

0.15% 0.38% 0.50% 0.75% 1.00% 1.50% 2.00% 2.50%

SWD-1

-20

30

(b)

60

-10

40

Length of the wall (mm)

(a)

50

0.15% 0.38% 0.50% 0.75% 1.00% 1.50% 2.00% 2.50%

50

-30 0

60

Normalised average strain

Normalised average strain

60

Maximum tensile strain

0.15% 0.38% 0.50% 0.75% 1.00% 1.50% 2.00% 2.50%

SWD-3

50 40 30 20 10 0 -10

Drift

SWD-2

+1.5 −1.52 +1.52 −1.03 +1.52 −2.01

Buckling mode

Drift

3

Drift

SWD-1

Drift

Normalised average strain

Boundary zone

Normalised average strain

Specimen

-20 -30

0

400

800

1200

1600

2000

Length of the wall (mm)

(d)

(e)

0

400

800

1200

1600

2000

Length of the wall (mm)

(f)

Fig. 12. Inelastic strain gradient in the tested wall specimens.

strains were concentrated and localised in the bottom 300 mm of all three tested wall specimens. The differences in distribution of plasticity in the tested specimens could also be observed visually by comparing the crack distribution along the wall height. Wall specimens SWD-1 and SWD-2 exhibited flexure-shear cracks distributed along the wall height, with predominant cracks (cracks with larger width) concentrated within the bottom 600 mm of the specimens (Figs. 13a and b). On the other hand, wide cracks in specimen SWD-3 extended further up to a height of 1200 mm from the base, clearly indicating a wider distribution of plasticity (Fig. 13c). As tensile and compressive strains were localised at the base of the wall, buckling and fracture of reinforcing bars also occurred within the bottom 300 mm of the wall. Buckling of reinforcing bars reduced their compressive stress capacity, thereby increasing the compressive strain demands at the base (as observed for specimen SWD-1, Fig. 13a). Thereafter, fracture of buckled reinforcing bars altered the strain profile along the wall length, resulting in an increased localisation of tensile strain at the base of specimens SWD-1 and SWD-3 (Figs. 13a and c).

4.3. Strain distribution along the wall height As outlined before, all the tested wall specimens responded flexurally, with flexure-shear cracks distributed along the wall height. In this section, average strains distributed along the wall height in different specimens are compared. Average strains at the wall boundaries were evaluated using the measurement of potentiometers located at the extreme ends of the two boundaries, i.e. close to the edge reinforcing bars (Fig. 6). Fig. 13 shows the distribution of normalised average vertical strains obtained by dividing the measured axial strain by the yield strain of reinforcing bars (0.0015) along the wall height. The average strain distribution along the wall height was similar for all three tested specimens, with tensile strains mostly distributed along the wall height. Large tensile strains were concentrated in the bottom 600 mm for specimens SWD-1 and SWD-2 (Figs. 13a and b), whereas for specimen SWD-3 the distribution of tensile strains extended further up to a height of 1200 mm, implying that plasticity was much better distributed in SWD-3 compared to the remaining two specimens. Contrary to the distribution of tensile strain along the wall height, compressive 11

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2000

0.75%

0.75%

1800

1.00%

1800

1.00%

1600

1.50%

1600

1.50%

Height of the wall (mm)

South boundary

Height of the wall (mm)

2000

2.00%

1400

Yield

1200 1000 800 600 400 200

2.00%

1400

North boundary

Yield

1200 1000 800 600 400 200

0

0 -30 -15

0

15

30

45

60

-30 -15

Normalised average strain

0

15

30

45

60

Normalised average strain

(a) SWD-1 2000

0.75%

1.00%

1800

1.00%

1600

1.50%

1600

1.50%

2.00%

1400

Yield

1200

Height of the wall (mm)

1800

Height of the wall (mm)

South boundary

2000

0.75%

2.00%

1400

Yield

North boundary

1200

1000

1000

800 600

800 600

400

400

200

200

0

0 -30 -15

0

15

30

45

60

-30 -15

Normalised average strain

0

15

30

45

60

Normalised average strain

(b) SWD-2 2000

0.75%

0.75%

1800

1.00%

1800

1.00%

1600

1.50%

1600

1.50%

1400

Yield

2.00%

1400

Yield

1200 1000 800 600

Height of the wall (mm)

South boundary

Height of the wall (mm)

2000

North boundary

1200 1000 800 600

400

400

200

200

0

2.00%

0 -30 -15

0

15

30

45

60

-30 -15

Normalised average strain

0

15

30

45

60

Normalised average strain

(c) SWD-3 Fig. 13. Normalised average vertical strain distribution along the wall height.

measure the vertical movement of the capping beam relative to the wall foundation. Fig. 14 shows the elongation plots for the tested specimens and Fig. 15a compares the permanent elongation measured during the tests. Here, permanent elongation is the residual vertical deformation of the wall measured after each loading cycle. The maximum permanent elongation for specimens SWD-1, SWD-2 and SWD-3 were 3.86 mm, 2.41 mm and 3.04 mm, respectively. Fig. 15a shows that a considerable reduction in residual elongation was observed at failure drift due to the loss in compression capacity of the walls. Here, the loss in compression capacity of the walls is inferred from their hysteretic response and is defined as the point at which a significant drop in lateral load-carrying

4.4. Wall elongation and hysteretic energy dissipation In this section, the wall elongation and hysteresis parameters (i.e. cumulative energy dissipation and secant stiffness) are evaluated for the tested walls and compared. Elongation in RC members has been observed during tests on RC beams and walls as a result of residual cracks in the plastic hinge region [58]. Elongation induces increased axial compressive demands on walls due to the restraint against vertical movement, which is generally imposed by other structural components, thereby altering their local and global response. Therefore, a draw-wire potentiometer was provided at the mid-length of the specimens to 12

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25

25

25

SWD-1

10

20

Elongation (mm)

Elongation (mm)

Elongation (mm)

15

SWD-3

SWD-2

20

20

15

10

5

5

-3

-2

-1

0

1

2

0 -3

3

10

5

0

0

15

Drift (%)

-2

-1

0

1

2

-3

3

-2

-1

Drift (%)

(b) SWD-2

(a) SWD-1

0

1

2

3

Drift (%)

(c) SWD-3

Fig. 14. Elongation of RC wall specimens measured during the tests.

200

Permanent elongation (mm)

SWD-1 SWD-2

4

SWD-3 3

2

1

120 SWD-1 SWD-2 SWD-3

180 160

SWD-1 100

Secant stiffness (kN/mm)

Cumulative dissipated energy (kN-m)

5

140 120 100 80 60 40

0

1

2

3

60 40 20

0

1

2

Drift (%)

Drift (%)

(a) Permanent elongation

SWD-3

80

20 0

0

SWD-2

(b) Cumulative energy dissipation

3

0 0

1

2

3

Drift (%)

(c) Secant stiffness

Fig. 15. Permanent elongation, cumulative energy dissipation and secant stiffness of the tested specimens.

initiated in the boundary regions. After the buckling of boundary zone reinforcing bars in compression, the secant stiffness of the walls reduced; however, the reduction in secant stiffness at this stage was minimal. However, at large drift levels significant buckling of longitudinal reinforcing bars in the boundary regions resulted in the development of secondary modes of failure, such as concrete crushing, bar fracture and development of local instability, thereby causing the wall to significantly lose its load-carrying capacity and a reduction of the wall’s secant stiffness.

capacity was observed. The cumulative energy dissipation and secant stiffness of the tested specimens are compared in Figs. 15b and c. The cumulative energy dissipation is calculated by integrating the area under the hysteresis curves at each loading cycle, whereas the secant stiffness is calculated as the ratio of the difference between the peak forces to the difference between the corresponding peak displacements. At smaller drifts, the cumulative energy dissipated by all three tested specimens was similar, but deviations in the energy dissipation patterns was observed at larger drifts due to the differences between their local responses. The cumulative energy dissipated by specimen SWD-3 was 24% and 77% higher than that of specimens SWD-1 and SWD-2, respectively, whereas the energy dissipation capacity of SWD-1 was 42% greater than that of SWD-2. This difference in energy dissipation capacity of the specimens is due to different transverse reinforcement detailing that altered the local and global response of the tested walls. Of all the tested specimens, specimen SWD-3 dissipated the most energy due to controlled buckling of reinforcing bars that resulted in an improved deformation capacity of the wall and consequently an increased energy dissipation capacity. On the other hand, it is evident that the secant stiffness of the tested specimens was mostly similar until reaching the failure drift. The similarity in secant stiffness of the tested specimens is associated with the fact that all three tested specimens had similar hysteretic response (due to identical dimension and detailing) until bar buckling was

5. Conclusions In this paper, the results of an experimental program aimed at evaluating the influence of transverse reinforcement detailing on the progression of bar buckling and the subsequent failure in RC structural walls was presented. A total of three slender RC walls with identical dimensions (length, height and thickness), longitudinal and shear reinforcement detailing but different transverse reinforcement detailing were tested under quasi-static reversed cyclic loading. The test observations, along with the progression of damage, failure mode and hysteresis behaviour, were presented. The tested RC wall specimens responded flexurally, with bar buckling being the primary mode of failure for all the specimens. The overall response of the specimens was governed by yielding, buckling and fracture of reinforcing bars, 13

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concrete crushing and development of localised out-of-plane instability. Based on the comparison of experimental test results, it can be concluded that bar buckling is a critical and common failure mode that restricts the seismic performance of slender rectangular RC walls. All three tested specimens (designed according to New Zealand Standards) exhibited bar buckling as the primary failure mode, followed by the development of localised out-of-plane instability. Hence, it can be concluded that slender RC walls designed according to the current New Zealand Standard are susceptible to compression-controlled failure associated with bar buckling. The deformability or ductility of slender RC walls can be enhanced/ improved by altering their local compression response (i.e. confinement and anti-buckling transverse reinforcement detailing at wall boundaries). In addition to improving the wall’s deformation capacity, enhancement in energy dissipation capacity can also be achieved by this modification. Furthermore, this research shows that complete avoidance of bar buckling is difficult due to the limitations associated with spacing and diameter of the transverse reinforcement. However, by following a mechanics-based approach to design the anti-buckling reinforcement (as used in this study), the buckling of reinforcing bars inside RC structures can be restricted to single tie spacing, thereby minimising/avoiding the post-buckling compressive stress degradation. Additionally, increasing the spacing of transverse reinforcement along the longitudinal reinforcement can help restrict bar buckling to within single tie spacing, which would subsequently delay the buckling-induced strength degradation in bars and, consequently, the walls. Nevertheless, spacing stirrups further apart degrades the confinement behaviour of concrete and hence the overall performance of the wall. This clearly outlines that in addition to the design of confinement reinforcement using the strength-based approach (as used in the design codes), a mechanics-based approach (as used in this study) should be used for the design of anti-buckling reinforcement. It can also be concluded that the tension and compression response of reinforcing bars (which directly controls the performance of an RC wall) cannot be relied upon in the post-buckling phase. Bar buckling accelerates the accumulation of low-cycle fatigue damage in reinforcing bars and fracture of buckled reinforcing bars was witnessed within a few subsequent cycles after the first visible buckling. This further highlights the need to use a low-cycle fatigue model that incorporates the effect of inelastic buckling while numerically simulating the seismic performance of slender RC walls.

[5] ACI318-14. Building code requirements for structural concrete (ACI 318–14) and commentary (ACI 318R–14). Farmington Hills (MI): American Concrete Institute; 2014. p. 519. [6] Eurocode-8, Design of structures for earthquake resistance-part 1: general rules, seismic actions and rules for buildings; 2005. [7] Vallenas JM, Bertero VV, Popov EP. Hysteretic behavior of reinforced concrete structural walls. Berkeley: University of California; 1979. [8] Dazio A, Beyer K, Bachmann H. Quasi-static cyclic tests and plastic hinge analysis of RC structural walls. Eng Struct 2009;31(7):1556–71. [9] Birely AC. Seismic performance of slender reinforced concrete structural walls. Civil and Environmental Engineering, University of Washington; 2012. [10] Rosso A, Almeida JP, Beyer K. Stability of thin reinforced concrete walls under cyclic loads: state-of-the-art and new experimental findings. Bull Earthq Eng 2016;14(2):455–84. [11] Dashti F, Dhakal RP, Pampanin S. 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Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements The authors would like to acknowledge the financial support provided by the Ministry of Business, Innovation and Employment (MBIE) and the Quake Centre at the University of Canterbury for carrying out the research. The technical support provided by Russell McConchie and Alan Thirlwell in Structural Engineering Laboratory at the University of Canterbury is greatly appreciated. References [1] Wallace JW, Massone LM, Bonelli P, Dragovich J, Lagos R, Luders C, et al. Damage and implications for seismic design of RC structural wall buildings. Earthquake Spectra 2012;28:S281–99. [2] Sritharan S, Beyer K, Henry RS, Chai YH, Kowalsky M, Bull D. Understanding poor seismic performance of concrete walls and design implications. Earthquake Spectra 2014;30(1):307–34. [3] Elwood KJ. Performance of concrete buildings in the 22 February 2011 Christchurch earthquake and implications for Canadian codes. Can J Civ Eng 2013;40(3):759–76. [4] NZS3101:2006. Concrete Structures Standard- The design of concrete structures. Wellington: Standards New Zealand; 2008.

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