shear wall 4

Engineering Structures 100 (2015) 356–368

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Engineering Structures

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Strength and drift capacity of squat recycled concrete shear walls undercyclic loading

http://dx.doi.org/10.1016/j.engstruct.2015.06.0250141-0296/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +61 7 34704711; fax: +61 7 34704129.E-mail address: [email protected] (Y. Zhuge).

Youkai Peng a, Hui Wu a, Yan Zhuge b,⇑a Beijing Higher Institution Engineering Research Center of Civil Engineering Structure and Renewable Material, Beijing University of Civil Engineering and Architecture, Beijing100044, Chinab School of Civil Engineering and Surveying, University of Southern Queensland, Brisbane, Queensland, Australia

a r t i c l e i n f o

Article history:Received 28 February 2014Revised 12 June 2015Accepted 15 June 2015Available online 26 June 2015

Keywords:Shear wallSquat wallRecycled concreteCyclic loadingDrift capacityStrength

a b s t r a c t

In order to provide an improved understanding of the behavior of squat reinforced concrete shear wallsand promote the application of recycled concrete in structures, six rectangular squat recycled concretewall specimens were tested under in-plane cyclic loading. The specimens were designed based onChinese code for design of concrete structures GB 50010-2010, which specified minimum horizontaland vertical reinforcement ratios of 0.25% in web, and vertical reinforcement ratio of 1.0% in boundaryelement. The main parameters investigated are axial load level and the amount of vertical and horizontalweb reinforcement. This research presents the experimental results which include test observation, lat-eral load versus drift response, and measured strain distribution of vertical and horizontal reinforcement,measured strength and drift capacity of wall specimens. It was found that increasing of axial load levelresulted in a higher peak load but less ultimate drift capacity, and increasing of horizontal web reinforce-ment had small effect on peak load but could improve the drift capacity. In this study, a mixed flexure anddiagonal compression mechanism was proposed to reflect the lateral load resisting behavior of squatwalls. Particularly, a simplified analytical method was developed to predict the peak loads of squat wallsfailed in flexure or a mixed flexural–diagonal compression mode, which was proved to accurately predictthe peak loads of specimens.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Recycled concrete is prepared by partially replacing the naturalaggregate in mix proportion by recycled aggregate which is theproduct of construction and demolition concrete waste. It providesa sustainable way of both preserving natural aggregate and solvingthe pollution problem. At present in China, with the rapid develop-ment of construction industry, shortage of resources is becomingan urgent matter. At the same time, billion tons of constructionwaste is generated each year. The traditional disposal method oflandfill or dumping will have fatal impact on environment, recy-cling and reuse of the huge amount of the construction wastebecomes an inevitable choice and is attracting more research activ-ities in the area.

Studies on the structural performance of using recycled con-crete have been carried out in the past decade [1–4]. Letelieret al. [1] investigated the seismic behavior of recycled concrete

beam–column joints under cyclic loading. Xiao et al. investigatedthe seismic behavior of plane frame under cyclic loading and con-ducted a shaking table test of a 1/4-scale recycled concrete frame[2]. Their testing results indicated that it was feasible to use recy-cled concrete in reinforced concrete structures. More recently, theflexural behavior of reinforced concrete beams that use recycledconcrete aggregates were studied by Arezoumandi et al. [3]. Theyfound out that recycled concrete aggregates beams have compara-ble ultimate flexural strength and approximately 13% higherdeflection corresponding to the ultimate flexural strength of theconventional concrete. Although a large amount of experimentalresearch has been conducted, additional studies should be per-formed to further the knowledge and use of recycled concrete inreinforced concrete building structures, especially laboratory test-ing on large-scale recycled concrete specimens. Previous study [4]carried out by the authors on the seismic behavior of full-scalerecycled concrete columns indicated that recycled concrete speci-mens exhibited more brittle characteristic than normal concretespecimen. In order to meet the requirements of seismic design, itis suggested that the seismic behavior of recycled concrete mem-bers must be carefully studied.

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A A

B-B

1800

Lateral load

All dimensions are in mm

Boundary element

Dowel Reinforcement4D14

Web180

A-A

360 36010801800

B

B 500

400

1600

450

1800

250

Foundation beam (length 3500)

Top beam

2100300

Fig. 1. Details of specimens.

Y. Peng et al. / Engineering Structures 100 (2015) 356–368 357

Squat reinforced concrete shear walls with a height hw to lengthlw ratio of less than 2 are commonly used in low-rise buildingsbecause they show good performance in lateral load resistanceand drift control. Since the 1950s, many research projects havebeen carried out in order to understand the behavior of squat rein-forced concrete walls under monotonic or simulated earthquakeloading. Some of them are shown in Refs. [5–15]. When shear wallsare used in the lateral force resisting system, it is highly desirablethat they are designed to exhibit a ductile behavior which meanssupplying sufficient shear strength to favor a flexural yielding[7,8]. However, for a squat wall, the behavior is dominated by ashear response or mixed modes of flexure and shear. Although arelatively large number of wall tests are reported in the literature[7], there is a significant uncertainty to predict the squat wallbehavior. This is due to the following factors: wall specimens expe-rienced different failure modes (flexure, shear and sliding shear)and the interaction between each failure mode was not welldefined; different parameters (e.g., material strength, geometryof wall cross section, amount and distribution of reinforcement)were used which resulted in different formulas; and small-scalespecimens used may not reflect the real behavior of full-scalewalls. Consequently, the deign equations derived from the experi-mental data probably give least predictable behavior of squat walls[15].

Currently, there is still a lack of studies on the behavior oflarge-scale squat recycled concrete walls. In this study, sixlarge-scale rectangular squat recycled concrete wall specimenswith a height to length ratio of 0.89 were designed and testedunder quasi-static cyclic loading. This research aimed at providingan improved understanding of squat recycled concrete shear wallsand giving design suggestions. The principal research objectivesare: (1) the lateral load-transferring mechanism and failure modesof squat recycled concrete shear walls; (2) the peak load and itsprediction method; (3) drift capacity; (4) the effect of verticaland horizontal web reinforcement; and (5) the adequacy of currentdetailing requirements for design of recycled concrete walls.

2. Research significance

This study presents the experimental results of six large-scalesquat recycled concrete shear walls under cyclic loading. It canbe used as reference for engineering practice and development ofdesign guidelines. Especially, the proposed mixed flexure and diag-onal compression mechanism is quite suitable for explaining thelateral load resisting behavior of squat walls with boundary ele-ments, and the simple analytical method for predicting the peakloads will be useful for the rational design of squat walls.

3. Experimental program

3.1. Specimen design

Six rectangular squat wall specimens were designed based onChinese code for design of concrete structures GB 50010-2010

Table 1Parameters of specimens.

Specimen hw (mm) lw (mm) lc (mm) bw (mm) fcu (MPa)

RCSW-1 1600 1800 360 180 50.3RCSW-2 1600 1800 360 180 50.3RCSW-3 1600 1800 360 180 51.9RCSW-4 1600 1800 360 180 51.0RCSW-5 1600 1800 360 180 53.4RCSW-6 1600 1800 360 180 49.3

Note: fcu = average compressive strength of three 150 mm cubs; fc = average compressiveload; N/(Acfc) = axial load ratio; Ac = lwbw.

[16], as shown in Table 1. The main variables are axial load level,the amount of vertical and horizontal web reinforcement. Allspecimens have a length of 1800 mm and a height of 1600 mm(hw/lw = 0.89), and a thickness bw of 180 mm. The height from wallbase to the action point of lateral loading (H) is 1800 mm. Thelength of boundary element lc is 360 mm, which is two times thethickness or 20% of the overall length of wall specimen. The detailsof specimens are illustrated in Fig. 1.

The boundary element of all specimens was vertically rein-forced with six hot rolled ribbed bars D14 (diameter = 14 mm),constituting a longitudinal reinforcement ratio q of 1.4%; andtransversely reinforced with hot rolled plain bars D10 (diame-ter = 10 mm) hoops and ties spaced at 75 mm (D10@75). Thedetails in boundary element meet the requirements of Chinesecode. Hot rolled plain bars D8 (diameter = 8 mm) spaced at180 mm (D8@180) were used as the vertical web reinforcementof specimens RCSW-1 through RCSW-4, and hot rolled plain barsD10 spaced at 135 mm (D10@135) were used as the vertical webreinforcement of specimens RCSW-5 and RCSW-6, constitutingvertical web reinforcement ratios qv of 0.310% (minimum require-ment 0.25%) and 0.646%, respectively. The horizontal web rein-forcement ratio qh varies from 0.186% to 0.873%. SpecimensRCSW-1 through RCSW-6 were horizontally reinforced in webregion by D10@100, D10@150, D10@150, D10@300, D8@150 andD8@300, respectively. In order to prevent a premature slidingshear failure at wall base, four hot rolled ribbed bars D14 with alength of 700 mm were added as dowel reinforcement for all spec-imens. The length of the dowel bars extended into the foundationand into the wall section was 400 mm and 300 mm, respectively.The axial load ratio of specimens RCSW-1, RCSW-3 and RCSW-4

fc (MPa) ft (MPa) q (%) qv (%) qh (%) N (kN) N/(Acfc)

42.0 2.26 1.4 0.310 0.873 1792 0.1342.0 2.26 1.4 0.310 0.582 870 0.0643.2 2.16 1.4 0.310 0.582 1818 0.1342.5 2.16 1.4 0.310 0.291 1791 0.1344.0 2.16 1.4 0.646 0.372 – –46.7 2.16 1.4 0.646 0.186 – –

strength of three 150 mm � 300 mm prisms; ft = splitting tensile strength; N = axial

Fig. 2. Stress–strain curves of reinforcement.

358 Y. Peng et al. / Engineering Structures 100 (2015) 356–368

was 0.13 while that of specimen RCSW-2 was 0.064, and the axialload was not applied for specimens RCSW-5 and RCSW-6.

In ACI 318 code [17], if hw/lw dose not exceed 2.0, it is requiredthat the vertical web reinforcement ratio shall not be less than thehorizontal web reinforcement ratio. This is mainly based on theobservation that in long and low shear walls, the vertical web rein-forcement will be more effective in restraining the inclined cracks,especially for walls with hw/lw less than 0.5. In this study, speci-mens RCSW-4 through RCSW-6 satisfy the requirement. For spec-imens RCSW-1 through RCSW-3, the amount of horizontal webreinforcement is more than that of vertical web reinforcement.They were designed to investigate the beneficial effect of horizon-tal web reinforcement on drift capacity. To attain nearly the sameflexural strength of specimens with similar axial load, the amountof vertical web reinforcement was kept constant for RCSW-1,RCSW-3 and RCSW-4 (0.310%), and for RCSW-5 and RCSW-6(0.646%), respectively.

3.2. Materials

The mix proportions per m3 of recycled concrete were 170 kgwater, 290 kg cement, 392 kg natural coarse aggregate, 308 kg nat-ural fine aggregate, 588 kg recycled coarse aggregate, 462 kg recy-cled fine aggregate, 91 kg flay ash, 82 kg mineral powder, and18.5 kg pumping agent. The recycled aggregate was producedproperly and supplied by a local production line. The average com-pressive and tensile strength of recycled concrete tested on the dayof cyclic testing are shown in Table 1. The mechanical properties ofreinforcement are show in Table 2 and stress–strain curves shownin Fig. 2.

3.3. Theoretical strengths and predicted failure modes

The average shear stress V/(lwbw) achieved by walls is closelyrelated to their failure mechanisms, where V is the applied shearforce. In the design applications, flexural failure is preferred sinceit is ductile and easy to predict the peak load with satisfactoryaccuracy. However, the squat shear walls are prone to fail in amixed flexure–shear or shear mode. Three typical shear failuremodes were summarized by Paulay et al. [8], namely, diagonal ten-sion, diagonal compression and sliding shear failure. Diagonal ten-sion failure, characterized by a corner to corner cracking, oftenoccurs when insufficient horizontal reinforcement is provided.Adding horizontal reinforcement can prevent diagonal tension fail-ure and lead to diagonal compression failure, characterized bycrushing of concrete struts near the base of the wall. This type offailure is common in walls with stiff boundary elements or witha high axial load. It usually attains a high shear stress. Sliding shearfailure differs from diagonal tension or compression, characterizedby resisting shear force by aggregate interlock in the compressionzone and dowel action of the vertical reinforcement at base sec-tion. It occurs in walls with adequate horizontal reinforcement toprevent diagonal tension failure, with low axial loads and no stiffboundary elements so that diagonal compression failure wouldbe avoided, or in walls with light vertical reinforcement. Sinceshear failures are brittle in nature, walls or other members are

Table 2Mechanical properties of reinforcement.

Type fy (MPa) fu (MPa) Es (MPa) ey (�10�6)

D8 398 518 2.1 � 105 1895D10 363 482 2.1 � 105 1729D14 477 628 2.0 � 105 2385

Note: fy is the yield stress; fu is the ultimate stress; Es is the modulus of elasticity; ey

is the yield strain.

designed to have shear strengths higher than their flexuralstrengths to suppress shear failures in seismic design.

The calculation of flexural strength is based on the plane sec-tions assumption which is applicable to flexure-dominant mem-bers. Thus, the assumption will not apply to the squat wallsbecause their shear deformations are expected to be considerable.Even so, the ideal and ultimate flexural strength (Vif and Vuf) of wallspecimens were calculated for comparison. The predicted flexuralstrengths according to Chinese code GB 50010 are shown inTable 3. The formulae for the calculation of Vif and Vuf are shownin Eqs. (1) and (2), where V represents Vif or Vuf. The strain limitof concrete in compression is 0.0033 and the tensile stress of con-crete is not considered. The only difference between Vif and Vuf isthat the latter takes into account of the strain-hardening ofreinforcement.

N ¼ a1f cbwxþX

A0si f 0si � f c

� ��X

Asif si ð1Þ

VH ¼ Nð0:5lw � 0:5xÞ þX

Asif siðdi � 0:5xÞ �X

A0sif0siðdi � 0:5xÞ

ð2Þ

where x = b1xn is the depth of the equivalent rectangular stressblock, xn is the actual depth of compression zone, a1 and b1 arethe coefficients of rectangular stress block (taken as 1.0 and 0.8for normal strength concrete, respectively), Asi

0is the area of bar i

in compression zone, fsi0

is the stress of compression bar i (positivein compression), Asi is the area of bar i in tension zone, fsi is thestress of tension bar i (positive in tension), di is the distance fromthe extreme compression fiber to the centroid of bar i. In calculationof Vif, it is assumed that fsi and fsi

0equal to the yield stress of vertical

reinforcement (Table 2). However, in calculation of Vuf, the stressesfsi and fsi

0are obtained from the testing stress–strain curves of rein-

forcement (Fig. 2). For example, the strain of the outermost bar intension in RCSW-1 is 0.012 and the corresponding stress is592 MPa.

Due to the uncertainty of shear strength of walls, design codesoften give a lower bound prediction to estimate the shear strengthconservatively. In Chinese code GB 50010 [16], the peak shearstrength of shear walls (hw/lw 6 1.5) can be simplified as Eq. (3).

VGB50010 ¼ 0:5f tbwh0 þ 0:13N þ f yAsh

sh0 ð3Þ

where h0 is the effective depth of cross section (taken as the dis-tance from the center of boundary element in tension to theextreme compressive fiber of concrete), N is axial load which is nomore than 0.2fcbwlw, fy is the yield stress of horizontal web rein-forcement, and Ash is the total cross-sectional area of horizontalweb reinforcement within the spacing s. In ACI 318 code [17], the

Table 3Calculated strengths and failure modes.

Specimen Vif (kN) Vuf (kN) Diagonal tensionstrength (kN)

Diagonal compression strength (kN) Sliding shear strength (kN) VWood (kN) Failure mode

VGB50010 VACI318 VBarda VPark Predicted Tests

RCSW-1 1200 1279 1486 1552 1626 2157 1050 F F-DCRCSW-2 867 984 1058 1209 1418 1235 1050 F F-SLRCSW-3 1215 1294 1167 1217 1644 2183 1065 F-DT F-DCRCSW-4 1203 1282 856 870 1631 2156 1056 DT DTRCSW-5 614 753 747 1017 1633 833 1075 F FRCSW-6 616 753 531 793 1660 833 1107 F F/DC⁄

Note: F – flexural; DT – diagonal tension; DC – diagonal compression; SL – sliding shear; F/DC⁄ – flexural failure in the negative direction, diagonal compression in the positivedirection.


peak shear strength for seismic design of walls (hw/lw 6 1.5) is acombination of the contribution of concrete and horizontal rein-forcement, as shown in Eq. (4), and the beneficial effect of axial loadis not considered.

VACI318 ¼ 0:25ffiffiffiffif 0c

qþ qhf y

� �lwbw ð4Þ

where fc0(in MPa) is the specified compression strength of concrete

(cylinder strength), which is equal to prism strength fc in this study(the small difference between them is ignored). Eqs. (3) and (4)assume a diagonal failure plane inclined as 45� and yielding of allhorizontal web reinforcement across the failure plane. In the pre-diction of failure modes, the maximum value of Eqs. (3) and (4)was regarded as a potential diagonal tension resistance of shearwalls. To estimate the potential diagonal compression strength ofwall specimens, the equation suggested by Barda et al. [6] was used.The Barda et al. equation was derived based on the test results ofeight squat walls with heavily reinforced flanges. Since diagonalcompression failure occurred in Barda’s study, it is reasonable touse the equation to predict the diagonal compression strength ofsquat walls for research purpose. Additionally, the equation sug-gested by Park and Paulay [18] was used to predict the sliding shearstrength of shear walls, which is shown in Eq. (5).

VPark ¼ N þ Av f y ¼ N þ qv lwbwf y ð5Þ

where Av is the total cross-sectional area of vertical reinforcementin web and boundary elements, which is taken as qvlwbw so thatthe contribution of heavy reinforcement in the boundary elementscould not be overestimated, qv is the vertical web reinforcementratio, and fy is the yield stress of web reinforcement. Moreover,the shear strength predicted by Wood [19] which was based onthe testing results of 143 specimens was also calculated.

As shown in Table 3, based on the calculated flexural and shearstrengths, all specimens except RCSW-4 could achieve the idealflexural strength. It was predicted that flexural failure would occurin RCSW-1, RCSW-2, RCSW-5 and RCSW-6, critical flexural–diago-nal tension failure would occur in RCSW-3, and diagonal tensionfailure would occur in RCSW-4. However, for squat walls withboundary elements, a significant portion of lateral load introducedat the top of a cantilever wall could be transmitted directly to thewall base by compressive struts, thus the lateral load resistancewould be the combined contribution of flexural and diagonal com-pression mechanisms and probably be lower or higher than theflexural strength of the critical section (evidenced by the resultsof this study). Since the relative contributions of the lateral loadresisting mechanisms are unknown, the peak loads and actual fail-ure modes are hard to predict accurately.

3.4. Construction

The specimens were constructed at the structural laboratory ofBeijing University of Civil Engineering and Architecture. For eachwall the foundation beam was cast by normal concrete first.Then the wall together with the top beam was cast vertically byrecycled concrete. After casting of walls, the specimens were curedat least 28 days before testing. The foundation beam and top beamwere designed to be elastic in loading process and sufficiently stiffto bear and transfer forces with negligible deformation.

3.5. Test setup

Fig. 3 shows the test setup. The specimen was stressed to thestrong floor and horizontally restrained to prevent rocking andsliding. The lateral load was applied by a horizontal actuator witha capacity of ±2000 kN. The axial load was applied vertically by aloading system which included two hydraulic jacks with a totalcapacity of 4000 kN, a stiff steel beam for transferring forces, twopost-tension bolts, and two hinged connections. Additionally, asteel beam was placed on the top of wall specimen to make surethat the axial load was applied uniformly to the wall.

3.6. Instrumentation

The applied lateral and vertical loads were monitored by loadcells. A series of linear variable displacement transducers (LVDTs)were used to measure the deformation. As shown in Fig. 4, thetop displacement at the application point of lateral load was mea-sured by a 250 mm stroke LVDT. Moreover, three LVDTs on eachside of the specimen and two LVDTs in diagonal directions wereinstalled for measuring the flexural and shear deformation respec-tively, and a LVDT was installed at the foundation beam to measurethe sliding displacement of the specimen. As shown in Fig.5, elec-trical resistance strain gages (3 mm length) were mounted on thevertical and horizontal reinforcement to monitor the steel strainduring testing. The selected locations of stain gauges of RCSW-2through RCSW-4 and RCSW-6 were same as those of RCSW-1and RCSW-5, respectively.

3.7. Loading procedure

The axial load remained constant when the specimen wastested under cyclic lateral load. In order to prevent unexpectedsudden shear failure in the loading process, force control was takenwith the increasing amplitude of 100 kN, and each target load wasapplied once before the minimum of 0.75Vif and VGB50010 (shearstrength based on Chinese code) was achieved. After that, displace-ment control was conducted. The target displacement or drift (dis-placement divided by wall height) was ±1, ±1.5, ±2, . . . times thedisplacement or drift corresponding to the minimum of 0.75Vif

Actuator

Hydraulic jack

Reaction wallStrong floor

Stiff steel beam

Post-tensionbolt

Steel beam

Specimen

Hingedconnection

PositiveNegative

(a) front view (b) side view

Fig. 3. Test setup.

Fig. 4. Instrumentation of wall specimen.


and VGB50010. For each target displacement or drift, three cycleswere applied.

4. Experimental results

4.1. RCSW-5 and RCSW-6: no axial load

Specimen RCSW-5 and RCSW-6 were designed to reflect thebehavior of squat recycled concrete shear walls without axialloads. They had same vertical web reinforcement (0.646%) butdifferent horizontal web reinforcement. The horizontal webreinforcement of RCSW-6 (0.186%) was one half of that ofRCSW-5(0.372%).

Strain gauge

300mm

Vertical:D8@180

(a) RCSW-1

Fig. 5. Measured s

In the test of RCSW-6, several short cracks formed in the lowerhalf of the boundary element at the end of the 300 kN cycle. In the0.3% drift cycle, the short cracks developed into the web regionobviously. In the following loading stages, inclined cracksincreased and climbed along the height of the specimen. In the1.29% drift cycle, the peak load was achieved. The crack patternof RCSW-6 at peak load is shown in Fig. 6(f), it was observed thatthe cover concrete at the toes of the specimen was slightly dam-aged and web concrete was divided into many compressive struts.An ultimate drift of +2.93% (corresponding to 85% of the peak load,namely, failure load) was achieved in the positive direction, andthe loss of load-carrying capacity was caused by the degradationof compressive struts. However, a lower ultimate drift of �2.54%was achieved in the negative direction, and the loss ofload-carrying capacity was caused by crushing of concrete in theleft boundary element (Fig.7(f)). The lateral load versus driftresponse of RCSW-6 is shown in Fig. 8(f). It should be noticed thatthe asymmetry of peak load and the degradation trend ofload-carrying capacity is obvious. In the positive direction, a peakload of +592 kN was achieved which was only 79% of the calculatedultimate flexural strength, and in the negative direction, the calcu-lated ultimate flexural strength (753 kN) was achieved. This couldbe a consequence of different controlling mechanism whichoccurred in two directions. Since flexural failure occurred in nega-tive direction and diagonal compression failure occurred in posi-tive direction (Table 3), two controlling mechanisms would resultin different capacity. In this test, the specimen was not symmetri-cally loaded in two loading directions due to unexpected horizon-tal sliding of the footing beam. Based on the test observation andmeasured vertical strain distribution of vertical reinforcementacross the base section, it was found that the depth of compression

Strain gauge

300mm

Vertical:D10@135

(b) RCSW-5

train gauges.

(a) RCSW-1 (b) RCSW-2 (c) RCSW-3

(d) RCSW-4 (e) RCSW-5 (f) RCSW-6

Fig. 6. Crack patterns of specimens at peak load.

(a) RCSW-1 (b) RCSW-2 (c) RCSW-3

(d) RCSW-4 (e) RCSW-5 (f) RCSW-6

Fig. 7. Crack patterns of specimens at failure load.


Fig. 8. Lateral load versus drift response: (a) RCSW-1; (b) RCSW-2; (c) RCSW-3; (d) RCSW-4; (e) RCSW-5; (f) RCSW-6.


zone in the positive direction was greatly larger than predicted,thus a shorter force arm would also result in a lower momentcapacity.

Specimen RCSW-5 developed less cracks than RCSW-6 at theend of 300 kN cycle due to larger amount of horizontal web rein-forcement. A peak load of +675 kN and �698 kN was achieved at+1.17% drift and �1.50% drift, respectively. The crack pattern atpeak load is shown in Fig. 6(e). Similar to RCSW-6, the calculatedultimate flexural strength of RCSW-5 was also not achieved.However, there was also substantial yielding of vertical reinforce-ment in the web and boundary element. Obvious crushing of coverconcrete in left boundary element was observed in the ±2.75% driftcycle. After that, the load-carrying capacity in negative directiondecreased rapidly to failure load at �2.84% drift, but the specimenstill kept stable lateral load-carrying capacity in positive directionuntil the spalling of web concrete (Fig. 7(e)) at +3.42% drift. Asshown in Fig. 8(e), it exhibited ductile behavior and could meetthe requirements of seismic design.

4.2. RCSW-2: axial load ratio 0.06

Specimen RCSW-2 was designed to reflect the behavior of thesquat wall with a small axial load ratio. The horizontal cracking

initiated in the lower half of boundary elements during the700 kN cycle. At the end of the 800 kN cycle, two cross inclinedcracks in web concrete were observed. A peak load of +1111 kNand �1093 kN was achieved at +1.36% drift and �1.92% drift,respectively. Different from specimen RCSW-5 and RCSW-6, thepeak load of RCSW-2 is higher than its calculated ultimate flexuralstrength. The crack pattern at peak load is shown in Fig. 6(b), finecompressive struts and the crushing of concrete at the toes of thespecimen could be observed. The loss of load-carrying capacitywas caused by horizontal sliding shear in web at a height of350 mm and crushing of boundary elements (Fig. 7(b)). The slidingsurface almost located at the end of dowel reinforcement. Asshown in Fig. 8(b), the specimen exhibited stable load-carryingcapacity until an average ultimate drift of 2.56% was achieved.

4.3. RCSW-1, RCSW-3 and RCSW-4: axial load ratio 0.13

Specimen RCSW-4 was lightly reinforced in horizontal directionand diagonal tension failure was expected. Horizontal cracking ini-tiated in the boundary elements during the 1000 kN cycle (0.2%drift). Cross diagonal cracking occurred at 0.75% drift. A peak loadof +1492 kN and �1499 kN was achieved at +1.21% drift and �1.0%drift, respectively. It is much higher than the predicted diagonal


tension strength. The crack pattern at peak load is shown inFig. 6(d). The specimen failed suddenly due to the spalling andcrushing of boundary elements and the main diagonal cracksdeveloped to the wall base (Fig. 7(d)), only an ultimate drift of1.455% was achieved (Fig. 8(d)).

Specimen RCSW-3 was designed with more horizontal webreinforcement (0.582%) than that of RCSW-4 (0.291%). Horizontalcracking initiated in the boundary elements during the 1000 kNcycle (0.25% drift). A peak load of +1467 kN and �1570 kN wasachieved at +1.18% drift and �0.81% drift, respectively. As shownin Fig. 6(c), vertical cracking in boundary elements could beobserved. In the following cycles, the cover concrete spalled grad-ually. The loss of lateral load-carrying capacity was caused byboundary crushing and immediately followed web crushing (seeFig. 7(c)). Compared with RCSW-4, an improved ultimate drift of1.83% was achieved.

Specimen RCSW-1 had a horizontal web reinforcement ratio of0.873%. Horizontal cracking was observed in the boundary ele-ments during the 0.36% drift cycle. A peak load of +1529 kN and�1535 kN was achieved at +1.28% drift and �0.90% drift, respec-tively. As shown in Fig. 6(a), the increasing of horizontal web rein-forcement resulted in finer compressive struts compared with thespecimens RCSW-3 and RCSW-4 with less horizontal web rein-forcement. The lateral load-carrying capacity was lost due to com-pressive failure of boundary elements and spalling of web concrete(Fig. 7(a)). Because of the brittle nature of diagonal compressionfailure, its ultimate drift (1.92%) was not greatly improved com-pared with RCSW-3.

Test results of specimens are summarized in Table 4.

4.4. Measured wall strain distribution

As shown in Fig. 5, the strains of four vertical bars in boundaryelements and three vertical bars in web were monitored by straingauges at a height of zero (wall base section) and 300 mm. Fivehorizontal bars located at a height of 50 mm, 350 mm, 650 mm,950 mm and 1250 mm were selected to measure their strains.

Table 4Test results.

Specimen Vpeak+ (kN) Vpeak

� (kN) Vpeak (kN) Dpeak/

RCSW-1 1529 1535 1532 1.090RCSW-2 1111 1093 1102 1.641RCSW-3 1467 1570 1518 0.996RCSW-4 1492 1499 1495 1.114RCSW-5 675 698 686 1.336RCSW-6 592 753 672 1.266

Note: Vpeak is the average peak load of positive direction Vpeak+ and negative direction Vpeak

lateral top displacement corresponding to 85% of the peak load (failure load); 0.73 and

(a) positive direction

Fig. 9. Measured vertical reinforcement str

For each horizontal bar, three strain gauges were installed at left,middle and right respectively. The measured vertical and horizon-tal reinforcement strains of specimens at various drift levels areshown in Figs. 9–16 (1le = 1 � 10�6). It can be observed that thestrain of vertical reinforcement varies linearly across the base sec-tion of the wall at small drift levels for all specimens. However, thestrain distribution of vertical reinforcement at base section doesnot satisfy the plane sections assumption after the wall developedobvious plastic deformations due to the yielding of reinforcementand cracking or spalling of concrete, especially for specimens withhigher axial load ratio (such as RCSW-1). As evidenced in Fig. 9,most of the vertical reinforcement of RCSW-1 (axial load ratio0.13) yield or enter strain-hardening phase at +0.95% and �0.90%drift (before the peak load was achieved). For specimen RCSW-5without axial load, the strain distribution approximately keeps lin-ear at +0.89% and �0.88% drift (Fig. 11). Even so, it is also foundthat most of reinforcement in tension zone yield at the peak load.For specimen RCSW-6, the depths of compression zone are differ-ent in two loading directions. As shown in Fig. 12, the depth ismore than 600 mm in positive direction at +0.51% drift, however,it is about 300 mm in the negative direction at �0.59% drift. Forboth RCSW-5 and RCSW-6 walls, the vertical strains in the bound-ary reinforcement appear to be relatively low and strain-hardeningis not obvious, therefore the stresses are much lower than the ulti-mate stress of reinforcement, which would result in a relativelylower moment. This is consistent with that the peak load waslower than the calculated ultimate flexural strength.

The maximum value of strain gauges located at left, middle andright (see Fig. 5) is taken as the representative strain of a horizontalbar. As shown in Figs. 13–16, the strains of horizontal reinforce-ment are very small at the initial drift levels for all specimens. Asthe increasing of drift, the strains become larger. The horizontalreinforcement of RCSW-1 and RCSW-5 did not yield when thespecimens achieved their peak loads. For other specimens, theyielding of some horizontal reinforcements was observed at theirpeak loads, but the yielding of all the horizontal reinforcementswas not measured, which was also observed in the studies of other

H (%) Du/H (%) Vpeak/Vif Vpeak/Vuf Vpeak/(Acp

fc)

1.915 1.28 1.20 0.73 (8.76)2.555 1.27 1.12 0.52 (6.30)1.833 1.25 1.17 0.71 (8.55)1.455 1.24 1.17 0.71 (8.49)3.132 1.12 0.91 0.32 (3.83)2.738 1.09 0.89 0.30 (3.64)

�; Dpeak is the average lateral top displacement corresponding to peak load; Du is the8.76 are the results when the value of fc in MPa and fc in psi is used respectively.

(b) negative direction

ain across the base section of RCSW-1.

(a) positive direction (b) negative direction

Fig. 10. Measured vertical reinforcement strain across the base section of RCSW-2.






researchers [20,21]. In the post peak load stages, the strainsincrease rapidly, and the maximum strain appears at a height of350 mm or 650 mm (nearly one third of the total height).

4.5. Analysis of wall strength

As shown in Table 4, the comparison of average peak load Vpeak

with Vif indicates that all specimens achieved the ideal flexuralstrengths. Moreover, the ratio Vpeak/Vuf shows that RCSW-1 throughRCSW-4 achieved the peak loads higher than calculated ultimateflexural strengths, and RCSW-5 and RCSW-6 did not achieve theirultimate flexural strength. In order to give a better prediction ofthe peak loads of squat walls in this study, a mixed flexural anddiagonal compression mechanism is proposed as shown inFig. 17(a). It is assumed that the lateral load resistance is a contri-bution of flexural mechanism (Vflexural) and diagonal compressionmechanism (Vdiagonal) which can transfer loads directly to the

foundation. The two mechanisms illustrated in Fig. 17(b) and (c)have the same compression zone. The ultimate condition is thatthe crushing of extreme compression fiber due to the contributionsof the two mechanisms. For simplicity, it is assumed that only thecompressive struts pointed into the compression zone are effectivein transferring lateral load. The analytical peak load (Vanalytical)could be expressed as Eq. (6).

Vanalytical ¼ Vflexural þ Vdiagonal ð6Þ

Then, the equilibrium of vertical forces at the base section givesEq. (7).

N þ Vdiagonal tan h ¼ a1f cbwxþX

A0siðf0si � f cÞ �

XAsif si ð7Þ

where h is the inclined angle of the effective compressive struts(taken as 45� in this study), Vdiagonaltanh is the total vertical compo-nent of compressive force in effective compressive struts, x = b1xn isthe depth of the equivalent rectangular stress block, xn is actual


Fig. 13. Measured horizontal web reinforcement strain of RCSW-1.








depth of compression zone, a1 and b1 are the coefficients of rectan-gular stress block (taken as 1.0 and 0.8, respectively), Asi is the areaof tension bar i, fsi is the stress of tension bar i (taken as the yield

stress), di is the distance from the extreme compression fiber tothe centroid of tension bar i. Since the contribution of diagonal com-pression to the peak load (Vdiagonal) will not produce moment at the

Compressivestruts

N

V

Bou

ndar

y el

emen

t in

com

pres

sion

Bou

ndar

y el

emen

t in

tens

ion

V

N

Vflexural

Vflexural

Compression zonexn

di

AsifsiAsi'fsi'Stress

block

Effective compressive

strut

Vdiagonal

Vdiagonal

xn

V

NV

Base section

Center line of lateral load

Vflexural

NVflexuralhw

is isfA∑Vflexural

Base section

Vdiagonal

θtandiagonalVVdiagonal

θtandiagonalV

(a) (b) (c)

Fig. 17. Mechanisms of lateral load resistance: (a) mixed flexure and diagonal compression mechanism; (b) flexural mechanism; (c) diagonal compression mechanism.


center of rectangular stress block (Fig. 17c), the equilibrium ofmoments at the center of rectangular stress block yields Eq. (8).

VflexuralH � Nð0:5lw � 0:5xÞ ¼X

Asif siðdi � 0:5xÞ�X

A0sif0siðdi � 0:5xÞ ð8Þ

Since the strain distribution of vertical reinforcement is notknown, the stress of vertical reinforcement in compression needsto be assumed. In this study, the vertical reinforcement in com-pression (Asi

0) in Eq. (7) and Eq. (8) is ignored in the calculation.

For Eq. (8), the componentP

Asi0fsi0(di � 0.5x) is small since the ver-

tical reinforcement in compression was symmetrical to the centerof compression zone in most cases. For Eq. (7), ignoring Asi

0will

have some effects on the results. According to the behavior of rein-forced concrete beam sections with and without compression rein-forcement under bending, ignoring Asi

0will give a relatively

conservative prediction of the ultimate load-carrying capacity.The analytical results are shown in Table 5. Since it is not pos-

sible to get four unknowns through Eqs. 6–8, it is assumed thatVanalytical equals Vpeak. Consequently, the compression zone x,Vflexural, Vdiagonal can be determined based on the tested peak loads.It is shown that 13–25% of peak load could be transferred by diag-onal compression mechanism. Particularly, as it is shown inTable 5, the lateral load resistance of flexural mechanism for allspecimens is nearly 95% of the ideal flexural strength, so that Eq.(9) can be proposed.

Vflexural ¼ 0:95Vif ð9Þ

Eq. (9) will be quite useful in the prediction of the peak load. Ifthe flexural component Vflexural is determined, the compressionzone x, Vdiagonal and Vanalytical can be obtained from Eqs. 6–8.

Table 5Analytical results.

Specimen xn (mm) x (mm) h (�) Vflexural (kN) Vdiagonal (kN)

RCSW-1 466 373 45 1142 385RCSW-2 294 235 45 834 266RCSW-3 453 362 45 1159 358RCSW-4 454 363 45 1148 346RCSW-5 172 138 45 582 103RCSW-6 160 128 45 585 89

5. Discussions

5.1. Application scope of mixed flexure and diagonal compressionmechanism

Due to the formation of compressive struts in web and frameaction of boundary elements, the diagonal compression mecha-nism will be effective in transferring lateral load to the foundation.The mixed flexural and diagonal compression mechanismdescribed above reasonably reflects the lateral load resistingbehavior of specimens and accurately predicts the peak loads ofall specimens if the uniform contribution of 0.95Vif (flexural mech-anism) is assumed. Since the number of specimens tested is lim-ited, the flexural component of 0.95Vif may only be used forsimilar walls to those in this study. However, the analyticalmethod applies to the squat walls failed in flexure or in a mixedflexure and diagonal compression mode, characterized by yieldingof vertical reinforcement out of compression zone and crushing orspalling of concrete in the boundary element. It is required that thediagonal tension or sliding shear strengths calculated by designequations are larger than the predicted loads by the proposedmodel.

5.2. Indication for design of squat recycled concrete walls

The axial load level, amount of horizontal and vertical web rein-forcement, and the details of boundary elements are regarded asthe main factors which affect the behavior of squat walls. As shownin Table 4, the experimental results show that the increasing ofaxial load level results in improvement of peak loads but decrease

Vflexural/Vif Vflexural/Vanalytical Vdiagonal/Vanalytical Vanalytical/Vpeak

0.95 0.75 0.25 1.000.96 0.76 0.24 1.000.95 0.76 0.24 1.000.95 0.77 0.23 1.000.95 0.85 0.15 1.000.95 0.87 0.13 1.00


of drift capacities. It is shown that an ultimate drift of 1.92% corre-sponding to an average shear stress of 0.73

pfc MPa can be achieved

by specimen RCSW-1 with sufficient horizontal web reinforce-ment. However, the average shear stress may be less than 0.5

pfc

MPa if an ultimate drift of more than 2.5% is expected.The effect of vertical and horizontal web reinforcement was dis-

cussed in previous studies. Barda et al. [6] found that both of thevertical and horizontal reinforcements were effective in producinga more distributed crack pattern and in reducing crack width,and suggested that minimum horizontal and vertical reinforce-ment should be provided for all walls. For the walls withheight-to-length ratio of 1.0, Cardenas et al. [22] reported that bothhorizontal and vertical web reinforcements were effective in con-tributing to the shear strength. As shown in Table 4, for the squatwalls failed in flexure or a mixed flexure and shear mode, the com-parison of the peak load and drift capacity of specimens RCSW-1,RCSW-3 and RCSW-4 indicates that the increasing of horizontalweb reinforcement has a small effect on the peak load when thevertical web reinforcement remains constant, however, it canimprove the drift capacity of specimens. Consequently, increasingof horizontal web reinforcement could be an effective method inorder to gain a more ductile behavior. In this study, the amountof vertical web reinforcement was not changed for the specimenswith the same axial load level, so that its effect on strength anddrift capacity was not investigated. The only design indication isthat the minimum requirement of vertical web reinforcement ratio0.25% will not be adequate to resist sliding shear for the squatwalls with low axial load level, such as RCSW-2, RCSW-5 andRCSW-6.

5.3. Equations for predicting the shear strengths of squat walls

The equations for predicting the shear strengths of squat wallscan be found in building codes, guidelines or literatures asdescribed in previous sections. Gulec et al. [23] found that theequation proposed by Wood [19] resulted in a median ratio ofthe predicted to measured strengths (of 120 rectangular walls)close to 1.0 with a small coefficient of variation. In this study, theshear strengths of specimens were calculated by equations incodes and equations suggested by researchers as shown inTable 3. Although the specimens tested failed in flexure or a mixedflexure and shear mode, the comparison of the predicted shearstrength VGB50010 with the peak load Vpeak shows that Eq. (3) alwaysgives a conservative prediction. ACI 318 (Eq. (4)) gives a slightlyhigher estimation of shear strength than Chinese code (Eq. (3)).Since the beneficial effect of boundary elements, the diagonal ten-sion strength of specimen with little horizontal web reinforcementsuch as RCSW-4 was greatly higher than that predicted by Chinesecode or ACI 318. The peak loads of specimens which failed in amixed flexure and diagonal compression mode such as RCSW-1and RCSW-3 are close to the predicted strength by Barda et al. Itis found that the Wood equation gives a conservative predictionof the shear strength for the specimens with axial loads.Additionally, Park equation was used to predict the sliding shearstrength of specimens. In this test, sliding shear failure onlyoccurred in RCSW-2 with a peak load of 1102 kN, which is 10%lower than the predicted 1235 kN.

6. Conclusions

Based on the experimental study on six large-scale squat recy-cled concrete walls, findings and conclusions may be summarizedas follows.

1. The peak loads and failure modes of wall specimens were notaccurately predicted by the existing formula. It is shown thatthe experimental peak loads may be 10% lower or 20% higherthan the predicted ultimate flexural strengths of squat wallswhich are predicted to fail in flexure.

2. In order to accurately predict the peak loads of squat walls, amixed flexural and diagonal compression mechanism is pro-posed, which assumes that the lateral load resistance of squatwalls is a combined contribution of the flexural mechanismand diagonal compression mechanism. It is found that 13–25%of peak load can be directly transferred to the wall foundationby diagonal compression according to the proposed analyticalmethod in this study.

3. The increasing of axial load level results in improvement ofpeak loads but decrease of drift capacities. An ultimate drift of1.92% corresponding to an average shear stress of 0.73

pfc

MPa can be achieved by providing sufficient horizontal webreinforcement. However, the average shear stress may be lessthan 0.5

pfc MPa if an ultimate drift of more than 2.5% is

expected.4. The increasing of horizontal web reinforcement had small effect

on peak load when vertical web reinforcement remains con-stant but could improve the drift capacity.

5. The explicit calculation of diagonal tension, diagonal compres-sion and sliding shear strength is recommended in the designof squat walls. However, the suitable equations for predictingthe shear strengths of squat walls should be further comparedand investigated.

Acknowledgements

The research reported in this paper was funded by BeijingNatural Science Fund (Grant No. 8091002). We would like tothank two anonymous reviewers for their specific and helpfulsuggestions.

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