1

Confinement of Rectangular Columns Made with Engineered Cementitious 1 Composites (ECC) 2

Wai Man Wong1, Carlos A. Cruz-Noguez 2, and Mohammad J. Tolou-Kian3 3

Keywords: Engineered Cementitious Composites (ECC), high-strength ECC, confined columns, 4 confinement model, compressive behaviour 5

ABSTRACT 6

Engineered Cementitious Composites (ECC) is a type of high-performance 7

fiber-reinforced cementitious composites (HPFRCC) designed to achieve 8

high tensile strain capacity with strain hardening effect during the post-9

cracking response. Previous studies show that ECC has high damage-10

tolerance capacity in tension, increasing the durability, safety, and 11

sustainability of structures susceptible to cracking and spalling under 12

moderate to severe loading. Under compression, however, there is a lack of 13

data regarding confinement effects on steel-reinforced ECC (RECC) 14

members. Thus, designing ECC structures is usually done by assuming the 15

ECC behaves in the same way as conventional concrete under compression. 16

With scarce experimental data available, this assumption may be inaccurate, 17

uneconomical, or even unsafe. An experimental test program on confined 18

ECC columns was performed in this study. Sixteen 100mm x 100mm x 19

300mm ECC square columns, consisting of one set of unconfined ECC and 20

1 Research Assistant, Dept. of Civil and Environmental Eng., University of Alberta, Edmonton, AB, T6G 2R3 2Associate Professor, Dept. of Civil and Environmental Eng., University of Alberta, Edmonton, AB, T6G 2R3. 3 PhD Candidate, Dept. of Civil and Environmental Eng., University of Alberta, Edmonton, AB, T6G 2R3.

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three sets of confined ECC with 1%, 1.5% and 2% transverse steel content 21

were fabricated and tested under monotonic compressive load until failure. 22

The force-displacement and stress-strain relationships in the longitudinal 23

direction were measured. The results show that confined ECC has a 24

compressive stress-strain behavior similar to that of confined high-strength 25

concrete, with a rapid compressive strength loss after peak strength, and a 26

gradual loss of strength that is inversely proportional to the amount of steel 27

reinforcement. An empirical stress-strain model for rectangularly confined 28

high-strength ECC was developed based on an existing model for high-29

strength conventional concrete. 30

1. INTRODUCTION 31

Conventional concrete has a high compressive strength, which is a useful mechanical property in 32

structural applications. However, due to its low tensile strength and strain, cracks develop 33

rapidly when subject to tension. Fibre-reinforced concrete (FRC) materials have been 34

developed to gain post-cracking and tensile strain capacity by adding certain types of natural and 35

synthetic fibres to the concrete mix. High-performance fibre-reinforced cementitious composites 36

(HPFRCC) are a type of FRC designed to achieve higher tensile strain capacity with strain 37

hardening effect during the post-cracking response (Li, 2008). An example of HPFRCC is 38

Engineered Cementitious Composites (ECC), which has a typical moderate tensile strength 39

ranging from 2 to 6 MPa and a tensile ductility of 1 to 5% (Li and Fischer 2002; Wong 2018). 40

ECC is made by mixing cement, fly ash, silica sand, water and polymeric, polyvinyl alcohol 41

(PVA) fibres. ECC can been successfully tailored to exhibit microcracking behaviour and high 42

tensile ductility (Li, 2008), preventing the opening of large, localized cracks, and allowing the 43

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development of large tensile strain capacities. The uniaxial tensile stress-strain curve from the 44

tensile test for this research shows that ECC is able to reach an ultimate tensile strain that is 110 45

times higher than a traditional high strength concrete. ECC exhibits multiple fine cracks with 46

crack widths below 100μm (Li, 2008). 47

While preserving the compressive behaviour of conventional concrete, the tensile ductility of 48

ECC reduces cracking and fracture problems associated with overloads and large imposed 49

deformations. The high damage tolerance capacity of ECC can increase durability, safety, and 50

sustainability of structures subjected to severe loading. Fischer and Li (2002) performed an 51

study on reinforced ECC beams under cyclic loading. The control specimen was an RC beam 52

with a longitudinal and transverse reinforcement ratio of 3.14% of 0.57%, respectively. One 53

ECC beam had identical reinforcement details, while two others had no transverse reinforcement. 54

The tests showed the superior damage tolerance and hysteretic response of the ECC beams 55

regardless of the presence of transverse reinforcement. No bond slipping, or cover spalling were 56

observed in the ECC specimens. Saiidi and Wang (2006) investigated bridge piers detailed with 57

ECC and SMA reinforcement at their plastic hinge locations. The test results indicated that the 58

proposed detailing results in minimal sustained damage and residual deformation when 59

compared to conventional RC. Cruz Noguez and Saiidi (2012) studied the seismic behaviour of 60

a quarter-scale, four-span bridge which was special in utilizing advanced materials. One of the 61

bents of the bridge model was detailed with superelastic, shape-memory alloy bars and ECC. 62

The ECC was incorporated in the lower parts of the bridge columns where the bottom plastic 63

hinges were expected to be formed. The rest of the columns including the top plastic hinges 64

were detailed with steel and normal concrete. Under dynamic excitation up to 1.0g, the plastic 65

hinges detailed with ECC sustained limited cracking and no spalling, while the plastic hinges 66

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detailed with conventional RC exhibited severe damage. Nagai et al. (2002) studied the 67

behaviour of low-rise ECC reinforced shear walls under lateral cyclic loading. They reported 68

that substituting normal concrete with ECC enhanced the performance of the shear walls in terms 69

of strength, deformability and damage tolerance. Yuan et al. (2018) studied the behaviors of 70

reinforced ECC columns bearing eccentric compressive loads. The study showed the superior 71

load-carrying, ductility and damage resistance of ECC columns in comparison to conventional 72

RC columns. The research also introduced a theoretical model regarding moment curvature 73

relationship in reinforced ECC columns and showed the effect of ECC properties such as tensile 74

ductility on the interaction diagrams of reinforced ECC columns. Al-Gemeel and Zhunge (2018) 75

studied concrete columns strengthened with ECC and three types of basalt fibre textile reinforced 76

ECC. According to the study, the strengthened square concrete columns showed 54%–77% 77

enhancement over un-confined specimen in terms of load bearing capacity. 78

Wu et al. (2017) studied the cyclic behavior of reinforced ECC short columns with different shear 79

span-to-depth, axial load and transverse reinforcement ratios. As the study showed, reinforced 80

ECC columns had enhanced ductility, energy dissipation and damage resistance properties with 81

respect to conventional RC columns. Also, fibre reinforcement in ECC provided adequate 82

confinement for the material so the additional confinement provided by transverse reinforcement 83

had insignificant effect on the response of the specimens. Xu et al. (2017) studied the lateral 84

hysteretic behaviour of three reinforced ECC and four composite concrete-ECC columns whose 85

concrete in the base of columns was substituted with ECC. Test results showed an improvement 86

in the ductility, energy dissipation, and stiffness degradation of the ECC and composite concrete-87

ECC columns over conventional RC columns. 88

Billington and Yoon (2004) studied the hysteretic response of five post-tensioned precast bridge 89

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piers detailed with ECC at their plastic hinging segment. The study showed that the ECC precast 90

piers dissipated higher levels of energy up to drift ratios of 3–6 % and showed higher damage 91

resistance under cyclic loads. Cruz Noguez and Saiidi (2012) also showed in a shake table test 92

that detailing the plastic hinging region of bridge piers with ECC and shape memory alloys will 93

notably increase the self-centering and damage resistance of the piers. 94

While the unconfined compressive characteristics of ECC has been found to be similar to those 95

of conventional compressive response of normal concrete (Motaref, 2011), the literature review 96

shows that there is scant data on the response of confined ECC elements. In conventional 97

concrete, through active or passive confinement, the lateral expansion of the material subjected 98

to axial stresses is restrained, and the resulting triaxial state of stresses increase the failure strain 99

of the concrete in the longitudinal direction. Normal-strength confined concrete has been widely 100

studied (Park and Paulay, 1975; Mander et al., 1988; Sheikh and Uzumeri, 1980), as well as 101

confined high-strength concrete (Yong et al., 1988; Bjerkeli et al., 1990) through a number of 102

different large-scale to small-scale experimental test programs. To the knowledge of the 103

authors, only one study of confined ECC has been conducted (Motaref 2011). Motaref tested 104

four groups of small-scale 100 × 200 mm circular ECC columns and developed a confined model 105

for circular ECC cylinders reinforced with steel spirals. However, no models for rectangular 106

columns made of ECC and confined with rectangular steel ties are available. This may present a 107

limitation for designers wishing to use ECC in members subjected to cyclic loading in which 108

understanding the confined properties of the ECC material is desirable. 109

In this study, the compressive response a number of confined, square, small-scale ECC columns 110

confined with different amounts of square steel stirrups is investigated. Using the experimental 111

results, an empirical model for confined ECC elements is proposed, based on one developed for 112

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high-strength concrete. 113

2. EXPERIMENTAL PROGRAM 114

2.1 ECC Material 115

The ECC material chosen for this study was PVA-ECC (M45), a commonly used type of ECC. It 116

has a minimum compressive strength of 45 MPa (Li 2008). The ECC was prepared by mixing: 117

(1) type GU Portland cement, (2) ASTM Class F fly ash, (3) silica sand, (4) superplasticizer 118

Glenium 7700, (5) water, and (6) 2% volume fraction of PVA fibres, according to the quantities 119

indicated in Table 1. The PVA fibre used was RECS-15, manufactured by Kuraray Co. from 120

Japan. RECS-15 fibres have a diameter of 40µm and a length of 12mm, with a proprietary 121

surface oil coating. The coating decreases the possibility of fibre fracture by preventing the 122

development of the high interfacial bond stresses, allowing slipping (Wang and Li, 2007). 123

RECS-15 fibres have a tensile strength of 1560 MPa, an elastic modulus of 40 GPa, and strain 124

capacity of 6.5%. The resulting mixture was viscous but workable, requiring just minor 125

vibration (5-10 seconds) to achieve satisfactory settlement in cylinder and column moulds. 126

2.2 ECC Characterization 127

Material testing was conducted to determine the tensile and compressive (unconfined) properties 128

of ECC. A standard uniaxial compression test was conducted on Ø75x150 mm cylinders as per 129

ASTM C469/C469M – 14. The average compressive stress-strain response (Fig. 1) shows that 130

the resulting ECC material had an average 28-day compressive strength of (f’c) of 74.1 MPa and 131

the typical compressive behaviour of high strength concrete. The secant modulus of elasticity (E) 132

at 0.4f’c was 16,400 MPa, and the Poisson's ratio (at a strain corresponding to 40% of peak 133

compressive strength) was 0.153. A uniaxial tensile test on ECC was conducted according to the 134

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procedures suggested by Zhou et al. (2012). It was performed in a hydraulic MTS 810 machine 135

by clamping the ends of 304.8 mm x 76.2 mm x 12.7 mm coupon specimens between two 136

aluminum plates. The average tensile response (Fig. 2) indicated that the ECC exhibited higher 137

tensile strain than that of conventional concrete, with an ultimate tensile strain of 0.015 and a 138

tensile strength of 2.6 MPa. A number of microcracks developed along the ECC specimen 139

during the tensile test (Fig. 3). 140

2.3 Specimen geometry 141

A test program was designed to investigate the stress-strain relationship of high-strength ECC 142

members with square ties as transverse reinforcement. A total of sixteen 100mm x 100mm x 143

300mm columns were fabricated. The specimens were divided into four sets that had different 144

amounts of transverse reinforcement, including an unconfined set: 0%, 1.0%, 1.5% and 2.0%. 145

One additional set of 4 unconfined 100mm x 100mm x 300mm columns were made with high-146

strength concrete designed to have approximately the same peak compressive strength as the 147

unconfined ECC columns. No superplasticizer was added to the concrete mixture and it 148

achieved a slump of 10 cm. In this study, the transverse reinforcement ratio is defined as the 149

ratio of the cross-sectional area of ties to the cross-sectional area of concrete tributary to the ties. 150

The transverse reinforcement consisted of 6.35-mm deformed bars with an average yield stress 151

of 416 MPa, ultimate stress of 602 MPa, and elastic Young’s modulus of 190,000 MPa. 152

The specimens were designed to have a height-to-width ratio of 3:1 in order to reduce the 153

confining effect produced by end loading plates, as suggested by Lai et al. (2014). The square 154

stirrups were placed around the column with no clear cover, as done in similar studies (Yong et. 155

al. 1988). To provide clearance for the transverse reinforcement in the 100 x 100 mm molds, the 156

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square ties were designed to be 95 x 95 mm with 135° hook anchorage at the corners. 157

Four 5-mm longitudinal plastic bars were placed in the corners of all the specimens to assist with 158

the positioning and tying of the square ties. These auxiliary bars were also placed on the 159

specimens with 0% transverse steel ratio for consistency. The cross section and the 160

configuration of ECC columns is shown in Figs. 4 and 5. 161

The steel cages were placed in molds in a horizontal manner to facilitate ECC pouring due to the 162

viscosity of the mixture (Fig. 6). After being cast, the specimens were vibrated for 5-10 seconds 163

using a small pencil vibrator. The specimens were kept in a curing room at approximately 25°C 164

and 95-100% relative humidity until one day before testing. It is to be noted that horizontal 165

pouring of ECC may lead to bottom side of the sample being denser than the uppermost one, an 166

effect that can be compounded by the vibration process. Vibration has also been reported to 167

cause fibre segregation in fibre-reinforced concrete, although this phenomenon was not observed 168

in this study. Tolou-Kian and Cruz-Noguez (2016) reported no appreciable segregation in a 1.0 169

x 1.8 x 0.15 m shear wall panel that was cast horizontally and vibrated, using a similar ECC 170

mixture than the one used in this research. They attributed this observation to the high viscosity 171

of the ECC. However, they did not perform differential density measurements through the 172

thickness of the panel. The compressive tests performed on the column specimens, described in 173

a latter section, did indeed show that some specimens failed preferentially in one side. This could 174

lend credibility to the idea that horizontal casting leads to significant density differentials 175

through the sample thickness, warranting further investigation as one of the limitations of this 176

study. However, other reasons may lead to similar observations, such as uneven loading plates, 177

geometric defects on the column specimen, and shifted reinforcement cages inside the column. 178

2.4 Instrumentation and Testing Procedure 179

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An overall view of the instrumentation of the specimen is shown in Figs. 7-8. To measure the 180

stress-strain compressive response of the specimens, two linear variable differential transducers 181

(LVDT’s) with swivel eyelets that permitted rotation were placed opposite each other at the 182

middle section of the specimen. The total deformation of the specimen was calculated by 183

averaging the reading of the two LVDT’s. Eight 6.35mm thumbscrews, with four at each end, 184

were screwed into the specimen surface to secure the aluminum frame. Four aluminum bars 185

were used to ensure that the top and bottom plates were parallel with respect to each other. After 186

fixing the aluminum frame on to the specimen, the aluminum bars were released to allow free 187

deformation during the tests. The specimens were loaded under a concentric monotonically 188

increasing axial compressive load in an MTS 815 machine (Fig. 9). The tests were conducted in 189

a displacement control system with a loading rate of 0.3 mm/s. The specimens were first pre-190

loaded (1-2 kN) to prevent slipping between the columns and the load cell. A QuantumX data 191

acquisition system was used to collect the LVDT readings and the axial load values. The tests 192

were terminated when either the load dropped to 40% of the maximum load or when the LVDT’s 193

were unable to record the displacement. All specimens were tested at 28 days of age. 194

4. EXPERIMENTAL RESULTS 195

The averaged load-displacement results for the ECC and concrete columns for each set are 196

presented in Figs. 10-11. Dividing the force from the actuator by the cross-sectional area and 197

dividing the displacement from the LVDT by the gauge length, averaged stress-strain 198

relationships are shown in Figs. 12-16. The cracking status and specimen deformation at 3 or 199

more different stages (elastic stage, peak, post-peak, residual, and failure) are also shown in figs 200

12-16. A comparison of the stress-strain responses of all tested specimen is shown in Fig. 17. 201

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The axial compressive test results are summarized in Table 2. The observations conducted 202

during the experiment are discussed below. 203

4.1 Unconfined Columns 204

Both Concrete-0% and ECC-0% columns had similar peak compressive strength. Concrete-0% 205

columns reached a peak compressive stress of 67.6 MPa at a strain of 0.0021, while ECC-0% 206

columns reached a peak compressive stress of 69.3 MPa at a strain of 0.0029. After the peak 207

strength, Concrete-0% columns had a sudden, explosive type of failure at the maximum axial 208

load, with a diagonal failure surface at a strain of 0.0025 (Fig. 12). In contrast, ECC-0% 209

columns developed a gradual failure with multiple longitudinal microcracks at the peak load, 210

with the strength dropping by 80% in average with the application of further compressive 211

displacement. At the post-peak stage, the unconfined ECC columns showed a stable, plateau-212

like residual strength response which continued up to relatively large strains (greater than 0.025) 213

that exceeded the range of the instrumentation used. The average residual strength was stable, 214

averaging 11 MPa (Fig. 13). It is noted that complete failure or crushing of the ECC specimens 215

was not observed in none of the tests – the residual stress plateau continued up to very high 216

compressive strains, which made necessary to remove the instrumentation frame to avoid 217

damaging it. 218

The peak compressive strength 0cf and modulus of elasticity Ec for Concrete-0% and ECC-0% 219

columns were found to be smaller by about 7% and 40%, respectively, than the corresponding 220

values recorded from cylinder tests (Fig. 18), while the modulus of elasticity Ec were found to be 221

larger by 10% and 70% respectively. The difference can be ascribed to both shape and boundary 222

effects. Similar findings have been discussed by Yong et al. (1988) and Martinez et al. (1984) 223

which tested concrete columns in different sizes, shapes (i.e. rectangular and circular shapes) and 224

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concrete materials (i.e. conventional and high-strength concrete). Shape effects are caused by 225

stress concentrations occurring at straight edges (Kotsovos, 1983), which translates into lower 226

strengths being observed in cube and prismatic samples when compared to cylindrical ones, but 227

higher pre-peak stiffness. Boundary effects are due to the restraints that loading plates impose 228

onto the specimen. Frictional restraint prevents the lateral expansion of the specimen at the 229

coupon-plate interfaces, effectively “confining” the specimen at the boundaries. This provides 230

additional strength. The boundary effect is more pronounced on shorter specimens, such as those 231

used in conventional cylinder tests. In specimens with higher height-to-width aspect ratios, the 232

confining effect of the plates is smaller and leads to a lower strength (Kotsovos, 1983). It is 233

noted that the tests showed that both shape and boundary effects influenced the ECC samples 234

more than the ones made with concrete. 235

4.2 Confined Columns 236

The general behaviour of the confined ECC columns showed four main stages: (1) an initial, 237

ascending, quasi-linear stage; (2) the attainment of peak compressive strength; (3) a gradual post-238

peak descending branch; and (4) a plateau-like region of residual stress that continued up to large 239

values of compressive strain. The compressive strengths for columns ECC-1%, ECC-1.5% and 240

ECC-2% was found to be similar, measured as 70.2 MPa, 70.4 MPa, and 71.4 MPa, respectively. 241

A few microcracks formed on the specimens at the attainment of the maximum axial load (Figs. 242

14-16). After microcracking occurred, the cracks developed into larger cracks as the specimen 243

entered the post-peak stage. At the plateau-like stage of the stress-strain curve where cracks 244

began to widen, specimens ECC-1%, ECC-1.5%, and ECC-2% reached a plateau stage with 245

residual stresses of 35 MPa, 48 MPa, and 50 MPa respectively. It is noted that minor cracking 246

and/or crushing at the boundaries was observed before reaching the maximum load (Figs. 16-18) 247

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in some of the specimens. 248

Overall, one of the most significant results of this investigation was that the transverse steel 249

content does not influence the peak strength of confined specimens in a significant manner. The 250

implication is that the column specimens failed before the lateral expansion due to transverse 251

cracking activated the confining ties. This could be due to several reasons. First, pouring the 252

columns horizontally (Fig. 6) and vibrating the mixture might have created a weaker upper side – 253

when the column was tilted up, the weaker side may have precipitated a premature failure. 254

Fig. 14 shows that the right side of column ECC-1% visibly failed before the left side. Another 255

explanation could be related to the unique response of ECC to tensile stress – instead of 256

developing large, localized cracks like conventional concrete, ECC develops multiple micro-257

cracks in its matrix that are not wide enough to activate the tie reinforcement. Lower strains in 258

the hoop reinforcement in ECC columns compared to RC columns of the similar size and subject 259

to similar loading was observed by Cruz-Noguez (2010). It is possible, although it was not 260

measured during the experiments, that the amount of lateral expansion of ECC in the square 261

columns tested in this study was significantly lower than conventional concrete at peak load, 262

with the axial capacity of ECC degrading before the tie reinforcement is activated. The 263

implication of these findings is that passive reinforcement is not as effective in ECC as in 264

conventional reinforced concrete for the range of reinforcement used. This warrants further 265

research with different ECC mixtures and tests in columns with different geometries and 266

amounts of reinforcement. 267

5. ANALYSIS MODEL 268

There are different confinement models for concrete. The model by Mander et al. (1988) is 269

widely used in structural applications that utilize normal-strength concrete. For high-strength 270

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concrete, several models are available. Due to its simplicity, the model proposed by Bjerkeli et 271

al. (1990) model, based on that developed by Martinez et al. (1984), was selected in this study as 272

a candidate to develop a model to describe the confined behaviour in ECC square columns. This 273

model, illustrated in Fig. 19, has an ascending branch, a post-peak branch, and a residual stress 274

plateau that corresponds well with the experimental observations from the ECC column tests. 275

The expressions that describe the stress-strain relationship for confined ECC are presented in 276

Eqs. (1-14). Note that the equations contain six adjustment constants, C1, C2, C3, C4, C5, and C6. 277

Using statistical regression analysis, Bjerkeli et al. (1990) determined values for these constants 278

that led to a best-fit adjustment between their experimental results and the confinement model. 279

A similar strategy was followed in this study to determine new values for the six coefficients that 280

are valid for ECC confined specimens. Table 3 shows a comparison between the coefficient 281

values proposed by Bjerkeli et al. (1990) for high-strength concrete and those obtained for the 282

ECC material. The parameter that exhibited a major change was C1 in Eq. 1, which accounts for 283

the increase in compressive strength due to the presence of transverse reinforcement. In high-284

strength concrete, Bjerkeli et al. (1990) found C1 to be 4.0. However, the experimental tests 285

conducted in this study found an almost negligible increment in compressive strength due to 286

stirrup reinforcement – as a result, the corresponding factor C1 was found to be 0.156. 287

The ascending branch of the confinement model, valid for ,c eccε ε≤ , is given by 288

2

0 , ,

1 2

ecc

ecc

c ecc c ecc

E

EE

σε ε

ε ε

=

+ − +

(1)

289 The post-peak branch, valid for ,c ecc residualε ε ε< < , is given by 290

( ), ,c ecc c eccf Zσ ε ε= − − (2)

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291 And the residual stress branch, valid for residualε ε≥ , is given by 292

1 ,0.7so sh syres c ecc

p ecc

d A fC f

s Aσ σ= = ≤ (3)

293 Where 294

,

,

c ecco

c ecc

fE

e= (4)

,

0.85 ,

0.15 c ecc

c ecc

fZ

ε ε=

− (5)

295 In Eq. 6, Eecc is the secant Young’s modulus of ECC. Based on data from the ECC cylinder tests 296

described in section 2.2, a best-fit equation that related Eecc with the peak compressive strength 297

of ECC, ,c eccf ′ , was determined (R2=0.92): 298

( )0.5,1900ecc c eccE f ′= (6)

299

The maximum confinement compressive strength, ,c eccf is defined as 300

, 2c ecc ecc g rf f C K fγ ′= + (7)

301

In Eq. (7), Kg is a section geometry factor and fr is a term for the confining reinforcement 302

pressure, defined later in Eqs. (12-14). The parameter γ is a modifier that allows the use of the 303

cylinder compressive strength in Eq. (7) instead of the cube compressive strength, which was a 304

required input in the original equation proposed by Bjerkeli et al. (1990). The term γ was added 305

to Eq. (7) since it was assumed that the unconfined compressive strength of ECC, eccf ′ would be 306

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more readily available to the analyst than the cube strength. The modified expression for the 307

compressive strength ,c eccf is shown in Eq. 7. The regressed value for γ was determined as 0.93, 308

which correlates well with earlier observations by Kotsovos (1983), who reported that cylinder 309

strength is slightly lower than cube strength, a phenomenon attributed to boundary and size 310

effects. 311

The strain at which the peak confined strength of ECC is achieved, ,c eccε , is given by 312

, 3 4r

c eccecc

fC Cf

ε

= + ′ (8)

313 While the strain parameters are defined by: 314

( )0.85 0.85 5 1

r eccg

f fK C

Fε ε

′ ′′= +

− (9)

2

70.85 6 1

ecc

CCf

ε

′ = + ′ (10)

( )0.25

1

1 1 r g

Ff K

= +

(11)

315 The confining pressure fr is defined in the usual way as: 316

sh syr

p

A ff

h s=

′ (12)

where Ash is the total effective area of ties and supplementary confining reinforcement, fsy is the 317

yield stress of confining reinforcement, h′ is the outer dimension of the hoop or stirrup 318

confining the section, and sp is the center-to-center distance between the confining hoop/ties. 319

The parameter Kg is the section geometry factor, defined by the larger value of Kg1 and Kg2, 320

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which represent the compression arches between the transverse confinement reinforcement and 321

laterally supported longitudinal reinforcement, respectively. 322

1 1 pg

so

sK

d= − (13)

Where dso is the shorter outer diameter of the confining hoop/ties. 323

2

2 15.5g

ecc

nCKA

= −′

(14)

Where n is the number of laterally supported longitudinal bars, C is the distance between 324

laterally supported longitudinal bars, and eccA′ is the gross area of the section measured to the 325

center line of the peripheral hoop. 326

The performance of the confinement model once the constants C1, C2, C3, C4, C5, and C6 from 327

Table 3 are substituted into Eq. (3) and Eqs. (7-10) is shown in Fig. 20. It is seen that the model 328

can predict the peak strength with satisfactory accuracy, including the initial elastic response. 329

The prediction of the residual strength is reasonable. 330

An important limitation of the model is that there was only one type of ECC mixture was used in 331

the experimental tests described in this study. As a result, the proposed model is only valid for 332

PVA-M45 ECC with a strength of about 74 MPa, made with the same types of sand, fly ash, 333

superplasticizer, and PVA fibres as in this study. It is recommended to investigate different 334

types of ECC mixes, in specimens with different aspect ratios and geometries, to further validate 335

the model presented above. 336

6. SUMMARY AND CONCLUSIONS 337

Sixteen 100 mm x 100 mm x 300 mm ECC square columns, which consisted of one set of 338

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unconfined ECC and three sets of confined ECC with 1%, 1.5%, and 2% steel were tested under 339

monotonic axial compressive load. A set of unconfined concrete columns was also tested as 340

control specimens. A test set-up was designed to investigate the behaviour of confined ECC 341

columns and the stress-strain response of rectangularly confined ECC in square columns was 342

studied. An empirical stress-strain model for rectangularly confined high-strength ECC was 343

developed with the test results from the small-scale ECC square columns. The conclusions below 344

highlight the findings obtained from this research: 345

1. The general behaviour of unconfined ECC columns and unconfined concrete columns 346

presented size effect and boundary effects. In comparison to the unconfined concrete columns, 347

unconfined ECC columns showed a gradual degradation instead of the sudden brittle failure like 348

unconfined concrete columns. 349

2. The general behaviour of confined ECC columns (ECC-1%, ECC-1.5%, ECC-2%) showed 350

four main stages: (1) an initial, ascending, quasi-linear stage; (2) the attainment of peak 351

compressive strength; (3) a gradual post-peak descending branch; and (4) a plateau-like region of 352

residual stress. The results showed that there is no significant increase in peak strength due to 353

transverse reinforcement. The only strength gain due to the use of more stirrups was observed as 354

a more stable post-peak behaviour in terms of residual stresses. 355

3. A few microcracks was observed on the all specimens at the maximum axial load. After 356

microcracking occurred, the cracks developed into larger cracks as the specimen entered the 357

post-peak stage. 358

4. An empirical stress-strain model of rectangularly confined ECC in square column was 359

proposed based on an existing confinement model for high-strength concrete. The maximum 360

compressive strength equation from Bjerkeli et al (1990) model was originally based on the 361

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unconfined compressive strength from concrete cubes. It was modified to account for the 362

unconfined compressive strength from conventional cylinder tests. 363

5. The proposed model showed reasonable correspondence with the test results and was able 364

to capture the main features of confined ECC rectangular columns with square stirrups. 365

ACKNOWLEDGEMENTS 366

This study was partly funded by the Natural Sciences and Engineering Research Council of 367

Canada (NSERC) and by LafargeHolcim through an Engage Grant. The authors thank 368

LafargeHolcim for the help in donating and casting concrete for the experiment, Kuraray Co., for 369

donating a portion of the PVA fibres, and BASF for donating the high-range water-reducing 370

admixture for this research. 371

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425

Table 1. Optimized ECC-M45 mix design 426

427 Table 2. Summary of axial compressive test results 428

Specimen ID

Modulus of elasticity (E)

Peak compressive stress (MPa)

Strain at peak stress

Residual Stress

ECC-M45 UofA Cement Fly Ash Sand Water SP

(Superplasticizer) Fibre

Weight Ratio 1 1.2 0.8 0.6±0.03 0.015 2% Vol kg/m3 556 667 445 311 8.3 26

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Concrete-0% 34476 67.56 0.002112 - ECC-0% 28201 69.26 0.002902 11 ECC-1.0% 25374 70.17 0.003352 35 ECC-1.5% 25211 70.41 0.004002 48 ECC-2.0% 25675 71.38 0.004752 50

429 Table 3. Coefficients for ECC confinement model 430

Coefficient Bjerkeli et al. 1990

Confined ECC

𝐶𝐶1 4.87 6.34 𝐶𝐶2 4.0 0.156 𝐶𝐶3 0.0025 0.0025 𝐶𝐶4 0.05 0.0217 𝐶𝐶5 0.05 0.015 𝐶𝐶6 0.0025 0.0025 𝐶𝐶7 17.07 16.92

431 432

433 Fig. 1 Averaged uniaxial compressive stress-strain graph of ECC 434

435 Fig. 2 Averaged uniaxial tensile stress-strain graph of ECC 436

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437 Fig. 3 Tensile cracking of ECC specimen 438

439 Fig. 4 Cross-sectional details of specimen 440

441 Fig. 5 Cross-sectional details of specimens with 0%, 1%, 1.5%, and 2% transverse steel content 442

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443 Fig. 6 Specimen fabrication 444

445 Fig. 7 Overall 2-D view of instrumentation of specimen 446

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447 Fig. 8 Overall 3-D view of instrumentation of specimen 448

449 Fig. 9 General view of specimen testing in MTS 815 machine 450

451

Fig. 10 Load-displacement response for columns with 0% transverse steel ratio 452

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453 Fig. 11 Load-displacement response for ECC square columns with 1.0%, 1.5%, and 2.0% transverse steel ratio 454

455 Fig. 12 Averaged stress-strain response for 0% confinement concrete square column (Concrete-0%) 456

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457 Fig. 13 Averaged stress-strain response for 0% confinement ECC square column (ECC-0%) 458

459 Fig. 14 Averaged stress-strain response for 1% confinement ECC square column (ECC-1%) 460

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461 Fig. 15 Averaged stress-strain response for 1.5% confinement ECC square column (ECC-1.5%) 462

463 Fig. 16 Averaged stress-strain response for 2% confinement ECC square column (ECC-2%) 464

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465 Fig. 17 Averaged stress-strain response for all square column 466

467 Fig. 18 Stress-strain graph of cylinder and unconfined square columns in (a) concrete and (b) ECC 468

469 Fig. 19 Proposed confinement model for Rectangular, Confined High-Strength ECC columns 470

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471

Fig. 20 Comparison between experimental results and proposed confinement model 472