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A new confinement model for FRCM confined concrete

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Abstract

Confined concrete by means of FRCM (Fabric Reinforced Cementitious Matrix), also known as TRM (Textile Reinforced Mortar), may exhibit alternative stress–strain behaviors, depending on different variables including the unconfined concrete strength, concrete cross-section, fibers type and number of layers. Specifically, increasing the confinement level, the experimental observed response changes from a softening to a hardening one, after an initial peak that coincides roughly to that of the unconfined strength. To consider the peculiar behavior of FRCM-confined concrete, a new analytical model is proposed in this work. The formulation allows to calculate both the first and ultimate peak strength values, being more adherent to the real observed experimental behavior of FRCM-confined concrete members. The model is calibrated on a set of experimental data obtained by the same authors, and then its accuracy is validated on a different, larger dataset. Model performance indicators are compared to those calculated for other existing formulations, demonstrating the goodness of the new proposal.

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Abbreviations

α :

Equation coefficient

ε c0 :

Unconfined axial strain at peak stress

ε cc ,1 :

Confined axial strain at first peak

ε ccu :

Confined axial strain at ultimate strength

ε f :

Strain capacity of fiber material

ε fu , rid :

Reduced strain capacity of fiber material

γ m :

Partial safety factor for material strength

η A :

Environmental conversion factor

ρ f :

Fiber reinforcement ratio

ρ mat :

Matrix reinforcement ratio

A c :

Concrete area

A e :

Effectively confined concrete area

b :

Short side of rectangular sections

D :

Diameter of circular sections or diagonal of rectangular ones

E f :

Fiber elastic modulus

f c0 :

Unconfined concrete strength

f cc :

Confined concrete strength

f cc,1 :

Confined concrete strength at first peak

f ccu :

Ultimate confined concrete strength

f cc,exp :

Experimental confined compressive strength

f cc,theo :

Predicted confined compressive strength

f l :

Confinement pressure

f l, eff :

Effective confinement pressure

f c,mat :

Matrix compressive strength

f f,mat :

Matrix flexural strength

h :

Long side of rectangular sections

k :

Equation coefficient

k a :

Shape factor (ACI549.4R)

k e :

Effectiveness coefficient

k f :

Fiber material effectiveness coefficient

k h :

Cross-section shape effectiveness coefficient

k m :

Matrix effectiveness coefficient (present paper)

k mat :

Matrix coefficient (CNR-DT 215)

k t :

Fabric thickness coefficient

K f :

Confinement jacket stiffness

K f, eff :

Effective confinement jacket stiffness

n f :

Number of layers

r c :

Corner radius of rounded edges for rectangular and square cross-sections

R 2 :

Coefficient of determination

RMSE:

Root mean square error

std:

Standard deviation

t mat :

Matrix layer thickness

t f :

Equivalent fabric thickness

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Author information

Authors and Affiliations

  1. Laboratoire de Mécanique and Matériaux du Génie Civil – L2MGC, CY Cergy Paris Université, 5 Mail Gay Lussac, 95000, Neuville-sur-Oise, France

    Klajdi Toska

  2. CY Institute for Advanced Studies, 1 Rue Descartes, 95000, Neuville-sur-Oise, France

    Klajdi Toska

  3. Department of Civil, Environmental and Architectural Engineering, University of Padova, Via Francesco Marzolo 9, Padua, Italy

    Flora Faleschini

Authors
  1. Klajdi Toska
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  2. Flora Faleschini
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Contributions

KT: conceptualization, methodology, data curation, investigation, formal analysis, visualization, writing. FF: conceptualization, methodology, investigation, writing, supervision, project administration.

Corresponding author

Correspondence to Klajdi Toska.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Appendix: Collected dataset of FRCM-confined concrete specimens

Appendix: Collected dataset of FRCM-confined concrete specimens

References

Specimen

D (mm)

b (mm)

h (mm)

rc (mm)

tmat (mm)

fc,mat (MPa)

nf (–)

Fiber (–)

tf (mm)

Ef (GPa)

ef (–)

fc0 (MPa)

fcc (MPa)

Colajanni et al. [28]

CF2M

200

–

–

–

3

31

2

C

0.047

240

0.02

16.44

20.71

 

CF3M

200

–

–

–

3

31

3

C

0.047

240

0.02

16.44

23.84

 

S15F2M

–

200

200

15

3

31

2

C

0.047

240

0.02

16.48

19.78

 

S15F4M

–

200

200

15

3

31

4

C

0.047

240

0.02

16.48

23.24

 

S30F2M

–

200

200

30

3

31

2

C

0.047

240

0.02

16.48

19.12

 

S30F4M

–

200

200

30

3

31

4

C

0.047

240

0.02

16.48

23.07

 

R15F2M

–

200

400

15

3

31

2

C

0.047

240

0.02

14.99

19.34

 

R15F4M

–

200

400

15

3

31

4

C

0.047

240

0.02

14.99

20.84

 

R30F2M

–

200

400

30

3

31

2

C

0.047

240

0.02

14.99

18.89

 

R30F4M

–

200

400

30

3

31

4

C

0.047

240

0.02

14.99

21.74

Bournas et al. [8]

U_M4

–

200

200

25

2

22

4

C

0.095

225

0.017

15.28

26.60

 

U_M6

–

200

200

25

2

22

6

C

0.095

225

0.017

15.28

31.55

Colajanni et al. [10]

CA_2L

154

–

–

–

3.5

16

2

PBO

0.046

206

0.015

24.20

31.23

 

CA_3L

154

–

–

–

3.5

16

3

PBO

0.046

206

0.015

24.20

36.57

 

CB_2L

200

–

–

–

3.5

16

2

PBO

0.046

206

0.015

24.40

31.17

 

CB_3L

200

–

–

–

3.5

16

3

PBO

0.046

206

0.015

24.40

33.55

 

SB_2L

–

200

200

20

3.5

16

2

PBO

0.046

206

0.015

25.50

28.27

 

SB_3L

–

200

200

20

3.5

16

3

PBO

0.046

206

0.015

25.50

31.63

Donnini et al. [29]

M15_CF

140

–

–

–

4

17

2

C

0.048

203

0.015

11.40

13.65

 

M45_PBO

140

–

–

–

4

50

2

PBO

0.046

206

0.025

11.40

17.71

 

M45_CF

140

–

–

–

4

50

2

C

0.048

203

0.015

11.40

13.66

Thermou et al. [30]

A3 × 2h1

150

–

–

–

5

22

1

S

0.562

230

0.021

15.12

22.26

 

A3 × 2m1

150

–

–

–

3.5

22

1

S

0.124

230

0.021

15.12

25.66

 

A3 × 2l1

150

–

–

–

3.5

22

1

S

0.062

230

0.021

15.12

22.80

 

A12 × h1

150

–

–

–

5

22

1

S

0.562

230

0.019

15.12

25.30

 

A12 × m1

150

–

–

–

3.5

22

1

S

0.124

230

0.019

15.12

26.64

 

A12 × l1

150

–

–

–

3.5

22

1

S

0.062

230

0.019

15.12

22.55

 

B3 × 2m2

150

–

–

–

3.5

22

1

S

0.124

230

0.021

26.20

36.07

 

B3 × 2l2

150

–

–

–

3.5

22

1

S

0.062

230

0.021

26.20

35.93

 

B12 × m2

150

–

–

–

3.5

22

1

S

0.124

230

0.019

26.20

40.42

 

B12 × l2

150

–

–

–

3.5

22

1

S

0.062

230

0.019

26.20

36.21

Kahangi et al. [31]

SQ-I-2-CE-LD-1L

–

150

150

25

3.5

50

1

S

0.084

190

0.02

19.88

25.23

 

SQ-I-2-CE-LD-2L

–

150

150

25

3.5

50

2

S

0.084

190

0.02

19.88

26.80

 

SQ-I-2-CE-MD-1L

–

150

150

25

3.5

50

1

S

0.169

190

0.02

19.88

25.38

 

SQ-II-6-CE-LD-1L

–

250

250

25

3.5

50

1

S

0.084

190

0.02

18.15

19.18

 

SQ-II-6-CE-LD-2L

–

250

250

25

3.5

50

2

S

0.084

190

0.02

18.15

21.28

 

SQ-II-3-CE-MD-1L

–

250

250

25

3.5

50

1

S

0.169

190

0.02

18.15

22.05

 

C-III-8-CE-LD-1L

150

–

–

–

3.5

50

1

S

0.084

190

0.02

20.47

25.40

 

C-III-8-CE-LD-2L

150

–

–

–

3.5

50

2

S

0.084

190

0.02

20.47

30.40

 

C-III-8-CE-MD-1L

150

–

–

–

3.5

50

1

S

0.169

190

0.02

20.47

26.87

Triantafillou et al. [11]

A_MI2

150

–

–

–

2

9

2

C

0.047

225

0.015

15.24

20.77

 

A_MII2

150

–

–

–

2

31

2

C

0.047

225

0.015

15.24

23.88

 

A_MI3

150

–

–

–

2

9

3

C

0.047

225

0.015

15.24

26.50

 

A_MII3

150

–

–

–

2

31

3

C

0.047

225

0.015

15.24

27.00

 

B_MII2

150

–

–

–

2

31

2

C

0.047

225

0.015

21.81

27.36

 

B_MII3

150

–

–

–

2

31

3

C

0.047

225

0.015

21.81

32.44

 

C_MII2

–

250

250

15

2

31

2

C

0.047

225

0.015

14.25

20.00

 

C_MII4

–

250

250

15

2

31

4

C

0.047

225

0.015

14.25

21.56

Garcìa et al. [32]

M1

150

–

–

–

5

32

1

B

0.043

52

0.022

21.80

26.20

 

M2

150

–

–

–

5

32

2

B

0.043

52

0.022

21.80

27.21

 

C1

150

–

–

–

5

22

1

B

0.043

52

0.022

21.80

28.67

 

C2

150

–

–

–

5

22

2

B

0.043

52

0.022

21.80

28.78

Di Ludovico et al. [26]

S3

150

–

–

–

4

30

2

G

0.043

72

0.02

15.52

22.35

 

S13

150

–

–

–

4

30

2

G

0.043

72

0.02

17.83

23.00

 

S10–S11–S12

150

–

–

–

4

30

1

G

0.043

72

0.02

17.83

20.03

 

S4

150

–

–

–

4

30

1

B

0.046

91

0.02

15.52

22.50

 

S14–S15

150

–

–

–

4

30

1

B

0.046

91

0.02

17.83

25.32

 

S5

150

–

–

–

4

30

2

B

0.046

91

0.02

15.52

22.81

 

S16–S17

150

–

–

–

4

30

2

B

0.046

91

0.02

17.83

28.35

 

S6

150

–

–

–

4

30

1

B

0.046

91

0.02

15.52

19.71

 

S18–S19

150

–

–

–

4

30

1

B

0.046

91

0.02

17.83

22.91

 

S

150

–

–

–

4

30

2

B

0.046

91

0.02

15.52

22.50

 

S20–S21

150

–

–

–

4

30

2

B

0.046

91

0.02

17.83

26.75

Basalo et al. [12]

LDG-A

152

–

–

–

4

31

2

G

0.21

72

0.045

20.40

26.85

 

LDG-H

152

–

–

–

4

31

2

G

0.21

72

0.045

20.40

30.00

 

HDG-A

152

–

–

–

4

31

2

G

0.366

72

0.045

20.40

24.50

 

HDG-H

152

–

–

–

4

31

2

G

0.366

72

0.045

20.40

30.00

 

BGP-A

152

–

–

–

4

31

2

B

0.046

74

0.047

20.40

28.80

 

BGP-H

152

–

–

–

4

31

2

B

0.046

74

0.047

20.40

31.80

 

1B

152

–

–

–

4

31

1

B

0.246

77

0.044

21.70

26.30

 

2B

152

–

–

–

4

31

2

B

0.246

77

0.044

21.70

35.52

 

2U

152

–

–

–

4

31

2

B

0.246

77

0.044

21.70

33.93

 

4B

152

–

–

–

4

31

4

B

0.246

77

0.044

21.70

47.90

Trapko et al. [33]

20M1

113

–

–

–

4

29

1

PBO

0.0455

206

0.0215

22.62

32.57

 

20M2

113

–

–

–

4

29

2

PBO

0.0455

206

0.0215

22.62

42.72

 

20M3

113

–

–

–

4

29

3

PBO

0.0455

206

0.0215

22.62

56.94

Colajanni et al. [34]

CF3M

200

–

–

–

3

38

3

C

0.047

240

0.02

15.10

21.77

 

S15F4M

–

200

200

15

3

38

4

C

0.047

240

0.02

16.30

22.50

 

S30F4M

–

200

200

30

3

38

4

C

0.047

240

0.02

16.30

22.00

 

R15F2M

–

200

400

15

3

38

2

C

0.047

240

0.02

16.40

20.60

 

R30F2M

–

200

400

30

3

38

2

C

0.047

240

0.02

16.40

20.10

Ombres et al. [35]

CRP1-I

150

–

–

–

3

30.4

1

PBO

0.0455

270

0.02

15.40

24.69

 

CRP2-I

150

–

–

–

3

30.4

2

PBO

0.0455

270

0.02

15.40

35.00

 

CRP3-I

150

–

–

–

3

30.4

3

PBO

0.0455

270

0.02

15.40

41.45

 

CRP4-I

150

–

–

–

3

30.4

4

PBO

0.0455

270

0.02

15.40

49.24

 

CRP1-II

150

–

–

–

3

30.4

1

PBO

0.0455

270

0.02

29.26

43.55

 

CRP2-II

150

–

–

–

3

30.4

2

PBO

0.0455

270

0.02

29.26

47.00

 

CRP3-II

150

–

–

–

3

30.4

3

PBO

0.0455

270

0.02

29.26

56.10

 

CRP4-II

150

–

–

–

3

30.4

4

PBO

0.0455

270

0.02

29.26

56.23

Ortlepp et al. [36]

B1

–

150

150

0

3

67

1

G

0.06

74.45

0.02

29.00

33.00

 

B2

–

150

150

15

3

67

1

G

0.06

74.45

0.02

27.00

34.00

 

B3

–

150

150

30

3

67

1

G

0.06

74.45

0.02

27.00

33.00

 

B4

–

150

150

45

3

67

1

G

0.06

74.45

0.02

27.00

32.00

 

B5

–

150

150

60

3

67

1

G

0.06

74.45

0.02

27.00

35.00

 

B6

150

–

–

–

3

67

1

G

0.06

74.45

0.02

26.00

35.00

 

B7

–

100

100

30

3

67

1

G

0.06

74.45

0.02

27.00

35.00

 

B8

–

300

300

30

3

67

1

G

0.06

74.45

0.02

27.00

40.00

 

C1

–

150

150

0

3

67

1

C(imp)

0.0617

223

0.0167

29.00

33.00

 

C2

–

150

150

15

3

67

1

C(imp)

0.0617

223

0.0167

27.00

34.00

 

C3

–

150

150

30

3

67

1

C(imp)

0.0617

223

0.0167

27.00

35.00

 

C4

–

150

150

45

3

67

1

C(imp)

0.0617

223

0.0167

27.00

36.00

 

C5

–

150

150

60

3

67

1

C(imp)

0.0617

223

0.0167

27.00

37.00

 

C6

150

–

–

–

3

67

1

C(imp)

0.0617

223

0.0167

26.00

39.00

 

C7

–

100

100

30

3

67

1

C(imp)

0.0617

223

0.0167

27.00

37.00

 

C8

–

300

300

30

3

67

1

C(imp)

0.0617

223

0.0167

27.00

41.00

 

D1

–

150

150

0

3

67

1

C(imp)

0.18

204

0.0167

29.00

33.00

 

D2

–

150

150

15

3

67

1

C(imp)

0.18

204

0.0167

27.00

34.00

 

D3

–

150

150

30

3

67

1

C(imp)

0.18

204

0.0167

27.00

40.00

 

D4

–

150

150

45

3

67

1

C(imp)

0.18

204

0.0167

27.00

46.00

 

D5

–

150

150

60

3

67

1

C(imp)

0.18

204

0.0167

27.00

52.00

 

D6

150

–

–

–

3

67

1

C(imp)

0.18

204

0.0167

26.00

57.00

 

D7

–

100

100

30

3

67

1

C(imp)

0.18

204

0.0167

27.00

57.00

 

D8

–

300

300

30

3

67

1

C(imp)

0.18

204

0.0167

27.00

38.00

Ates et al. [37]

C-BG-1

150

–

–

–

12.5

43.5

1

B

0.115

32

0.05

9.00

15.40

 

C-BG-3

150

–

–

–

6.25

43.5

3

B

0.115

32

0.05

9.00

17.10

 

S-BG-1

–

200

200

30

12.5

43.5

1

B

0.115

32

0.05

8.50

13.50

 

S-BG-3

–

200

200

30

6.25

43.5

3

B

0.115

32

0.05

8.50

14.70

 

R1.5-BG-1

–

200

300

30

12.5

43.5

1

B

0.115

32

0.05

9.60

12.70

 

R1.5-BG-3

–

200

300

30

6.25

43.5

3

B

0.115

32

0.05

9.60

12.60

 

R2-BG-1

–

200

400

30

12.5

43.5

1

B

0.115

32

0.05

10.00

12.70

 

R2-BG-3

–

200

400

30

6.25

43.5

3

B

0.115

32

0.05

10.00

13.60

 

R3-BG-1

–

200

600

30

12.5

43.5

1

B

0.115

32

0.05

10.50

11.60

 

R3-BG-3

–

200

600

30

6.25

43.5

3

B

0.115

32

0.05

10.50

12.00

Thermou and Hajirasouliha [38]

A1#1

150

–

–

–

3

22

1

S

0.062

110

0.019

23.14

28.75

 

A2#1

150

–

–

–

3

22

1

S

0.062

120

0.021

23.14

32.30

 

A2#2

150

–

–

–

3

22

2

S

0.062

120

0.021

23.14

38.56

 

A3#1

150

–

–

–

3

4

1

S

0.062

110

0.019

23.14

29.80

 

A4#1

150

–

–

–

3

4

1

S

0.062

120

0.021

23.14

30.12

 

A4#2

150

–

–

–

3

4

2

S

0.062

120

0.021

23.14

34.02

 

A5#1

150

–

–

–

3

20

1

S

0.062

110

0.019

23.14

33.07

 

A6#1

150

–

–

–

3

20

1

S

0.062

120

0.021

23.14

32.15

 

A6#2

150

–

–

–

3

20

2

S

0.062

120

0.021

23.14

38.02

 

B1#1

150

–

–

–

3

22

1

S

0.062

110

0.019

16.62

30.45

 

B3#1

150

–

–

–

3

4

1

S

0.062

110

0.019

16.62

26.64

 

B5#1

150

–

–

–

3

20

1

S

0.062

110

0.019

16.62

28.32

 

C7#1

150

–

–

–

3

55

1

S

0.0845

190

0.015

20.73

31.36

 

C8#1

150

–

–

–

3

55

1

S

0.0845

190

0.015

20.73

34.10

 

C7#2

150

–

–

–

3

55

2

S

0.0845

190

0.015

20.73

40.24

 

C8#2

150

–

–

–

3

55

2

S

0.0845

190

0.015

20.73

44.63

 

D8#1

150

–

–

–

3

55

1

S

0.0845

190

0.015

18.27

27.68

 

D7#2

150

–

–

–

3

55

2

S

0.0845

190

0.015

18.27

36.44

 

D9#1

150

–

–

–

3

55

1

S

0.254

190

0.015

18.27

40.64

 

D10#2

150

–

–

–

3

55

2

S

0.254

190

0.015

18.27

53.53

 

E8#1

150

–

–

–

3

55

1

S

0.0845

190

0.015

29.98

40.51

 

E7#2

150

–

–

–

3

55

2

S

0.0845

190

0.015

29.98

45.21

 

E9#1

150

–

–

–

3

55

1

S

0.254

190

0.015

29.98

45.87

 

E10#2

150

–

–

–

3

55

2

S

0.254

190

0.015

29.98

64.19

Ombres [27]

CR-2

150

–

–

–

3

22.5

2

C

0.047

240

0.0142

19.52

26.88

 

CR-3

150

–

–

–

3

22.5

3

C

0.047

240

0.0142

19.52

31.42

 

CR-4

150

–

–

–

3

22.5

4

C

0.047

240

0.0142

19.52

35.08

 

R-Q11

–

150

150

30

3

22.5

1

C

0.047

240

0.0142

17.42

20.02

 

R-Q12

–

150

150

30

3

22.5

2

C

0.047

240

0.0142

17.42

21.46

 

R-Q24

–

150

150

30

3

22.5

3

C

0.047

240

0.0142

17.42

26.90

 

R-Q27

–

150

150

30

3

22.5

4

C

0.047

240

0.0142

17.42

29.73

 

R-T1-1-R1

–

150

300

30

3

22.5

1

C

0.047

240

0.0142

27.05

28.50

 

R-T1-1-R3

–

150

300

30

3

22.5

2

C

0.047

240

0.0142

27.05

30.53

 

R-T1-1-R5

–

150

300

30

3

22.5

3

C

0.047

240

0.0142

27.05

33.33

Gonzalez–Libreros et al. [25]

CCML1D0-1

150

–

–

–

4

25

1

C

0.047

240

0.018

36.80

40.10

 

CCML1D0-2

–

150

150

20

4

22.9

2

C

0.047

240

0.018

17.50

21.80

 

CCML1D0-3

–

150

150

20

4

22.9

2

G

0.05

70

0.03

17.50

18.70

Bhuvaneshwari et al. [40]

20M1

113

–

–

–

5

29

1

PBO

0.046

270

0.0215

22.60

32.57

 

20M2

113

–

–

–

5

29

2

PBO

0.046

270

0.0215

22.60

42.72

 

20M3

113

–

–

–

5

29

3

PBO

0.046

270

0.0215

22.60

56.94

Ombres [13]

C1-1-20

150

–

–

–

3

30.4

1

PBO

0.046

270

0.0215

33.83

35.80

 

CIII-1-20

150

–

–

–

3

30.4

1

PBO

0.046

270

0.0215

52.39

54.90

 

CIII-2-20

150

–

–

–

3

30.4

2

PBO

0.046

270

0.0215

52.39

51.45

 

CIII-3-20

150

–

–

–

3

30.4

3

PBO

0.046

270

0.0215

52.39

55.94

Toska and Faleschini [19]

C_C1_C1

150

–

–

–

3.5

21.56

1

C

0.047

240

0.018

13.79

14.85

C_C2_C1

150

–

–

–

3.5

21.56

2

C

0.047

240

0.018

13.87

15.91

C_C3_C

150

–

–

–

3.5

21.56

3

C

0.047

240

0.018

18.90

21.82

C_C4_C

150

–

–

–

3.5

21.56

4

C

0.047

240

0.018

18.90

25.54

C_G1_C

150

–

–

–

3.5

21.56

1

G

0.05

70

0.03

19.36

19.84

C_G2_C

150

–

–

–

3.5

21.56

2

G

0.05

70

0.03

19.36

20.77

S_C2_C

–

150

150

20

3.5

21.56

2

C

0.047

240

0.018

17.45

18.70

R1_C2_C

–

100

150

20

3.5

21.56

2

C

0.047

240

0.018

18.45

19.38

R2_C2_M

–

150

250

20

3.5

21.56

2

C

0.047

240

0.018

12.34

12.98

Toska and Faleschini [20]

C200_1D_C

150

–

–

–

3.5

25.00

2

C

0.047

240

0.018

22.45

26.72

C200_2D_C

150

–

–

–

3.5

22.47

2

C

0.061

240

0.018

22.45

26.50

C200_1D_D

150

–

–

–

3.5

22.63

2

C

0.047

240

0.018

22.45

27.46

C300_1D_C

150

–

–

–

3.5

21.29

2

C

0.047

240

0.018

22.45

26.26

C200_1FC_C

150

–

–

–

3.5

26.36

2

C

0.047

240

0.018

22.45

26.59

C200_1ER_C

150

–

–

–

3.5

25.87

2

C (imp)

0.047

240

0.018

22.45

28.38

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Toska, K., Faleschini, F. A new confinement model for FRCM confined concrete. Mater Struct 56, 98 (2023). https://doi.org/10.1617/s11527-023-02186-w

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