4th November 2005

Towards Unified Bond Modelling for the Structural Behaviour of GFRP-RC

Kypros PilakoutasHarsha Sooriyaararachchi

Maurizio Guadagnini

Centre for Cement and ConcreteDepartment of Civil and Structural Engineering, University of Sheffield,

Sheffield, United Kingdom

4th November 2005

GFRP bars

Use of GFRP for bridge deck construction(Franklin county bridge Virginia)

Stiffness of GFRP compared to Steel

0

200

400

600

800

0 5000 10000 15000

Strain (micro strain)

Str

es

s (

MP

a)

GFRP Bare bar

Steel bare bar

GFRP-RC in Construction

4th November 2005

Outline

• Hierarchy of bond modelling

• Macro level Modelling

• Meso level modelling

• Average bond stress slip relation

• Formulation of bond modelling using strain distribution

• Local bond stress-slip-strain relation

s

4th November 2005

Steel reinforcement FRP reinforcement

Hierarchy of bond Modelling

Macro-level modelling

4th November 2005

Steel reinforcement FRP reinforcement

Macro-level modelling

Hierarchy of bond Modelling

Meso-level modelling

4th November 2005

Steel reinforcement FRP reinforcement

Macro-level modelling

Meso-level modelling

Micro-level modelling

Hierarchy of bond Modelling

4th November 2005

Tension stiffening effect Average Strain

Av

era

ge

Str

es

s

Bare bar response

RC response

Tension stiffening of concrete is defined as: the ability of concrete to carry tension between cracks and provide

extra stiffness for RC in tension.

Macro Level Bond Modelling

4th November 2005

Test results bar stress Vs overall strain Average stress strain behaviour of concrete

0

200

400

600

800

0 5000 10000 15000 20000

Strain (Microstrain)

Str

es

s (

MP

a)

C90/13/150

C50/13/150

13mm Bar

0

0.5

1

1.5

2

2.5

3

3.5

0 5000 10000 15000 20000

Strain (Microstrian)

Str

es

s (

MP

a)

C90/13/150

C50/13/150

Strain Softening Behaviour Concrete

4th November 2005

Reinforced concrete in tension

Typical Test Results

c

f N

N

Strain of the composite specimen at

Strain of the bar at crack

Average Strain

Ave

rag

e S

tres

s

N

f

c

Sta

ge I

Pre

Cra

ckin

g

Sta

ge II

Cra

ck P

rop

agat

ion

Sta

ge III

Po

st C

rack

ing

Response of composite section

Bare bar response

Tension Stiffening Behaviour

4th November 2005

1st crack2nd 3rd

Internally strain gauged bar

0

2000

4000

6000Just before first crack (37 kN)

0

2000

4000

After second crack (43 kN)

0 200 400 600 800 1000 12000

2000

4000

Length along the bar (mm)

Ba

r s

tra

in

( )

After third crack (53 kN)

Strain Distribution while Cracking

Stage I

Stage II

4th November 2005

0 200 400 600 800 1000 12000

1000

2000

3000

4000

5000

6000

7000

510152025303641465156606670 kN

Length along the specimen (mm)

Str

ain

( )

0 200 400 600 800 1000 12000

0.1

0.2

0.3

0.4

0.5

0.6

5152025303641465156606670 kN

Length along the specimen (mm)

Sli

p (

mm

)

Post cracking slip and strain

Stage III

4th November 2005

Typical strain and bond stress distribution between cracks

650 700 750 800 850 900 950 10000

5000

10000

15000

20000

Distance between cracks # 1 & # 2 mm

Ba

rs s

tra

in

( )

35 kN

55 kN75 kN95 kN115 kN135 kN155 kN

35.8 kN

650 700 750 800 850 900 950 1000-15

-10

-5

0

5

10

15

Distance between cracks # 1 & # 2 mm

Bo

nd

str

ess

(MP

a)

55 kN

155 kN

Strain and bond between cracks

4th November 2005

Meso Level Bond Modelling

Direct tension test

Pullout test

Magnified images showing bond failure

4th November 2005

Average Bond Stress Vs. Slip

(a) (d) (b) (c)

0

1

2

3

4

5

6

7

8

9

10

11

12

0 0.5 1 1.5 2 2.5 3 3.5

Slip (mm)

Bo

nd

str

es

s (

MP

a)

19-45-5D - Loaded end

19-45-5D - Free end

Comparison of average bond stress slip behaviour for the two test in almost identical circumstances

0 0.5 1 1.5 2 2.5

0

1

2

3

4

5

6

7

8

9

10

11

12

a (0~150)

(b) (175~325)(d) (900~1050)

(d) (750~900)

(d) (750~900) (d) (750~900)

(c) (750~900)(a) (0~175)

Slip (mm)

Bo

nd

Str

ess

(N/m

m2 )

50%

4th November 2005

Stress Conditions During Testing

Direct tension test

Pull out test

4th November 2005

Bond Stress based on strain distribution

dxd

4dE fff

x

0 f dxs 115.2 kN

135.6 kN

155.7 kN

dxd

4dE fff

dxd f

x

0 f dxs

Str

ain

Distance between cracks

2262

2473

2677

2874

3079

3267

dxd

4dE fff

dxd f

free

x

0 f sdxs

Str

ain

Distance along the embedment length

4th November 2005

Local Bond Stress Slip Relationship

0 50 100 1500

5000

10000

15000

Distance from centre of the crack (mm)

Str

ian

( )

0 0.5 1 1.5 2

0

2

4

6

8

10

12

0

25

50

75100

125

150

175

Slip (mm)

Bo

nd

str

ess

(N

/mm2 )

0 50 100 1500

5000

10000

15000

Distance from centre of the crack (mm)

Str

ain

( )

0 0.5 1 1.5

0

2

4

6

8

10

12

12.5

37.5

62.587.5

112.5

137.5

Slip (mm)

Bo

nd

str

ess

(N

/mm

2 )

0 25 50 75 100

150

175

125

0 25 50 75 100

150

125

4th November 2005

0 50 100 1500

5000

10000

15000

Distance from centre of the crack (mm)

Str

ain

( )

dxd

4dE fff

dxd f

x

0 f dxs

x

f

0 0.1 0.2 0.3 0.4 0.5 0.60

2

4

6

8

10

*8474

940610464

1130312317

13241 14159

Different Slip at (mm)D

iffe

ren

t b

on

d s

tre

ss (

N/m

m2)

*f

f

s

4th November 2005

0 0.5 1 1.50

2

4

6

8

10

352

1196

2071

310039144854 5740

665375858474

940610464

1130312317

1324114159

Slip at different strain levels (mm)

Bo

nd

str

ess

(N/m

m2 )

Bond stresses slip at different strain

4th November 2005

0 0.5 1 1.50

1

2

3

4

5

6

7

8

9

10

1196

3100 48546653

847410464

12317

14159

Slip at different strain levels (mm)

Bo

nd

str

es

s (

N/m

m2)

00

e14 25053

.

)()( ..max

S.

1

251.

cal

icalS

Scal= Slip at peak bond stress at calibrated strain

cal = Referred strain for calibration

s Relation for BOND

4th November 2005

0 0.5 1 1.5 2

0

2

4

6

8

10

0

25

25

50

50

7575

100

100

125125

150150

175

175

Local slip (mm)

Lo

cal

bo

nd

str

ess

(N/m

m2 )

Comparison of Results

4th November 2005

Local Bond Stresses in Pull-out 5D

0 20 40 60 80 100

0

1

2

3

4

length (mm)B

on

d s

tre

ss

(

N/m

m2)

0 20 40 60 80 100

0

200

400

600

800

Length (mm)

Str

ain

(

)

0 0.005 0.01 0.015 0.020

0.5

1

1.5

2

2.5

3

91mm

Slip at various section mm

Bo

nd

str

ess

(N

/mm

2)

19mm

38 mm

57 mm

76 mm

95.5mm

0 0.05 0.1 0.15 0.20

2

4

6

8

10

Slip at various sections mmB

on

d s

tre

ss

(N/m

m2)

19 mm

38 mm

57 mm

76 mm

95 mm

0 20 40 60 80 100

0

2

4

6

8

10

Length(mm)

Bo

nd

str

es

s

(N

/mm

2)

0 20 40 60 80 100

0

1000

2000

3000

Length (mm)

Str

ain

(

)

Grade 90

Grade 45

4th November 2005

Local Bond Stresses in Pull-out 10D

0 50 100 150 2000

2

4

6

8

10

12

length(mm)

Bo

nd

str

es

s

(N

/mm

2)

0 0.05 0.1 0.15 0.20

2

4

6

8

10

12

0mm

Slip at various section (mm)B

on

d s

tre

ss

(N/m

m2)

57mm76mm

96 mm

115 mm

134mm

153 mm

172mm

191mm

0 50 100 150 200

0

1000

2000

3000

4000

Length (mm)

Str

ain

(

)

0 50 100 150 2000

1

2

3

4

Length(mm)

Bo

nd

str

es

s

(N

/mm

2)

0 0.02 0.04 0.06 0.080

1

2

3

4

0mm

Slip at various section (mm)

Bo

nd

str

es

s

(N

/mm

2)

38.2mm57.3mm

95mm115 mm

134 mm

153 mm172mm

191mm

0 50 100 150 200

0

500

1000

1500

Length (mm)

Str

ain

(

)

Grade 90

Grade 45

4th November 2005

Comparisons of results

Local bond behaviour in pull out test 19/45/10D

0 0.02 0.04 0.06 0.080

0.5

1

1.5

2

2.5

3

3.5

4

Local slip mm

Bo

nd

str

ess

(N/m

m2 )

19.1 mm19 mm

57 mm57 mm

96 mm

96 mm

115 mm115 mm

134 mm

134 mm

153 mm

153 mm

171 mm171mm

191 mm

191mm

4th November 2005

Conclusions

• -s- approach proposed

• Is Average bond stress slip relationship useful?

• Different levels of bond modelling

• More work to be done

• Bond stress profile changes with increasing load

• Testing conditions affect bond behaviour