Seminar Fibre reinforced concrete and durability:

“Fiber Reinforced Concrete, Chalmers research “

- an exposé

From ”micro to macro” - or ”small-scale” to ”large-scale”

• Carlos Gil Berrocal. ”Corrosion of steel bars in fibre reinforced concrete: corrosion

mechanisms and structural performance”. PhD thesis, 2017.

• Jonas Ekström. “Concrete Structures Subjected to Blast Loading: Fracture due to dynamic

response”. Licentiate Thesis, 2015. (PhD defence November 10th)

• Natalie Williams Portal. “Usability of Textile Reinforced Concrete: Structural Performance,

Durability and Sustainability”. PhD thesis, 2015.

• David Fall. “Steel Fibres in Reinforced Concrete Structures of Complex Shapes: Structural

Behaviour and Design Perspectives”. PhD thesis, 2014.

• Ulrika Nyström. “Modelling of Concrete Structures Subjected to Blast and Fragment

Loading”. PhD thesis, 2013.

• Anette Jansson. “Effects of Steel Fibres on Cracking in Reinforced Concrete”. PhD thesis,

2011.

• Peter Harryson. “Industrial Bridge Engineering—Structural developments for more efficient

bridge construction”. PhD thesis, 2008.

• Ingemar Löfgren. “Fibre-reinforced Concrete for Industrial Construction—a fracture

mechanics approach to material testing and structural analysis”. PhD thesis, 2005.

Chalmers research (PhD & licentiate):

Fibre-reinforced concrete σ

fct

∆l

w

FRC

Concrete

w l

∆l

wc ≈ 0.3 mm wc = lf / 2 w ≈ 0.05 mm

Fibre

contribution Residual tensile

stress

Schematic description of the tensile behaviour

When fibre-reinforcement is added an additional material property have to be

taken into account, i.e. the σσσσ-w relationship, or the “fibre bridging” or the

“residual tensile strength”.

Material testing approch

The approach is based on three steps:

1) Material testing (fracture mechanics based)

2) Invers analysis ⇒ σ-w relationship

3) Adjustment of σ-w relationship considering the number of fibres in the specimen

Material testing

UTT Three-Point Bending

Test

RILEM TC 162-TDF

WST

Indirect methods

Direct method

load cell

steel loading

device with

roller bearings wedging

device

linear support

Clip

gauge

cube

specimen

piston with

constant cross-

head displacement

starter notch

(cut-in)

groove (cast)

Fsp

Mateial testing & structural analysis

Material testing

Sectional analysis

Inverse analysis

Structural analysis

Analytical model – “non-linear hinge”

Moment

Curvature

δ

R

d

x

N

w

M

s

M

N

σc (ε

,y)

y

y 0

σs

d1

σc (w

,y)

a

h /

2

h /

2

a

εc (y)

εs

θ* θ / 2

‘Non-linear hinge model’

Stress-strain

relationship

Concrete

-110

-90

-70

-50

-30

-10

-5 -4 -3 -2 -1 0

Strain, εc, [10-3

]

Str

ess,

σc,

[M

Pa]

0

εs

σs

Stress-strain

relationship

Reinforcement

Ec

fct

σ (ε)

ε

1

wc w1

b2

a1

a2 w

( )

ctf

wσ

Stress-crack opening relationship

Concrete

Comparison: experiments / analysis

-50

-40

-30

-20

-10

0

0 10 20 30 40

Nedböjning [mm]

Las

t [k

N]

FE 'bond-slip'

FE 'embedded

reinforcement'

Analytisk

Experiment

S1:2 7-150/700

(Mix 1)

-70

-60

-50

-40

-30

-20

-10

0

0 10 20 30 40 50

Nedböjning [mm]

Las

t [k

N]

FE 'bond-slip'

FE 'embedded

reinforcement'

Analytisk

Experiment

S4:2 7-150/700

(Mix 4)

R2 = 0.982

-80

-60

-40

-20

0

-80-60-40-200

FE analyses

Q E

xp

. [k

N]

Q Model [kN]

Correlation: 0,99

R2 = 0.882

-80

-60

-40

-20

0

-80-60-40-200

Analytical

Bi-linear

Q E

xp

. [k

N]

Q Model [kN]

Correlation: 0,94

Midspan deflection [mm]

Midspan deflection [mm]

Load

[kN

]Load

[kN

]

Comparison – conventional vs. FRC

0

15

30

45

60

75

90

0.0 0.2 0.4 0.6 0.8 1.0

Crack opening [mm]

Mom

ent

[kN

m]

Conventional

φ10-s150

FRC 40 kg/m3

φ7-s150

FRC 60 kg/m3

φ7-s150

Comparison:

crack opening

crack opening

MM

-70

-60

-50

-40

-30

-20

-10

0

0 10 20 30 40 50

Nedböjning [mm]

Las

t [k

N]

Plain: φ10-s150

FRC: 39 kg/m3 &

φ7-s150

FRC: 59 kg/m3 &

φ7-s150

Plain: φ12-s175

Load-deflection rel.

Load

[kN

]

Midspan deflection [mm]

Effect of fibres on the cracking process

N N

u Crack

u u

N N

Stadium II

(neglecting tension

stiffening)

Tension

stiffening Ncr Ncr

u

N

Ncr

Small reinforcement

ratio

Force Imposed deformation

Large reinforcement

ratio

Imposed deformation

When cracking is caused by an external applied force the crack width depends on the

applied force.

If cracking is caused by an imposed deformation the force in the member depends on

the actual stiffness and the crack width on the number of cracks formed.

However, most codes do not distinguish between these two cases.

Force induced cracking Ncr Ncr

Forces acting on the concrete:

cc tcfbmaxr,bm AfAs ⋅=⋅+⋅⋅⋅ σφπτ )5.0(

Stress introduced to concrete

through bond, σc (x)

Fibre bridging stress, σfb (w)

Total concrete stress, σct (x,w)

lt,max

σct ≈ fct

Possible location of new crack

New crack

Crack Crack

σfb τbm

σct ≈ fct

Ac

As

φ

lt,max

sr,max

lt,max

0.5 sr,max

Can be used to derive the crack

spacing expression

(+ effect of concrete cover & spacing)

Force induced cracking

−=

ct

fb

ff

kσ

1

effs

r kkkcks,

4213max,ρ

φ⋅⋅⋅+⋅=

According to EC 2 the crack spacing can be

calculated using the following expression:

⋅⋅⋅⋅+⋅⋅=

effs

fmr kkkkcks,

4213,7.1

1

ρ

φThis can be modified to take into account the

effect of fibres (the “residual tensile strength”)

by introducing a new coefficient (k5):

( )mcmsmrm sw ,,, εε −⋅=and the crack width can be calculated as:

( )( ) ( )( ) ( )

s

effsef

effs

ctftts

mcmsE

fkkk ,

,

,,

111 ραρ

σ

εε

⋅+⋅⋅−⋅−+−

=−e.g. DAfStb (UA SFB N 0171):

Experiments

1800

2000

600

Q Q

C L

LVDT

b=150

h=

22

5

d=

20

0

A-A ELEVATION

A

A

Reinf.

600 600

Roller Roller

Test series without and with fibre reinforcement (type Dramix®

RC-65/35

from Bekaert) and amount of conventional reinforcement.

Fibre dosage Reinforcement Beams

Series [vol-%] and [kg/m3] Number and diameter [mm] [No.]

1 Vf = 0 % (0 kg/m3) 3 φ 8 3

2 Vf = 0.5 % (39.3 kg/m3) 3 φ 8 3

3 Vf = 0.25 % (19.6 kg/ m3) 3 φ 6 3

4 Vf = 0.5 % (39.3 kg/ m3) 3 φ 6 3

5 Vf = 0.75 % (58.9 kg/ m3) 3 φ 6 3

Results

78

59

71

66

55

77

60

81

66

54

40

50

60

70

80

90

100

Av

era

ge c

rack

sp

acin

g [

mm

]

Experiment Model

3φ8

V f = 0%

3φ8

V f = 0.5%

3φ6

V f = 0.25%

3φ6

V f = 0.5%

3φ6

V f = 0.75%

Vf = 0.5% and φ 8

Gustafsson, M. and Karlsson, S. (2006): Fiberarmerade betongkonstruktioner – Analys av sprickavstånd och sprickbredd.

MSCe thesis 2006:105, Dep. of Civil & Environmental Eng., Chalmers Technical University, Göteborg, Sverige, 2006.

Results

Vf = 0.5% and φ 8

0

5

10

15

20

0.00 0.05 0.10 0.15 0.20 0.25

Crack width [mm]

Mo

men

t [k

Nm

]

0

5

10

15

20

0.00 0.05 0.10 0.15 0.20 0.25

Crack width [mm]

Mo

men

t [k

Nm

]

Vf = 0.5% and φ 8

Vf = 0.75% and φ 6

Non-linear hinge model

DAfStb

Focus on:

• Combined reinforcement, i.e. steel bars + (steel) fibres

• Crack control

• Service state

Effects of Steel Fibres on Cracking in Reinforced Concrete

Investigation of:

• Cracking process, i.e. crack width and crack spacing.

• Bond-slip relationship

• Material properties

Experiments: tension rods

For investigation of the cracking process – Digital Image Correlation

Tensile member

Relative elongation , δ / L

Axia

l fo

rce,

N

Reinforcement bar

N cr

N y1

N y2

N s

N c

Fibre reinforced

concrete

Concrete

Yield load for reinforcemen t bar

N

L

N

0

0.1

0.2

0.3

0.4

0 0.2 0.4 0.6 0.8 1

No

rmali

zed

bo

nd

str

ess

τ/f

c

Active slip [mm]

1.0b

0.25

0.5

1.0a

0.0

Bond-slip relationship

For confined conditions, the fibres (steel fibres, Dramix RC-65/35-BN) showed no

effect on the bond-slip relationship.

For unconfined conditions (i.e. splitting cracks) the fibres provide confinement and

inhibit splitting cracks.

Bond-slip relationship – confinement effect

0

10

20

30

0 2 4 6 8

Bo

nd

str

ess

[MP

a]

Slip [mm]

Series 0.25ExpConfinedSplit-stirrups

0

10

20

30

0 2 4 6 8Slip [mm]

Series 0.5ExpConfinedSplit-stirrups

0

10

20

30

0 2 4 6 8

Bo

nd

str

ess

[MP

a]

Slip [mm]

Series 1.0aExpConfinedSplit-stirrups

0

10

20

30

0 2 4 6 8

Bo

nd

str

ess

[MP

a]

Slip [mm]

Series 1.0bExpConfinedSplit-stirrups

Series

φ-stirrup

[mm]

Sv

[mm]

Ktr

[%]

0.25 6 300 1.2

0.5 10 200 4.9

1.0a 12 80 18

1.0b 12 80 18

Corresponding transversal reinforcement:

0.0

0.2

0.4

0.6

0.8

1.0

20 40 60 80 100

Cra

ck w

idth

[mm

]

Load [kN]

0.0

0.25

0.5

1.0a

1.0b

0 kg

14 kg

35 kg

78 kg

66 kg

Cracking & tension stiffening

0

20

40

60

80

100

0 0,5 1 1,5 2 2,5

Ten

sile

load

[k

N]

Deformation [mm]

66 kg78 kg35 kg14 kg0 kg

Reinf.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.001 0.002 0.003

Bon

d f

acto

rβ

[ -

]

Member strain [ - ]

a. - βc

b. -βFRC

b.

a.

εc(x)

εs(x)

εsm

εcm

ε

ββββ is used to calculate the

average steel strain

between cracks

Result show higher ββββ and that at

high fibre dosage almost constant

and no degradation

Tension rod

Restraint induced cracking – combined reinf.

l

Crack, modelled as

non-linear springs

w(σs)

( ) φσσφ

σ 4

122.0

42.0

826.0

2

⋅+

⋅+⋅⋅⋅

⋅⋅=

s

s

ef

s

c

sscm

ss

E

A

A

E

EEf

w

Bond-slip relationship => crack width as a

function of the steel stress:

N(σs)

N(σs)

N(σs)

N(σs)

N(σs)

N(σs)

N(σs)

N(σs)

Forces acting on un-cracked parts

(with only bar reinforcement)

N(fft.res) N(fft.res) Forces acting on un-cracked parts for

combined reinforcement (fibre and bar reinforcement), with fft.res as FRCs

residual tensile strength

Friction between slab and

sub-base is neglected

Engström, B. (2006): Restraint cracking of reinforced

concrete structures, Chalmers University of Technology.

The response during the cracking process can described with the following

deformation criteria:

( ) lRwnAE

lfNcssef

Ic

resfts⋅⋅=⋅++⋅

⋅

⋅εσϕ

σ)(1

),( .

where N(σs, fft.res) is the force acting on un-cracked parts, n is the

number of cracks and R is the degree of restraint. N(σs, fft.res) can be

calculated as:

( )sefresftssresfts AAfAfN −⋅+⋅= .. ),( σσ

If N(σs, fft.res) is larger than the force required to initiate a new crack, N1, more

cracks will be formed. However, if it is smaller only one crack will be

formed. The force required to initiate a new crack, N1, can be calculated as:

⋅

−+⋅= s

c

sefctm A

E

EAfN 11

Engström, B. (2006): Restraint cracking of reinforced

concrete structures, Chalmers University of Technology.

Exemple

A reinforced “slab” on grade, 20 meter long, with full restraint (R=1).

Reinforced with φ 8, 10 or 12 (0.2% < ρ < 0.8%)

Material properties, concrete C30/37 (vct ≈ 0.55):

Tensile strength: fctm = 2.9 MPa (fctk, 0.05 = 2.0 MPa)

Residual tensile strength: 0 MPa < fft.res < 2.5 MPa

Creep coefficient: ϕef = 2.5

Concrete shrinkage: εcs = 600 10-6

250

1 m c = 30

20 m

Exampel – crack widths with combined reinforcement

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Crack width [mm]

Resi

du

al

ten

sile

str

en

gth

[M

Pa]

0.3%

0.4%0.5%0.6%

C 30/37 φ 10

ρ = 0.8%0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Crack width [mm]

Resi

du

al

ten

sile

str

en

gth

[M

Pa]

0.3%

0.4%

0.5%0.6%ρ = 0.8%

C 30/37 φ 12

The ”normal / recommended” reinforcement ratio is typically 0.4-0.6%.

A conservative estimate on the residual strength with steel fibres:

20 kg/m3 => 0.8 MPa residual strength

30 kg/m3 => 1.1 MPa residual strength

40 kg/m3 => 1.3 MPa residual strength

Concrete structures – square and boring ?

TailorCrete - Rationel design and production of

structures with complex geometries

TailorCrete - Rationel design and production of

structures with complex geometries

Tailorcrete

Interesting results regarding:- Load redistribution

- Membrane action

Blast and Fragment Impacts – effect of fibres

From PhD thesis, by Jonas Ekström, to be presented November 10th

Blast and Fragment Impacts – effect of fibres

From PhD thesis, by Jonas Ekström, to be presented November 10th

Durability – Effect of fibres on corrosion

Crack morphologyno fibres

Crack morphologywith fibres