fiber reinforced concrete, chalmers research “ - an exposé...• david fall. “ steel fibres in...
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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
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