crack spacing of overlay strengthened rc members...crack spacing of overlay strengthened rc members...
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Crack Spacing of Overlay Strengthened RC MembersCrack Spacing of Overlay Strengthened RC Members
国際共同研究国際共同研究国際共同研究国際共同研究のののの推進推進推進推進「「「「コンクリートコンクリートコンクリートコンクリート構造物構造物構造物構造物のののの国際共同研究国際共同研究国際共同研究国際共同研究のののの推進推進推進推進「「「「コンクリートコンクリートコンクリートコンクリート構造物構造物構造物構造物ののののLCMLCM国際標準国際標準国際標準国際標準のののの確立確立確立確立」」」」国際標準国際標準国際標準国際標準のののの確立確立確立確立」」」」
Zhang Dawei Zhang Dawei
Contents
Research Background1
Analytical Approach2
Experimental Database3
Conclusions4
Research Background
Deterioration problems of highways or bridgesDeterioration problems of highways or bridges
Continuous increase in traffic amount
Insufficient slab thickness in the past design
Repair or strengthening of deteriorated
concrete structures are necessary
Traffic Safety
concrete structures are necessary
Overlay Strengthening FRP BondingSteel Plate bonding
Overview of Overlay Strengthening
A
Overlay materials
Cover materials Reinforcement materials
PCM HPFRCC Steel bars FRP Grid
RC beam
overlay
A
A
Section A-A
h
t
lR
lE
Typical view of overlay strengthening method
Problems of Overlay Strengthening
Bending failure Shear failure
Concrete cover separation
Peeling at intermediate crack zone Localized debonding
Peeling at overlay end
Design of Overlay Strengthening
Calculate the reinforcement area necessary to
strengthen the concrete section
Check shear capacity of strengthened member
Check flexure capacity of strengthened member
Check intermediate cracks zone Check overlay end zone
Predict debonding load Predict debonding load
Predict failure mode
Check overlay end zone
Predict debonding load
Life Cycle Management
Current Achievements
IC DebondingConcrete Cover
Separation
∆V
Bond strength Poj
Lp
A
B
C D
Ld DStatic Load
Average Crack Spacing
PPcm Pcs Pys Pyy
∆Voj
Pd
Transferred shear
force
Pojy
B
h0
τ τ σs
A
B
Scr
La
a
d0
σA
σA
D
Effects of Crack on Overlay Strengthening
Serviceability and durability
�Shear, tensile and bending stiffness
�Energy absorption capacityCrack Spacing
Scr Scr Scr Scr Scr Scr ScrScr ScrScr
Pre-mature failure
�Energy absorption capacity
�Ductility
�Corrosion resistance
�Transferred shear stress-----IC or end zone debonding
�Transferred normal stress-----Concrete cover separation
Crack Spacing
Crack Width
Crack Distribution
Current Structural Codes
h
ht
Overlay strengthened beam Multiplayer reinforced beam
BB
NS 3473 E 1992
PredictionPrediction
equationsequations
EE
CC
DD
AACSA S474 2004 Eurocode EC2
JSCE, 2007 CEB-FIP 1990
Current Equations
Code EquationMain
Parameters
CSA S474 2004 C: concrete cover (mm)
S: bar spacing (mm)NS 3473 E 1992
(((( )))) tNscr kkSCS ρφ /.. 211002 ++++++++====
(((( )))) tNscr kkSCS ρφ /.. 211002 ++++++++==== (mm)
Ф: Bar diameter (mm)
(External layer)
Ast: Bar area (mm2)
Act: Effective concrete tension area (mm2)
NS 3473 E 1992
Eurocode EC2
CEB-FIP 1990
JSCE, 2007
(((( )))) tNscr kkSCS ρφ /.. 211002 ++++++++====
st
ctcr
A
AkkCS
φ212 ++++====
efscrS
,. ρφ
45====
(((( )))){{{{ }}}}φ−−−−++++==== SckkkScr 70411 321 ..
ctsttNs AA /====ρ
Comparison with Experimental Data-1
0 50 100 150 2000
50
100
150
200
Scal.(mm)
Sexp.(
mm
)
Scal.=Sexp.
CEB-FIP
0 50 100 150 2000
50
100
150
200
Scal.(mm)
Sexp.(
mm
)
Scal.=Sexp.
JSCE
0 50 100 150 2000
50
100
150
200
Scal.(mm)S
exp.(
mm
)
Scal.=Sexp.
NS
R2 =0.326 R2 =0.343 R2 =0.365
26 Overlay Strengthened Beams
c. CEB-FIP 1990 provisions
Scal.(mm)
d. Eurocode EC2 provisions e. CSA S474 2004
a. JSCE 2007 b. NS 3473 E 1992
0 50 100 150 2000
50
100
150
200
Scal.(mm)
Sexp.(
mm
)
Scal.=Sexp.
EC2
Scal.(mm)
0 50 100 150 2000
50
100
150
200
Scal.(mm)
Sexp.(
mm
)
Scal.=Sexp.
CSA
Scal.(mm)
R2 =0.203 R2 =0.343
Initiation Location of Flexural Crack
Arc
Ar
As
hodr
b
ds
ε’cc
εtc
xg
drc
hc
εto
tcgc
ccc f
xh
IM
−−−−====
Crack at substrate concrete
Concrete
Overlay
(((( )))) togo
c
o
cco f
xh
I
E
EM
−−−−====
Crack at overlay material
(((( ))))
(((( ))))(((( )))) togcc
tcgoo
togo
c
o
c
tcgc
c
co
ccc
fxhE
fxhE
fxh
I
E
E
fxh
I
M
MR
−−−−
−−−−====
−−−−
−−−−========
�Multilayer reinforced concrete beam
�Overlay strengthened RC beam
Rc>1 Rc Max:0.52 Min: 0.33 Mean: 0.45
Crack always initiates near the bottom
Crack always initiates from substrate concrete
Comparison with Experimental Data-2
0 50 100 150 2000
50
100
150
200
Se
xp
.(m
m)
Scal.=Sexp.
JSCE
0 50 100 150 2000
50
100
150
200
Sexp
.(m
m)
Scal.=Sexp.
NS
0 50 100 150 2000
50
100
150
200
Sexp
.(m
m)
Scal.=Sexp.
CEB-FIP
R2=0.456 R2=0.563 R2=0.723
S: bar spacing, Ф: Bar diameter (Internal layer)
0 50 100 150 200
Scal.(mm)
0 50 100 150 2000
50
100
150
200
Scal.(mm)
Se
xp
.(m
m)
Scal.=Sexp.
EC2
d. Eurocode EC2 provisions e. CSA S474 2004
a. JSCE 2007 b. NS 3473 E 1992 c. CEB-FIP 1990 provisions
0 50 100 150 2000
50
100
150
200
Scal.(mm)
Se
xp
.(m
m)
Scal.=Sexp.
CSA
0 50 100 150 200
Scal.(mm)0 50 100 150 200
Scal.(mm)
R2=0.429 R2=0.563
Steel Bar
FRP Grid
S
ssjAσ
rriAσ
ssiAσ
rrjAσ
x
Concrete
Overlay dx
bcτ
bpτ
bcτ
bpτ
Overlay
S S
P P
Analytical Approach-1
SOverlay
Concrete
FdFF ++++
bcτ
Overlay
dx
boτb
b
t
ch
(((( ))))
(((( ))))
++++−−−−====++++
++++−−−−====
++++++++++++====
∑∑∑∑∑∑∑∑
∑∑∑∑∑∑∑∑
∑∑∑∑∑∑∑∑
bosbcroto
ctc
bosbcr
bosbcr
OOAdx
dA
dx
d
OOdx
dF
dxOdxOdFFF
ττσσ
ττ
ττ
Free Body Diagram
S
ssjAσ
rriAσ
ssiAσ
rrjAσx
Concrete
Overlay
bcτ
bpτ
bcτ
bpτ
o
o
c
co
EE
maxmax σσε ========Zero-slip point
(((( ))))(((( ))))bomsbcmr
Sbosbcrotosctcs
OOS
dxxOxOAA
++++−−−−====
++++−−−−====++++
∑∑∑∑∑∑∑∑∫∫∫∫ ∑∑∑∑∑∑∑∑
3
0
2
ττ
ττσσ/
)()(
Analytical Approach-2
S
)(0cσ
mobc )(τ
(((( ))))
(((( ))))ot
oto
cct
bomsbcmr
os
ct
c
ootct
bomsbcmr
cs
f
AE
EA
OOS
f
E
EAA
OOS
≤≤≤≤
++++
++++====
≤≤≤≤
++++
++++====
∑∑∑∑∑∑∑∑
∑∑∑∑∑∑∑∑
3
3
ττσ
ττσ
(((( ))))bomsbcmr
c
ootctt
csOO
E
EAAf
Sττ ∑∑∑∑∑∑∑∑ ++++
++++
====
3
),min( oscss SSS ====
�Stabilized crack spacing of
substrate concrete layerUniaxial tension load
Stabilized cracking
under flexure load
Analytical Approach-3
(((( ))))bomsbcmr
oto
ccto
osOO
AE
EAf
Sττ ∑∑∑∑∑∑∑∑ ++++
++++
====
3
),min( oscssf SSkS 1====
ε1
ε2hec+t
ho
xc
�Stabilized crack spacing of
overlay layer
k1= (ε1 + ε2)/2ε1
26 Overlay with steel bars
10 Overlay with FRP grid
Verification-1
150
200
Sexp. (m
m)
Scal.=Sexp.
Steel Bar
FRP Grid
Scal/Sexp.
Mean: 1.01
Standard Deviation: 0.11
R2: 0.833
0 50 100 150 2000
50
100
Scal. (mm)
Sexp. (m
m)
100
150
200
Sexp. (m
m)
Scal.=Sexp.New ModelJSCE 2007EC2 2004CSA & NSCEB-FIP 1990
(((( ))))bomsbcmr
c
ootctt
csfOO
E
EAAfk
Sττ ∑∑∑∑∑∑∑∑ ++++
++++
====13
(((( ))))bomsbcmr
oto
ccto
osfOO
AE
EAfk
Sττ ∑∑∑∑∑∑∑∑ ++++
++++
====13
Verification-2
6 Conventional beams
0 50 100 150 2000
50
100
Scal. (mm)
Sexp. (m
m)
Scal/Sexp
Mean: 1.05
Standard Deviation: 0.08
R2= 0.982
∑∑∑∑====
rsbcm
tcts
O
AfkS
τ13
(((( ))))bomsbcmr ∑∑∑∑∑∑∑∑
JSCE-- most conservative
Conclusions
Current structural codes can not predict the
crack spacing of overlay strengthened members
1
The initiation location of flexural crack has2 The initiation location of flexural crack has
predominantly effect on the crack prediction
2
The newly developed analytical model can
predict well the average crack spacing of overlay
strengthened members as well as conventional
RC members
3
Next Step
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Analytical Approach -2
S
ssjAσ
rriAσ
ssiAσ
rrjAσx
Concrete
Overlay
bcτ
bpτ
bcτ
bpτ
250
55
.
)(
)(
'.
⋅⋅⋅⋅====
oc
mobc
fτ
entreinforcem sversewith tran
failure splitting of casein
Bond Stress at
stabilized crack stage
S
)(0cσ
mobc )(τ
2055)( .
⋅⋅⋅⋅====mobcτ
20
05
250.
)(
)(
'.
⋅⋅⋅⋅====
oc
mobc
fτ
failureout -pull of casein
entreinforcem rseut transve witho
)()( '. ocmobc f251 ====τ
Analytical Approach -2
For a certain steel bar or FRP grid, the maximum area of the reinforced
concrete (Acmax) or overlay (Aomax) zone within which stable crack can
develop is,
where As(F) and fy(Fy) denote the area, the yielding strength of steel bar (FRP Grid)
respectively, fc(o)t is the tensile strength of concrete (overlay).
toc
FyyFs
ocf
fAA
)(
)()(
max)(
⋅⋅⋅⋅==== hmax
(neutral axis depthrespectively, fc(o)t is the tensile strength of concrete (overlay).
In a two-dimensional consideration, the maximum size of square bond
effective zone for steel bar (hcmax) or FRP Grid (homax) can then be
calculated as,
max)(max)( ococ Ah ====
≤tension area in bending
xgc
Actf
Aotf
ε2
ε1
The lesser of
hcmax and hc-xgchc
tThe lesser of
homax and t
(neutral axis depth
of cracked section)