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

PreparePreparePreparePrepare aaaa detaileddetaileddetaileddetailed designdesigndesigndesign approachapproachapproachapproach forforforforoverlayoverlayoverlayoverlay strengtheningstrengtheningstrengtheningstrengthening underunderunderunder staticstaticstaticstatic loadingloadingloadingloading

1

FatigueFatigueFatigueFatigue designdesigndesigndesign ofofofof overlayoverlayoverlayoverlay strengthenedstrengthenedstrengthenedstrengthened2 FatigueFatigueFatigueFatigue designdesigndesigndesign ofofofof overlayoverlayoverlayoverlay strengthenedstrengthenedstrengthenedstrengthenedRCRCRCRC membersmembersmembersmembers

2

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)