thThe 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China

LOCAL BOND SPLITTING BEHAVIOR OF RC MEMBERS
WITH LATERAL REINFORCEMENT
1

Akira YASOJIMA and Toshiyuki KANAKUBO

2

1

2

Assistant Professor, Graduate School of Engineering, Hiroshima University, Japan
Associate Prof., Graduate School of Systems and Information Engineering, University of Tsukuba, Japan
Email: yasojima@hiroshima-u.ac.jp

ABSTRACT :This research features local bond splitting behavior and bond splitting strength of reinforced concrete memberswith confinement of lateral reinforcements. Lateral reinforcements contribute to confinement of main
reinforcements, increase bond splitting strength and improve brittle failure. To make clear the correlation
between local bond splitting behavior with confinement of lateral reinforcement in RC members, it is necessary
to quantify effect of lateral confinement in bond splitting behavior. To obtain the local bond stress versus
slippage relationship with confinement of lateral reinforcement, pull-out bond test is conducted. The test results
show that maximum bond stress has an increment as lateral confinement stress also increases, and the slippageat maximum bond stress is influenced by splitting crack width and shape of main reinforcement. A new
relationship between bond stress and slippage in case of confinement of lateral reinforcement is proposed using
these results and effect of lateral confinement. A numerical analysis is performed to confirm the model withexperimental results. The analytical results show a good agreement in bond splitting strength with experimental
results of previous studies.
KEYWORDS:

bond splitting, local behavior, lateral confinement, shape of main bar, crack width

1. INTRODUCTION
In many studies related to bond splitting behavior of reinforced concrete (RC) members, it is reported that many
local bond stress versus slippage relationships and bond splitting strength calculation formulas and are proposedby the present [1,2]. It is essentially considered that local bond splitting behavior and average one in RC
members are same destruction mechanism, regardless of with or without lateral reinforcement. However, theevaluation of bond splitting strength based on relationship between local bond splitting behavior and average
one have not been developed. Most calculation formulas are proposed by regression analysis of experimental
results and mechanical meaning considerations is not always done. And the relationship between local bondstress and slippage of reinforcement with lateral reinforcement has not been yet completely clear.
The authors focus attention on bond splitting behavior failed by splitting crack of surrounding concrete,investigate bond splitting behavior of RC members through pull-out bond test of which specimens have a shortbond length, and have quantified local bond stress - slippage of reinforcement relationships without lateralreinforcement. From the results of the numerical analysis conducted to obtain average bond behavior using thismodel, analyzed bond splitting strengths showed a good correlation with experimental values observed [3]. The
formula for bond splitting strength built up by solving second differential equation of bond problem using EBSB,
which is defined as the area of EBSB has the same area of local bond stress versus slippage, agreed well withexperimental results reported previously [4].
The purpose of this study is to derive local bond stress versus slippage relationship with lateral reinforcement
based on effect of lateral confinement and correlation between local bond splitting behavior with lateralreinforcement. To obtain the relationship and the effect, pull-out bond test is conducted with lateral confinement
force as a main parameter, and comparison of numerical analysis results using the model with experimental
results reported previously is investigated.

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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
2. LOCAL BOND EXPERIMENT WITH LATERAL CONFINEMENT
2.1. Outline of Experiment
To investigate local bond splitting behavior with lateral confinement, the authors have conducted pull-out bondtest with lateral confinement force. The specimen is shown in Fig.1. The specimen with a bond length of fourtimes of the diameter of reinforcement (db) is concrete block inserted one main reinforcement. The dimensionsof specimen are 14db x 14db x 7db in rectangle. To apply the lateral confinement force to only the main
reinforcement, the specimen has slits by steel and urethane form, which correspond to splitting crack ofsurrounding concrete. In order not to restrain the deformation inside and outside concrete of surrounding themain reinforcement, the specimen is set up on the loading plate provided the hole through four teflon sheets.
The lateral confinement force is applied by two oil jacks to concrete block directly, which is kept constantduring loading. A monotonic pull-out load is applied until failure occurred. The measured items are the pull-out
load, the lateral confinement load, the slip of the free end of the main reinforcement and the crack width of
concrete.
LVDT

14db
1.5db
4 db

Test
region1.5db
Casting
Oil jacks direction

Loading
direction

Plaster
LVDT

Loading plate
Teflon sheet

Cdb
Steel +
urethaneform

Fig.1 Outline of the specimen
2.2. Specimens and Materials
Two series of specimens is consisted in order to investigate the influence of shape of main reinforcement in thebond stress transfer mechanism. In series A, specimens is provided with generic deformed-bars andexperimental factors are concrete strength (24, 30, 48 and 60MP), diameter of reinforcement (16 and 25mm),
shape of reinforcement (lateral-type rib and screw-type rib), thickness of concrete cover (C/db: 1.5, 2.5 and 3.5)
and lateral confinement force (2, 4, 6, 8, 10, and 12kN). In series B, specimens are provided with scraped andcutting deformed-bars. The test variables in series B are rib angle (45 and 90 degree), rib spacing (9.6, 16.0 and
24.0mm), rib height (1.2 and 2.4mm) of deformed-bars and lateral confinement force (2, 6, and 10kN). The
material characteristics of concrete and deformed-bars used in this study are shown in Table 1, Table 2, andFig.2. The list of specimens in series A and B is shown in Table 2.3 and Table 2.4 with test results, respectively.
The concrete is normal weight concrete using coarse aggregate of maximum diameter of 20mm and specifiedcompressive strength of 30, 60, 24, and 48MPa.
Table 1 Mechanical properties of concrete

B

Elastic
modulus Ec
(GPa)
23.1
28.2
22.6
29.2
23.8

1.2

16.0

F075
45°

2.0

2.4

9.6

2.0

16.0

2.0

2.4

F250
45°

R150

φ13.2

Splittingstrength σt
(MPa)
2.75
3.60
2.01
3.79
2.72

φ18.0

Compressive
strength σB
(MPa)
32.9
62.8
23.6
55.5
32.9

φ13.2

A

Specifiedcompressive
strength
30MPa
60MPa
24MPa
48MPa
36MPa

φ15.6

series90°[mm]

Fig.2 Shape of scraped bar in series B

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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China

Table 2 Mechanical properties of reinforcement
seriesA

B

Reinforcing
bar type
T (D16)Lateral-type rib
N (D16)Screw-type rib
LT (D25)
Lateral-type rib
LN (D25)
Screw-type rib
F050
F075
F150
F250
R150

(degrees)

Rib height-spacing
ratio h/ln

Yieldstrength sσy(MPa)

Elastic
modulus Eb
(GPa)

10.60

36

0.097

399

197

1.25

8.38

41

0.149

376

197

78.1

2.02

17.81

34

0.113

403

199

25.0

78.6

1.73

9.96

39

0.174

393

197

16.0
16.1
14.6
15.7
13.9

50.2
50.6
46.0
49.4
43.6

1.20
1.20
2.40
2.40
2.40

24.0
16.0
16.0
9.6
16.0

45
45
45
45
90

0.050
0.075
0.150
0.250
0.150

568

206

Cross-sectional
area ab(mm2)

Diameterdb(mm)

Perimeterφb

Rib spacingln(mm)

Rib angle(mm)

Rib height
h
(mm)

191

15.6

49.0

1.03

193

15.7

49.2

485

24.8

492
201
204
168
194
152

θ

2.3. Experimental Results
Experimental results at the maximum load in series A and B are listed in Table 3 and Table 4, respectively. The
bond stress is derived by dividing the tensile load by the surface area of main reinforcement. The loaded end slip
is derived by adding the elongation of the reinforcement to the free end slip ignoring concrete deformation andassuming constant bond stress. The lateral confinement stress is calculated by dividing lateral confinement force
by diameter of bar and bond length. The splitting crack width is half of slit deformation. Each experimental
value in series A is average value of three specimens in same factors, one in series B is value of one specimen.
Table 3 List of specimens and test results in series A
Specimen
T3015-2
T3015-6
T3025-2
T3025-4
T3025-6
T3025-8
T3025-10
T3025-12
T3035-6
T3035-10
N3025-2
N3025-6
N3025-10
T6025-2
T6025-4
T6025-6
T6025-8
T6025-10
T6025-12
LT2425-12.5
LN2425-12.5
LT4825-12.5
LN4825-12.5

Reinforcement
Rib height
Shape(Bar type) -spacing
ratio

concretestrength

Thicknessof concrete
cover
1.5

T
(D16)

0.097

Compressive
32.9MPa
Splitting
2.75MPa

N
(D16)

0.149

T
(D16)

0.097

LT
(D25)
LN
(D25)
LT
(D25)
LN
(D25)

0.113
0.174
0.113
0.174

2.5

3.5
2.5

Compressive
62.8MPa
Splitting
3.60MPa
Compressive
23.6MPa
Splitting
2.01MPa
Compressive
55.5MPa
Splitting
3.79MPa

2.5

Lateral confinement

13.45
24.82
12.29
20.09
21.58
24.98
29.09
30.22
20.53
27.46
15.71
24.16
30.70
22.15
28.36
32.71
38.03
40.12
43.26

At maximum load
Slip (mm)Bondstress(MPa) Loaded end Free end
4.29
0.609
0.597
7.92
0.421
0.400
3.92
0.678
0.667
6.41
0.555
0.538
6.88
0.762
0.743
7.96
0.824
0.803
9.28
0.533
0.509
9.64
0.784
0.758
6.55
0.658
0.641
8.75
0.848
0.825
4.99
0.396
0.383
7.67
0.398
0.378
9.75
0.407
0.381
7.06
0.538
0.519
9.04
0.691
0.667
10.43
0.655
0.627
12.13
0.467
0.435
12.79
0.582
0.548
13.79
0.437
0.401

Crack
width
(mm)
0.220
0.101
0.275
0.146
0.117
0.071
0.088
0.110
0.101
0.059
0.121
0.121
0.042
0.412
0.287
0.210
0.136
0.124
0.102

5.03

52.28

6.70

0.812

0.785

0.179

12.5

4.99

45.03

5.73

0.677

0.651

0.083

12.5

5.03

62.16

7.96

1.253

1.221

0.506

12.5

4.99

69.30

8.81

0.655

0.619

0.337

Force
(kN)

Stress
(MPa)

Load
(kN)

2.0
6.0
2.0
4.0
6.0
8.0
10.0
12.0
6.0
10.0
2.0
6.0
10.0
2.0
4.0
6.0
8.0
10.0
12.0

2.00
6.01
2.00
4.01
6.01
8.02
10.02
12.02
6.01
10.02
1.99
5.98
9.97
2.00
4.01
6.01
8.02
10.02
12.02

12.5

2.5

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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China

Table 4 List of specimens and test results in series B
Specimen
F050-2
F050-6
F050-10F075-2
F075-6
F075-10
F150-2
F150-6
F150-10F250-2
F250-6
F250-10
R150-2
R150-6
R150-10

Reinforcement
Rib height
Rib angle-spacing(Diameter)ratio
45 degrees(16.0mm)0.050

45 degrees(16.1mm)0.075

45 degrees(14.6mm)0.150

45 degrees(15.7mm)0.250

90 degrees(13.9mm)

0.150

Thicknessof concrete
cover

Concretestrength

Compressive
32.9MPa
Splitting
2.72MPa

2.5

Lateral confinement
Force
(kN)

Stress
(MPa)

Load
(kN)

2.0
6.0
10.0
2.0
6.0
10.0
2.0
6.0
10.0
2.0
6.0
10.0
2.0
6.0
10.0

1.96
5.87
9.78
1.94
5.82
9.70
2.13
6.40
10.67
1.99
5.96
9.94
2.25
6.75
11.25

10.09
21.18
27.68
16.40
26.72
31.48
15.30
25.44
36.87
15.19
23.87
34.21
14.82
27.38
34.67

At maximum load
Slip (mm)BondstressLoaded
Free
(MPa)
end
end
3.14
1.422
1.414
6.59
1.012
0.996
8.62
1.359
1.338
5.06
0.782
0.769
8.25
0.624
0.604
9.72
0.888
0.864
5.20
0.466
0.452
8.64
0.716
0.692
12.53
0.612
0.578
4.80
0.368
0.356
7.55
0.481
0.442
10.82
0.369
0.342
5.31
0.439
0.424
9.80
0.506
0.478
12.41
0.684
0.648

Crack
width
(mm)
0.297
0.172
0.156
0.310
0.213
0.193
0.241
0.268
0.206
0.245
0.177
0.075
0.222
0.202
0.207

2.3.1 Maximum Bond StressFig.3 shows the relationship between maximum bond stress and lateral confinement stress (a formula in the
figure mentioned later). Maximum bond stress and lateral confinement stress are normalized by concrete
compressive strength to remove the influence by the difference of concrete compressive strength. Maximum
bond stress increases linearly as lateral confinement stress increases in almost specimens, not influenced by thedifference of diameter, rib height, rib spacing, rib angle of reinforcing bar, and thickness of concrete cover.
2.3.2 Slippage of Reinforcement
Fig.4 shows slippage of reinforcement at maximum load versus rib height of reinforcement, one versus rib
spacing of reinforcement. Slippage of reinforcement at maximum load decreases slightly as rib height ofreinforcing bar increases, increases approximately linearly as rib spacing of reinforcement increases. In
specimens used deformed-bar of D25 in series A, slippage of reinforcement at maximum load increases
markedly as concrete compressive strength increases. It is observed that the difference of concrete compressive
strength on the front of rib affects slippage of reinforcing bar, which regarded as tri-axial compressive stress by
the effect of lateral confinement.

0.5

1.5

0.4
0.3
0.2
0.1

1

0.5

y = 0.681 x + 0.100

0.1 0.2 0.3 0.4 0.5
Confinement stress/ concrete compressive strength0

0.8
Crack width δw (mm)20.6Slip at max. smax (mm)Maximum bond stress/ concrete compressive strength

2.3.3 Crack Width
Fig.5 shows splitting crack width at maximum load versus concrete compressive strength and rib height ofreinforcing bar. Splitting crack width at maximum load increases as concrete compressive strength and ribheight of reinforcement increase. It is recognized that splitting crack width strongly relates to concrete stiffness
on the front of rib, bearing strength of concrete, and effect of lateral confinement.

0

1
2
30
10
20
30
Rib height (mm) Rib spacing (mm)

0.6
0.4
0.2

0

30 60 90
1
2
3
Concrete comp. Rib height (mm)strength (MPa)

T3015
T3025
T3035
N3025
T6025
LT2425
LN2425
LT4825
LN4825
F050
F075
F150
F250
R150

Fig.3 Maximum bond stressFig.4 Loaded end slip - rib heightFig.5 Crack width - concrete- confinement stress relationship and rib spacing relationshipstrength and rib height relationshipth

The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
2.4. Local Bond Stress - Slip Model
It is considered that bearing strength and effect of lateral confinement are greatly affected by lateral confinement
condition of surrounding concrete on bond action between deformed bars and concrete assumed that bearing
stress acts on the front of rib of main reinforcement, which are depending on mechanical interaction andsplitting crack width. A new relationship between local bond stress and slip with lateral reinforcement is
proposed based on concrete stress condition on the front of rib and consideration of mechanical behavior.
2.4.1 Maximum Bond StressMechanical interaction is regarded as being dominant on bond action between deformed bars and concrete withlateral confinement after the occurrence of splitting crack, thus bond stress and splitting stress are described asshown in Eq.(1). Because it is recognized that relationship between bond stress and splitting stress is linear as
shown in Fig.3, the angle between the principal bond stress and the axis of the main reinforcement is 56 degrees
from the slop of linear curve calculated by least square method.
τ bs , max = σ l ⋅ cot θ(1)where, τbs,max : maximum bond stress, σl : lateral confinement stress,
θ : angle between the principal bond stress and the axis of reinforcement (= 56degrees)
2.4.2 Effect of Lateral Confinement
The coefficient of bearing strength (fbear) is described as Eq.(2), which is defined as ratio of bearing stressexerted apparently on all area of the front of rib at maximum load to concrete compressive strength. Fig.6 shows
coefficient of bearing strength versus crack width relation as maximum load. It is observed that bearing strengthof the front of rib is 1-3 times of concrete compressive strength, also that coefficient of bearing strength
decreases as splitting crack width increases. Maximum bond stress, bearing strength, and mechanical interaction
can be expressed by relationship between lateral confinement stress and crack width, considering that maximum
bond stress versus lateral confinement stress relation is described by Eq.(1).
f bear =(τ bs , max ⋅ φb ⋅ lb ) 2 + (σ l ⋅ d b ⋅ lb ) 2 l n⋅
φb ⋅ hlb(2)

σB

where, σB : concrete compressive strength, φb : perimeter of reinforcement,h : rib height, ln : rib spacing, db : diameter of reinforcing bar, lb : bond length

5
4
3
2
1
0

0.1
0.2
0.3
0.4
Crack width δw (mm)0.5

Fig.6 Coefficient of bearing strength
versus crack width relationship

T3015
T3025
T3035
N3025
T6025
LT2425
LN2425
LT4825
LN4825
F050
F075
F150
F250
R150

Confinement stress/concrete compressive strength

bearing strength/concrete compressive strength

Lateral confinement stress versus crack width relation is shown in Fig.7. Lateral confinement stress and crack
width are normalized by concrete compressive strength and rib height of reinforcing bar, respectively, to remove
the influence by concrete strength and shape of main reinforcements. It is confirmed that crack width decreases
as lateral confinement stress increases to enhance effect of lateral confinement. Formula calculated by leastsquare method is obtained as shown in Fig.7, thus, bearing strength on the front of rib and least upper bound oflateral confinement effect given by bearing strength are expressed by function of crack width.
0.5
0.4
0.3
0.2

y = 0.018 / x

0.1
0

0.1
0.2
0.3
0.4
Crack width/Rib height

0.5

Fig.7 Lateral confinement stressversus crack width relationship

T3015
T3025
T3035
N3025
T6025
LT2425
LN2425
LT4825
LN4825
F050
F075
F150
F250
R150

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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
2.4.3 Slip at Maximum Bond StressSlip has been influenced by rib spacing and lateral confinement stress from investigation of test results. Slip at
maximum bond stress versus crack width relation normalized by lateral confinement stress is shown in Fig.8. It
is observed that slip at maximum bond stress increases linearly as splitting crack width increases. As results
calculated by least square method, slip at maximum bond stress can be described as shown in Fig.8. It indicatesthat slip at maximum bond stress and crack width are proportion relations, also which rib spacing increases asslippage increases.

0.05
0.04

y = 0.447 x

0.03
0.02
0.01
0

0.01 0.02 0.03 0.04 0.05 0.06
Crack width ( δw / h )／( σB / σl )

T3015
T3025
T3035
N3025
T6025
LT2425
LN2425
LT4825
LN4825
F050
F075
F150
F250
R150

Fig.8 Normalized Slip at maximum stressversus crack width relationship

1.5
Bond stress τbs / τbs,max

Slip ( smax / ln )／( σB / σl )2.4.4 Relationship between Bond Stress and Slippage
Typical relationships between bond stress and loaded end slip are shown in Fig.9, which is normalized bymeasured maximum bond stress. The shape of the curve is not influenced by experimental factors, and eachcurve after the maximum stress trends to decrease linearly with slip of main reinforcement. The objective of thisresearch is to present bond stress - slip model that has two stages. The increase stage is expressed by parabolic
curve considering tri-axial compression state and failure progress of mechanical interaction and effect of lateralconfinement. Because the area in which rib spacing concrete resists to shear force decreases linearly to the slipof the reinforcement after maximum load, the decrease stage is expressed by the straight line determined by rib
spacing, as that the bond stress becomes zero when the slip of main reinforcement is equal to rib spacing. Bondstress - slip model is shown in Fig.9, which can express basically experimental results.
T3025-4
T3025-6
T6025-8
T6025-12
Model

1

F075-10
F150-10
R150-10
Model

0.5

0

0

5

10

15 0
Slip (mm)

5

10

15

Fig.9 Relationship between bond stress and slip

3. BOND SPLITTING BEHAVIOR WITH LATERAL REINFORCEMENT
3.1. Confinement Stress Exerted by Lateral Reinforcement
Lateral confinement stress is provided by lateral reinforcement which restrain increase of crack width, andcorrelate with lateral reinforcement stress occurred by deformation of lateral reinforcement and crack width.
Assuming that bond force of lateral reinforcement is distributed uniformly throughout entire bond effective
length at maximum bond stress, lateral confinement stress can be expressed by Eq.(3), which is provided bystress of lateral reinforcement that is proportional to crack width. It represents lateral confinement stress thatexerts uniform confinement force to orthogonal direction of crack side in side-splitting bond failure. On theother hand, because lateral confinement stress has upper limit of confinement effect determined by bearing
strength as shown in Fig.10, lateral confinement stress at maximum bond stress is derived as Eq.(4) which is
given by point at the intersection of Equation as shown in Fig.7 with Eq.(3) as shown in Fig.10. Also, in casethat stress of lateral reinforcement calculated by Eq.(4) is more than yield strength, lateral confinement stress isgiven by Eq.(5).
σ l b ⋅ pw δ w Est=⋅⋅
σ B N ⋅ db lwe σ B
σ l , max = k ⋅b ⋅ pw h⋅⋅ Est ⋅ σ B
N ⋅ db lwe

(3)
(4)

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The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China

σ ly =b ⋅ pw⋅ σ wyN ⋅ db(5)

where, b : width of member, pw : lateral reinforcement ratio, σwy : yield strength of lateral reinforcement,
N : number of reinforcing bar, lwe : bond effective length, Est : Elastic modulus of lateral reinforcement
3.2. Bond Stress - Slip Relationships
It is possible to express local bond behavior of RC members with lateral reinforcement as adding bondincrement to local bond behavior without lateral reinforcement. Moreover, the local bond stress versus slip
relation without lateral reinforcement has been quantified as shown in Eq.(7) [1]. Therefore, a new proposed
relationship between local bond stress and slip with lateral reinforcement, which is described by adding bondstress of Eq.(7) to bond stress obtained from test results, becomes as follows:τ b = τ bc + τ bs

(6)

τ bc = 2 ⋅ σ t ⋅ β ⋅ s ⋅(ru d b ) − ( β ⋅ s )2

2(ru d b ) 2 + ( β ⋅ s ) 2
τ bs = τ bs , max ⋅ ( s s max ) ⋅ (2 − s s max )τ bs = −τ bs ,maxl n − s max⋅ cot α⋅ (s − l n )(7)(s ≤ smax)(8)(s > smax)(9)τ bs , max = σ l , max ⋅ cot θ(10)s max = 0.008 ⋅ l n ⋅σBσ l ,max(11)

σ l ,max = 0.018 ⋅b ⋅ pw h⋅⋅ E st ⋅ σ B
N ⋅ d b l we

(12)

σ l , max ≤ σ ly = b ⋅ p w ⋅ σ wy ( N ⋅ d b )(13)where, τb : local bond stress, s : slip, β : coefficient between internal crack depth and slip (=10.2 (1/mm)),
α : angle between the principal bond stress and the axis of reinforcing bar (= 34 degrees),σt : concrete tensile strength, ru : C + db/2 (C : thickness of concrete cover), db : diameter of reinforcing bar

Conf inement stressat maximum load
○ at elasticity□ at y ield
Conf inement stress which
is proportional to crack width

10

5

Fig.10 Lateral confinement stressversus crack width relationshippw = 1.00%
pw = 0.15%

0Crack width δw

σB=24MPa, σt=2MPa
b=65mm, ru=32.5mm
Rebar: D19, N=1
h=1.2mm, ln=12.8mm
Lateral reinf orcement: D6
lwe =9dw(dw:diameter of stirrups）

0

2

4
6
8
Slip (mm)10Fig.11 Local bond stressversus slip relationship

Average bond stress (MPa)Upper limitof conf inement ef f ect

Local bond stress (MPa)Confinement stress σl / σB

Examples of local bond stress - slip relation are shown in Fig.11, where bond effective length is 9 times ofdiameter of lateral reinforcement. Analytical results by numerical calculation of pull-out test are shown in
Fig.12, which is conducted to obtain average bond behavior using this model and analysis method indicated in
Reference 3. The dimensions and mechanical properties of specimens in the model and the analysis are shownin Fig.11 and Fig.12. Proposed local bond stress - slip relations have two extreme values, that one is at theoccurrence of splitting crack and the other is at bearing strength of concrete on the front of rib by the acting oflateral confinement effect. Therefore, average bond stress - loaded end slip relations also have two peaks, that
one is given by concrete splitting and the other is given by lateral confinement of reinforcement.
σB=24MPa, σt=2MPa

Bond length=400mm, b=65mm
Rebar: D19, Eb=206GPa
h=1.2mm, ln=12.8mm
Lateral reinf orcement: D6
lwe =9dw (dw:diameter of stirrups）

10

5

pw = 1.00%
pw = 0.15%

0

0

2
4
6
8
10
Loaded end slip (mm)Fig.12 Average bond stressversus loaded end slip relationshipth

The 14 World Conference on Earthquake Engineering
October 12-17, 2008, Beijing, China
4. ADAPTATION OF PROPOSED MODEL4.1. Confinement Contribution Ratio of Lateral reinforcement
It is confirmed that the effect of lateral confinement at the corner main reinforcement and at the middle one isdifferent. Because the difference of bond splitting strength between at the corner main reinforcement and at the
middle one is closely related to quantity of lateral reinforcement and effect of lateral confinement, confinement
contribution ration of Lateral reinforcement is determined by ratio of bond splitting strength at corner and at
middle versus ratio of lateral reinforcement relationship using previous test results. From test results ofspecimens that concrete compressive strength is under 30 MPa, and ratio of lateral reinforcement is over 0.5 %,average of bond splitting strength ratio is 0.62, which corresponds to confinement contribution ratio.
4.2. Bond Splitting Strength

10

5
Av erage : 1.07
COV : 19%

0

5
10
15
Analytical values (MPa)15

σB ≦ 30MPa10

Av e. : 1.03
COV : 16%53 specimens

5
Conf inement stressEq.(12)
Eq.(13)0

51015
Analytical values (MPa)1530 < σB ≦ 60MPa
10

Av e. : 1.02
COV : 18%
47 specimens

5
Conf inement stressEq.(12)
Eq.(13)0

51015
Analytical values (MPa)Experimental values (MPa)132 specimens
14≦σB ≦104MPa

Experimental values (MPa)15Experimental values (MPa)Experimental values (MPa)To evaluate adaptation of the proposed model, the comparison between results of numerical analysis using the
proposed model and experimental results is investigated. Experimental values are obtained by bond test of
cantilever and beam type specimens done in previous studies. Fig.13 shows the comparison between
experimental bond strength and analytical values calculated by the proposed model. The ratio of experimental
values to analysis values is 1.07 in average, and the coefficient of variation is 19 percent. The predicted values
show a good agreement with experimental results for most specimens.
15

σB > 60MPa
10

Av e. : 1.04
COV : 14%32 specimens

5
Conf inement stressEq.(12)
Eq.(13)0

51015
Analytical values (MPa)Fig.13 Comparison between experimental results and analytical results
5. CONCLUSIONS
To investigate the effect of lateral confinement on local bond behavior, pull-out bond test was conducted. A
local bond stress versus slip model was proposed based on mechanical meaning considerations, which wasderived from relationship between effect of lateral confinement and splitting crack width. The model was also
verified by comparing the test results form previous studies with the analytical results obtained from the present
model.
REFERENCES[1] S. Morita and S. Fujii (1982). Bond Capacity of Deformed Bars Due to Splitting of Surrounding Concrete,
Proceedings of the International Conference on Bond in Concrete[2] M. Maeda, S. Otani and H. Aoyama (1992). A Proposal of A Formula for Bond Splitting Strength ofReinforced Concrete Members, AIJ Journal of Structural Engineering, Vol.38B, pp.293-306[3] T. Sakai, T. Kanakubo, K. Yonemaru and H. Fukuyama (1999). Bond Splitting Behavior of Continuous
Fiber Reinforced Concrete Members, Fiber Reinforced Polymer for Reinforced Concrete Structures, ACI
SP-188, pp.1131-1144[4] A. Yasojima, T. Kanakubo (2005). Bond Splitting Strength of RC Members Based on Local Bond Stressand Slip Behavior, 11th International Conference on Fracture, Proceedings CD-ROM, No.4486