The 2019 World Congress on
Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 - 21, 2019

Study on pullout behavior of single steel fiber in SFRCC*Saki Echizen1) and Toshiyuki Kanakubo2)
1)

2)

GSSIE, University of Tsukuba, Ibaraki, 305-8573, Japan
Dept. of Eng. Mechanics and Energy, Univ. of Tsukuba, Ibaraki, 305-8573, Japan1)s1820881@s.tsukuba.ac.jp

ABSTRACTThe purpose of this study is to investigate the pullout behavior of a single steel
fiber in a mortar matrix, and its influence on tensile behavior of SFRCC (Steel FiberReinforced Cementitious Composite). The test parameters are the thickness of thematrix and orientation angle of fiber. The orientation angle is set by two methods, i.e.,
angled pullout load to specimen (called set angle), and angled fiber embedded inmatrix (called embedded angle). The test results indicate that first peak load becomes
greater with increasing of bond length and orientation angle. The snubbing coefficientobtained from the specimens with set angles is larger than that obtained from thespecimens with embedded angle. The bridging law (tensile stress-crack width relation)is calculated using modeled pullout load – slip curves considering fiber orientation
distribution.

1. INTRODUCTION
Steel Fiber-Reinforced Cementitious Composite (SFRCC) is cementitious
composite with mixing short steel fibers in mortar. SFRCC improves tensile andbending characteristics of cementitious composites by bridging effect of short fibers
thorough the crack after first cracking. By applying SFRCC to components in concrete
structures, it is expected to improve durability and to prolong the service life ofstructures. However, there are few applications using SFRCC to structural elements
because of the difficulty of the evaluation of bridging effect in SFRCC. Therefore,
establishing the evaluation method of SFRCC is an important subject.
Previous researches have showed that the tensile performance of SFRCC ischaracterized by the bridging law (tensile stress-crack width relationship). The bridging
law can be expressed by the sum of pullout properties of single fiber, which is based on
1)
2)

Graduate StudentProfessor

The 2019 World Congress on
Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 - 21, 2019fiber-matrix bond characteristic and influenced by the orientation angle of fiber(Kanakubo et al. 2016). Orientation angle is defined by two factors as shown in Fig. 1.
One is that cracking surface angled against pullout direction of the fiber (Fig. 1 center,called set angle). The other one is that the fiber has angle against normal direction ofcracking surface (Fig. 1 right, called embedded angle). When the fiber embedded withan orientation angle, pullout strength of the fiber in matrix increases by snubbing effect(Li et al. 1990). Snubbing effect is considered to be caused by reaction force at thebending point of the fiber, and also it depends on the quantity of matrix at the bending
point of the fiber. It is considered that the difference of fiber orientation angles, such as
set angle and embedded angle, causes an influence on snubbing effect.
In this study, to evaluate the influence of fiber orientation angles set by two cases,
single steel fiber pullout test was conducted. By using the test results, the bridging law
is calculated.

Fig. 1 Definition of set angle and embedded angle

2. OUTLINE OF PULLOUT TEST
2.1 Materials
Table. 1 shows the material properties of steel fiber. Straight steel fiber before
cutting in the specified length was utilized in this study. Table 2. shows the matrix
mixture proportion.

Table 1 Material properties
Fiber diameter
(mm)
0.16

FiberSteel

Tensile strength(MPa)2825

Elastic modulus
(GPa)
210

Table 2 Mixture proportion
Watercement ratio(%)
56.0

Unit weight(kg/m3)
WaterCementSand

Fly ash380678484291

Waterreducing
admixture
6

The 2019 World Congress on
Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 - 21, 2019

2.2 Specimens
Casting mold is shown in Fig. 2 (left figure). Three rubber plates are sandwichedby two acrylic plates, and they are fixed by bolts. Molds have four holes for pouringmatrix into. A punched hole has been made in the center of the mold to let the fiber gothrough the mortar matrix, as shown in Fig. 2 (middle figure). In case of embedded
angle specimens, the upper and bottom holes have an eccentricity to ensure the initialembedded angle of fiber, as shown Fig. 2 (right figure). The parameters are specimen
thickness (1mm, 2mm, 3mm, 4mm, and 6mm), orientation angle (0°, 30°, 60°) andtypes of orientation angle (set and embedded). Five specimens were prepared for eachparameters. Bond length is calculated by specimen thickness divided by cosθ, as which
θ is embedded angle.

Fig. 2 Mold and its cross section

2.3 Method of loading and measurements
Pullout test was conducted using a screw-type testing machine. The
measurement items for all specimens were pullout load and displacement of theloading head of the testing machine. Set angle specimens were loaded by set standangled, as shown in Fig. 3 (left figure), embedded angle specimens were loaded asshown in Fig. 3 (right figure). Both specimens were set on the stand by steel platebonded under the specimen.

Fig. 3 Loading method

The 2019 World Congress on
Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 - 21, 2019

3. TEST RESULTS
Fig. 4 shows the relationships between load and slip for each specimen except
fractured specimens. The case of orientation angle is noted above each graph. Slip isobtained substituting the elongation of fiber out of the matrix from the displacement of
the loading head of the testing machine. The number of curves is less than five in small
thickness specimens that were fractured during removing the mold.
As shown in Fig. 4, pullout load of orientation angle 0° is smaller than that of otherorientation angles in same bond length. In case of orientation angle 0° specimens,pullout load increases linearly to the peak, decreases follows due to pullout of thefiber. In the other specimens, pullout load increases to the peak (first peak, Pmax), andthen keep a constant load, increases again and the fiber was pulled out completely.
Pmax is plotted in graphs.

Set0°-Embedded0°

40First peakSpecimenthickness
6mm
4mm
3mm
2mm
1mm

Load P (N)3020100051015

Slip s (mm)

Set0°-Embedded30°
First peak

Load P (N)3020Specimen
thickeness
6mm
4mm
3mm
2mm

510015

Slip s (mm)Set30°-Embedded0°3020

Specimenthickness
6mm
4mm
3mm
2mm

1004051015

Slip s (mm)Set60°-Embedded0°
First peak

30
Load P (N)

0First peak
Load P (N)2010400First peak load
Specimenthickeness
6mm
4mm
3mm
2mm

30100

Set0°-Embedded60°

40

Load P (N)4020

Specimenthickness
6mm
4mm
3mm
2mm
1mm

100510Slip s (mm)1500510

Slip s (mm)Fig. 4 Relationship between pullout load and slip

15

The 2019 World Congress on
Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 - 21, 2019

4. CALCULATION OF BRIDGING LAW
4.1 Modeling of single fiber pullout behavior
According to the pullout test results, single fiber bridging model has beenmodeled by bilinear model as same as the previous research (Hashimoto et al. 2016).
Bilinear model represents that pullout load increases linearly to the peak, anddecreases due to pullout of the fiber.
Fig. 5 shows the relationship between the first peak load and bond length, the left
figure shows those in set angle specimens, and the right figure shows those inembedded angle specimens. Bond length was calculated by measured specimen
thickness before loading. In each orientation angle, results are approximated by theleast square method as represented by Eq.(1). P1,θ represents the peak load per unit
bond length at θ orientation angle.
Pmax  P1,  lb

(1)

The approximation results in the Fig. 5 gives that P1,30 = 0.831(N/mm) and P1,60 =3.45(N/mm) in case of set angle, P1,30 = 1.31 and P1,60 = 2.00 for embedded angle.

Set 0°-Embedded 0°Set 30°-Embedded 0°
Set 60°-Embedded 0°
Pmax=3.45lb

3020

Pmax=0.831lb
Pmax=0.739lb

1000540First peak load Pmax (N)First peak load Pmax (N)40

Set 0°-Embedded0°
Set 0°-Embedded30°
Set 0°-Embedded60°

Pmax=1.31lb

20Bond length lb (mm)Pmax=0.739lb

10010

Pmax=2.00lb

3005

配向角0°
配向角30°
配向角0°
配向角30° between
配向角60°
nn
Fig.5 Relationships
first peakload
y=Σanx and bondy=Σanlengthx
y=Σan xn
y=Σan xn
y=Σan xna0=0.00000000e+00
a1=7.39051106e-01
3.25606550e+00|r|=3.23470359e-01

a0=0.00000000e+00
a0=0.00000000e+00(left : set angle,right : embeddedangle)
a0=0.00000000e+00
a0=0.00000000e+00

a1=8.31026979e-01
3.18751683e+00|r|=3.25098741e-01

10

Bond length lb (mm)a1=7.39051106e-01
a1=3.44535342e+00
3.25606550e+00
4.87760577e+00|r|=3.23470359e-01|r|=6.97678362e-01

a1=1.31450011e+00
1.68515765e+00|r|=7.19188121e-01

配向角60°y=Σan xna0=0.00000000e+00
a1=1.99866852e+00
5.28760196e+00|r|=7.33924917e-01

4.2 Snubbing coefficient
The snubbing effect is represented by snubbing coefficient as shown by Eq. (2).
P  P0  e f(2)The 2019 World Congress on
Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 - 21, 2019

First peak load per unit bond lengthP1,θ（N/mm)

First peak load per unit bond lengthP1,θ（N/mm)

In Eq. (2), P is the maximum pullout load, P0 is the maximum pullout load at 0degree orientation angle, f is snubbing coefficient, θ is orientation angle. In this study,
snubbing coefficient is calculated by the first peak load per unit bond length obtained
from Fig. 5. Fig. 6 shows the relationship between the first peak load per unit bondlength and orientation angle. Exponential approximations are carried out by the leastsquare method. The results are shown as the curves in Fig. 6, which indicate thesnubbing coefficients of 1.2 and 0.98 in the case of set angle and embedded angle,
respectively.

54
3

ln y=a + b x
a=-3.02457358e-01
b=1.70912905e-02
3.85657356e-02
P1,θ=exp(-0.302+0.98 θ)|r|=9.95783822e-01

1015 30 45 60 75 90
Orientation angle θ(度)ln y=a + b x
a=-3.02457358e-01
b=1.70912905e-02
3.85657356e-02|r|=9.95783822e-01

ln f' =a + b θ（θの単位は度）
a=-2.77563283e-01
b=1.65934090e-02
3.52055389e-02|r|=9.96269782e-01

10

ln f' =a + b θ（θの単位は度）
a=-2.77563283e-01
b=1.65934090e-02(θ:rad)3

ln f' =a + b θ（θの単位は度）
a=-2.77563283e-01
2b=1.65934090e-02
3.52055389e-02|r|=9.96269782e-01

205

ln f' =a + b θ（θの単位は度）
a=-2.77563283e-01
4
b=1.65934090e-02

P1,θ=exp(-0.302+1.2 θ)(θ(rad))015 30 45 60 75 90

Orientation angle θ(degree)

Fig. 6 Relationships between first peak load per unit bond length and orientation angle(left : set angle, right : embedded angle)

Fig. 7 shows the relationship of slip at first peak and bond length. The plots in Fig.
7 are approximated linearly by the least square method as expressed by Eq. (3).

smax  s1  lb

(3)

In Eq. (3), smax is slip at first peak load, s1 is slip at first peak load per unit bondlength. The approximation result shows that s1 is 0.19.

Slip at first peak smax (mm)5y=Σan xn

smax=0.19lb

a0=0.00000000e+00
a1=1.85550016e-01
8.53586535e-01|r|=4.66025821e-01
ny=Σan x0a0=0.00000000e+00
a1=1.91682095e-01
8.63131387e-01|r|=4.73859124e-01

0510

Bond length lb (mm)Fig. 7 Relationship between slip at first peak and bond length

The 2019 World Congress on
Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 - 21, 2019

To calculate the bridging law which is expressed by tensile stress-crack width
relationship, the model should be given by crack width. Crack width is assumed to betwo times slip by considering that the fiber is pulled out from the both ends in matrix, as
given by Eq. (4).
𝛿𝑚𝑎𝑥 = 2𝑠𝑚𝑎𝑥(4)

By considering the influence of bond length and orientation angle, the single fiber
pullout model is expressed by Pmax and δmax as Eq. (5).
Pi , j ( ,  , lb ) Pmax

 max

Pi , j ( ,  , l b )  Pmax (δ≦δmax)Pmax
 (   max )l b   max(δmax<δ)(5)

4.3 Calculation of bridging law
In FRCC, fibers bridge across the crack as shown Fig. 8. The bridging law iscalculated by applying the single fiber pullout model to each fibers. In this study, thebridging law is calculated by assuming the sectional area of 50mm x 50mm. Each fiber
follows the elliptic distribution as same as previous researches (Kanakubo et al. 2016).
The elliptic distribution is expressed by the orientation intensity k and the principal
orientation angle θr. The principal orientation angle θr expresses principal orientation
direction of fibers in crack plane. The orientation intensity k shows the fiber orientation
tendency to principal orientation angle. In this study, k is set to 1 expressing therandom orientation. The bridging law can be calculated by the sum of pullout load ofeach single fiber, as given by Eq. (6).
P( )   {N f  Pij ( , , l b )  p( i )  p(i )  p d ( y h , z h )      A}
hi

(6)

j

P(δ) = tensile force
Pij(δ,ψ) = tensile force of single fiberP(θi), p(φj) = probability based on elliptic distribution for x-y plane and z-x planePd(yh,zh) = probability of fiber distribution along x axis (constant)θ, φ = refer to Fig.8
Nf = number of fibers in crack plane
Nf can be expressed by Eq. (7).
𝑁𝑓 = 𝑉𝑓 ∙ 𝐴𝑚 / 𝐴𝑓
Vf = volume fraction of fiber
Am = cross sectional area of matrix
Af = cross sectional area of fiber
Table. 3 shows the parameters for calculation of bridging law.

(7)

The 2019 World Congress on
Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 - 21, 2019

Fig. 8 Bridging fibers in crack plane

Table 3 Input parameters to calculation of bridging law
Input item
Cross sectional area of matrix Am (mm2)Fiber length lf (mm)Snubbing coefficient f
Peak load per unit bond length at orientation
angle 0 degree P1,θ (N/mm)
Crack width at first peak load per unit bondlength of orientation angle 0 degree δ1 (mm)Fiber volume fraction Vf (%)
Orientation intensity k

Input number
EmbeddedSet
50 x 50130.981.2
0.739
0.38 (0.19 x 2)
1.01

4.3 Result of calculation
The calculation results of tensile stress-crack width relationships are shown in Fig.
9. Tensile stress in the case of set angle is larger than that of embedded angle.

Tensile stress  (MPa)1.5Set angle
Embedded angle

10.5001234Crack width  (mm)Fig. 9 Result of calculation

56

The 2019 World Congress on
Advances in Structural Engineering and Mechanics (ASEM19)
Jeju Island, Korea, September 17 - 21, 2019

5. CONCLUSIONS
The result of single steel fiber pullout test shows that the snubbing coefficient in
the case of set angle is larger than that of embedded angle. The results of calculationof bridging law using those snubbing coefficients show that the difference of snubbing
effect causes the difference in tensile stress.
REFERENCES
Hashimoto, H., Yamada, H., Yasojima, A., Kanakubo, T., (2016) “Pullout Behavior ofSteel Wire and Calculation of Bridging Law”, Proceedings of the Japan Concrete
Institute, Vol.38, No.1, pp.249-254. (in Japanese)
Kanakubo, T., Miyaguchi, M., Asano, K., (2016) “Influence of Fiber Orientation onBridging Performance of Polyvinyl Alcohol Fiber-Reinforced Cementitious
Composeite”, ACI Materials Journal. Vol.113, No.2, pp.131-141.
Li, V.C., Wang, Y., Backer, S., (1990) “Effect of Inclining Angle, Bundling, and Surface
Treatment on Synthetic Fiber Pull-out from a Cement Matrix”, Composites, Vol.21(2),pp.132-140