Engineering Structures 139 (2017) 59–70

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Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct

Seismic behavior of reinforced concrete sacrificial exterior shear keys

of highway bridges
Qiang Han a,⇑, Yulong Zhou a, Yuchen Ou b, Xiuli Du a
a
Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing, China
b
Department of Civil and Construction Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan, China

a r t i c l e i n f o a b s t r a c t

Article history: Shear keys as sacrificial members are widely used in cap beams and abutments of highway bridges, to
Received 21 September 2016 limit the transverse displacement of superstructures and control damage to substructures. An experi-
Revised 9 February 2017 mental program to study the seismic behavior of reinforced concrete (RC) sacrificial exterior shear keys
Accepted 13 February 2017
was presented. The influence of reinforcement ratios and construction joint types on the mechanical
behavior of the shear keys was investigated, and three failure modes of the exterior shear keys under
reversed loads were observed during testing. Two analytical models for predicting the force-
Keywords:
displacement backbone curves of the exterior shear keys with sliding shear failure and sliding friction
Highway bridge
Exterior shear key
failure were developed, respectively. The analytical models proposed in this paper were in good agree-
Seismic behavior ment with the experimental data, indicating that they can be used as a reliable tool for predicting the
Failure mode response of exterior shear keys of highway bridges.
Analytical model Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction earthquake, Priestley et al. [4] and Moehle et al. [5] indicated that
shear keys failed to play a role of structural fuses during the earth-
Exterior shear keys between the superstructure and substruc- quake. Subsequently, Megally et al. [6] and Silva et al. [7–9] studied
ture, as shown in Fig. 1, are important seismic components for the seismic performance and load transfer mechanism of shear
small to medium span bridges, and are used to provide transverse keys, and developed the shear-friction model and strut-and-tie
support for superstructure under earthquakes. Exterior shear keys model to predict the capacity of shear keys in abutments. Bozorg-
do not carry gravity loads, and seismic damage to such keys is zadeh et al. [10–12] carried out a series of experimental study on
easier to be detected and repaired than other bridge components, the behavior of bridge exterior shear keys subjected to lateral load-
such as abutment stem walls and piles. Therefore, exterior shear ing. Based on the test results, they developed a simplified model to
keys can be utilized as structural fuses to limit the magnitude of predict the capacity of sacrificial shear keys that fail in sliding
the force transmitted to the substructure. However, the use of shear mode, and proposed several recommendations for construc-
exterior shear keys as structural fuses, also known as sacrificial tion details of sacrificial shear keys. For shear-off failure of concrete
shear keys, have not received sufficient attention from bridge engi- key joints, Buyukozturk et el. [13] and Kaneko et el. [14] investi-
neers in seismic regions around the world. Failure of shear keys gated the shear behavior and proposed simplified formula. In addi-
with severe damage in abutments and cap beams was reported tion, Zhou et al. [15] and Shamass et al. [16] further investigated
in recent major earthquakes [1–3]. Fig. 2a shows diagonal tension the behavior of the concrete key joints through both experimental
failure in an abutment, and Fig. 2b shows the bridge girders com- studies and numerical simulations.
pletely shear off from the bearing pads due to the failure of the In the current design practice, exterior shear keys are generally
exterior shear keys. assumed to provide no further support once their maximum capac-
In the past few decades, experimental studies were performed ity has been exceeded [17]. Therefore, the determination of the
to investigate the seismic behavior of bridge exterior shear keys, maximum load-carrying capacity of exterior shear keys is impor-
and analytical models were proposed to evaluate their seismic tant. The determination of the post-peak behavior of exterior shear
behavior and maximum load-carrying capacity. Based on the keys under seismic loading is also important if the bridge is to be
investigation of damage to bridges during the 1994 Northridge evaluated for seismic performance. However, previous
studies [6,9] only provided analytical models for predicting the
⇑ Corresponding author. force-displacement behavior of shear keys with diagonal tension
E-mail address: qhan@bjut.edu.cn (Q. Han). failure. This paper presents an experimental study on ten exterior

http://dx.doi.org/10.1016/j.engstruct.2017.02.034
0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.
60 Q. Han et al. / Engineering Structures 139 (2017) 59–70

Superstructure
Backwall

Wing Exterior
wall Exterior Stem wall shear key Cap
shear key beam
Cap
Exterior
Exterior shear key
shear key

Pile Pier

(a) Abutment (b) Cap beam

Fig. 1. Schematics of exterior shear keys in the abutment and cap beam of bridges.

(a) Diagonal tension (b) Offset of girders

failure in an abutment from cap beams
Fig. 2. Failure of exterior shear keys with damage in abutments in earthquakes.

shear key specimens with different reinforcement ratios and types the interface of shear key-stem wall was monolithic construction,
of construction joints. The main objectives of this paper were: (1) consisted of Specimens S1 to S6. The second group, whose construc-
to investigate the seismic behavior and load transfer mechanism tion joint surface preparation was a seismic resilient construction,
of exterior shear keys under reversed lateral loading, (2) to develop consisted of Specimens S7 to S10. The configurations of the resilient
appropriate reinforcement detailing and construction joints at the construction joints shown in Fig. 3c are as follows: (1) an artificial
interface of shear key-abutment stem wall for shear keys to func- sliding surface is set on the interface between the shear key and stem
tion as structural fuses, and (3) to develop analytical models that wall by a piece of kraft paper, to limit the damage through aggregate
can accurately predict the load-displacement backbone behavior interlocking to the stem wall when the shear key moves, (2) poly-
of exterior shear keys with sliding shear failure mode and sliding styrene foam blocks are disposed adjacent to the vertical reinforce-
friction failure mode. ment on the top of the artificial sliding surface to control the bending
range of vertical reinforcement and avoid shear failure of the rein-
2. Experimental program forcement. Fig. 3 presents the elevation view and the layout of the
reinforcing bars of typical shear key specimens with monolithic
The experimental program consists of testing ten shear key spec- and resilient construction joints.
imens under lateral reversed loading to investigate the seismic The same concrete and reinforcement materials in the proto-
behavior of sacrificial exterior shear keys of highway bridges. The type shear keys were used for all the specimens, resulting in a
specimens with different reinforcement ratios and construction stress scaling factor of 1.0. Grade C40 concrete (Chinese concrete
joint between the shear key and stem wall were designed and built grade) with a measured compressive strength of 64.9 MPa from
at 1:1.25 scale of the prototype shear key designed according to Chi- the compression tests of concrete cubic specimens
nese design code, Guideline for Seismic Design of Highway Bridges [18]. (150
150
150 mm) after 28-day curing process at room tem-
The detailed configuration of vertical and horizontal reinforcement perature was used for the concrete of the specimens. HRB335 steel
in the shear key specimens, including the number of reinforcing (Chinese steel grade) were used for the vertical and horizontal
bars, reinforcement ratios, total cross-sectional areas of reinforcing reinforcement. HPB235 steel (Chinese steel grade) was used for
bars, are listed in Table 1. The vertical and horizontal reinforcement the hoops in both the shear key and stem wall and horizontal dis-
refer to the reinforcement crossing the interface between the shear tributing reinforcement in the stem wall (Fig. 3d), respectively. The
key and stem wall and the reinforcement in the stem wall right diameter, yield strength, ultimate strength and elongation of the
below the shear key-stem wall interface, respectively (Fig. 3). The vertical, horizontal, hoops and horizontal distributing reinforce-
ten exterior shear key specimens were divided into two groups. ment mentioned previously were obtained from standard tensile
The first group, whose construction joint surface preparation at coupon tests as presented in Table 2.
 Q. Han et al. / Engineering Structures 139 (2017) 59–70 61

Table 1
Reinforcement design parameters of specimens.

Specimen Vertical reinforcement Horizontal reinforcement Ash/Asv Construction joint type

Number of bars 2
Total area Asv (mm ) Ratio qsv (%) Number of bars 2
Total area Ash (mm )
S1 12/12 1358 0.91 6/12 679 0.5 Monolithic
S2 8/12 905 0.6 6/12 679 0.75
S3 4/12 452 0.3 6/12 679 1.5
S4 12/12 1358 0.91 12/16 2412 1.8
S5 8/12 905 0.6 12/16 2412 2.7
S6 4/12 452 0.3 12/16 2412 5.3
S7 12/12 1358 0.91 12/18 3054 2.2 Resilient
S8 10/12 1131 0.75 12/18 3054 2.7
S9 8/12 905 0.6 12/18 3054 3.4
S10 4/12 452 0.3 12/18 3054 6.8

The test setup is shown in Fig. 4. All the specimens were S1 and S2, and sliding shear failure was observed in Specimens
mounted vertically to a strong floor using post-tensioned bolts. S3 to S6. Their capacity is mainly contributed by the total resis-
Lateral loading simulating the force from the bridge superstructure tance from the vertical reinforcement and the concrete (see
was applied to the shear key by a servo-controlled hydraulic actu- Fig. 9a and b). For the specimens with monolithic construction
ator. The reversed lateral loading protocol consisted of joints, the failure modes can be determined based on the ratio of
displacement-controlled cycles, as shown in Fig. 5. For each target the total cross-sectional area of the horizontal reinforcement to
loading amplitude, three repeated loading cycles were performed that of the vertical reinforcement (Ash/Asv) (Table 1), whose bound-
on each specimen. The amplitude of the loading was increased ary value is between 0.75 and 1.50. Sliding friction failure was
until failure of the shear key. Strain gauges were attached to both observed in Specimens S7 to S10 with resilient construction joints,
the vertical/horizontal reinforcement and the hoops/horizontal- whose capacity is mainly contributed by the total resistance from
distributing reinforcement to monitor the deformation of the rein- the vertical reinforcement and friction along the interface between
forcement during tests. Displacement transducers were installed at the shear key and stem wall (see Fig. 9c).
the top of the shear key at a space of 100 mm to monitor the lateral
displacement of the key. 3.3. Load-displacement hysteretic response and envelop curves

3. Experimental observations and results Fig. 10a, b and c show the lateral load-displacement hysteretic
loops of the typical three shear key specimens with different fail-
3.1. General test observations ure modes. For all the specimens, the stiffnesses of loading and
unloading are almost the same. Therefore, the lateral load-
In Specimens S1 and S2, diagonal cracks initiated from the inner displacement back-bone curves can qualitatively evaluate and
side of the shear key at the shear key-stem wall interface during compare the seismic behavior of the shear key specimens, as
the second cycles at the displacement of 1 mm. As the tests contin- shown in Fig. 11.
ued, the diagonal cracks propagated to the outer side. The initial Several characteristics of Specimens S1 to S6 with monolithic
diagonal crack was the major crack during the tests, and a low construction joints are summarized as follows: (1) during the
horizontal reinforcement ratio in the stem wall caused it to propagating of concrete cracks, the specimens reached their peak
widen significantly. The damage process of Specimens S1 as the load with a small displacement in the range of 5.7 mm–26.3 mm,
representative is shown in Fig. 6. (2) after reaching the peak load, a significant drop in the lateral
In Specimens S3 to S6, horizontal cracks close to the loading load was caused by the reduction of concrete contribution to the
point initiated at the shear key-stem wall interface during the first resistance and then resulted in a shear failure. In addition, the
cycles. As the tests continued, an increase in the number of hori- number of rows of vertical reinforcement had significant influence
zontal cracks at the interface and inclined cracks at the stem wall on the force-displacement behavior of shear key specimens. For
was observed. The initial horizontal crack was the major crack dur- Specimens S4 and S5 with double rows of vertical reinforcement
ing the tests, and a low amount of vertical reinforcement in the (see Specimen S4 in Fig. 3b), local peak appeared after the peak
shear key caused it to widen significantly. The damage process of load, which did not appear in Specimens S3 and S6 with single
Specimens S3 as the representative is shown in Fig. 7. row of vertical reinforcement (see Specimen S3 in Fig. 3b).
In Specimens S7 to S10, horizontal cracks initiated from the Several characteristics of Specimens S7 to S10 with resilient
inner side of the shear key at the shear key-stem wall interface construction joints are summarized as follows: (1) local maximum
during the second cycles. As the tests continued, the concrete cover values of lateral loads appeared at a very small displacement in the
spalled and the shear key slid on the stem wall. The stem wall range of 0.7 mm–1.8 mm, (2) after the spalling of concrete cover,
remained in a good condition with only some minor spalling of obvious lateral sliding was observed on the interface between
the concrete cover even in the finial failure state, verifying the the shear key and stem wall inducing a minor loss in capacity,
desirable damage of shear keys with resilient construction joints. (3) prior to the peak value of loads, a rise of lateral loads and resid-
The damage process of Specimens S9 as the representative is ual displacement was recorded due to the hardening of the vertical
shown in Fig. 8. reinforcement, (4) after the peak value of loads, a significant drop
was recorded due to fracture of the vertical reinforcement.
3.2. Failure modes of shear key specimens
3.4. Maximum load-carrying capacity of specimens
Three different failure modes, diagonal tension failure in the
stem wall (Fig. 9a), sliding shear failure (Fig. 9b) and sliding friction In order to ensure shear keys function as structural fuses, the
failure (Fig. 9c) were observed during the tests of the shear key maximum load-carrying capacity of the shear key should be lim-
specimens. Diagonal tension failure was observed in Specimens ited by the lateral capacity of the stem wall within both
62 Q. Han et al. / Engineering Structures 139 (2017) 59–70

I-I section S1 S2 II-II section

300
I II 300 500
500
40 420 40 40 40 40 40 40 420 40

50

50
Erection Erection
reinforcement reinforcement

600

600
Hoops Hoops
Vertical Vertical
reinforcement reinforcement

I II

(a) Specimens S1 and S2 with monolithic construction joints

I-I section S3 S4 II-II section

500 300
I II 300 500
40 420 40 40 40 40 40 40 420 40
50

50
Erection Erection
reinforcement reinforcement
600

600
Hoops Hoops
Vertical Vertical
reinforcement reinforcement

I II

(b) Specimens S3 and S4 with monolithic construction joints

I-I Section S7 S8 II-II Section

I II
500 300 300 500
40 420 40 32 32 32 32 40 420 40
100 100
48

48

Erection Erection
reinforcement reinforcement
500

500

Kraft Kraft
paper paper
Foam Foam
blocks Hoops Hoops blocks
Vertical Vertical
reinforcement reinforcement

I II

(c) Specimens S7 and S8 with resilient construction joints

III-III section
500
45 410 45
III
Horizontal
Shear distributing Shear Horizontal
key reinforcement key reinforcement
1200

Hoops
38
500
424 38

III
(d) Reinforcement layout of the cap beam and footing
Fig. 3. Elevation view and reinforcement layout of typical specimens (Unit: mm).
 Q. Han et al. / Engineering Structures 139 (2017) 59–70 63

Table 2
Material properties of reinforcement.

Reinforcement Steel class Diameter (mm) Yield strength (MPa) Ultimate strength (MPa) Elongation (%)
Vertical HRB335 12 437 638 20.6
Horizontal HRB335 12, 16, 18 433 599 26.1
Hoops HPB235 8 422 542 13.8
Horizontal distributing HPB235 8 422 542 13.8

Force sensor
Hydraulic jack

Hinge
Shear key Shear key
Load cell
Spread girder

Box Box
Girder Girder

Actuator
Loading Smooth pad
head
Reaction Anchor Cap beam
wall

Fig. 4. Test setup of exterior shear key specimens.

respectively, it is found that the horizontal reinforcement ratio

has insignificant influence on the lateral load carrying capacity of
11.5
the shear key specimens. As shown in Fig. 11a, the lateral displace-
10 ments at peak load of those specimens decrease generally with the
Displacement (cm)

increase of Ash/Asv, except for Specimen S6.

8.5
For Specimens S7 to S10 with resilient construction joints, the
7.0 lateral capacity decreases and the extent of descending branch
5.5 increases, with the decrease of the vertical reinforcement ratio.
4.0
The values of the displacement ductility factor in Table 3 show that
3.0 the specimens with resilient construction joints have superior duc-
2.0 tility capacity compared with specimens with monolithic construc-
1.0 tion joints.
0 3 4 5 6 7 8 9
1 2
Number of loading levels 4. Analytical model of force-displacement back-bone response

Fig. 5. Loading protocol. 4.1. Mechanical characteristics of shear key specimens

capacity- and performance-based design frameworks. Table 3 lists Based on the experimental work above, the mechanical charac-
the measured maximum load-carrying capacity and corresponding teristics of the shear key specimens with different failure modes
displacement together with the vertical reinforcement ratio and are illustrated in Fig. 12a, b and c. The hysteretic model of exterior
the total cross-sectional area of the horizontal reinforcements to shear key with diagonal shear failure has been proposed by Silva
that of the vertical reinforcements for the shear key specimens. et al. [8], which is applicable to specimens with diagonal shear fail-
Comparing the experimental results of Specimens S1, S2 and S3, ure in the stem wall. Therefore, only the analytical models of the
it can be seen that the vertical reinforcement ratio has significant sliding shear failure mode and sliding friction failure mode were
effects on the lateral load carrying capacity of shear keys. Both investigated in this paper.
the capacity and displacement at peak load of the shear key spec- The resisting force of shear keys can be computed by Eq. (1),
imens decrease with the decrease of the vertical reinforcement considering the contributions of the concrete and reinforcement
ratio. A similar pattern can be observed for the lateral load carrying [6].
capacities of Specimens S4, S5 and S6. However, for Specimen S6,
V ¼ Vc þ Vs ð1Þ
the lateral displacement at peak load increases compared to that
of Specimen S5 with a higher vertical reinforcement ratio, which where, Vc and Vs are the concrete and reinforcement contributions
is primarily caused by the significant increase of horizontal rein- to the resisting force of shear keys, respectively.
forcements in Specimen S6. Moreover, comparing the experimen- The concrete contribution is provided by the shear capacity of
tal results of Specimens S1 and S4, S2 and S5, S3 and S6, the concrete of the interface between the shear key and stem wall.
64 Q. Han et al. / Engineering Structures 139 (2017) 59–70

(a) Initial cracking (at the (b) Cracks propagating (at (c) Cracks widening (at the (d) End of test (at the
displacement of 1mm) the displacement of 26mm) displacement of 80mm) displacement of 180mm)
Fig. 6. Damage process of Specimen S1.

(a) Initial cracking (at the (b) Cracks propagating (at (c) Cracks widening (at the (d) End of test (at the
displacement of 1mm) the displacement of 5mm) displacement of 25mm) displacement of 175mm)

Fig. 7. Damage process of Specimen S3.

(a) Initial cracking (at the (b) Cover spalling (at the (c) Shear key sliding (at the (d) End of test (at the
displacement of 1mm) displacement of 3mm) displacement of 80mm) displacement of 110mm)
Fig. 8. Damage process of Specimen S9.

The peak value of concrete contribution can be obtained by Priest- envelope curves of steel with a yielding plateau are provided by
ley et al. [19]. Chinese design code, Concrete Structure Design [20] as shown in
qffiffiffiffi Fig. 13. The stress-strain relationship of steel is given by Eq. (3).
0
V c max ¼ 0:2 f c Acv ðMPaÞ ð2Þ 8
>
>
Ee e 6 ey
>
>
where, f0c is the concrete compression strength; Acv is the total sec- >
> r ey < e 6 euy
>
< y
tional area of the monolithic shear key but the cover area of the
r ¼ ry þ kðe  euy Þ euy < e 6 eu ð3Þ
resilient shear key. >
>
>
In the following sections, the reinforcement contribution to the >
>
> ry þ kðe  euy Þ þ k ðe  eu Þ eu < e 6 eup
0
>
:
resisting force of shear keys with sliding shear failure and sliding 0 e > eup
friction failure were investigated, respectively. The stress-strain
 Q. Han et al. / Engineering Structures 139 (2017) 59–70 65

Tensile failure of
horizontal
reinforcements Tensile failure of
vertical Tensile failure of
reinforcements vertical
reinforcements

Vertical reinforcement
Horizontal reinforcement

(a) Diagonal shear failure (b) Sliding shear failure (c) Sliding friction failure
Fig. 9. Failure modes observed during the tests.

500 500 250

Diagonal shear failure Sliding shear failure Sliding friction failure

400 400 200

Lateral force (kN)

Lateral load (kN)

Lateral load (kN)

300 300 150

200 200 100

100 100 50

0 0 0
0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120
Lateral displacement (mm) Lateral displacement (mm) Lateral displacement (mm)
(a) S1 (b) S4 (c) S9
Fig. 10. Measured load-displacement curves of typical specimens with different failure modes.

500 400
S1 350 S7
S2 S8
400 S3 S9
300
S4 S10
Lateral load (kN)

Lateral load (kN)

S5
S6 250
300
200

200 150

100
100
50

0 0
0 50 100 150 200 0 25 50 75 100 125 150

Lateral displacement (mm) Lateral displacement (mm)

(a) S1 to S6 with monolithic joints (b) S7 to S10 with resilient joints

Fig. 11. Lateral load-displacement envelop curves of specimens.

where, ey , euy , eu and eup are the yield strain, hardening strain, ulti- 4.2. Analytical model of sliding shear failure mode
mate strain and fracture strain of steel, respectively; ry and ru are
the yield stress and ultimate stress, respectively; E is the elasticity According to the geometrical relationship shown in Fig. 12b, the
modulus; k is the tangent of the hardening stage; and k0 is the tan- reinforcement strain, eðhÞ, and the reinforcement bending rotation,
gent of the softening stage. hs(h), can be expressed by the shear key rotation angle, h, as follows
66 Q. Han et al. / Engineering Structures 139 (2017) 59–70

Table 3
Maximum load carrying capacity and corresponding displacement.

Specimen Vertical reinforcement ratio qsv Ash/ Maximum capacity Vnmax Corresponding displacement Dnmax Displacement ductility factor
(%) Asv (kN) (mm) lD
S1 0.91 0.5 483 26.7 12.0
S2 0.6 0.75 355 11.5 5.9
S3 0.3 1.5 262 2.7 10.0
S4 0.91 1.8 463 12.4 6.9
S5 0.6 2.7 371 5.8 3.4
S6 0.3 5.3 303 12.3 9.5
S7 0.91 2.2 344 79.6 131.2
S8 0.75 2.7 326 89.0 102.1
S9 0.6 3.4 234 76.4 46.8
S10 0.3 6.8 136 70.8 44.1

V V V
m
fyhAsh m s

fysAss fyvAsv
m s
θ

fyvAsv fyvAsv
fysAss R fyvAsv

(a) Diagonal shear failure (b) Sliding shear failure (c) Sliding friction failure
Fig. 12. Mechanical characteristics of specimens with different failure modes.

8
>
< m1 e 6 euy
u e e
1 m ¼ m2 ¼ n eu euyuy m1 euy < e 6 eu ð6Þ
k k >
:
1 m3 ¼ nm1 e > eu
y
where, the value of m1 is listed in Table 4 for each specimen, n is the
modified coefficient for the bending length of the vertical reinforce-
ment after yielding, relating to the reinforcement diameter, and can
be calculated by Eq. (7)
2cdb þ m1
n¼ ð7Þ
m1
ε where, db is the diameter of the vertical reinforcement, c is a coef-
0 εy εuy εu εup ficient equal to 5.283 derived from the measurement of the bending
length of the vertical reinforcement after the testing.
Fig. 13. Stress-strain envelope curves of steel in Chinese design code. For the shear keys with sliding shear failure, the reinforcement
contribution contains the lateral resisting force of vertical reinforc-
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ing bars and friction force between the shear key and stem wall,
2 which is given by Eq. (8)
½hðR þ mÞ cos h2 þ ½m  hðR þ mÞ sin h
e ¼ eðhÞ ¼ 1 ð4Þ V S ¼ Asv rðlr cos hs ðhÞ þ sin hs ðhÞÞ ð8Þ
m
where, lr is the coefficient of friction on the rough concrete surface
hðR þ mÞ cos h
tan hs ðhÞ ¼ ð5Þ and determined to be 0.35 by Bozorgzadeh et al. [11].
m  hðR þ mÞ sin h
Therefore, the reinforcement contribution can be obtained by
where, R is equal to 357 mm from test observation and geometrical substituting the stress-strain relationship of steel into Eq. (8).
relationship; m is the bending length of the vertical reinforcement The finial equations predicting the force-displacement back-bone
(Fig. 12b), and is calculated by Eq. (6) from test observation. curves of shear keys with sliding shear failure are listed as follows
 Q. Han et al. / Engineering Structures 139 (2017) 59–70 67

Table 4
Values of parameters in analytical models.

Specimen Acv (mm2) E (Gpa) k (Mpa/mm) k0 (Mpa/mm) m1 (mm) ey euy eu eup

S3 150,000 218.5 4467 4467 100 0.002 0.005 0.05 0.10
S4
S5
S6
S7 44,400 218.5 4785 14,355 80 0.002 0.005 0.05 0.10
S8
S9
S10

8 I
>
> V c þ V Is eðhÞ 6 ey For the shear keys with sliding friction failure, the reinforce-
>
>
< V II þ V II ey < eðhÞ 6 euy ment contribution contains the lateral resisting force of vertical
c s
V¼ ð9Þ reinforcing bars and friction force between the shear key and cap
>
> Vs
III
euy < eðhÞ 6 eu
>
> beam, which is given by Eq. (21)
: IV
Vs eu < eðhÞ 6 eup
Asv r
V S ¼ Asv rðls cos hs þ sin hs Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðD þ ls mÞ ð21Þ
D ¼ hðR þ hÞ ð10Þ D2 þ m2
where, ls is the coefficient of friction on the smooth concrete sur-
eðhÞ
V Ic ¼ V ð11Þ face and determined to be 0.123 by the kraft paper manufacturer.
ey c max Therefore, the reinforcement contribution can be obtained by
substituting the stress-strain relationship of steel into Eq. (21).
euy  eðhÞ
V IIc ¼ V ð12Þ The finial equations predicting the force-displacement back-bone
euy  ey c max curves of shear keys with sliding friction failure are listed as
follows
V Is ¼ Asv Eeðlr cos hs ðhÞ þ sin hs ðhÞÞ ð13Þ 8 pffiffiffiffiffiffiffiffiffiffi2ffi
> m 2ey þe
>
> V Ic þ V Is D6 1 2 y
Shear key specimens with single vertical reinforcement row: >
> pffiffiffiffiffiffiffiffiffiffi2ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
>
> m1 2ey þey
>
> V IIc þ V Is < D 6 m1 2ey þ e2y
V IIs ¼ Asv ry ðlr cos hs ðhÞ þ sin hs ðhÞÞ ð14Þ >
>
> 2
< qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
V ¼ V IIs m1 2ey þ e2y < D 6 m1 2euy þ e2uy ð22Þ
s ¼ Asv ðrs þ kðe  euy ÞÞðlr cos hs ðhÞ þ sin hs ðhÞÞ
V III ð15Þ >
>
>
> qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
> V III
> m1 2euy þ e2uy < D 6 m2 2eu þ e2u
>
>
>
>
s
s ¼ Asv ðry þ kðeu  euy Þ þ k0ðe  eu ÞÞðlr cos hs ðhÞ
V IV >
> pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
: V IV m2 2eu þ e2u < D 6 m3 2eup þ e2up
s
þ sin hs ðhÞÞ ð16Þ
Shear keys with double vertical reinforcement rows: 2D
  V Ic ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V c max ð23Þ
e  ey   m1 2ey þ e2y
V IIs ¼ Asv ry 1  w1 lr cos hs ðhÞ þ sin hs ðhÞ ð17Þ
euy  ey
 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 
  2 m1 2ey þ e2y  D
e  euy  
V III ¼ Asv 1  w1  w2 ry þ kðe  euy Þ ðlr cos hs ðhÞ V IIc ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V c max ð24Þ
s
eu  euy m1 2ey þ e2y
þ sin hs ðhÞÞ ð18Þ
0qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1
 
e  euy   B D 2
þ m 2
 m 1C
V IV
s ¼ Asv 1  w2 ry þ kðeu  euy Þ þ k0 ðe  eu Þ V Is ¼ Asv E@ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi AðD þ ls m1 Þ
1
ð25Þ
eu  euy 2
m1 D þ m1 2

ðlr cos hs ðhÞ þ sin hs ðhÞÞ ð19Þ
where, h is the distance between the displacement transducer and Asv ry
V IIs ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðD þ ls m1 Þ ð26Þ
bottom of the shear key; D is the displacement at the top of the
D2 þ m21
shear key specimens corresponding to the displacement measured
in the tests; w1 and w2 are the reduction coefficients of the
Asv
s ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½ry þ kðe  euy ÞðD þ ls m2 Þ
contribution of the vertical reinforcement in double row and V III ð27Þ
approximately equal to 0.35 and 0.15, respectively derived from D2 þ m22
test results and the analytical model developed in this paper.

As v
s ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½ry þ kðeu  euy Þ þ k ðe  eu Þðx þ ls m3 Þ
0
4.3. Analytical model of sliding friction failure V IV ð28Þ
x2 þ m23
According to the geometrical compatibility relationship in
Fig. 12c, the relationship between the reinforcement strain, e, and
the shear key lateral displacement, D, is as following 4.4. Comparison with the experimental results
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
D2 þ m2 The values of the parameters in the analytical models are listed
e¼ 1 ð20Þ
m in Table 4. Using these parameters, the force-displacement back-
68 Q. Han et al. / Engineering Structures 139 (2017) 59–70

300 500
Experimental data
450 Experimental data
250 Analytical curves
Analytical curves
400
Lateral load (kN)

Lateral load (kN)

200 350

300
150 250

200
100
150

100
50
50

0 0
0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180
Lateral displacement mm Lateral displacement (mm)
(a) S3 (b) S4
400 350

Experimental data
350 300 Experimental data
Analytical curves
Analytical curves
300
250
Lateral load (kN)

Lateral load (kN)

250
200
200
150
150
100
100

50 50

0 0
0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140
Lateral displacement (mm) Lateral displacement (mm)
(c) S5 (d) S6

400 350
Experimental data Experimental data
350 Calculated curves 300 Calculated curves

300
Lateral load (kN)
Lateral load (kN)

250
250
200
200
150
150
100
100

50 50

0 0
0 30 60 90 0 20 40 60 80 100
Lateral displacement (mm) Lateral displacement (mm)
(e) S7 (f) S8
300 160
Experimental data Experimental data
Calculated curves 140 Calculated curves
250
120
Lateral load (kN)

Lateral load (kN)

200
100

150 80

60
100
40
50
20

0 0
0 30 60 90 0 30 60 90
Lateral displacement (mm) Lateral displacement (mm)
(g) S9 (h) S10
Fig. 14. Comparison of calculated and experimental load-displacement envelop curves.
 Q. Han et al. / Engineering Structures 139 (2017) 59–70 69

Table 5
Comparison of peak point of back-bone curves.

Specimen Peak point

Lateral load (kN) Lateral displacement (mm)
Test Calculation Deviation (%) Test Calculation Deviation (%)
S3 262 293 11.83 2.70 8.93 230.74
S4 463 458 1.08 12.4 8.93 27.98
S5 371 376 1.35 5.80 8.93 53.97
S6 303 293 3.30 12.3 8.93 27.40
S7 344 374 8.72 73.11 66.21 9.44
S8 326 311 4.60 71.97 66.21 8.00
S9 234 249 6.41 60.49 66.21 9.46
S10 136 124 8.82 63.68 66.21 3.97

bone curves were calculated by the analytical models and com- (3). Two different analytical models to assess the force-
pared with the experimental results, as shown in Fig. 14. It can displacement back-bone response of shear keys are devel-
be seen that the calculated force-displacement back-bone curves oped for sliding shear failure mode and sliding friction
are in good agreement with those from the experiment. The com- mode, respectively. Compared with the experimental data,
parison is shown in Table 5 on the peak point of force- these two analytical models can well predict the force-
displacement back-bone curves of the specimens, indicating that displacement back-bone response of the shear key
the analytical methods were able to accurately evaluate the maxi- specimens.
mum load-carrying capacity with a deviation less than 12%. How-
ever, the effect of vertical reinforcement ratios on the displacement
is not considered in the analytical models. Therefore, the two ana- Acknowledgments
lytical models provide a same value of displacement at peak point
for the specimens with sliding shear failure and sliding friction fail- This research is jointly funded by the National Natural Science
ure, respectively. This leads to a significant difference between the Foundation of China (NSFC) [grant numbers 51578022,
calculated and experimental displacement at the peak load for the 51421005]. This support is gratefully acknowledged. The results
shear key specimens with monolithic construction joints. Further and conclusions presented in the paper are those of the authors
research is needed to address this significant difference. and do not necessarily reflect the view of the sponsors.

5. Conclusions
References
An experimental program was performed to investigate the [1] Han Q, Du X, Liu J, Li Z, Li L, Zhao J. The seismic damage of highway bridges
seismic behavior of reinforced concrete exterior shear keys of high- during 2008 Wenchuan earthquake. Earthquake Eng Eng Vib 2009;8:263–73.
way bridges. Ten shear key specimens with different reinforcement [2] Sarrazin M, Moroni O, Neira C, Venegas B. Performance of bridges with seismic
isolation bearings during the Maule earthquake, Chile. Soil Dyn Earthquake
ratios and construction joints were tested under lateral reversed Eng 2013;47:117–31.
loading. Important conclusions of this research are summarized [3] Schexnayder C, Alarcón L, Antillo E, Morales B, Lopez M. Observations on
as follows: bridge performance during the Chilean earthquake of 2010. J Constr Eng
Manage 2014;140:B4013001.
[4] Priestley MJN, Seible F, Uang CM. The Northridge earthquake of January 17,
(1). Three types of failure modes were observed during the tests 1994: Damage analysis of selected freeway bridges. San Diego, La Jolla
of the shear key specimens: diagonal shear failure, sliding (California): University of California; 1994.
[5] Moehle J, Fenves G, Mayes R, Priestley MJN, Seible F, Uang CM, et al. Highway
shear failure and sliding friction failure. It is found that the
bridges and traffic management. Earthquake Spectra 1995;11:287–372.
shear key specimens with monolithic construction joints [6] Megally SH, Silva PF, Seible F. Seismic response of sacrificial shear keys in
exhibited diagonal shear failure and sliding shear failure, bridge abutments. San Diego, La Jolla (California): University of California;
which is determined by the ratios between the total cross- 2001.
[7] Silva PF, Megally S, Seible F. Performance of sacrificial exterior shear keys
sectional area of the horizontal reinforcement to that of under simulated seismic loading. ACI Special Publication 2002;209:681–700.
the vertical reinforcement (Ash/Asv). The shear key specimens [8] Silva PF, Megally S, Seible F. Seismic performance sacrificial interior shear keys.
with resilient construction joints failed in sliding friction ACI Struct J 2003;100:177–87.
[9] Silva PF, Megally S, Seible F. Seismic performance of sacrificial exterior shear
mode, and minor damage occurred in the stem wall. keys in bridge abutments. Earthquake Speactra 2009;25:643–4.
(2). With the decrease of the vertical reinforcement ratio of the [10] Bozorgzadeh A, Megally SH, Restrepo JI, Ashford SA. Seismic response and
specimens with monolithic construction joints, the maxi- capacity evaluation of exterior sacrificial shear keys in bridge abutments. San
Diego, La Jolla (California): University of California; 2004.
mum load-carrying capacity and corresponding displace- [11] Bozorgzadeh A, Megally SH, Restrepo JI, Ashford SA. Capacity evaluation of
ment decreases significantly Lateral displacements at peak exterior sacrificial shear keys of bridge abutments. J Bridge Eng
force of the specimens with monolithic construction joints 2006;11:555–65.
[12] Bozorgzadeh A, Megally SH, Ashford S, Restrepo JI. Seismic response of
decrease generally with the increase of Ash/Asv (except for sacrificial exterior shear keys in bridge abutments. San Diego, La Jolla
Specimen S6). With the decrease of the vertical reinforce- (California): University of California; 2007.
ment ratio of the specimens with resilient construction [13] Buyukozturk O, Bakhoum MM, Beattie SM. Shear behavior of joints in precast
concrete segmental bridges. J Struct Eng 1990;116:3380–401.
joints, the maximum load-carrying capacity decreases sig-
[14] Kaneko Y, Connor JJ, Triantafillou TC, Leung CK. Fracture mechanics approach
nificantly, and the extent of descending branch increases. for failure of concrete shear key. I: theory. J Eng Mech 1993;119:681–700.
The specimens with resilient construction joints have higher [15] Zhou X, Mickleborough N, Li Z. Shear strength of joints in precast concrete
displacement ductility factor than the specimens with segmental bridges. ACI Struct J 2005;102:3–11.
[16] Shamass R, Zhou X, Alfano G. Finite-element analysis of shear-off failure of
monolithic construction joints at the expense of lower max- keyed dry joints in precast concrete segmental bridges. J Bridge Eng
imum lateral force. 2014;20:04014084.
70 Q. Han et al. / Engineering Structures 139 (2017) 59–70

[17] Caltrans. Bridge design specifications. Sacramento: California Department of [19] Priestley MJN, Seible F, Calvi GM. Seismic design and retrofit of bridges. New
Transportation; 1990. York: John Wiley & Sons; 1996.
[18] JTG/T B02-01. Guideline for seismic design of highway bridges. Beijing: China [20] GB50010. Concrete structure design. Beijing: China Building Industry Press;
Communications Press; 2008. 2010.