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Elasto plastic behavior of 3 dimensional reinforced concrete abutments considering the effect of the wing wall
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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014), pp. 79-96 © IAEME
97
ELASTO-PLASTIC BEHAVIOR OF 3-DIMENSIONAL
REINFORCED CONCRETE ABUTMENTS CONSIDERING
THE EFFECT OF THE WING WALL
Desy Setyowulan1, Tomohisa Hamamoto
2, ToshitakaYamao
3
1Graduate School of Science and Technology, Kumamoto University, 2-39-1 Kurokami,
Kumamoto, 860-8555, Japan 2Departement of Civil Engineering, Gunma National College of Technology, 580, Tribamachi,
Maebashi, Gunma 371-8530, Japan 3Graduate School of Science and Technology, Kumamoto University, 2-39-1 Kurokami,
Kumamoto, 860-8555, Japan
ABSTRACT
This study presents the elasto-plastic behavior of 3-dimensional reinforced concrete
abutments with wing wall as a parametric. To analyze the structure, we used ABAQUS, the finite
element software, with geometrical modeling of three dimensional solid elements (C3D8R) and two
dimensional trusses (T3D2) for concrete and reinforcing bar, respectively. Four static horizontal
loads were applied at half-height of parapet wall with the fixed boundary condition at the footing of
abutment. Firstly, the analytical and experimental result of reinforced concrete beam was compared
in this paper in order to check the validity of the numerical analysis. Then, numerical studies were
carried out in four different abutment modeling approaches including the proposed model of Type 4
in order to generate an appropriate abutment model. According to the numerical results, it was
demonstrated that effect of the wing wall in reducing the displacement of the proposed model was
significant in the wing wall part. Furthermore, cracking and stress distribution in the proposed model
were also affected by the wing wall.
Keywords: Reinforced concrete abutment, concrete damaged plasticity, elasto-plastic behavior,
parapet wall, wing wall
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
TECHNOLOGY (IJCIET)
ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 11, November (2014), pp. 97-113
© IAEME: www.iaeme.com/Ijciet.asp
Journal Impact Factor (2014): 7.9290 (Calculated by GISI)
www.jifactor.com
IJCIET
©IAEME
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
98
I. INTRODUCTION
Reinforced concrete (RC) materials have been widely used as the main constituent material in
the structural engineering structure, such as in the buildings, bridges, dams, etc. This material has the
complex behavior which is mainly due to non-linear stress-strain relation of the concrete under
multi-axial stress conditions, strain softening and anisotropic stiffness reduction, progressive
cracking caused by tensile stresses, both between concrete and reinforcement, aggregation interlock
and dowel action of reinforcement, time dependent behavior as creep and shrinkage [1].
Consequently, a proper material modelshould be capable to represent the behavior of materials,
including elastic and elasto-plastic behavior of concrete in tension and compression, within finite
element packages.
Recently, many studies have investigated the behavior of concrete using finite element
analysis. Model verifications of RC beam structures with the damage identification by Concrete
Damaged Plasticity model in ABAQUS [2] have performed by some researchers. This code has
shown the adequate reliability and accuracy to perform nonlinear behavior of RC structure in
comparison with the experimental results [3-5].
In structural engineering, abutment refers to the end support of the bridge superstructure. It
plays an important role on the performance of bridge, such as transferring load from superstructure
to its foundation, resisting and/or transferring self-weight and lateral loads from earth pressure and
wind loads, also supporting one end of an approach slab. Its behavior has been found to significantly
influence the response of an entire bridge system under strong intensity dynamic excitation [6].On
many bridges, abutment damage was the only damage reported indicating that it attracted a large
portion of seismic force [7].
The parapets and wing walls of abutment are designed based on the Japan Specification for
Highway Bridges, Part IV Substructures [8]. In earthquake prone area, the unseating prevention
structures (UPS) are needed to be installed in the bridge structure in order to prevent unseating of the
superstructure against unforeseen conditions such as unexpected seismic force, destruction of the
surrounding ground, or unexpectedly complicated vibrations in the structural members. However,
falling of the superstructure may lead by the breakage of the parapet when UPS are installed to the
parapet.
Previous study [9] has carried out an investigation on the elastic behavior of parapet
considering to the wing wall. In comparison with the plate structure fixed three sides, it is found that
the bending moment and shear force at the base of the parapet wall decrease and elastic deformation
behavior is similar. In addition, an investigation on elastic and elasto-plastic behavior of the parapet-
unified wing walls of abutment subjected to horizontal loads through unseating prevention structure
of bridge has been conducted by another researcher [10]. From this study, it has been recognized that
the effect of the wing walls on the behavior and bending moment at base of the parapet is very large.
In past large earthquake, many abutments collapsed due to strong intensity of dynamic excitation.
The collapsed mainly due to high stress as the most common problems observed during the
inspection of the abutment failure. Therefore, it is needed to analyze the new type of abutment as the
proposed model in order to generate an appropriate abutment model. This study is focused on
determination of the elasto-plastic behavior of 3-D reinforced concrete abutments considering to the
effect of the wing wall. The finite element software of ABAQUS with the Concrete Damaged
Plasticity method was used as the finite element analysis method. In verification method, modeling
technique of reinforced concrete beamwas verified by comparing the model prediction of RC beam
to the experimental work in the previous research [10]. Then, numerical studies were carried out in
four different abutment modeling approaches including a proposed model of abutment, subjected to
horizontal loads through the unseating prevention structures. The results were used to predict the
effect of the wing wall in the behavior of abutment.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
99
II. NUMERICAL PROCEDURES
2.1 Finite element modeling
Numerical modeling of reinforced concrete beam and abutments were performed using
ABAQUS [2] software. The concrete beam was idealized by homogenous material and modeled with
eight-node solid (brick) elements, identified as C3D8R elements. Furthermore, the reinforcing bar
was idealized by three dimensional truss elements called T3D2.
2.2 Constitutive model of steel reinforcing bar (rebar)
The constitutive model for steel rebar has approximately linear elastic behavior when the
stiffness is governed by the Young’s modulus at low strain magnitudes. At higher strain magnitudes,
it begins to behave nonlinear, inelastic behavior, which is referred to as plasticity [3]. The plastic
behavior is described by its yield point and post-yield hardening, with the shift from elastic to plastic
behaviors occurs at a yield point on a material stress-strain curve. Once the stress in rebarexceeds the
yield stress, permanent (plastic) deformation begins with decreasing of the stiffness. The plastic
deformation of this material increases its yield stress for subsequent loadings.
2.3 Constitutive model of concrete
In ABAQUS [2], there are three methods to simulate the damage criterion in reinforced
concrete elements, including brittle crack concrete model, smeared crack concrete model and
concrete damaged plasticity model (CDP). The CDP method allows in defining the complete
inelastic behavior of concrete under tension and compression including the damage parameters. It
provides a general capability for modeling concrete and other quasi-brittle materials in all types of
structures (beams, trusses, shells, and solids), so it can be used with rebar to model concrete
reinforcement.In the mechanical behavior of CDP, tensile cracking and compressive crushing are
assumed to be the main failure mechanisms of concrete. Failure of the yield surface is controlled by
tensile and compressive equivalent plastic strains, pl
c
pl
t εε ~ and ~ , respectively.
The concrete behavior is considered independently with rebar. Effect of the bond slip and
dowel action are modeled by introducing some “tension stiffening”, as shown in Fig. 1(a), in order to
simulate load transfer across cracks through the rebar and to define cracking and post cracking
properties for the concrete.The stress-strain response under uniaxial tension follows a linear elastic
relationship up to the failure stress, 0tσ , corresponds to the onset of micro-cracking in the concrete
material. The compressive equivalent cracking strain and plastic strain values, pl
t
ck
t εε ~ and ~ , are
defined by (1) and (2), respectively.
el
ott
ck
t εεε −=~ (1)
( )(2)
1
~~
o
t
t
tck
t
pl
tEd
d σεε
−−=
where: tε : total tensile strain
el
otε : The elastic tensile strain corresponding to the undamaged material, ot
el
ot Eσε =
Eo : Young’s modulus
tσ : tensile stress
dt : tension damage parameter
The compressive behavior of plain concrete under uniaxial compression outside the elastic
range can be defined, as shown in Fig. 1(b). The stress-strain response under uniaxial compression is
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
linear up to the initial yield, 0cσ . The response in plastic regime is characterized by stress hardening
followed by strain softening beyond the ultimate stress,
plastic strain values, pl
c
in
c εε ~ and ~ , are defined by (3) and (4), respectively.
of the elastic modulus in compressive and tensile behavior,
respectively.
el
occ
in
c εεε −=~
( )1
~~
o
c
c
cin
c
pl
cEd
d σεε
−−=
( )occ EdE −= 1
( )ott EdE −= 1
where: cε : total compressive strainel
ocε : The elastic tensile strain corresponding to the
cσ : Compressive stress
dc : compression damage parameter
(a) Tension behavior associated with
tension stiffening
Figure 1.
(a) Compressive stress-strain relationship [
Figure 2. Numerical properties of RC structure
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
100
. The response in plastic regime is characterized by stress hardening
ing beyond the ultimate stress, cuσ . The inelastic (or crushing) strain and
, are defined by (3) and (4), respectively. In addition, the reduction
of the elastic modulus in compressive and tensile behavior, Ec and Et, are given
(3)
)4(
(5)
(6)
: total compressive strain
elastic tensile strain corresponding to the undamaged material,
stress
damage parameter
Tension behavior associated with
tension stiffening
(b) Compression behavior associated
with compression hardening
Figure 1.Concrete damaged plasticity model [2]
strain relationship [11] (b) Modified tension stiffening model [
Figure 2. Numerical properties of RC structure
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
. The response in plastic regime is characterized by stress hardening
The inelastic (or crushing) strain and
In addition, the reduction
, are given in (5) and (6),
undamaged material, ot
el
oc Eσε =
Compression behavior associated
with compression hardening
(b) Modified tension stiffening model [5]
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
In this analysis, modeling of the
previous research [11], which can be used for
shown in Fig. 2(a). The compressive stress value
cuσ3.0 in the descending portion is calculated by (
for the concreteis shown in Fig.2(b).
through the rebar and to define cracking and post cracking prope
ocuc E and,σσ are in kip/in2 with the conversion factor of 1MPa = 0.145 kip/in
( )( ) cu
oc
oc
c σεεβ
εεβσ
β
+−=
1
( )[ ]oocu Eεσβ
−=
1
1
35 10114.2109.8 −− += xx cuo σε
32 10283.310243.1 xxE cuo += σ
2.4 Numerical modeling of reinforced concrete
In order to ensure the validity of the numerical analysis, a model comparison to actual
behavior was performed. A simple model of RC beam structure shown in
including its material properties [1
b of 100 mm, the height h of 400 mm,
230 mm from the beam ends.The shear span ratio (
respectively. Other structural properties were shown in Table 1. It was subjected to two identical
point loads and applied symmetrically on the rigid plates. Moreover, the stress
the concrete and rebar are shown in
was measured by means of LVDTs.
Figure 3. Position of the tested RC beam [1
According to the experimental test setup data, RC beam was then simulated in X
coordinate system with a half-length by symmetry condition, as shown in Fig.5. X, Y, and Z axes
were parallel to the longitudinal, depth and width of beam. The compressive strength of the
were 27.214 MPa (taken as yielding strength
The density, Young modulus Eo
kg/m3, 33342.61 MPa, 3.315 MPa, and 0.167. In addition, rebar was assumed as steel material with
the density of 7850 kg/m3, yield stress
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
101
In this analysis, modeling of the compressive stress-strain curve was d
can be used for normal strength concrete with σ
The compressive stress value, cσ , between the yield point at
descending portion is calculated by (7). Furthermore, modified tension stiffening
2(b). It is introduced in order to simulate load transfer across cracks
through the rebar and to define cracking and post cracking properties for the concrete.
with the conversion factor of 1MPa = 0.145 kip/in
(7)
(8)
(9)
(10)
Numerical modeling of reinforced concrete (RC) beam structure
In order to ensure the validity of the numerical analysis, a model comparison to actual
behavior was performed. A simple model of RC beam structure shown in
material properties [10]. As shown in this set-up, a rectangular RC beam
of 400 mm, 900 mm long Lwas positioned horizontally and supported at
The shear span ratio (a/d) and the depth d wer
respectively. Other structural properties were shown in Table 1. It was subjected to two identical
point loads and applied symmetrically on the rigid plates. Moreover, the stress
the concrete and rebar are shown in Fig. 4(a) and Fig. 4(b), respectively.The deflection at mid
was measured by means of LVDTs.
Figure 3. Position of the tested RC beam [10]
Table 1. Structural properties of RC
beam
Descriptions Dimensions (mm)
l
t
r
e experimental test setup data, RC beam was then simulated in X
length by symmetry condition, as shown in Fig.5. X, Y, and Z axes
were parallel to the longitudinal, depth and width of beam. The compressive strength of the
were 27.214 MPa (taken as yielding strength fco) and 54.427 MPa (taken as ultimate strength
o, tensile stress 0tσ , and Poisson’s ratio cυ of concrete were 2400
MPa, 3.315 MPa, and 0.167. In addition, rebar was assumed as steel material with
, yield stress fyof 375.3 MPa, Young modulus Es of 205939.65 MPa, and
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
strain curve was developed based on the
cuσ less than 62 MPa, as
between the yield point at cuσ5.0 and the
modified tension stiffening model
It is introduced in order to simulate load transfer across cracks
rties for the concrete.The equations,
with the conversion factor of 1MPa = 0.145 kip/in2.
)
In order to ensure the validity of the numerical analysis, a model comparison to actual
behavior was performed. A simple model of RC beam structure shown in Fig. 3was chosen,
up, a rectangular RC beam with the width
was positioned horizontally and supported at
were 0.5 and 320 mm,
respectively. Other structural properties were shown in Table 1. It was subjected to two identical
point loads and applied symmetrically on the rigid plates. Moreover, the stress-strain relationship of
4(b), respectively.The deflection at mid-span
Table 1. Structural properties of RC
beam
Dimensions (mm)
440
30
100
e experimental test setup data, RC beam was then simulated in X-Y-Z
length by symmetry condition, as shown in Fig.5. X, Y, and Z axes
were parallel to the longitudinal, depth and width of beam. The compressive strength of the concrete
) and 54.427 MPa (taken as ultimate strength fcu).
of concrete were 2400
MPa, 3.315 MPa, and 0.167. In addition, rebar was assumed as steel material with
of 205939.65 MPa, and
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
Poisson’s ratio sυ of 0.3. The damaged variables,
Fig.6(a) and Fig.6(b).
(a) Stress-strain curve for concrete
Figure
(a) Applied load and boundary condition
Figure
(a) Tension damage
Figure
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
102
of 0.3. The damaged variables, dt and dc, are defined based on plot presented in
strain curve for concrete (b) Stress-strain curve for steel rebar [10
Figure 4. Model input of RC beam
Applied load and boundary condition (b) Solid element (c) Rebar element
Figure 5. Model of RC beam in ABAQUS
Tension damage (b) Compression damage
Figure 6. Damage variables of the concrete
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
are defined based on plot presented in
strain curve for steel rebar [10]
(c) Rebar element
(b) Compression damage
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
2.5 Numerical modeling of reinforced concrete abutments
According to Japan Specifications for
three different types of the wing wall shapes. The shapes and dimensions vary according to the
installation site of the abutment, backfill height, and gradient of the slope. The numerical model of
RC abutment Type 2 as the typical model of abutment in Japan is representative for actual model, as
shown in Fig.7. In order to increase the strength of abutment, abutment Type 4 was analyzed as a
proposed model to be developed from Type 1 (without wing wall
Moreover, based on this specification, the wall of a T
cantilever with the fixed end at the node connected to the top of the footing. Therefore, in order to
reduce the number of nodes and elements in the modeling, it needs to simplify the model by omitting
the footing of abutment and modeling support with fixed boundary condition. Summary of the
comparison results in Type 1, with and without footing are described in Table
recognized that the analytical method of RC
behavior of abutment with footing.
(a) Numerical model
Figure 7. Model of abutment Type 2 as the typical model in Japan
Table 2. Summary of the maximum result in each model
Descriptions
S11
S33
PE11
AC Yield
dt
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
103
Numerical modeling of reinforced concrete abutments
According to Japan Specifications for Highway Bridges, Part IV (Substructures) [
three different types of the wing wall shapes. The shapes and dimensions vary according to the
installation site of the abutment, backfill height, and gradient of the slope. The numerical model of
abutment Type 2 as the typical model of abutment in Japan is representative for actual model, as
. In order to increase the strength of abutment, abutment Type 4 was analyzed as a
proposed model to be developed from Type 1 (without wing wall) and Type 3 (full wing wall).
Moreover, based on this specification, the wall of a T-shaped abutment can be designed as a
cantilever with the fixed end at the node connected to the top of the footing. Therefore, in order to
elements in the modeling, it needs to simplify the model by omitting
the footing of abutment and modeling support with fixed boundary condition. Summary of the
comparison results in Type 1, with and without footing are described in Table
recognized that the analytical method of RC abutment without footing is able
abutment with footing.
Numerical model (b) Real bridge
. Model of abutment Type 2 as the typical model in Japan
Summary of the maximum result in each model
Type 1
(with footing)
Type 1
(without footing)
1.591 e+8 1.592 e+8
2.493 e+6 2.507 e+6
2.955 e-4 2.956e-4
Similar value and position
Similar value and position
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
ges, Part IV (Substructures) [8], there are
three different types of the wing wall shapes. The shapes and dimensions vary according to the
installation site of the abutment, backfill height, and gradient of the slope. The numerical model of
abutment Type 2 as the typical model of abutment in Japan is representative for actual model, as
. In order to increase the strength of abutment, abutment Type 4 was analyzed as a
) and Type 3 (full wing wall).
shaped abutment can be designed as a
cantilever with the fixed end at the node connected to the top of the footing. Therefore, in order to
elements in the modeling, it needs to simplify the model by omitting
the footing of abutment and modeling support with fixed boundary condition. Summary of the
comparison results in Type 1, with and without footing are described in Table 2 and Fig.8. It was
abutment without footing is able to represent the
(b) Real bridge
. Model of abutment Type 2 as the typical model in Japan
Summary of the maximum result in each model
Diffe-rences
0.06%
0.56%
1.30%
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
Four different abutment modeling approach were carried out with a half
symmetry condition, as shown in Fig.9. The dimensional configurations are depicted in Fig.
Table 3, respectively, with parameter of
Furthermore, the rebar arrangement is given in Fig. 11.
(a) Type 1 (b) Type 2
Fig
Figure 10. Dimensional configurations of abutments (unit:
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
104
Figure 8. Load vs displacement
Four different abutment modeling approach were carried out with a half
symmetry condition, as shown in Fig.9. The dimensional configurations are depicted in Fig.
Table 3, respectively, with parameter of t represents the thickness of parapet wall and wing wall.
Furthermore, the rebar arrangement is given in Fig. 11.
Type 1 (b) Type 2 (c) Type 3
Figure9. Numerical models of abutments
. Dimensional configurations of abutments (unit:
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
Four different abutment modeling approach were carried out with a half-length model by
symmetry condition, as shown in Fig.9. The dimensional configurations are depicted in Fig.10 and
represents the thickness of parapet wall and wing wall.
(d) Type 4
. Dimensional configurations of abutments (unit: m)
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
Table 3.Dimensional configurations of four abutments
Figure 11. Rebar arrangement of Type 4
Material property of the concrete was assumed from previous research [1
12, while for the rebar was similar with RC beam input. The compressive strengths were 13.75 MPa
(taken as yielding strength fco) and 27.5 MPa (taken as ultimate strengt
modulus Eo,tensile stress 0tσ , and Poisson’s ratio
MPa, and 0.2.
2.6 Loading conditions
There are two types of loading condition for RC beam and
weight as a gravity load g of 9.8
amplified under force control. Design seismic force of the unseating prevention structure
be taken as 1.5 times dead load
abutment with full wing wall and applied the unseating prevention structure (UPS), as shown in
13. In this research, four static horizontal loads through UPS were applied in the half
parapet wall, with the dead load reaction of the superstructure was 2900 kN, obtained from the deck
weight. Therefore, each UPS will transfer the external load to the parapet wall of 543.75 kN.
HF = 1.5 RD
Descrip
tions
Type 1
(m)
Type 2
(m)
Type 3
(m)
b2 - -
h3 - 1.0 8.0
h4 - 3.3 0.0
h5 5.5 5.5 5.5
h6 - -
t 0.5 0.5 0.5
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
105
Dimensional configurations of four abutments
Figure 12. Stress-strain curve for concrete
. Rebar arrangement of Type 4 Figure 13. Side view of abutment [1
ial property of the concrete was assumed from previous research [1
12, while for the rebar was similar with RC beam input. The compressive strengths were 13.75 MPa
) and 27.5 MPa (taken as ultimate strength fcu
, and Poisson’s ratio cυ of concrete were 2400 kg/m
There are two types of loading condition for RC beam and RC abutments, including the self
of 9.8 m/s2 and the external load. The external load in RC beam was
Design seismic force of the unseating prevention structure
be taken as 1.5 times dead load reaction, RD [13]. Previous research [14] developed a model of
abutment with full wing wall and applied the unseating prevention structure (UPS), as shown in
. In this research, four static horizontal loads through UPS were applied in the half
parapet wall, with the dead load reaction of the superstructure was 2900 kN, obtained from the deck
weight. Therefore, each UPS will transfer the external load to the parapet wall of 543.75 kN.
Type 3
(m)
Type 4
(m)
- 0.5
8.0 8.0
0.0 0.0
5.5 1
- 1
0.5 0.5
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
strain curve for concrete
Side view of abutment [14]
ial property of the concrete was assumed from previous research [12], as shown in Fig.
12, while for the rebar was similar with RC beam input. The compressive strengths were 13.75 MPa
cu). The density, Young
of concrete were 2400 kg/m3,25000 MPa, 2.75
abutments, including the self-
external load. The external load in RC beam was
Design seismic force of the unseating prevention structure, HF, may
] developed a model of
abutment with full wing wall and applied the unseating prevention structure (UPS), as shown in Fig.
. In this research, four static horizontal loads through UPS were applied in the half-height of
parapet wall, with the dead load reaction of the superstructure was 2900 kN, obtained from the deck
weight. Therefore, each UPS will transfer the external load to the parapet wall of 543.75 kN.
(11)
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
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2.7 Interaction Properties
General contact surface algorithm was considered to determine the modeling of contact
behavior in the interacting surfaces between concrete and steel plate in RC beam. The friction
coefficients of contact point was
analysis, the steel plate was used in order to transfer the external load to RC beam and to set down
the support. The embedment was defined using an embedded constraint and was achieved by
constraining rebar elements into solid element
2.8 Boundary conditions
The RC beam and abutments were modeled as a half
conditions in support were hinged
RC beam was constrained with boundary condition in X
in the mid-span of RC abutments was constrained in Z direction
III. RESULTS AND DISCUSSIONS
3.1 Analysis of RC beam structure
The load-displacement curves for experime
are shown in Fig. 14. The displacement
mid-span of RC beam structure and
From this figure, it can be seen that the
data up to 40 tf. Moreover, the maximum load
48.54 tf, which is slightly larger than experimental result of 45 tf.
In order to visualize the cracking distribution within the FEM, the positive plastic strain can
be mapped with color coded contours shown in
flexural cracks initiate first in the mid
The maximum plastic strain occurs in the “red” regions where the plastic strain equals 0.00255
corresponds to the maximum tension damage parameter of approximately 0.9. Dark blue regions
correspond to areas of no tension damage. According to the analysis, it could be concluded that the
cracking distribution of RC beam is more localized within the support and mid
Figure 14. Vertical load vs displacement curves Figure 1
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
106
ral contact surface algorithm was considered to determine the modeling of contact
behavior in the interacting surfaces between concrete and steel plate in RC beam. The friction
coefficients of contact point was set to be 0.1 and hard contact for pressure
analysis, the steel plate was used in order to transfer the external load to RC beam and to set down
The embedment was defined using an embedded constraint and was achieved by
constraining rebar elements into solid element, in order to create a proper bond action.
The RC beam and abutments were modeled as a half-length model with the boundary
hinged and fixed, respectively. The surface of YZ in the middle length of
s constrained with boundary condition in X-direction (U1=0), whether the surface of XY
of RC abutments was constrained in Z direction (U3=0).
DISCUSSIONS
beam structure
curves for experimental result and numerical analysis by ABAQUS
displacementand load shown correspond to the vertical displacement at
and the total vertical force imposed on the structure, respectively.
, it can be seen that the numerical resultcorrelate well with those from experimental
aximum load to be transmitted in RC beam by numerical analysis
slightly larger than experimental result of 45 tf.
In order to visualize the cracking distribution within the FEM, the positive plastic strain can
be mapped with color coded contours shown in Fig. 15. The beam exhibit flexure
flexural cracks initiate first in the mid-span of structure, followed by inclined flexure
The maximum plastic strain occurs in the “red” regions where the plastic strain equals 0.00255
corresponds to the maximum tension damage parameter of approximately 0.9. Dark blue regions
tension damage. According to the analysis, it could be concluded that the
cracking distribution of RC beam is more localized within the support and mid
. Vertical load vs displacement curves Figure 15. FEM magnitude of plastic strain
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
ral contact surface algorithm was considered to determine the modeling of contact
behavior in the interacting surfaces between concrete and steel plate in RC beam. The friction
0.1 and hard contact for pressure-over closure. In this
analysis, the steel plate was used in order to transfer the external load to RC beam and to set down
The embedment was defined using an embedded constraint and was achieved by
, in order to create a proper bond action.
length model with the boundary
and fixed, respectively. The surface of YZ in the middle length of
, whether the surface of XY
ntal result and numerical analysis by ABAQUS
to the vertical displacement at
force imposed on the structure, respectively.
resultcorrelate well with those from experimental
by numerical analysis is
In order to visualize the cracking distribution within the FEM, the positive plastic strain can
. The beam exhibit flexure-shear failure where
followed by inclined flexure-shear cracks.
The maximum plastic strain occurs in the “red” regions where the plastic strain equals 0.00255
corresponds to the maximum tension damage parameter of approximately 0.9. Dark blue regions
tension damage. According to the analysis, it could be concluded that the
cracking distribution of RC beam is more localized within the support and mid-span of the beam.
agnitude of plastic strain
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
(a) Figure 16. RC beam cracking pattern with the external load of 20 tf
The comparison between analytical and experimental results of this behavior due to external
load of 20 tf is shown in Fig. 16. “L
correspond to the cracking of the concrete. Due to an automatic step increment in analysis, the result
is figured out at load of 22 tf. It indicates that the cracking distributions in analytical
good agreement with those from experimental results.
3.2 Analysis of RC abutments
3.2.1 Longitudinal displacement
The longitudinal displacements of abutmentswere investigated in the wing wall part and half
part of abutment, three levels in each side
longitudinal displacement of the wing wall part
parapet and bottom of abutment, respectively. Otherwise, in
UB2, and U2.
Figure 1
(a) Middle part
Figure 18. Longitudinal displacement of abutment (mm)
Load = 22 tf
U2 = 0.229 mm
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107
Analysis (b) Experiment
. RC beam cracking pattern with the external load of 20 tf
The comparison between analytical and experimental results of this behavior due to external
load of 20 tf is shown in Fig. 16. “Light blue and deep colors” regions with positive plastic strain
the cracking of the concrete. Due to an automatic step increment in analysis, the result
is figured out at load of 22 tf. It indicates that the cracking distributions in analytical
good agreement with those from experimental results.
butments
isplacement
The longitudinal displacements of abutmentswere investigated in the wing wall part and half
in each side, as shown in Fig. 17. UT1, UB1
the wing wall part in different level positions, top
, respectively. Otherwise, in the middle part are depi
Figure 17. Position of the nodal displacement
Middle part (b) Wing wall part
. Longitudinal displacement of abutment (mm)
Load = 22 tf
U2 = 0.229 mm
Middle partWing wall
part
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
. RC beam cracking pattern with the external load of 20 tf
The comparison between analytical and experimental results of this behavior due to external
ht blue and deep colors” regions with positive plastic strain
the cracking of the concrete. Due to an automatic step increment in analysis, the result
is figured out at load of 22 tf. It indicates that the cracking distributions in analytical study are in a
The longitudinal displacements of abutmentswere investigated in the wing wall part and half-length
UB1 and U1 represent the
top of parapet, bottom of
part are depicted as UT2,
(b) Wing wall part
. Longitudinal displacement of abutment (mm)
Middle part
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
Total static horizontal load which can be expected to be
prevention structures for half-length model was 2175 kN. Applying external load affect the
longitudinal displacement of each abutment, are depicted in Fig. 18(a) and Fig. 18(b) as
displacement in the middle and wing wall p
wall part UT1 of 10.64 mm, 3.16 mm, 0.59 mm, and 0.36 mm for abutment Type 1, Type 2, Type 4,
and Type 3, respectively. It signifies in reducing of 59.20%, 94.33% and 92.06% for abutment Type
2, Type 3 and Type 4, respectively. These results prove that installation of the wing wall in abutment
have a capability in decreasing of the longitudinal displacement.
In addition, a static pushover analysis was carried out with the external load amplification i
order to characterize the maximum load to be transmitted in abutment. The result of load versus
displacement curve is shown in Fig. 19. The study reported that the maximum load for abutment
Type 1 is the smallest one of 2792.25 kN. Type 3 and Type 4 have
which are smaller than Type 2 of 3244.43 kN. This condition is possibly due to design of the wing
walls in Type 4 as slabs fixed on two sides to a wall and footing, which can reduce the longitudinal
displacement and flexibility of the structure. Consequently, it leads crack at the parapet wall.
(a) Figure 19. Longitudinal displacement of abutment (mm)
3.2.2 Cracking Distribution of RC Abutments
(a) Initial cracking
Figure 20. Contour plot of tensile damage in RC abutment Type
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
108
Total static horizontal load which can be expected to be transmitted through the unseating
length model was 2175 kN. Applying external load affect the
longitudinal displacement of each abutment, are depicted in Fig. 18(a) and Fig. 18(b) as
displacement in the middle and wing wall part, respectively. Interesting results occur in the wing
of 10.64 mm, 3.16 mm, 0.59 mm, and 0.36 mm for abutment Type 1, Type 2, Type 4,
and Type 3, respectively. It signifies in reducing of 59.20%, 94.33% and 92.06% for abutment Type
3 and Type 4, respectively. These results prove that installation of the wing wall in abutment
have a capability in decreasing of the longitudinal displacement.
In addition, a static pushover analysis was carried out with the external load amplification i
order to characterize the maximum load to be transmitted in abutment. The result of load versus
displacement curve is shown in Fig. 19. The study reported that the maximum load for abutment
Type 1 is the smallest one of 2792.25 kN. Type 3 and Type 4 have similar value of 3009.27 kN,
which are smaller than Type 2 of 3244.43 kN. This condition is possibly due to design of the wing
walls in Type 4 as slabs fixed on two sides to a wall and footing, which can reduce the longitudinal
y of the structure. Consequently, it leads crack at the parapet wall.
Middle part (b) Wing wall part
. Longitudinal displacement of abutment (mm)
of RC Abutments
Initial cracking at 1093.11 kN (b) Final cracking at 2792.25 kN
. Contour plot of tensile damage in RC abutment Type 1 at different external load
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
transmitted through the unseating
length model was 2175 kN. Applying external load affect the
longitudinal displacement of each abutment, are depicted in Fig. 18(a) and Fig. 18(b) as
art, respectively. Interesting results occur in the wing
of 10.64 mm, 3.16 mm, 0.59 mm, and 0.36 mm for abutment Type 1, Type 2, Type 4,
and Type 3, respectively. It signifies in reducing of 59.20%, 94.33% and 92.06% for abutment Type
3 and Type 4, respectively. These results prove that installation of the wing wall in abutment
In addition, a static pushover analysis was carried out with the external load amplification in
order to characterize the maximum load to be transmitted in abutment. The result of load versus
displacement curve is shown in Fig. 19. The study reported that the maximum load for abutment
similar value of 3009.27 kN,
which are smaller than Type 2 of 3244.43 kN. This condition is possibly due to design of the wing
walls in Type 4 as slabs fixed on two sides to a wall and footing, which can reduce the longitudinal
y of the structure. Consequently, it leads crack at the parapet wall.
. Longitudinal displacement of abutment (mm)
at 2792.25 kN
1 at different external load
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
(a) Initial cracking at 1093.11 kN
Figure 21. Contour plot of tensile damage in RC abutment Type 2 at different
(a) Initial cracking at 1093.11 kN
Figure 22. Contour plot of tensile damage in RC abutment Type 3 at different external load
(a) Initial cracking at 1093.11 kN
Figure 23. Contour plot of tensile damage in RC abutment Type 4 at different external load
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
109
Initial cracking at 1093.11 kN (b) Final cracking at 3244.43 kN
Figure 21. Contour plot of tensile damage in RC abutment Type 2 at different
Initial cracking at 1093.11 kN (b) Final cracking at 3009.27 kN
Figure 22. Contour plot of tensile damage in RC abutment Type 3 at different external load
Initial cracking at 1093.11 kN (b) Final cracking at 3009.27 kN
our plot of tensile damage in RC abutment Type 4 at different external load
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
(b) Final cracking at 3244.43 kN
Figure 21. Contour plot of tensile damage in RC abutment Type 2 at different external load
(b) Final cracking at 3009.27 kN
Figure 22. Contour plot of tensile damage in RC abutment Type 3 at different external load
(b) Final cracking at 3009.27 kN
our plot of tensile damage in RC abutment Type 4 at different external load
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014),
Figs.20-23 show contour plot of output variable DAMAGET, which is a scalar degradation
measure used to express the reduced tensile elastic modulus of concrete after it has sustaine
cracking damage. Sequence of the concrete cracking are described as initial and final cracking, as
shown in section (a) and (b), respectively. “Dark blue” regions correspond to areas of no tension
damage or no cracking. The maximum tension damage occurs
strain equals 0.00264 corresponds to the maximum tension damage parameter of approximately 0.9.
From these figures, it can be discovered that the initial cracking of all abutments occur in two
different positions, in peripheral of the external load and intersection between parapet wall and
abutment wall due the external load of 1093.11 kN. In addition, cracking is also found at bottom of
abutment wall near the footing for Type 1 and Type 2. Type 1 is found as a structur
critical damage due to the cracking propagation in region through its width. Moreover, it propagates
from the middle width to the edge position, lead the connection part between wing wall and parapet
wall to crack.
3.2.3 Load-tensile strain plot for reinforcing bar
Fig. 24(a) shows the maximum tensile stress versus tensile strain relationship of the rebar,
located at the reverse side of parapet wall. According to this figure, it can be seen that the tensile
steel rebar is not yield at failure in abutment with all types of the wing wall. Otherwise, yielding
occurs at Type 1. Furthermore, the relationship between load and maximum tensile strain in the rebar
is depicted in Fig. 24(b). From these results, it is recognized that installation of t
increases the stiffness of abutment, resulting on strain reduction in the rebar.
(a) Stress-
Figure 2
3.2.4 Shear stress distribution of RC abutments
Stress distribution is one of the important aspects to be evaluated in abutment. The areas
subjected to high stress is the most common problems observed during the inspection of the failure
of abutment in the past large earthquake.
are studied in numerical analysis
these figure, it can be determined that
wallnearly the intersection with the wi
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
110
23 show contour plot of output variable DAMAGET, which is a scalar degradation
measure used to express the reduced tensile elastic modulus of concrete after it has sustaine
cracking damage. Sequence of the concrete cracking are described as initial and final cracking, as
shown in section (a) and (b), respectively. “Dark blue” regions correspond to areas of no tension
damage or no cracking. The maximum tension damage occurs in “red” regions, where the cracking
strain equals 0.00264 corresponds to the maximum tension damage parameter of approximately 0.9.
From these figures, it can be discovered that the initial cracking of all abutments occur in two
eripheral of the external load and intersection between parapet wall and
abutment wall due the external load of 1093.11 kN. In addition, cracking is also found at bottom of
abutment wall near the footing for Type 1 and Type 2. Type 1 is found as a structur
critical damage due to the cracking propagation in region through its width. Moreover, it propagates
from the middle width to the edge position, lead the connection part between wing wall and parapet
in plot for reinforcing bar
Fig. 24(a) shows the maximum tensile stress versus tensile strain relationship of the rebar,
located at the reverse side of parapet wall. According to this figure, it can be seen that the tensile
ure in abutment with all types of the wing wall. Otherwise, yielding
occurs at Type 1. Furthermore, the relationship between load and maximum tensile strain in the rebar
is depicted in Fig. 24(b). From these results, it is recognized that installation of t
increases the stiffness of abutment, resulting on strain reduction in the rebar.
-strain ratio (b) Load versus tensile strain
Figure 24. Tensile strain plot for the rebar
Shear stress distribution of RC abutments
ribution is one of the important aspects to be evaluated in abutment. The areas
subjected to high stress is the most common problems observed during the inspection of the failure
of abutment in the past large earthquake. Shear stress distributions around vertical wall of abutments
studied in numerical analysis, with the results for each abutment are shown in
these figure, it can be determined that maximum shear stresses occur at the region of parapet
wallnearly the intersection with the wing wall.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
23 show contour plot of output variable DAMAGET, which is a scalar degradation
measure used to express the reduced tensile elastic modulus of concrete after it has sustained
cracking damage. Sequence of the concrete cracking are described as initial and final cracking, as
shown in section (a) and (b), respectively. “Dark blue” regions correspond to areas of no tension
in “red” regions, where the cracking
strain equals 0.00264 corresponds to the maximum tension damage parameter of approximately 0.9.
From these figures, it can be discovered that the initial cracking of all abutments occur in two
eripheral of the external load and intersection between parapet wall and
abutment wall due the external load of 1093.11 kN. In addition, cracking is also found at bottom of
abutment wall near the footing for Type 1 and Type 2. Type 1 is found as a structure with the most
critical damage due to the cracking propagation in region through its width. Moreover, it propagates
from the middle width to the edge position, lead the connection part between wing wall and parapet
Fig. 24(a) shows the maximum tensile stress versus tensile strain relationship of the rebar,
located at the reverse side of parapet wall. According to this figure, it can be seen that the tensile
ure in abutment with all types of the wing wall. Otherwise, yielding
occurs at Type 1. Furthermore, the relationship between load and maximum tensile strain in the rebar
is depicted in Fig. 24(b). From these results, it is recognized that installation of the wing wall
Load versus tensile strain
ribution is one of the important aspects to be evaluated in abutment. The areas
subjected to high stress is the most common problems observed during the inspection of the failure
ertical wall of abutments
abutment are shown in Fig. 25. From
maximum shear stresses occur at the region of parapet
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
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(a) Type 1
(c) Type 3
Figure 2
IV. CONCLUSIONS
The elasto-plastic behavior of 3
effect of the wing wall were investigated in this study
different abutment modeling approaches subjected to static
prevention structure with consideration of the wing wall. The conclusions are summari
following.
1) The analytical method of Concrete Damaged Plasticity by
the elasto-plastic behavior of RC structure. The material modeling was
experimental results in showing the behavior of RC beam in
cracking distribution.
2) Installation of the wing wall in abutments ha
displacement of 59.20%, 94.33% and 92.06% for abutment Type 2, Type 3 and Type 4
proposed type, respectively.
in abutment. Otherwise, there was no significant
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976
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111
Type 1 (b) Type 2
(d) Type 4
Figure 25. Shear stress distribution of abutments
plastic behavior of 3-dimensional reinforced concrete abutments considering the
e investigated in this study. Numerical studies were carried out in four
approaches subjected to static horizontal loads through the unseating
prevention structure with consideration of the wing wall. The conclusions are summari
The analytical method of Concrete Damaged Plasticity by ABAQUS was capable to analyze
plastic behavior of RC structure. The material modeling was
experimental results in showing the behavior of RC beam in case of
Installation of the wing wall in abutments had a capability in decreasing of the longitudinal
9.20%, 94.33% and 92.06% for abutment Type 2, Type 3 and Type 4
ely. This condition was affected by the increasing number of stiffness
Otherwise, there was no significant effect in half-length part of abutment.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
© IAEME
(b) Type 2
(d) Type 4
dimensional reinforced concrete abutments considering the
Numerical studies were carried out in four
horizontal loads through the unseating
prevention structure with consideration of the wing wall. The conclusions are summarized as
ABAQUS was capable to analyze
plastic behavior of RC structure. The material modeling was said to be valid as
case of displacement and
a capability in decreasing of the longitudinal
9.20%, 94.33% and 92.06% for abutment Type 2, Type 3 and Type 4 as the
This condition was affected by the increasing number of stiffness
length part of abutment.
International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),
ISSN 0976 – 6316(Online), Volume 5, Issue 11, November (2014), pp. 97-113 © IAEME
112
3) According to the static pushover analysis, the maximum load that could be expected to be
transmitted for the proposed type of abutment of 3009.27 kN was smaller than Type 2 of
3244.43 kN.It was possibly due to design of the wing walls in Type 4 as slabs fixed on two
sides to a wall and footing, which reduced the longitudinal displacement and flexibility of the
structure.
4) The initial cracking for all abutments occurred in two different positions, at the peripheral of
the external load and intersection between parapet wall and abutment wall. Installation of the
wing wall in the proposed model reduced the cracking at the bottom of wall and compressive
strain of the concrete.
5) The stress distribution was affected by the wing wall. From numerical analysis, it was
depicted that the maximum shear stress occurred at the region of parapet wall nearly the
intersection of the wing wall. Furthermore, the tensile steel of the rebar was not yielded at
failure in abutments with the wing wall which was affected by the reduction of the axial
strain.
6) Although the present study found better evidence on the proposed model of abutment Type 4
in its behavior, no earth pressure was applied. Therefore, further studies are necessary in
order to determine the behavior of RC abutment under earth pressure and strong ground
excitation.
ACKNOWLEDGEMENT
The first author acknowledges DIKTI (Directorate General of Higher Education) as the
financial supporter of the scholarship and University of Brawijaya as the home university. The
support in completing the doctoral study in Kumamoto University is gratefully appreciated.
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