8 ELASTO PLASTIC BEHAVIOR OF 3 DIMENSIONAL …...2.2 Constitutive model of steel reinforcing bar...

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

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ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 5, Issue 11, November (2014), pp. 97-113

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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.



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


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


© 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]



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



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


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


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


© 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.

)


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,


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



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



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


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are defined based on plot presented in

strain curve for steel rebar [10]

(c) Rebar element

(b) Compression damage



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



103

Numerical modeling of reinforced concrete abutments

According to Japan Specifications for Highway Bridges, Part IV (Substructures) [



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


elements in the modeling, it needs to simplify the model by omitting


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


© IAEME

ges, Part IV (Substructures) [8], there are



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


elements in the modeling, it needs to simplify the model by omitting


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%



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:



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:


© 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)



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



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


) 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



Type 3

(m)

Type 4

(m)

- 0.5

8.0 8.0

0.0 0.0

5.5 1

- 1

0.5 0.5


© 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.


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



(11)



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



106

ral contact surface algorithm was considered to determine the modeling of contact


coefficients of contact point was set to be 0.1 and hard contact for pressure


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.


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



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


© IAEME

ral contact surface algorithm was considered to determine the modeling of contact


0.1 and hard contact for pressure-over closure. In this


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


. The beam exhibit flexure-shear failure where

followed by inclined flexure-shear cracks.



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



(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



107

Analysis (b) Experiment

. RC beam cracking pattern with the external load of 20 tf


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


© IAEME

. RC beam cracking pattern with the external load of 20 tf


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


Middle part



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



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


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,


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



Type 1 is the smallest one of 2792.25 kN. Type 3 and Type 4 have similar value of 3009.27 kN,



y of the structure. Consequently, it leads crack at the parapet wall.

Middle part (b) Wing wall part


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


© IAEME

transmitted through the unseating

length model was 2175 kN. Applying external load affect the


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,


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



similar value of 3009.27 kN,



y of the structure. Consequently, it leads crack at the parapet wall.


at 2792.25 kN

1 at different external load



(a) Initial cracking at 1093.11 kN

Figure 21. Contour plot of tensile damage in RC abutment Type 2 at different


Figure 22. Contour plot of tensile damage in RC abutment Type 3 at different external load





109


Figure 21. Contour plot of tensile damage in RC abutment Type 2 at different




our plot of tensile damage in RC abutment Type 4 at different external load


© IAEME

(b) Final cracking at 3244.43 kN





our plot of tensile damage in RC abutment Type 4 at different external load



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



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



damage or no cracking. The maximum tension damage occurs in “red” regions, where the cracking



eripheral of the external load and intersection between parapet wall and


abutment wall near the footing for Type 1 and Type 2. Type 1 is found as a structur



in plot for reinforcing bar



ure in abutment with all types of the wing wall. Otherwise, yielding


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


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.


© 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



in “red” regions, where the cracking



eripheral of the external load and intersection between parapet wall and


abutment wall near the footing for Type 1 and Type 2. Type 1 is found as a structure with the most





ure in abutment with all types of the wing wall. Otherwise, yielding


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


ertical wall of abutments

abutment are shown in Fig. 25. From

maximum shear stresses occur at the region of parapet



(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



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.


© 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.



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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8 ELASTO PLASTIC BEHAVIOR OF 3 DIMENSIONAL …...2.2 Constitutive model of steel reinforcing bar...

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