International Journal of Advanced Structural Engineering (2018) 10:199–210

https://doi.org/10.1007/s40091-018-0192-2

ORIGINAL RESEARCH

Finite‑element modeling of UHPC hybrid bridge deck connections

Sabreena Nasrin1 · Ahmed Ibrahim1

Received: 26 December 2017 / Accepted: 10 July 2018 / Published online: 17 July 2018
© The Author(s) 2018

Abstract
In recent years, linked bridge deck elements have gained popularity for facilitating more durable components in bridge
decks, but these components require field-applied connections for constructing the entire bridge. Ultra-high-performance
concrete (UHPC) is started to be a major material for closure pours in bridges and various Department of Transportations
have been developing guidelines. UHPC is known by its superior quality than conventional concrete in terms of constructa-
bility, strength and durability. So far, very limited data are available on the finite-element modeling (FEM) of hybrid bridge
deck connections. In this study, FEMs have been presented to define the crucial factors affecting the response of bridge
hybrid deck panel system under monotonic loads. The commercial software ABAQUS was used to validate the modes and
to generate the data presented herein and the concrete damage plasticity was used to simulate both conventional concrete and
UHPC. Numerical results were validated using available experimental data. The key parameters studied were the mesh size,
the dilation angle, reinforcement type, concrete models, steel properties, and the contact behavior between the UHPC and
the conventional concrete. The models were found to capture the load–deflection response of experimental results, failure
modes, crack patterns and ductility indices show satisfactorily response. A sensitivity test was also conducted by consider-
ing various key parameters such as concrete and steel constitutive models and their associated parameters, mesh size, and
contact behavior. It is perceived that increasing the dilation angle leads to an increase in the initial stiffness of the model. The
damage in concrete under monotonic loading is found higher in normal concrete than UHPC with no signs of de-bonding
between the two materials. Changing the dilation angle from 20° to 40° results in an increase of 7.81% in ultimate load for the
panel with straight reinforcing bars, whereas for the panel with headed bars, the increase in ultimate load was found 8.56%.

Keywords  Nonlinear static analysis · Ultra-high-performance concrete (UHPC) · Bridge deck connections · Sensitivity
analysis · Accelerated construction

Introduction the long-term structural performance, and currently, the use

of UHPC has becoming more popular in the construction
The ASCE 2017 report card listed that about 9% of bridges industry for its superior properties such as its early very high
in the USA are classified structurally deficient and each strength that might reach 96 MPa (14,000 psi) in 3 days, its
year more than 3000 new bridges are being constructed promising toughness, and long-term steadiness. The term
(Bhide 2008). It has been always a challenge for the bridge UHPC is classified as innovative cementitious composite
engineers to find new ways to build better bridges with materials, where ground-breaking technology of cement and
reduced construction time. So far, significant efforts have concrete industry grouped together (Graybeal 2010).
been provided in developing innovative ways to increase In fact, the concept of using UHPC for connection
between precast concrete panels started in the mid 90s. At
that time, a building was being constructed at Aalborg Uni-
* Ahmed Ibrahim versity using UHPC as a closure pour material, and addi-
aibrahim@uidaho.edu tional project was completed, where UHPC was used for
Sabreena Nasrin slab-column connections and its bond characteristics, (Aarup
nasr2701@vandals.uidaho.edu et al. 2009; Hansen and Jensen 1999; Nielsen et al. 1996;
1
Department of Civil and Environmental Engineering,
Aarup and Jensen 1998). Additional research, was com-
University of Idaho, 875 Perimeter Dr. MS1022, Moscow, pleted at Chalmers University focusing on the application
ID 83844, Russia

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200 International Journal of Advanced Structural Engineering (2018) 10:199–210

of UHPC as closure material (Broo and Broo 1997; Har- Experimental program
ryson 1999, 2000). Simplicity in construction and outstand-
ing performance made UHPC connection more popular Two full-scale experimentally tested deck panels were
than conventional modular-component connections, where selected from Graybeal (2010). The two specimens had
conventional concrete connections require post-tensioning, two different UHPC connections, where straight and
complex confinement reinforcement, large volume of con- headed bars were used. Table 1 provides the details of the
crete, etc., (Graybeal 2010). An ample amount of studies two test specimens.
has been conducted to investigate the bond strength between The details for each of the specimens, the location of
UHPC and various materials. Perry and Seibert (2012) UHPC filled connection, and normal strength concrete
reported on applications related to precast joints of UHPC. deck panels are provided in Figs. 1 and 2. In all cases,
The bond characteristics between timber and UHPC were the size of the test specimens was 2400 × 2152  mm
studied by Schäfers and Seim (2011). The interfacial behav- (94.5 × 84.7 inch). The diamond shape UHPC connection
ior of hollow glass fiber-reinforced plastic beams having a runs parallel to the length of the slab specimen with a
UHPC filled compressive zone was examined by El-Hacha 152 mm (6 inch) nominal width, as shown in Fig. 1. No
and Chen (2012). Graybeal and Swenty (2012) investigated post-tensioning was included in the test panels and the
the performances of precast deck joints with variable cross connection reinforcements were extended from the adja-
sections. More research has been conducted on develop- cent precast slabs into the UHPC connection, (Graybeal
ing analytical models to predict that the compressive and 2010).
tensile strength are also conducted. As this is not always
feasible to conduct large-scale test of UHPC connection of
bridge deck elements, a need for developing dependable 3D
finite-element model is now time worthy. Graybeal (2006a, Finite‑element modeling
b, 2008, 2009a, b), performed comprehensive experimental
tests on UHPC characterization, full-scale flexural and shear The modeling UHPC connected bridge deck panels under
of I-girders, and pi-girders. monotonic loading using computer-aided program is
Numerical modeling of UHPC connected deck panels needed to broaden the current knowledge and provide
has been always challenging due to non-availability of post- some reliable results, especially with the high cost of
peak behavior of UHPC either under compression or tension experimental testing of UHPC connections. The numeri-
loads. The post-peak behavior is very important to predict cal simulations were conducted using the ABAQUS
the damage parameters needed for numerical modeling (ABAQUS Inc. 2016) code, which is a general FE analy-
(Chen and Graybeal 2012). Different modeling approaches sis software for modeling the nonlinear material behav-
considering diverse assumptions have been proposed, but ior, interaction between different materials, heat transfer,
sensitivity analyses are needed for identifying the major fluid dynamics problem, etc. Both implicit and explicit
parameters affecting the numerical results. In this paper, an numerical methods are available in ABAQUS for solving
effort has been made to develop a finite-element model that problems associated with large deformation and multi-
can be applied for a variety of UHPC bridge connections loading environments. ABAQUS/explicit method was used
subjected to monotonic loading. It is needed to recognize for simulating the FE models as it can effectively handle
the major factors which affects the numerical results and severely nonlinear behavior.
evaluate the sensitivity of the material input parameters on
the variability and response of the models.

Table 1  Test specimen Specimen Orientation Depth (mm) Reinforcement

(Graybeal 2010)
8H Transverse 200 16 M (#5) headed black reinforce-
ment with 90 mm lap length and
450 mm (top) and 180 mm (bot-
tom) spacing
8G Transverse 200 16 M (#5) galvanized straight bars
with 150 mm lap length and
450 mm (top) and 180 mm (bot-
tom) spacing

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International Journal of Advanced Structural Engineering (2018) 10:199–210 201

Fig. 1  Reinforcement details for

panel 8H (Graybeal 2010)

Precast panels These parameters are used to identify and validate dam-
age and crack patterns of the developed model and compare
To model the concrete material in ABAQUS, various it with experimental results. Three different concrete con-
models are available in the software library. The “concrete stitutive models were adopted in this study to identify the
damaged plasticity” model is used in this paper and was most suitable concrete model for this study. These models
developed by Lubliner et al. (1989) and then elaborated were only used to predict the behavior of the precast con-
by Lee and Fenves (1998). The constitutive relationship crete panels.
requires the following material input parameters:
Concrete model proposed by Hsu and Hsu (1994)
• uniaxial stress–strain constitutive relation under com-
pressive and tensile loading; The concrete model derived by Hsu and Hsu (1994) is limited
• damage parameters dc and dt for compressive and ten- to a concrete compressive strength of 62 MPa. For other con-
sile load, respectively. crete grades, modifications should be made by referring to the
original work reported by Hsu and Hsu (1994). This model

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202 International Journal of Advanced Structural Engineering (2018) 10:199–210

Fig. 2  Reinforcement details for

panel 8G (Graybeal 2010)

assumes a linear stress–strain relationship up to 50% of the

ultimate compressive strength (σcu) in the ascending portion.
𝜀0 = 8.9 × 10−5 𝜎cu + 2.114 × 10−3 . (3)
The model was only used to predict the compressive stresses The initial tangential modulus, E0, is given by
from 0.5σcu to 0.3σcu in the descending portion: E0 = 1.243 × 102 𝜎cu + 3.28312 × 103 . (4)
� �
⎛ 𝜀 ⎞ Concrete model proposed by Park and Paulay (1975)
⎜ 𝛽 𝜀c ⎟
(1)
0
𝜎c = ⎜ � �𝛽 ⎟𝜎cu ,
⎜ 𝛽 − 1 + 𝜀c ⎟ This model considers concrete as an elastic–plastic and strain
⎝ 𝜀0 ⎠ hardening material. The constitutive relation in compression
is assumed to follow the expression given below:
where the parameter β depends on the shape of the [ ( )2 ]
stress–strain diagram and is given by � 2𝜀c 𝜀c
fc = f − , (5)
1 𝜀0 𝜀0
𝛽= [ ],
1−
𝜎cu (2)
𝜀0 E0

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International Journal of Advanced Structural Engineering (2018) 10:199–210 203

where f’ is the cylinder compressive strength of concrete in UHPC

MPa. ε0 is the strain at peak stress, and εcu is the crushing
strain. Very limited analytical model has been developed for pre-
dicting the compressive and tensile behavior of UHPC up
Concrete model proposed by Saenz (1964) to the knowledge of the authors. The UHPC compressive
strength was 210 MPa and the tensile strength was taken as
The uniaxial compressive stress–strain relationship proposed 6.40 MPa (Graybeal 2006a). Figure 3 shows the stress–strain
by Saenz (1964) is as follows: history of the UHPC used in this study and provided as input
EC 𝜀C in ABAQUS. Concrete compression damage parameter that
𝜎C =
( )( 𝜀C ) ( )2 ( )3 , was used based on Eqs. (7) and (8) (Birtel and Mark 2006).
𝜀 𝜀
1 + R + RE − 2 𝜀 − (2R − 1) 𝜀C + R 𝜀C Table 3 shows the input parameters used in the damage
model.
0 0 0

(6)
where
Reinforcing steel
( )
RE R𝜎 − 1 1 EC fC�
R= − , RE = , E0 = , Reinforcing steel has been modeled using a 2-noded lin-
(R𝜀 − 1)2 R𝜀 E0 𝜀0 ear 3D truss element (T3D2); however, solid elements were
used to model the headed end. The reinforcing bars within
where RE = 4 and R𝜎 = 4.
the concrete slab were simulated using the embedded ele-
Concrete compression and tension damage parameters
ment technique available in ABAQUS. Both elastic-perfectly
were calculated using the following equations which were
plastic and bilinear stress–strain curves are tested for the
proposed by Birtel and Mark (2006)
𝜎c Ec−1
dc = 1 − ( ) , (7) 250
pl
𝜀c 1
− 1 + fc Ec−1 (a)
Axial Stress (MPa)

bc
200 UHPC

where dc = concrete compression damage parameter, fc = 150

compressive stress, Ec = modulus of elasticity of concrete, 100
𝜀c = plastic strain corresponding to compressive strength,
pl
50
and bc = constant ranges 0 < bc < 1:
0
𝜎t Ec−1 0 0.001 0.002 0.003 0.004 0.005
dt = 1 − ( ) , (8)
pl 1 Axial Strain (mm/mm)
𝜀t bt
− 1 + ft Ec−1
7
(b)
where dt = concrete tension damage parameter, ft = tensile 6
stress, Ec = modulus of elasticity of concrete, 𝜀t = plastic
pl 5
Stress [MPa]

strain corresponding to tensile strength, and bt = constant 4

ranges 0 < bt < 1. 3
The concrete parameters used in the plastic damage 2
model are shown in Table 2. 1
0
0 0.01 0.02 0.03
Strain [%]

Fig. 3  Axial stress–strain behavior for UHPC (a) in compression and

(b) in tension (Graybeal 2006a)

Table 2  Concrete parameters used in the plastic damage model

Concrete strength Mass density (ton/ Young’s modulus Poisson’s ratio Dilation angle ψ (°) Eccentricity (ε) fbo/fco bc ∕bt
(MPa) mm3) (MPa)

45 2.4E − 009 26,764.7 0.2 20, 36, 40 0.1 1.16 0.7

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Table 3  Ultrahigh-performance concrete parameters used in the plastic damage model (Chen and Graybeal 2012)
Concrete strength Mass density (ton/ Young’s modulus Poisson’s ratio Dilation angle Eccentricity (ε) Concrete strength bc ∕bt
(MPa) mm3) (MPa) ψ (°) (MPa)

210 2.565E−009 53,000 0.18 15 0.1 1.16 0.7

Table 4  Parameters of reinforcing steel Sensitivity analysis

Type Poisson’s ratio Elastic modu- Mass density Yield stress
lus (MPa) (ton/mm3) (MPa) In this section, sensitivity analysis of the numerical mod-
els was conducted based on the constitutive models of con-
Steel 0.3 200,000 7.85E−009 414/517
crete and steel, concrete input properties such as dilatancy
angle and mesh size of the elements. Numerical models
for both headed and straight bars were named SB-XYZ-Pφ
60 and HB-XYZ-Pφ. Where SB and HB stand for straight bar
50
and headed bars, respectively, X represents the initial letter
of the concrete constitutive model being used (H, S, and
40 P), Y is the mesh size (5, 10, and 20 mm), Z represents the
Displacement (mm)

30 contact model type used (T for Tie contact and F for fric-
tion model), P stands for steel model (E for elastic—per-
20
fectly plastic and B for bilinear model), and φ is the angle
10 of dilatancy. All these variables are shown in Table 5.

0
0 0.2 0.4 0.6 0.8 1 1.2
Time (s) Effect of concrete model

Fig. 4  Displacement time history (8H) Three different constitutive models of concrete were
considered to investigate the overall behavior the UHPC
hybrid connections. The ultimate load carrying capac-
simulation. The other parameters used to define the behavior ity for the models HB-S20T-E35°, HB-P20T-E35°, and
of reinforcing steel are shown in Table 4. HB-H20T-E35° was found 480.21, 486.07, and 469.811
Panel 8H has been reinforced at the connection using kN, respectively. For SB-S20T-E35°, SB-P20T-E35°,
headed bars of 16M (#5) as normal reinforcement, whereas and SB-H20T-E35°, the ultimate load carrying capacity
panel 8G was reinforced by straight, lapped bars of 16M was found 486.98, 473.76, and 482.62 kN. Though all
(#5). The thickness of the headed bars was 12.7 mm (0.5 in) the models predicted the ultimate load quite satisfacto-
and a diameter of 50.5 mm (1.987 in.). For panel 8H and 8G, rily, but these models showed stiffer behavior compared
the minimum lap length in the connection was 90 mm (3.54 to the experimental results and that was expected due to
inch) and 150 mm (5.9 inch), respectively. Two additional the initial cracking developed in the real specimens due to
16M (#5) bars were provided along the length of the con- casting and shrinkage. It is observed from Fig. 6 that the
nection between the top and bottom layers. Steel reinforce- model proposed by Saenz (1964) indicates a decrease in
ment is assumed to have perfect bond with concrete as an initial stiffness which is 2 and 45% less than the models
embedded element in ABAQUS. The mesh configuration proposed by Hsu and Hsu (1994) and Park and Paulay
and reinforcement details are shown in Fig. 5a. A displace- (1975), respectively, for headed bar. Concrete damage
ment controlled loading was applied to the panels through plasticity (CDP) model is used for modeling both nor-
a rigid steel plate placed on the top of the panels until the mal strength concrete and UHPC which incorporates both
failure occurs as reported in the test program which is shown tensile cracking and compressive crushing of concrete.
in Fig. 4. In the experiment, the deck panels were supported Defining tension stiffening in CDP model is necessary as
by elastomeric pads on the top of steel plates. The roller it allows to model strain-softening behavior for cracked
supports represent the elastomeric pads at both sides of the concrete. Due to unavailability of post-peak behavior of
deck panels. The load was applied in very small increments UHPC, the ratio of the strength in the biaxial state to the
using the explicit dynamic option in ABAQUS. The edge of strength in the uniaxial state, the eccentricity is assumed
the loading plate was parallel to the precast–UHPC interface as input to the CDP model.
(Fig. 5).

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International Journal of Advanced Structural Engineering (2018) 10:199–210 205

Fig. 5  a Concrete mesh configuration, b reinforcement details ▸

(straight bars), c reinforcement details (headed bars)

Effect of dilation angle

In this section, the angle of dilatancy of concrete was varied

from 20° to 40° for the precast concrete. Figure 7 shows that
the results are not varying drastically as the dilation angle
changes. Numerical results from both panels 8G and 8H also
showed that higher dilation angle results in slightly higher
ultimate load without effect in initial stiffness. For panel
8G, changing the dilation angle from 20° to 40° results in
an increase of 7.81% in ultimate load, whereas for panel 8H,
the increase in ultimate load was found 8.56%. The amount
of dilation depends strongly on the density of the material
(ABAQUS). For this reason, increasing confinement results
in an increase in the angle of friction. In both 8G and 8H
panels, higher dilation angle produced slightly higher initial
stiffness which was expected. In case of headed bar speci-
mens, the stiffness of the composite panel for a dilation angle
of 40° was found 9.69% greater than the stiffness found for
dilation angle 20°, whereas for the 8G panel, 5.47% higher
value of initial stiffness was found for 40° dilation angle.

Effect of steel properties

Both elastic–plastic and bilinear models of the reinforcement

steel were implemented to investigate their effect on the
overall performance of the panels. It is evident from Fig. 8
that the bilinear model of the steel showed lesser stiffness
than the elastic-perfectly model and both models showed
low stiffness compared to the experimental load–displace-
ment response. The initial stiffness decreased 8 and 20%
for 8G and 8H panels, respectively, which justifies that the
bilinear model could predict the experimental results quite
satisfactorily in both panels.
The highest strain in steel bars was observed at mid span
in the connection between UHPC and normal strength pre-
cast concrete. The stress–strain history of the steel bar for
both elastic-perfectly plastic and bilinear cases is shown in
Fig. 9. In both cases, the steel bar reached the yield stress
which was provided as 414 MPa. It also verifies that the
finite-element model is in good agreement with the input
data provided for steel properties.

Convergence study

A sensitivity test was carried out to investigate an optimum

mesh size for the simulation to capture the load–displace-
ment response accurately. The numerical simulation was
performed for 5, 10, and 20 mm mesh size. Figure 10 shows
that there is no significant change observed between 20 and
5 mm mesh size. The ultimate load is found 486.98 and

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206 International Journal of Advanced Structural Engineering (2018) 10:199–210

Table 5  Variables used for Sensitivity test Parameters Straight bars Headed bars
sensitivity analysis
Mesh size 20 mm SB-H20T-E35° HB-H20T-E35°
10 mm SB-H10T-E35° HB-H10T-E35°
5 mm SB-H5T-E35° HB-H5T-E35°
Dilation angle φ = 20 SB-H20T-E20° HB-H20T-E20°
35 SB-H20T-E35° HB-H20T-E35°
40 SB-H20T-E40° HB-H20T-E40°
Concrete model Hsu and Hsu (1994) SB-H20T-E35° HB-H20T-E35°
Saenz (1964) SB-S20T-E35° HB-S20T-E35°
Park and Paulay (1975) SB-P20T-E35° HB-P20T-E35°
Steel properties Elastic-perfectly plastic SB-H20T-E35° HB-H20T-E35°
Bilinear SB-H20T-B35° HB-H20T-B35°
Contact modeling Perfect bond (tie) SB-P20T-E35° HB-P20T-E35°
Penalty (friction) SB-P20F-E35° HB-P20F-E35°
UHPC All parameters were constant for all cases

(a) 600 (a) 600

500 500

400
Load (KN) 400
Load (KN)

Experiment 300
300
Hsu and Hsu (1994)
200 Experimental
200 Park and Paulay (1975) Dialon angle-40
saenz (1964) Dialaon Angle-35
100
100 Dialon angle -20
0
0
0 20 40 60 80
0 20 40 60 80
Displacement(mm)
Displacement(mm)

(b) 600
(b) 600
500
500

400 400
Load (KN)

Load (KN)

Experiment
300 300
Hsu and Hsu (1994) Experimental
200 Park and Pauley (1975) Dialaon Angle-35
200
saenz (1964)
Dilaon angle-20
100 Dilaon angle-40
100
0
0 10 20 30 40 50 60
0
Displacement(mm) 0 10 20 30 40 50 60
Displacement(mm)
Fig. 6  Effect of concrete models; a 8G and b 8H
Fig. 7  Effect of dilation angle; a 8G and b 8H

490.31 kN for 20 and 5 mm mesh, respectively, which are

very close. In consequence, all the simulations were con- ABAQUS, because no numerical data available about the
ducted for 20 mm mesh. behavior of this kind of hybrid connection. Two different
kinds of contact properties were in ABAQUS to predict this
Contact modeling behavior. First, a perfect bond between the UHPC and the con-
ventional concrete was assumed and later, a friction model
The contact between the normal strength precast concrete considering a friction coefficient of 1.09 (Hussein et al. 2016)
deck panels and UHPC is the most crucial part to model in was implemented in which little slip between the interfaces

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International Journal of Advanced Structural Engineering (2018) 10:199–210 207

(a) 600 600

500 500

400 400

LOAD (KN)
Load (KN)

300 300
Experiment EXP
200 Elasc-perfectly plasc 200 FEM 20 mm
Bilinear FEM10 mm
100 100 FEM 5 mm

0 0
0 10 20 30 40 50 60 70 80
0 20 40 60 80
Displacement(mm) Displacement (mm)

(b) 600
Fig. 10  Convergence study for 8G
500

400 600

300 500
Experiment
Load (KN)

200 Elasc-perfectly plasc 400

Load (KN)
Bilinear
100 300
8H Experiment
8H Tie
0 200 8G Experiment
0 10 20 30 40 50 60 8G-e
Displacement(mm) 100 8H-fricon
8G-fricon
0
Fig. 8  Effect of steel properties; a 8G and b 8H 0 20 40 60 80
Displacement(mm)

Fig. 11  Effect of contact model

600
Validation of the finite‑element model
500
The proposed finite-element model has been validated
Axial Stess (MPa)

400 with two full-scale experimentally tested deck panels as

300 described in all the previous sections, which includes both
Headed elasc
headed and straight reinforcement bars under monotonic
200 Headed bilinear
Straight elasc
loading. The failure mode of deck panels was due to the
100
straight bilinear large deformemin associated with a reduction in ultimate
0 load. A comparison of full-scale experimentally tested and
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 the finite-element model is presented in Figs. 12 and 13
Strain (mm/mm) to validate the competency of FEM to foresee the failure
load, mode of failure, and overall behavior of UHPC con-
Fig. 9  Axial stress vs axial strain response for the reinforcement steel nection in precast deck panels.
at the UHPC connection Figure 12 shows that inelastic cracking response con-
tinued to increase until the load reaches to approximately
370–390 kN, and up to this level, the numerical models
showed higher initial stiffness than the experimental ones.
Above that load level, the displacement has been changed
(normal concrete and UHPC) was allowed. Figure 11 shows significantly without noticeable increase in the failure
that both models were quite capable of predicting the response loads. The same behavior is also observed in the experi-
of experimental program satisfactorily. It seems that the fric- mental results. Figure 13 shows the damage in concrete
tion model has less stiffness than the perfect bond model which panels both in compression and tension. As UHPC could
was anticipated, though the predicted ultimate load was less endure higher compressive strength than normal strength
than the experimental one

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208 International Journal of Advanced Structural Engineering (2018) 10:199–210

600

500

400
8G EXP
Load (kN)

300 8G FEM
8H Exp
200
8H FEM

100

0
0 10 20 30 40 50 60 70 80
Displacement (mm)

Fig. 12  Load vs displacement response at mid span

concrete so less damage was found in the UHPC connec-

tion. It is also apparent from the figure that there is no
indication of slip or de-bonding along either of the two
connection interfaces which is in good agreement with the
experiments. The crack pattern found in the tension side
of the deck panels is in good agreement with the cracks
observed from the experiment. Figure 14 shows the dam-
age pattern found around the reinforcement bars in tension.
It is evident from Fig. 14a, b that less damage is found
around headed bar.
The axial stain history of normal precast concrete and
the UHPC both in panel 8H for compression and tension is
shown in Fig. 15. The ultimate axial compressive strain was
found 0.01 and 0.0065 mm/mm for normal concrete and
UHPC, respectively. As UHPC can withstand more tensile
strain, it was observed that the tensile strain is found higher
in UHPC which is 0.08 mm/mm.
The overall comparison between the FEM and experimen-
tal results is summarized in Table 6. The energy absorption
was calculated for each case (AFEM) and compared with the
respective experimental results (Aexp). The ratio between the
energy absorption in the experiments to the energy absorp-
tion in the FEM ranges from 0.91 to 1.01. It was also shown
in Table 6 that the FEM considering the bilinear steel prop-
erties accompanied by friction model predicts more close
results than other parameters.
Fig. 13  Damage a in compression, b in tension (FEM) and c in ten-
sion (Graybeal 2010)
Conclusions

This paper presents a sensitivity analysis based on numeri- • The damage in concrete under monotonic loading is
cal simulations of the behavior of UHPC bridge deck con- found higher in normal concrete than UHPC with no
nections under monotonic loading. The software package signs of de-bonding between the two materials.
ABAQUS was used to perform all the simulations. Various • The FE model captured the damage pattern of the com-
key parameters were investigated such as the concrete con- posite slab deck quite satisfactorily.
stitutive models for the normal concrete, steel stress strain • The numerical model is well capable of predicting
behavior, mesh size, contact properties, and concrete dilation the load displacement response, though it experiences
angles with the following conclusions were drawn: higher stiffness initially.

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International Journal of Advanced Structural Engineering (2018) 10:199–210 209

Fig. 14  Damage in tension
around; a headed bar, b straight
bar

0.090 angle of 40° was found 9.69% greater than the stiffness
0.080
found for dilation angle 20°, whereas for the straight
Axial Strain (mm/mm)

0.070
0.060
NSC (compression)
bar panel, 5.47% higher value of initial stiffness was
0.050
0.040
NSC (Tension)
found for 40° dilation angle.
0.030
0.020 UHPC (Compression)
• The initial stiffness decreased 8 and 20% for panel with
0.010
UHPC (Tension) straight bars and panels with headed bars, respectively,
0.000
-0.010 0 0.2 0.4 0.6 0.8 1 1.2 which justifies that the bilinear model could predict the
-0.020
Time (sec) overall panel performance closely to the experimental
results.
Fig. 15  Strain response of NSC and UHPC in compression and ten-
• The energy absorption ratios of all the experimental
sion (8H) results compared to the developed FEM models were in
the range of 89–110%, which justifies that the FEM mod-
els are in good agreement with the experimental results.
• Changing the dilation angle from 20° to 40° results in
an increase of 7.81% in ultimate load for the panel with
straight reinforcing bars, whereas for panel with headed Open Access  This article is distributed under the terms of the Crea-
tive Commons Attribution 4.0 International License (http://creat​iveco​
bars, the increase in ultimate load was found 8.56%. mmons​.org/licen​ses/by/4.0/), which permits unrestricted use, distribu-
• It was fund that for the panel with straight reinforce- tion, and reproduction in any medium, provided you give appropriate
ment bars, higher dilation angle produced slightly credit to the original author(s) and the source, provide a link to the
higher initial stiffness. In case of headed bar speci- Creative Commons license, and indicate if changes were made.
mens, the stiffness of the composite panel for a dilation

13

210 International Journal of Advanced Structural Engineering (2018) 10:199–210

Table 6  Comparison between FEM and experimental results

Sensitivity test Variables Straight bar Aexp/AFEM Ultimate load (kN) Headed bar Aexp/AFEM Ultimate load (kN)

Mesh size 20 mm SB-H20T-E35° 0.95 486.98 HB-H20T-E35° 0.92 469.81

10 mm SB-H10T-E35° 0.95 445.21 HB-H10T-E35°  N/A N/A
5 mm SB-H5T-E35° 0.94 490.31 HB-H5T-E35°  N/A N/A
Dilation angle (φ) 20 SB-S20T-E20° 0.93 453.17 HB-S20T-E20° 1.01 442.33
35 SB-S20T-E35° 0.94 473.76 HB-S20T-E35° 0.91 467.13
40 SB-S20T-E40° 0.93 488.54 HB-S20T-E40° 0.98 480.21
Concrete model Hsu and Hsu (1994) SB-H20T-E35° 0.95 486.98 HB-H20T-E35° 0.92 469.81
Saenz (1964) SB-S20T-E35° 0.94 473.76 HB-S20T-E35° 0.92 480.21
Park and Paulay (1975) SB-P20T-E35° 0.93 482.62 HB-P20T-E35° 0.92 486.07
Steel properties Elastic-perfectly plastic SB-H20T-E35° 0.95 486.98 HB-H20T-E35° 0.91 469.81
Bilinear SB-H20T-B35° 0.94 515.74 HB-H20T-B35° 0.97 465.59
Contact modeling Perfect bond (tie) SB-P20T-E35° 0.93 482.62 HB-P20T-E35° 0.92 486.07
Penalty (friction) SB-P20F-E35° 0.95 462.05 HB-P20F-E35° 1.01 462.02

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