Flexural behavior modeling of ultrahigh- Performance concrete prestressed T-girder using 3D finite element method

Tóm tắt Flexural behavior modeling of ultrahigh- Performance concrete prestressed T-girder using 3D finite element method: ...d in Table1. This concrete contains no coarse aggregate and is internally reinforced by 13 mm long, 0.2 mm diameter straight steel fibers that are included at a volumetric ratio of 2%. The UHPC mix proportions and mixing procedure show in Figure 2. 480 (a) (b) (c) Figure 2. Cementitious mat... width is probably larger and more visible. Figure 6. SOLID65 element in Ansys [10] The BEAM188 is suitable for analyzing slender to moderately stubby/thick beam structures. The element is based on Timoshenko beam theory which includes shear-deformation effects. The element provides option...l of cable 4.4. Loads and Boundary Conditions Displacement conditions were needed to constraint the model to get a unique solution. The support was modelled as a fixed support at left supporting plate and hinged support at the right one (Figure 10 (a)). Then we applied displacements on two l...

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478 
FLEXURAL BEHAVIOR MODELING OF ULTRAHIGH-
PERFORMANCE CONCRETE PRESTRESSED 
T– GIRDER USING 3D FINITE ELEMENT METHOD 
Do Van Trinh
1,a
, Le Ba Danh
2,b
, Khong Trong Toan
3,c
, Ta Quoc Bao
4,d
, 
Tran Quoc Tinh
5,e
, Doan Dac Truong
6,f 
1
Institute for computational science, 
Ton Duc Thang University, Ho Chi Minh, Vietnam 
2
Department of Bridge and Tunnel Engineering, 
National University of Civil Engineering, Hanoi, Vietnam 
3,5,6
Faculty of Civil Engineering, Hutech University, Ho Chi Minh, Vietnam 
4
Department of Ocean Engineering, Pukyong National University, Busan, Korea. 
a
dovantrinh39@gmail.com, 
b 
danhlb@nuce.edu.vn 
c 
kt.toan@hutech.edu.vn, 
d 
tabao838@pukyong.ac.kr 
e
 tq.tinh@hutech.edu.vn, 
f 
dd.truong@hutech.edu.vn 
ABSTRACT 
This paper presents a 3D finite element modeling of the flexural behavior of ultrahigh-performance 
concrete (UHPC). A four-point flexural test on a UHPC prestressed T girder is considered. The flexural 
strength and cracks pattern of girder are addressed. UHPC material is supposed to be homogeneous and 
isotropic material. It follows a nonlinear fracture model. The results are compared with experimentally 
captured measurements and qualitatively discussed. 
Keywords: Ultra-high performance concrete; Prestressed; Flexural behavior; T Girder; Nonlinear 
behaviour; Finite element method. 
1. INTRODUCTION 
Ultrahigh-performance concrete (UHPC) is a new class of concrete that has been developed in recent 
years. The Federal Highway Administration (FHWA) defines UHPC as follows [1]: UHPC is a 
cementitious composite material composed of an optimized gradation of granular constituents, a water-to-
cementitious materials ratio less than 0.25, and a high percentage of discontinuous internal fiber 
reinforcement. The mechanical properties of UHPC include compressive strength greater than 120 MPa 
and sustained post-cracking tensile strength greater than 5 MPa. Compare with conventional concrete, 
UHPC tends to exhibit superior properties such as advanced strength, durability, and long-term stability. 
UHPC in its present form started to become commercially available in North America by the late 1990s; 
first in Canada in the late 1990s followed by the US in the early 2000s. The first North American bridge to 
use UHPC was constructed in Sherbrooke, Quebec, Canada in 1997 (Blais and Couture 1999). This was a 
precast, prestressed open-web space truss pedestrian bridge that contained nonprestressed (passive) steel 
reinforcement. FHWA began investigating the use of UHPC for highway infrastructure in 2001 and has 
been working with State transportation departments to deploy the technology since 2002. The first US 
479 
bridge to employ UHPC was constructed in Wapello County, Iowa in 2006; this bridge is known as the 
Mars Hill Bridge. The bridge features three precast, prestressed UHPC girders. By the conclusion of 2016, 
there have been more than 180 bridges built in the US and Canada that employ UHPC [2]. Fig.1 presents 
the graphs of UHPC in bridge construction in the United States and Canada. 
In Viet Nam, research on UHPC materials has been conducted in the last 10 years. The research focused 
on changing the composition of local materials available to improve the quality of concrete. Nguyen Cong 
Thang et al. have researched and fabricated UHPC using silica fume and fly ash available in Vietnam in 
2013 [3]. Nguyen Van Tuan et al. have researched and development of UHPC with a compressive strength 
of 200MPa using materials available in Vietnam in 2014 [4]. 
(a) 
(b) 
Figure 1. Graph. Timeline of UHPC in bridge construction in the United States (a) and Canada (b) [2]. 
The use of this new class of concrete in structural applications has been limited. One reason for the slow 
implementation is the perceived complexity of the structural behaviors of UHPC components as compared 
to conventional concrete components as well as the lack of full-scale UHPC component test results. 
Graybeal [5] reseached the flexural behavior of the UHPC was investigated through the testing and related 
analysis of a full-scale prestressed I-girder. Test results are compared to predictions based on standard 
analytical procedures. A relationship between tensile strain and crack spacing is developed. The uniaxial 
stress-strain response of UHPC when subjected to flexural stresses in an I-girder is determined and is 
verified to be representative of both the stress and flexural stiffness behaviors of the girder. A flexural 
design philosophy for this type of girder is proposed. The research of flexural behavior of girder is 
important. It allows to determine, predict the flexural strength and the crack appear. 
In this paper, the general concept of UHPC is first recalled. Then, the UHPC property characterization. 
Next, the experiment setup of flexural test of UHPC prestressed T girder is described. The following 
sections are devoted to numerical modeling by the finite element method. Then, the results of stress-strain 
and cracks pattern between numerical simulations and experimental result were compared. Finally, the 
conclusion of work. 
2. UHPC PROPERTY CHARACTERIZATION 
The constituent material proportions of UHPC in this study are listed in Table1. This concrete contains no 
coarse aggregate and is internally reinforced by 13 mm long, 0.2 mm diameter straight steel fibers that are 
included at a volumetric ratio of 2%. The UHPC mix proportions and mixing procedure show in Figure 2. 
480 
(a) (b) (c) 
Figure 2. Cementitious matrix (a), steel fibers reinforcement (b) and mixing procedure (c) of UHPC 
Table 1. UHPC mix proportions 
Material kN/m
3
Portland Cement 9.02 
Sand Quart 11.30 
Silica Fume 2.26 
Water 1.65 
Steel Fibers (2%) 1.58 
HRWR (%) 0.40 
The mechanical properties of UHPC are determined by a series tests in laboratory (Figure 3): 
– The Modulus of elasticity and Poisson‟s ratio measure from a compression tests on cylinders 
specimen with a nominal diameter of 100 mm and nominal height of 200 mm [6]. 
– The elastic tensile strength and tensile stress-strain curve are determined based on flexural tests (3-
point bending tests on notched prisms and 4-point bending tests). The prisms have a cross-section 
of 100 ×100 mm and a length of 400 mm [7]. 
The results of mechanical properties of UHPC show in Table 2. 
Figure 3. Concrete properties test setup 
481 
Table 2. Mechanical Properties of UHPC 
Fiber volume 
fractions (%) 
Compressive strength 
 (MPa) 
Tensile 
strength (MPa) 
Modulus of 
elasticity 
(GPa) 
Poisson‟s ratio 
2.0 120 8 40 0.2 
3. EXPERIMENTAL SETUP OF FLEXURAL TEST UHPC PRESTRESSED T GIRDER 
The test specimen for this research effort was designed base on recent releases [5][8]. The cross section of 
T girder shows in Figure 4. The length of girder is 6.3 m. It contains 2 strands 15.7 mm diameter and 1860 
MPa low relaxation prestressing. 
Figure 4. Cross section and strands pattern of T girder 
The girder was loaded in four point bending test, with the point loads each located 0.5 m from midspan as 
is shown in Figure 5. The stress in girder are measured by 11 strain gauges, and 5 LVDT for identify the 
vertical deflections. The majority of strain gauges were placed on the midspan cross section in order to 
capture the strains and the neutral axis location during the test. 
Figure 5. Instrumentation used and experiment setup for T girder flexural test 
4. FINITE ELEMENT (FE) MODELING 
In this study, the ANSYS APDL software was used to model the flexural behavior of prestressed T girder. 
4.1. Element types 
The SOLID65 is used for 3-D modeling the UHPC. The solid is capable of cracking in tension and 
crushing in compression. The concrete element is similar to a 3-D structural solid but with the addition of 
482 
special cracking and crushing capabilities [9]. The most important aspect of this element is the treatment 
of nonlinear material properties. 
The SOLID65 element is used to model for concrete and cables are smeared within the element and can be 
defined in three different axes, it is represented by BEAM188 element in Ansys. Frictional contact 
between concrete and rebar and is assumed. The geometry and node locations for SOLID65 element are 
shown in Figure 6. The element is defined by eight nodes with three degrees of freedom at each node in 
the nodal x, y, and z directions [10]. Crack widths are not supplied by the element and therefore existence 
of a crack does not mean that it is visible to the eye. Crack profiles with “third” cracks are usually more 
consistent with the experimental ones than the ones with “first” and “second” cracks. An integration point 
with a “third” crack is cracked at all three axes; therefore, the crack width is probably larger and more 
visible. 
Figure 6. SOLID65 element in Ansys [10] 
The BEAM188 is suitable for analyzing slender to moderately stubby/thick beam structures. The element 
is based on Timoshenko beam theory which includes shear-deformation effects. The element provides 
options for unrestrained warping and restrained warping of cross-sections. The element is a linear, 
quadratic, or cubic two-node beam element in 3-D. BEAM188 has six or seven degrees of freedom at each 
node. These include translations in the x, y, and z directions and rotations about the x, y, and z directions. 
A seventh degree of freedom (warping magnitude) is optional. This element is well-suited for linear, large 
rotation, and/or large strain nonlinear applications [10]. 
SOLID185 is used for 3-D modeling of solid structures, they are support and loading plates here. It is 
defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z 
directions. The element has plasticity, hyper elasticity, stress stiffening, creep, large deflection, and large 
strain capabilities [10]. It also has mixed formulation capability for simulating deformations of nearly 
incompressible elastoplastic materials, and fully incompressible hyperplastic materials 
(a) 
(b) 
Figure 7. BEAM188 element (a) and SOLID185 element (b) in Ansys [2] 
483 
4.2. Material Properties 
To define concrete and strand, in Ansys platform all the following properties are to define; that is, (i) 
Young modulus, (ii) stress – strain relationship, (iii) ultimate uniaxial tensile strength, (iv) ultimate 
uniaxial compressive strength and (v) Poisson‟s ratio. All the values are provided from experimental 
(Tab.2). William and Warnke [11] failure criterion is applied to model the concrete to define crack 
propagation. Four important parameters, that is, (i) shear transfer coefficients for an open crack, (ii) shear 
transfer coefficients for a closed crack, (iii) uniaxial tensile cracking stress, and (iv) uniaxial crushing 
stress, are also considered to model the concrete. Typical shear transfer coefficients range from 0.0 to 1.0, 
with 0.0 representing a smooth crack (complete loss of shear transfer) and 1.0 representing a rough crack 
(no loss of shear transfer). The William and Warnke criterion‟s parameters use show in Table 3. 
Table 3. FE governing parameters 
FE governing parameters Concrete Cable 
Modulus of elasticity (MPa) 40000 195000 
Stress – Strain relationship From experiment From experiment 
Poisson‟s ratio 0.2 0.3 
Shear transfer coefficients for an open crack 0.15 
Shear transfer coefficients for a closed crack 0.85 
Uniaxial tensile cracking stress (MPa) 8 
Uniaxial crushing stress (MPa) 120 
The stress – strain relationship will be applied for both concrete and cable via hardening model 
Multilinear Isotropic Hardening and Multilinear Kinematic Hardening. 
4.3. Modeling and Meshing 
All beam and plate will be built as 3D full model, has the same dimensions with the test specimen and 
cables are modeled as links. 
In order to obtain the actual results from the SOLID65 element, a mesh was recommended. The meshing 
of the reinforcement was a special case compared to volumes. The beam was meshed such that it is 
considered of 100mm along the length of beam and 50mm along the width of beam. The total number of 
node is 6200 and element is 3186. 
Figure 8. Meshing of the 3D full model 
Loading Plate 
Supporting Plate 
484 
Figure 9. Meshing and model of cable 
4.4. Loads and Boundary Conditions 
Displacement conditions were needed to constraint the model to get a unique solution. The support was 
modelled as a fixed support at left supporting plate and hinged support at the right one (Figure 10 (a)). 
Then we applied displacements on two loading plates and down wards along Y direction as Figure 10 (b). 
(a) 
(b) 
Figure 10. Boundary conditions (a) and forced displacement conditions (b) 
5. RESULTS AND DISCUSSION 
In order to investigate the flexural behavior and crack profiles of the girder, the FE results are partially 
compared with the experimental data. Convergence using nonlinear element types such as SOLID65 is so 
sensitive to the analysis and element options. The size of the load increment is initially set to an optimum 
value and then, let ANSYS change automatically according to the number of nonlinear iterations 
performed at each load step. 
Figure 11 shows the relationship between the bending forces and the measured displacements at mid-span 
obtained from experiment and FE analyses. The displacement is increased when the force increases. In 
first part, these cures are linear (P < 58 KN). Compared with the experiment results, a similar part is 
obtained in both curves. The bending strength obtain is197 kN. 
The stress contours of the FE models are shown in Figure12 (a). The stress concentration is found higher 
at the bottom face of beam in the position that opposite with two loading plates, conforming to the 
experimental observation of first cracks found in similar locations (Figure 12 (b)). 
Figure 11. Comparison of analyses results between FEM modeling and the 
experimental data 
485 
(a) (b) 
Figure 12. Diagram of von Mises Stress (a) and first crack appear in experimental test (b) 
The model developed using ANSYS is capable of predicting failure for concrete materials. Both 
cracking and crushing failure modes are needed to define a failure surface for the concrete. Cracking 
occurs when the principal tensile stress in any direction lies outside the failure surface. Figure 13 shows 
the cracks appeared on the bottom face of beam first (red lines); after that they propagated along the 
vertical direction between plates, caused by the constant moment. However, the shear crack (near and 
outside plates) has not yet properly. It influences by the shear transfer coefficients used in the William 
and Warnke criterion. The same result of cracks pattern is obtained by experiment test (white lines) 
(Figure 14). 
Figure 13. Crack pattern obtain by FE modeling 
(a) 
(b) 
Figure 14. Cracks pattern obtain by experiment 
6. CONCLUSIONS 
This paper presents a 3D finite element modeling of the flexural behavior of ultrahigh-performance 
concrete (UHPC). A four-point flexural test on a UHPC prestressed T girder is considered. ANSYS APDL 
software was used. The numerical flexural strength and cracks pattern in tension appear during the test 
correspond well to the experiment. However, the shear crack has not yet properly. It influences by the 
486 
shear transfer coefficients used in the William and Warnke criterion. In this study, UHPC material is 
supposed to be homogeneous and isotropic material. It follows a nonlinear fracture model. Influence of 
fibers distribution on the cracks pattern is not yet considered. The shear transfers coefficients, influence of 
fibers distribution, contact interface UHPC/cable are content of the future research. 
REFERENCES 
[1] B. A. Graybeal, “Design and Construction of Field-Cast UHPC Connections,” FHWA, no. October, 
pp. 1–36, 2014. 
[2] Z. B. Haber, I. De La Varga, and B. A. Graybeal, “Properties and Behavior of UHPC-Class 
Materials,” no. FHWA-HRT-18-036, p. 153, 2018. 
[3] N. T. L. Nguyen Cong Thang, Nguyen Van Tuan, Pham Huu Hanh, “Research and fabricate UHPC 
using silica fume and fly ash available in Vietnam,” J. Build. Sci. Technol., vol 2. No. 201, pp. 24–
31, 2013. 
[4] N. C. T. Nguyen Van Tuan, Pham Huu Hanh, “research and development of UHPC with a 
compressive strength of 200MPa using materials available in Vietnam,” Constr. Journal, Minist. 
Constr., 2014. 
[5] [5] B. A. Graybeal, “Flexural Behavior of an Ultrahigh-Performance Concrete I-Girder,” J. 
Bridg. Eng., vol. 13, no. 6, pp. 602–610, 2008. 
[6] ASTM, “ASTM C469/C469M-14 Standard Test Method for Static Modulus of Elasticity and 
Poisson‟s Ratio of Concrete in Compression,” ASTM Int., pp. 1–5, 2014. 
[7] A. F. de G. Civil, “Documents scientifiques et techniques - Ultra High Performance Fibre-
Reinforced recommendations,” Recommandations provisoires.Janvier, no. June, 2013. 
[8] JSCE, “Recommendations for design and construction of ultra high strength fiber reinforced 
concrete structures (draft)”, JSCE guidelines for concrete , no. 9 ed. Japan Society of Civil 
Engineers, 2006. 
[9] K. P. Nimiya, R.J., Saibabu, S. and Siva, “Finite Element Analysis of Reinforced and Pre-
Tensioned Concrete Beams”, International Journal of Emerging Technology and Advanced 
Engineering, vol. 4, Issue 10, pp. 449–457, 2014. 
[10] Ansys Help, “Element Reference,” vol. Ansys Inc. 
[11] K. Willam and E. Warnke, “Constitutive model for the triaxial behavior of concrete”, Intl. Assoc. 
Bridge Structl. Engrt 19 (III), pp. 1–30, 1975. 

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