Numerical Simulation of Prestressed Precast Concrete Bridge Deck Panels Using Damage Plasticity Model
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Abstract
This paper describes a three-dimensional approach to modeling the nonlinear behavior of partial-depth precast prestressed concrete bridge decks under increasing static loading. Six full-size panels were analyzed with this approach where the damage plasticity constitutive model was used to model concrete. Numerical results were compared and validated with the experimental data and showed reasonable agreement. The discrepancy between numerical and experimental values of load capacities was within six while the discrepancy of mid-span displacement was within 10 %. Parametric study was also conducted to show that higher accuracy could be achieved with lower values of the viscosity parameter but with an increase in the calculation effort.
Keywords
bridge decks concrete concrete damage plasticity cracking finite element simulation1 Introduction
This paper presents the results of numerical simulations conducted using ABAQUS on hybrid partial-depth precast prestressed concrete (PPC) bridge deck panels using the concrete damage plasticity model to investigate the behavior and failure mechanism. The term “hybrid panel” in this paper describes a PPC panel that contains two different types of prestressing tendons: either epoxy-coated steel or carbon fiber reinforced polymer (CFRP) tendons at the panel edges, and uncoated steel tendons at the interior of the panel. Previous studies have shown that substitution of steel tendons with epoxy-coated steel could effectively reduce the occurrence of corrosion (Kobayashi and Takewaka 1984) and using FRP tendons as the addition of reinforced tendons, the ductility of the prestressed beams can be significantly improved (Saafi and Toutanji 1998).
2 Background
2.1 Bridge Deck Description
Partial-depth prestressed precast concrete deck panels span between girders and serve as stay-in-place (SIP) forms for a cast-in-place (CIP) concrete bridge deck. Typical panel geometries are 75–90 mm (3.0–3.5 in.) thick, 2.4 m (8 ft) long in the longitudinal direction of the bridge, and sufficiently wide to span between the girders in the bridge transverse direction. The panels are typically pretensioned with prestressing steel strands located at the panel mid-depth. Panels are placed adjacent to one another along the length of the bridge and typically are not connected to each other in the longitudinal bridge direction. After the panels are in place, the top layer of reinforcing steel is placed, and the CIP concrete portion of the deck [typically 125–140 mm (5.0–5.5 in) thick] is cast on top of the panels. At the bridge service state, the CIP concrete and SIP panels act as a composite deck slab.
2.2 Problem Statement
The most common problem reported with the use of partial-depth deck panels is reflective cracking on the top surface of the deck. Cracks in the transverse direction of the bridge may form at locations at which adjacent panels are placed (panel edges), while cracks in the longitudinal direction may form at the locations at which the panels are supported on the girders (panel ends).
3 Experimental Program
Test matrix.
Test specimen | Edge tendon type | Concrete type |
---|---|---|
ST-NC | Steel | Normal |
ST-FRC | Steel | FRC |
ECT-NC | Epoxy-coated steel | Normal |
ECT-FRC | Epoxy-coated steel | FRC |
CFRP-NC | CFRP | Normal |
CFRP-FRC | CFRP | FRC |
Material parameters (MPa/Psi).
Concrete compressive strength | Concrete tensile strength | Concrete modulus of rupture | Tendon f_{ y } | Tendon f_{ u } | ||||
---|---|---|---|---|---|---|---|---|
ST | Epoxy-coated steel | ST | Epoxy-coated steel | CFRP | ||||
ST-NC | 37.2/6,360 | 3.36 | 31,342/600 | 1,737/2.52 × 10^{5} | – | 1,889/2.74 × 10^{5} | – | – |
ST-FRC | 32.6/5,580 | 3.08 | 29,357/855 | 1,737/2.52 × 10^{5} | – | 1,889/2.74 × 10^{5} | – | – |
ECT-NC | 34.5/5,900 | 3.20 | 30,187/765 | 1,793/2.6 × 10^{5} | 1,882/2.73 × 10^{5} | 1,924/2.79 × 10^{5} | 1,999/2.9 × 10^{5} | – |
ECT-FRC | 37.8/6,460 | 3.40 | 31,587/745 | 1,793/2.6 × 10^{5} | 1,882/2.73 × 10^{5} | 1,924/2.79 × 10^{5} | 1,999/2.9 × 10^{5} | – |
CFRP-NC | 40.9/700 | 3.58 | 32,881/620 | 1,793/2.6 × 10^{5} | – | 1,924/2.79 × 10^{5} | – | 2,576.5 |
CFRP-FRC | 37.4/6,390 | 3.37 | 31,416/585 | 1,793/2.6 × 10^{5} | – | 1,924/2.79 × 10^{5} | – | 2,576.5 |
4 Modeling Approach
4.1 Material Models
The finite element models of the tested specimens were built and analyzed with software ABAQUS. For linear elastic materials, at least two material constants are required: Young’s modulus (E) and Poisson’s ratio (v). For nonlinear materials, the steel and concrete uniaxial behaviors beyond the elastic range must be defined to simulate their behavior at higher strains. ABAQUS provides different types of concrete constitutive models including, (1) a smeared crack model; (2) a discrete crack model; and (3) a damage plasticity model (ABAQUS Theory Manual 2010). The concrete damage plasticity model, which can be used for modeling concrete and other quasi-brittle materials, was used in this study. This model combines the concepts of isotropic damage elasticity with isotropic tensile and compressive plasticity to model the inelastic behavior of concrete. The model assumes scalar (isotropic) damage and can be used for both monotonic and cyclic loading conditions. Elastic stiffness degradation from plastic straining in tension and compression is accounted for (Lubliner et al. 1989; Lee and Fenves 1998). Cicekli et al. (2007) and Qin et al. (2007) proved that damage plasticity model provides an effective method for modeling the concrete behavior in tension and compression.
4.1.1 Concrete Constitutive Model and Damage Indices
The concrete damage plasticity model requires input of parameters including the constitutive relationship of concrete, which can be customized by the user. This paper used the constitutive model of concrete developed by Zhenhai (2001) and Xue et al. (2010).
4.1.2 Other Data of Concrete Models
- (1)
The dilation angle ψ is a ratio of vertical shear strain increment and strain increment, which is taken as 38 degrees.
- (2)
Flow potential eccentricity ɛ is a small positive number that defines the rate at which the hyperbolic flow potential approaches its asymptote. This paper takes a value of 0.1.
- (3)National standard of the people’s republic of China (2002) recommend,$$-{f}_{3}/{f}_{c}^{\ast}=1.2+33{({\mathit{\sigma}}_{1}/{\mathit{\sigma}}_{3})}^{1.8}$$(3)From FE model analysis, σ_{1} = −16.66 Mpa, σ_{3} = −1.73 Mpa, before the concrete cracks. So$$-{f}_{3}/{f}_{c}^{\ast}=1.2+33{(16.66/1.73)}^{1.8}=1.7585$$
The ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress σ_{ bo }/σ_{ co } was taken as 1.76.
- (4)
The ratio of the second stress invariant on the tensile meridian, q(TM), to that on the compressive meridian K_{ c } was taken as 2/3.
- (5)
The viscosity parameter μ used for the visco-plastic regularization of the concrete constitutive equations in Abaqus/Standard was taken as 0.0005.
4.1.3 Prestressing Tendons
4.2 Finite Element Model Description
4.2.1 Symmetry
4.2.2 Element Type and Meshing Scheme
4.2.3 Bonding Between Reinforcement and Concrete
4.2.4 Boundary Conditions
Due to symmetry, only a quarter of the panel was modeled as shown in Fig. 8. The nodes on symmetry surfaces were constrained in X and Y directions, respectively. At the supports, nodes were constrained in the z direction.
4.2.5 Prestressing Effect
4.2.6 Convergence Considerations
- (1)
Loading steps were adjusted in consideration of the anticipated time of concrete cracking and the automatic time step was adopted.
- (2)
Constitutive relationship was modified by introducing the coefficient of viscosity. A higher viscosity coefficient would make the structure of “harder”. Through extensive trials, a viscosity coefficient of 0.0005 was found to be helpful with convergence.
- (3)
In cases of computation time being more critical than accuracy (Jiang 2005), the force and displacement convergence criteria were adjusted to reduce the computation time.
5 Validation of FE Model
5.1 Force–Displacement Relationships
Failure loads and corresponding displacements.
Failure load | Midspan displacement at failure load | |||||
---|---|---|---|---|---|---|
P_{ Test } (kN) | P_{ FE } (kN) | P_{ Test }/P_{ FE } | δ_{Test} (mm) | δ_{FE} (mm) | δ_{Test}/δ_{FE} | |
ST-NC | 98.21 | 101.4216 | 0.97 | 54.31 | 51.82 | 1.05 |
ST-FRC | 90.55 | 88.1972 | 1.03 | 42.75 | 34.8868 | 1.23 |
94.4248^{a} | 0.96^{a} | 42.5018^{a} | 1.01^{a} | |||
ECT-NC | 82.51 | 88.3596 | 0.93 | 27.46 | 34.8623 | 0.79 |
85.5892^{a} | 0.96^{a} | 29.4543^{a} | 0.93^{a} | |||
ECT-FRC | 94.36 | 93.43 | 1.01 | 44.02 | 41.05 | 1.07 |
CFRP-NC | 93.39 | 99.5872 | 0.94 | 36.45 | 45 | 0.81 |
91.4712^{a} | 1.02^{a} | 33.4368^{a} | 1.09^{a} | |||
CFRP-FRC | 92.85 | 97.0472 | 0.96 | 44.11 | 40.00 | 1.10 |
The error of the failure loads was within 6 % and the error of the midspan displacement was within 10 % with the adjusted concrete model.
5.2 Failure Modes
6 Parametric Analysis
The influence of the concrete dilation angles, viscosity parameters, and prestressing effect on the analytical results was investigated through parametric analysis of panel ST-NC-SL.
6.1 Effect of Concrete Dilation Angle $\mathbf{\psi}$
6.2 Effect of µ Viscosity Parameter
Material models exhibiting softening behavior and stiffness degradation often lead to severe convergence difficulties in implicit analysis programs, such as Abaqus/Standard. A common technique to overcome these convergence difficulties is the use of a visco-plastic regularization of the constitutive equations, which causes the consistent tangent stiffness of the softening material to become positive for sufficiently small time increments.
6.3 Effect of Prestressing Force
7 Conclusions
- (1)
The concrete damage plasticity model in ABAQUS can predict the concrete crushing failure mode in PPC panels. The numerical error of the failure loads and mid-span displacement was within 6 % and 10 %, respectively.
- (2)
It was feasible and accurate enough to simulate the prestressing effect by applying temperature load to prestressing strands or tendons.
- (3)
Under tri-axial compression state in the case of this paper, the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress σ_{ bo }/σ_{ co } was taken as 1.76 and was shown accurate to predict the behavior of PPC panels.
- (4)
Increasing prestressing effect resulted in increasing of, the cracking load and decreasing of displacement capacity of the PPC panels as shown in the parametric study in this paper.
- (5)
Lower values of viscosity of parameter increased calculation accuracy and increased the calculation time.
Notes
Acknowledgments
The experimental program was funded by the Missouri Department of Transportation (MoDOT) and the National University Transportation Center (NUTC) at Missouri University of Science and Technology (Missouri S&T). Ministry of Transport of the People’s Republic of China (2012 319 812 100) and the Shaanxi Department of Transportation (14–17 k) funded the other part of this study.
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