Research Article  Open Access
Experimental Study and MixedDimensional FE Analysis of TRib GFRP PlateConcrete Composite Bridge Decks
Abstract
In order to extend the understanding of structural performance of a Trib glass fibrereinforced polymer (GFRP) plateconcrete composite bridge deck, four GFRP plateconcrete composite bridge decks were tested, which consist of castinplace concrete sitting on a GFRP plate with Tribs. Subsequently, a mixeddimensional finite element (FE) analysis model was proposed to simulate the behavior of the test models. The test and simulation results showed that the composite specimens had an excellent interface bonding performance between GFRP plate and concrete throughout flexural response until specimens failure occurred. The failure mode of those composite specimens was shear failure in concrete structures. It was found that the interface roughness of the GFRP plate could not affect the ultimate bearing capacity and stiffness of composite specimens significantly. However, the height of concrete structures had a strong effect on those structural behaviors. In addition, the longitudinal compressive reinforcing CFRP rebars had a little influence on ultimate bearing capacity of composite specimens, while it had a significant influence on ductility of composite specimens. The mixeddimensional FE analysis model can accurately simulate the local complex stress state of GFRP plates, ultimate loads, stiffness, and midspan deflections and simultaneously can significantly reduce computational time. Therefore, mixeddimensional FE analysis can provide a suitable solution to simulate the structural performance of Trib GFRP plateconcrete composite bridge decks.
1. Introduction
Compared with the FRP structure, the FRPconcrete composite/hybrid structures have more advantages, such as preventing the buckling phenomena of pultruded FRP profiles [1, 2], improving the usage of FRP profiles strength [3], reducing material costs [4], and improving stability, flexural stiffness, and bearing capacity of structures [5]. Furthermore, the FRP profiles/plates can act as a temporary formwork when pouring the castinplace concrete [6]. Hence, the application of FRPconcrete composite bridge decks becomes more and more widespread in recent years [7–14].
Researchers proposed some FRPconcrete composite structures with different shapes of cross sections, such as a rectangular [15–17], box [18, 19], or Ishape section [8, 20–22], as shown in Figure 1. The failure modes of these composite structures are primarily interface bonding failure between FRP profiles/plates and concrete [23–29]. The material strength of these composite structures cannot be effectively used due to interface bonding failure. Therefore, increasing the bonding behaviors between FRP profiles/plates and concrete is significantly critical for these structures.
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In order to obtain an improved interface bonding performance between FRP profiles/plates and concrete, some composite structures with different shapes of cross sections were proposed, as shown in Figure 2(a) [30], Figure 2(b) [31], and Figure 2(c) [32]. In addition, a Trib glass fibrereinforced polymer (GFRP) plateconcrete composite bridge deck was also proposed in this paper, which consists of castinplace concrete sitting on a GFRP plate with Tribs, as shown in Figure 2(d).
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The finite element method (FEM) is widely used to analyse the structural performance of FRPconcrete composite structures, due to the better accuracy and feasibility of FEM than the other analysis methods (e.g., Euler–Bernoulli beam theory [33], Timoshenko beam theory [3, 15, 21, 34], and orthotropic plate theory [4]). According to element types used in simulation composite structures, the FEA model can be divided into three types, namely, FEA model with truss elements, shell elements, and solid elements, respectively. (1) The FEA model with truss elements was the twodimensional truss elements adopted to simulate FRP profiles/plates and concrete [35]. (2) The FEA model with shell elements was the twodimensional shell elements and threedimensional solid elements adopted to simulate FRP profiles/plates and concrete [3, 4, 8, 15, 22, 36–38], respectively. (3) The FEA model with solid elements was the threedimensional solid elements adopted to simulate concrete and FRP profiles/plates [34, 39–41].
The FEA model with truss elements and shell elements is unable to simulate the stress state of FRP profiles/plates along the thickness direction and also unable to simulate the threedimensional stress state of FRP profiles/plates (e.g., box section, rectangular section, and Ishape section) at the intersection or near the Tribs. By contrast, though the FEA model with solid elements can overcome the above deficiency, the computational time is very long and computational efficiency is very low.
As a result, the flexural experiments on the proposed Trib GFRP plateconcrete composite bridge decks in this paper were performed to examine the feasibility and indepth understanding of structural performance. Furthermore, a mixeddimensional FEA model is proposed for high efficiency analysis of the GFRP plateconcrete composite bridge deck and accurately simulating the local complex stress state of GFRP plates.
2. Experimental Program
2.1. Description of Specimens
A total of four rectangular GFRPconcrete composite bridge decks were designed and conducted. The GFRP plate was used to carry tensile force, and the castinplace concrete was poured on the upper surface of the GFRP plate to carry compressive force. The details, including geometric dimensions and test parameters, of all specimens used in the test are shown in Table 1.

For the convenience of the experiment, the pultruded GFRP plate was halved according to the symmetry of the structure. Then, the halved GFRP plate with five Ttype ribs and one specialshaped rib is shown in Figure 3(a). The specimens GC1, GC2, and GC4 had identical geometric dimensions of 305 mm in width, 200 mm in height, and 1300 mm in length; while specimen GC3 had a same geometric dimension in width and length, expect the 150 mm height, as shown in Figures 3(b) and 3(c).
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To investigate the effect of CFRP rebars on the structural performance of composite specimens, two 8 mm diameter CFRP rebars were placed in the compressive zone of the composite specimen as the longitudinal compressive reinforcement. Moreover, the horizontal CFRP rebars spacing at 165 mm center to center were tied with two longitudinal CFRP rebars at the intersections to form a reinforcement mesh, as shown in Figure 3(c).
Two types of interfaces (i.e., type I and type II) were generated by treating the GFRP plate surface bonded with castinplace concrete. The interface of specimens coded as GC1, GC3, and GC4 was interface type I, while interface type II was used in specimen GC2.
The interface type I was that the 2 mm even thick epoxy brushed onto the GFRP plate, 2–5 mm aggregates immediately spread onto the epoxy resin, and then the rough interface of the GFRP plate formed. The type II interface was the concrete placed directly against the GFRP plate. A set of the device, which consisted of a dial indicator and flat base, was designed to measure the interface roughness, as shown in Figure 4. The average value of the vertical height difference between protruding and concave portions of the interface was used to quantitatively assess the interface roughness [42]. The measured interface roughness values of type I was 3.33 mm.
The manufacturing process of all composite specimens is described in detail as follows: the GFRP plate acts as the bottom formwork of the composite specimen and four wooden boards as the side formwork. For specimens GC1, GC3, and GC4 with the interface type I, the interface was manufactured according to the abovementioned method. According to previous research results conducted by Zhang et al. [43], the best initial placement time of castinplace concrete onto the adhesive resincoated GFRP plate is about 30 minutes. So, after 30 minutes curing of the adhesive layer, the castinplace concrete was poured into the moulds against the adhesive layer to form the composite specimens. For specimen GC2 with the type II interface, the castinplace concrete was directly poured into the moulds to form the composite specimen after cleaning of the GFRP plate. All the specimens were cured under the temperature of 20 ± 2°C and humidity of 95% for 28 days.
2.2. Material Properties
Ordinary Portland cement (CEM Ι 42.5N) was used for the castinplace concrete. The fine aggregate was natural sand with sizes below 1.7 mm, and the coarse aggregate was crushed limestone with sizes between 5 mm and 20 mm. The polycarboxylicbased waterreducing agent produced by Subote New Material Co., Ltd of China was used to obtain good workability. The mass ratio of the castinplace concrete was 1 (cement) : 0.39 (water) : 1.06 (fine aggregate) : 2.72 (coarse aggregate) : 0.0075 (waterreducing agent). The measured average compressive strength, tensile strength, and elastic modulus of the castinplace concrete were 34.6 MPa, 2.2 MPa, and 31.4 GPa, respectively, according to the methods reported in GB/T 500812002 [44].
The GFRP plate and CFRP rebar were all produced by Nanjing Hitech Composites Co., Ltd of China. Sikadur330 epoxy resin was produced by Sika Corporation of Switzerland. Material parameters of the GFRP plate, CFRP rebar, and Sikadur330 epoxy resin were provided by the manufacturers. The ultimate tensile strength, tensile elastic modulus, and elongation of the GFRP plate were 471 MPa, 26.6 GPa, and 1.9%, respectively. The ultimate tension strength, elastic modulus, and elongation of the CFRP rebars were 2100 MPa, 147 GPa, and 1.5%, respectively. The ultimate tension strength, elastic modulus, and elongation of Sikadur330 epoxy resin were 30 MPa, 3.8 GPa, and 1.6%, respectively. A summary of material properties is shown in Table 2.

2.3. Experimental Setup and Instrumentations
The experimental setup is shown in Figure 5. All specimens were simply supported on two rollers spaced at 1000 mm. And all specimens were applied in fourpoint bending under monotonically increasing loads, through a 350 kN capacity hydraulic jack. The whole loading process was controlled at a speed of 0.5 mm/min. The load values were determined through a load cell between the jack and the reaction frame.
A fully instrumented specimen is also shown in Figure 5. Three linear variable displacement transducers (LVDTs) were applied to measure deflection of midspan and two supporting points. Five 100 mm long strain gauges on the specimen side were applied to measure strain distributions at midspan cross section.
2.4. Test Results and Discussion
2.4.1. Failure Mode and Characteristics Data
Detailed test phenomena of all specimens under monotonically increasing load are described as follows: for the specimens GC1, GC2, GC3, and GC4, when applied loads of 55 kN, 50 kN, 40 kN, and 55 kN, respectively, the first microcrack was found at the bottom of the concrete. And then with the increasing loads, the first microcrack widened and extended upward, and the new cracks also formed. For instance, the cracks distribution of specimen GC2 is shown in Figure 6 (not all are shown here for brevity).
For the specimens GC1, GC2, GC3, and GC4, when applied loads beyond 80 kN, 200 kN, 180 kN, and 200 kN, respectively, the specimens began to make a continuous noise in the process of increasing loads. When the applied loads were 242.3 kN, 226.3 kN, 192.5 kN, and 267.1 kN, respectively, the shear failure of concrete occurred (diagonal racks through concrete cross section), while the concrete remained better bonded to the GFRP plates/Tribs, and there was almost no slip between the concrete and GFRP plate throughout the flexural response until concrete shear failure occurred. For instance, the failure mode of specimen GC3 is shown in Figure 7 (not all are shown here for brevity).
The test results, including crack load, ultimate load, midspan deflection at the ultimate load, ultimate relative slip between GFRP plate and concrete, and failure mode, of all specimens are shown in Table 3.

It can be found that failure mode of all specimens was concrete shear failure and there was almost no slip between the concrete and GFRP plate, indicating that the interface roughness of the GFRP plate, the height of concrete cross section, and the longitudinal compressive reinforcing CFRP rebars had no influence on the failure mode of the composite specimens.
It can also be seen that the crack loads of specimens GC2 and GC3 were 9% and 27% lower than that of specimen GC1, respectively, while the crack load of specimens GC1 and GC4 was identical, indicating that the interface roughness of the GFRP plate and height of concrete cross section had a significant influence on crack loads, while the longitudinal compressive reinforcing the CFRP rebars had almost no influence on crack loads.
2.4.2. LoadDeflection Curve at Midspan Cross Section
The loaddeflection curves of all specimens at the midspan section are shown in Figure 8. It can be found that variations of loaddeflection curves of specimens were basically similar. Before ultimate loads of 70%, the loaddeflection curves of all specimens were linear. Hereafter, the stiffness of all specimens decreased slightly, and the loaddisplacement curves showed nonlinearity. After the ultimate loads, the loaddisplacement curves presented a sharp decline because the shear failure of concrete occurred.
By comparing the loaddeflection curves of specimens GC1 and GC2, it can be found that, before the ultimate load of 70%, the stiffness of specimens GC1 and GC4 was basically identical. Hereafter, the stiffness of specimen GC2 was slightly lower than that of specimens GC1, and the ultimate load of specimen GC2 was also 6.6% lower than that of specimen GC1. It can be concluded that the interface roughness of the GFPR plate had a slight influence on the ultimate bearing capacity and stiffness of composite specimens.
By comparing the loaddeflection curves of specimens GC1 and GC3, it can be found that the stiffness of specimen GC3 was significantly lower than that of specimen GC1, and the ultimate load of specimen GC3 was also 20.6% lower than that of specimen GC1. It can be concluded that the height of concrete cross section had a significant influence on ultimate bearing capacity and stiffness of composite specimens.
By comparing the loaddeflection curves of specimens GC1 and GC4, it can be found that the stiffness of specimens GC1 and GC4 was basically identical before the ultimate loads of composite specimens. However, the ultimate load of specimen GC4 was 10.2% higher than that of specimen GC1, and the midspan deflection of specimen GC4 at the ultimate load was 29.8% higher than that of specimen GC1. It might be explained by the fact that the concrete shear failure of composite specimens was delayed because the CFRP bars restricted development of concrete cracks and assisted the concrete to bear compressive stress. Therefore, it can be concluded that the longitudinal compressive reinforcing CFRP rebars had a little influence on ultimate bearing capacity while had a significant influence on ductility of composite specimens.
2.4.3. Strain Distributions at Midspan Cross Section
The strain distribution at midspan cross section of all specimens is shown in Figure 9. In Figure 9, indicates the ultimate load of the specimens, and the height of cross section is zero at the bottom of the GFRP plates. It can be found that the strain distributions of all specimens were generally linear, and there was almost no strain redistribution caused by the interface slip. Combining the test results of the relative slip between the concrete and GFRP plate (Table 3), it can be concluded that the Trib GFRP plateconcrete composite bridge deck proposed in this paper had an excellent interface bonding performance between GFRP plate and concrete throughout the flexural response until concrete shear failure occurred.
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3. Finite Element Analysis of MixedDimensional Model
3.1. Constitutive Modeling and Failure Criterion
Before FE analysis of the GFRP plateconcrete composite specimens, some assumptions of the constitutive models and failure criterions of all materials were made for simplicity.(1)Subjected to the tensile force, the stressstrain relationship of concrete is linear before ultimate tensile strain . Subjected to the pressure force, the stressstrain relationship of concrete is a quadratic parabola before the compressive strength and then keeps a constant value until ultimate pressure strain ; the stressstrain curve of concrete is as shown in Figure 10(a), and the stressstrain equation of concrete is as shown in Equation (1). In Equation (1), the ultimate tensile strain , peak stress pressure strain , and ultimate pressure strain are −0.00007, 0.002, and 0.0033, respectively:(2)The stressstrain relationship of the GFRP plate and CFRP rebar is all linear, and the stressstrain curves of the GFRP plate and CFRP rebar are as shown in Figures 10(b) and 10(c), respectively. And the stressstrain equations of the GFRP plate and CFRP rebar are shown in Equations (2) and (3), respectively. In Equations (2) and (3), the ultimate tensile strain of the GFRP plate and ultimate pressure strain of the CFRP rebar are 0.0177 and 0.002, respectively:(3)The failure criterion of concrete is the fiveparameter Willam–Warnke failure criterion. The failure criterions of the GFRP plate and CFRP rebar are that the tensile strain and pressure strain reached ultimate tensile strain and ultimate pressure strain , respectively.
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3.2. GFRPConcrete Interface
The experimental results of this paper showed that the Trib GFRP plateconcrete composite specimens with an excellent interface bond between concrete and GFRP plate and the insignificant or almost no slip between the concrete and GFRP plate throughout the flexural response until concrete shear failure occurred. Moreover, the destruction of composite specimens with type I and II interface was all determined by the concrete (i.e., shear failure of concrete). As a result, a bondslip criterion between the GFRP plate and concrete was not necessary, and assume a perfect bond between GFRP plate and concrete.
3.3. Interface Coupling of Solid and Shell Elements in the MixedDimensional Model
Since different types of solid element and shell element have different numbers of degreesoffreedom (DOFs), the mixeddimensional FE model needs a rational FE coupling method to combine mixeddimensional finite elements at their interfaces into a single FE model. The constraint equations can be used to establish the interface coupling for elements of different DOFs [45].
The relationship between solid element and shell element at the coupling interface is shown in Figure 11. At the coupling interface, the solid elements nodes are 1, 2, and 3, respectively, while the shell element node is only . In the global coordinate system, displacement parameters of solid elements nodes 1, 2, and 3 are , , , , , , , , and , respectively, while the displacement parameters of shell elements node are , , , , and , respectively.
The displacement parameters of nodes at the coupling interface are transferred from the global coordinate system to the local coordinate system according to the following equation:
In Equation (4), the , , and are nodes displacement components along the xaxis, yaxis, and zaxis in the local coordinate system, respectively. The , , and are nodes displacement components along the xaxis, yaxis, and zaxis in the global coordinate system, respectively.
In order to achieve displacement compatibility at the coupling interface, the constraint equations were used to establish the interface coupling for solid elements and shell elements in the local coordinate system [46], as shown in following equations, respectively:
The above formulas can also be rewritten as follows:
Equation (9) is the constraint equations of solid elements and shell elements in the coupling interface.
3.4. MixedDimensional Model
The commercial software ANSYS was applied to facilitate the mixeddimensional FE analysis of Trib GFRP plateconcrete composite bridge decks. A mixeddimensional FE model was proposed for high efficiency analysis of the GFRP plateconcrete composite bridge deck and accurately simulating the local complex stress state of GFRP plates. In the model, threedimensional solid elements were adopted to simulate concrete, while twodimensional shell elements and threedimensional solid elements were simultaneously adopted to simulate the GFRP plate. The section of Tribs and GFRP plates at the intersection under the relatively complex stress state was simulated using threedimensional solid elements, while the rest of the section under the relatively simple stress state was simulated using twodimensional shell elements.
The specimen GC1 as the research object and the relevant material parameters of the GFRP plate and concrete are listed in Table 1. For comparison purposes, three FE models with different methods were established. (1) Model I: GFRP plates/Tribs were simulated using shell 63 elements, and concrete was simulated using solid 65 elements, as shown in Figure 12(a); (2) Model II: GFRP plates/Tribs were simulated using solid 64 elements, and concrete was simulated using solid 65 elements, as shown in Figure 12(b); and (3) Model III: GFRP plates at the intersection and Tribs were simulated using solid 64 elements, while the rest of the section was simulated using shell 63 elements, and concrete was simulated using solid 65 elements, as shown in Figure 12(c). The FEA method of the mixeddimensional model (i.e., Model III) was named the mixed elements method for brevity in this paper.
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The constraint equation of Equation (9) in this paper was used to establish the interface coupling for shell 63 elements and solid 64 elements. The shell element nodes were used as main nodes, while the solid element nodes are used as attached nodes. The DOFs of main nodes in all three directions (i.e., X, Y, and Z directions) were coupled, as shown in Figure 12(d).
The comparisons of the three different FE modes are shown in Table 4. Model I had the minimum total number of elements and the shortest computational time; however, the twodimensional shell elements are unable to simulate the stress state of GFRP plates along the thickness direction and unable to simulate the threedimensional stress state of GFRP plates at the intersection or near the Tribs. Although Model II could overcome the above deficiency, it had the maximum total number of elements and the longest computational time. Model III could significantly decrease the total number of elements and the computational time as compared to that of Model II, but it still could simulate the stress state of GFRP plates along the thickness direction and simulate the threedimensional stress state of GFRP plates at the intersection or near the Tribs. As a result, when the stress state of GFRP plates need detailed analysis, the mixed elements method (named for brevity in this paper) is a good alternative for the analysis of the structural performance of Trib GFRP plateconcrete composite bridge decks.

3.5. Comparison of LoadDeflection Curves at Midspan Cross Section
The comparison loaddeflection curves at midspan section between experiment and mixed elements method (named for brevity in this paper) of specimens GC1, GC2, GC3, and and GC4 are shown in Figure 13. It can be seen that the loaddeflection curves of the mixed elements method and experiment for specimens GC1, GC2, GC3, and GC4 were basically identical before the maximum loads. After the maximum loads, the curves variations of the experiment and mixed elements method were basically consistent. Namely, the curves of the mixed elements method and experiment all presented sharp declines after the maximum loads. Therefore, it can be concluded that the mixeddimensional FEA model proposed in this paper can accurately simulate the loaddeflection curves of the GFRP plateconcrete composite bridge deck.
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3.6. Comparison of Experimental Results and Simulation Results
The comparison of the predicted results of the mixed elements method (named for brevity in this paper) and experimental results for the crack loads, ultimate loads, and midspan deflection of all specimens is shown in Table 5. The ratio of experiment and prediction had a mean value of 0.986, a very small standard deviation (SD) of 0.027, and a coefficient of variation (COV) of 0.028 for ultimate loads, and corresponding values were 1.791, 0.181, and 0.101 for crack loads, and corresponding values were 1.033, 0.058, and 0.056 for midspan deflection at the ultimate load, respectively.

It can be seen that the predictions of the mixed elements method had a good agreement with experimental results in ultimate loads and midspan deflection at the ultimate load. However, there are some discrepancies existing between predicted results and experiment results in crack loads, and the crack loads experiment values of all specimens were all bigger than predicted values. It might due to the fact that the microcracks could not timely and accurately be found in the process of increasing load; however, when the cracks were found, the microcracks already had developed a certain width.
Therefore, it can be concluded that the mixeddimensional FEA model proposed in this paper can accurately simulate the ultimate loads and midspan deflection of the GFRP plateconcrete composite bridge deck, expect the crack loads.
4. Conclusions
The experimental study and finite element analysis of the mixeddimensional model for the Trib GFRP plateconcrete composite bridge decks have been presented in this paper.(1)The test results showed that the Trib GFRP plateconcrete composite bridge deck proposed in this paper had an excellent interface bonding performance between the concrete and GFRP plate. There was almost no slip between the concrete and GFRP plate throughout the flexural response until specimens failure occurred. The failure mode of all specimens was shear failure in concrete structures. Moreover, the strain distributions of all specimens were generally linear, and there was almost no strain redistribution caused by the interface slip.(2)The height of concrete cross section had a significant influence on ultimate bearing capacity and stiffness of composite specimens, while the interface roughness of the GFPR plate had a slight influence on ultimate bearing capacity and stiffness of composite specimens. The longitudinal compressive reinforcing CFRP rebars had a significant influence on ductility of composite specimens, while it had a little influence on ultimate bearing capacity of composite specimens. The interface roughness of the GFRP plate and height of concrete cross section had a significant influence on crack loads of composite specimens, while the longitudinal compressive reinforcing CFRP rebars had almost no influence on crack loads of composite specimens.(3)The mixeddimensional FEA model proposed in this paper can accurately simulate the local complex stress state of Tribs and GFRP plates at the intersection and simultaneously can significantly reduce computational time. The predicted and experiment results of ultimate loads, stiffness, and midspan deflection at the ultimate load all had a good consistency, expect the crack loads. Therefore, the mixeddimensional FE analysis can provide a suitable solution to simulate the structural performance of Trib GFRP plateconcrete composite bridge decks.
Data Availability
All data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
The authors would like to thank the National Natural Science Foundation of China (Program nos. 51809046, 51678149, and 51808562), Scientific Research Foundation for Introduce Talent by Dongguan University of Technology (GC30050229 and GC30050232), Guangdong Science and Technology Planning (2016A010103045), and Innovation Research Project by Department of Education of Guangdong Province (2015KTSCX141) for providing funds for this research work.
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