# Study on the Shear Capacity of the Wet Joint of the Prefabricated Bridge Panel with a Special-Shaped Shear Key

Authors: Fan Feng; Fanglin Huang; De Zhou; Weibin Wen; Yong Tao
Journal: Advances in Civil Engineering
 (2021)

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## Abstract

Steel-concrete composite beam has been widely applied in civil engineering, and the concrete during operation may crack due to the large shear force at the wet joint. A new concrete panel shear key with the boss is designed to strengthen the shear capacity of the wet joint part. Three different configurations of specimens are tested to study the shear capacity of the wet joint. These specimens include plain concrete specimens with shear keys, specimens with reinforcement and no shear key, and specimens with both shear keys and reinforcements. An experimental study is designed and conducted to verify the shear capacity of each specimen. The experimental results show that the ultimate shear capacity of the new wet joint structure is 73% higher than the conventional one. Meanwhile, the shear capacity of the new wet joint structure is theoretically predicted, and the finite element models are established to demonstrate the effectiveness of the experiment and the good performance of the new wet joint design.


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## Body

## 1. Introduction

The steel-concrete composite beam is suitable for the construction of long-span bridges, such as cable-stayed bridges and x-style arch bridges. The deck system of the steel-concrete composite beam bridge is composed of steel beams and concrete panels. The bridge deck is usually prefabricated according to the size of the steel beam and installed on-site. This bridge deck system has the advantage of fast construction. However, in operation, the wet joints connecting precast bridge panels of the bridge deck system often endure shear and durability failure.In recent years, a large number of research studies have been conducted to improve the shear capacity and durability of wet joints. These researches can be roughly categorized into three aspects: (1) improving the material performance of the wet joint, (2) improving the connecting form of reinforcement at the wet joint, and (3) optimizing the shape of the wet joint.To improve the material performance of the wet joint, epoxy resin is adopted for the joints of the segment girder to improve the crack resistance under cyclic load [1]. At the joints of decked bulb tees and adjacent box-girder bridge, due to the action of environmental load, the two joints will bear high tensile stress. The tensile stress between the old and new concrete can be increased by using ultrahigh-performance concrete (UHPC) as the filling material of the joint [2]. UHPC is very suitable for the wet joint of the steel-concrete composite bridge [3, 4]. The ultrahigh-performance fiber-reinforced concrete (UHPFRC) joints between two precast panels reinforced with the glass-fiber-reinforced polymer (GFRP) bars can improve the mechanical performance of the wet joint [5, 6]. For the connecting form of reinforcement at the wet joint, an effective headed-bar reinforcement was designed to improve durability [7–11]. Through experiment study, Haber [12] verified the good bonding performance and crack resistance of noncontact lap splices joint combined with UHPC. As for the shape of the wet joint, the traditional construction technology of wet joint is to set a shear pocket where its surface is made of exposed aggregate finish [3]. The sawtooth, rectangular, and other special-shaped wet joints have similar mechanical properties as the traditional wet joints but have higher crack resistance [13]. Shear keys are widely used in the joints of segment bridges. Previous studies have been conducted to investigate the shear capacity of one or more shear keys [14–17]. An internal connector in the joint of the segment bridge can reduce the negative moment of the girder [18]. A large number of research studies have also been devoted to study the mechanical properties of the shear key in an adjacent box-girder bridge by experiment or finite element methods [19–21].To solidify the connection between the panels of the steel-concrete composite bridge, Noel et al. [22] proposed three types of shear pockets and verified the desirable shear capacity of the specimens by experiment. Zhao et al. [23] proposed a dovetail-type wet joint and studied its crack resistance under a negative bending moment. Qi et al. [7] proposed an innovative dovetail shear key that can effectively improve the crack resistance of concrete at wet joints. However, it is found that most of the present wet joints can only improve the shear capacity along a single direction vertical to the normal direction of cross section. This study is focused on a novel shear connector design to improve the shear capacity of the wet joint. The new wet joint can be used in a deck system and wet joint of an X-arch bridge as shown in Figure 1. In fact, during the operation, the wet joint is inevitably subjected to the vertical shear force and the horizontal inertia force resulted from the moving vehicle. The new shear connector of the wet joint as shown in Figure 2 is expected to have enhanced shear capacity along both the horizontal and vertical directions.Figure 1
Photos of the construction site. (a) Xincheng bridge. (b) Bridge deck construction. (c) Wet joint. (d) Details of the wet joint.
(a)(b)(c)(d)Figure 2
New type of the bridge panels and experimental specimen.The content of this paper is organized as follows. First, in Section2, the experiment schedule is designed to test the ultimate shear capacity of the wet joint. The experimental results are analyzed in Section 3 where the load-displacement response, strain analysis, and crack pattern are exclusively discussed. In Section 4, theoretical analysis is conducted to predict the ultimate shear capacity of the new wet joint and traditional wet joint. In Section 5, finite element analysis is provided to confirm the effectiveness of experiment analysis. Finally, some conclusions are summarized in Section 6.


## 2. Experimental Program

### 2.1. Experimental Specimens

Three different types of specimens are designed to simulate the bridge panels which are the specimens with shear keys and no reinforcement (Type 1), the specimens with reinforcements and no shear key (Type 2), and the specimens with both shear keys and reinforcements (Type 3). Each type is composed of three parts, i.e., two bridge panels and the wet joint. The bridge panels are prefabricated, and the wet joint is then cast between the two bridge panels. Figure3 shows the assembly diagram of the experimental specimens. Figure 4(a) shows the formworks of the specimens. The formworks of the shear key are made of wood plates and steel bars. The white bars in Figure 4(a) are the PVC pipes designed to facilitate transport. Since the PVC pipes are away from the wet joint and do not affect the experiment analysis, the strain gauges are fixed on the steel bars. Figure 4(b) shows the panel-to-panel alignment. Figure 4(c) shows the fabricated experiment specimens.Figure 3
Assembly diagram of the experiment specimens. (a) Type 1. (b) Type 2. (c) Type 3.
(a)(b)(c)Figure 4
Fabrication of experiment specimens. (a) Formworks of the specimens. (b) Panel-to-panel alignment. (c) Experiment specimens.
(a)(b)(c)The panels measure 600 mm long, 250 mm wide, and 250 mm thick. The wet joints measure 150 mm long, 250 mm wide, and 250 mm thick (see Figure5). The experiment specimens measure 1350 mm long, 250 mm wide, and 250 mm thick (see Figure 6). The dimensions of Type1 and Type 3 with boss-type shear keys are shown in Figure 5. The cross sections of the steel bars are selected with 16 mm diameter. The overlap width of two steel bars is 80 mm.Figure 5
Dimension of the panels. (a) Dimension of Type 1. (b) Dimension of Type 2. (c) Dimension of Type 3.
(a)(b)(c)Figure 6
Dimension of the experiment specimens.


### 2.2. Loading Method and Implementation

All specimens were tested with a 1000-kN servo tester. There were two supports under the specimen. As shown in Figure7, two concentrated loads were acted on the wet joints of the specimen, and strain gauges were pasted on the specimens. The LVDT (Linear Variable Differential Transformer) and electrical-resistance strain gauges were located at the wet joint (see Figure 8). The displacement of the wet joint under the loading was measured by LVDT. Three strain gauges (CSG1-CSG3) for the concrete test were pasted on the wet joint. Four strain gauges (RSG1-RSG4) for reinforcement (i.e., steel bar) test, near the interface of the panels and the wet joint, were pasted.Figure 7
Loading process.Figure 8
Sensors setting.


### 2.3. Material Properties

Panels and wet joints are cast separately with the same proportion of concrete as shown in Table1. All specimens are fabricated with the concrete of compressive strength 19.21 MPa and tensile strength 1.64 MPa. The mechanical properties of the steel bars embedded in Type 2 and Type 3 are listed in Table 2.Table 1
Mix proportion of concrete for specimens.
Cement (kg/m3)Stone (kg/m3)Sand (kg/m3)Water (kg/m3)4501092735118Table 2
Mechanical properties of the reinforcements.
drmmGradeEfGPafyMPafuMPa16HRB400202424601Note. dr is the diameter for steel bars; Ef is the modulus of elasticity; fy is the yield stress; fu is the ultimate stress.


## 2.1. Experimental Specimens

Three different types of specimens are designed to simulate the bridge panels which are the specimens with shear keys and no reinforcement (Type 1), the specimens with reinforcements and no shear key (Type 2), and the specimens with both shear keys and reinforcements (Type 3). Each type is composed of three parts, i.e., two bridge panels and the wet joint. The bridge panels are prefabricated, and the wet joint is then cast between the two bridge panels. Figure3 shows the assembly diagram of the experimental specimens. Figure 4(a) shows the formworks of the specimens. The formworks of the shear key are made of wood plates and steel bars. The white bars in Figure 4(a) are the PVC pipes designed to facilitate transport. Since the PVC pipes are away from the wet joint and do not affect the experiment analysis, the strain gauges are fixed on the steel bars. Figure 4(b) shows the panel-to-panel alignment. Figure 4(c) shows the fabricated experiment specimens.Figure 3
Assembly diagram of the experiment specimens. (a) Type 1. (b) Type 2. (c) Type 3.
(a)(b)(c)Figure 4
Fabrication of experiment specimens. (a) Formworks of the specimens. (b) Panel-to-panel alignment. (c) Experiment specimens.
(a)(b)(c)The panels measure 600 mm long, 250 mm wide, and 250 mm thick. The wet joints measure 150 mm long, 250 mm wide, and 250 mm thick (see Figure5). The experiment specimens measure 1350 mm long, 250 mm wide, and 250 mm thick (see Figure 6). The dimensions of Type1 and Type 3 with boss-type shear keys are shown in Figure 5. The cross sections of the steel bars are selected with 16 mm diameter. The overlap width of two steel bars is 80 mm.Figure 5
Dimension of the panels. (a) Dimension of Type 1. (b) Dimension of Type 2. (c) Dimension of Type 3.
(a)(b)(c)Figure 6
Dimension of the experiment specimens.


## 2.2. Loading Method and Implementation

All specimens were tested with a 1000-kN servo tester. There were two supports under the specimen. As shown in Figure7, two concentrated loads were acted on the wet joints of the specimen, and strain gauges were pasted on the specimens. The LVDT (Linear Variable Differential Transformer) and electrical-resistance strain gauges were located at the wet joint (see Figure 8). The displacement of the wet joint under the loading was measured by LVDT. Three strain gauges (CSG1-CSG3) for the concrete test were pasted on the wet joint. Four strain gauges (RSG1-RSG4) for reinforcement (i.e., steel bar) test, near the interface of the panels and the wet joint, were pasted.Figure 7
Loading process.Figure 8
Sensors setting.


## 2.3. Material Properties

Panels and wet joints are cast separately with the same proportion of concrete as shown in Table1. All specimens are fabricated with the concrete of compressive strength 19.21 MPa and tensile strength 1.64 MPa. The mechanical properties of the steel bars embedded in Type 2 and Type 3 are listed in Table 2.Table 1
Mix proportion of concrete for specimens.
Cement (kg/m3)Stone (kg/m3)Sand (kg/m3)Water (kg/m3)4501092735118Table 2
Mechanical properties of the reinforcements.
drmmGradeEfGPafyMPafuMPa16HRB400202424601Note. dr is the diameter for steel bars; Ef is the modulus of elasticity; fy is the yield stress; fu is the ultimate stress.


## 3. Experimental Results

### 3.1. Crack Pattern and Failure Mode

Figure9 shows the crack pattern of specimens. For Type 1, when the load increases to the ultimate load, the specimen suddenly fails. The crack, through the whole specimen, appears at one of the interfaces of the panel and wet joint. After the failure, as shown in Figure 10(a), the shear key breaks.Figure 9
Crack pattern for specimens. (a) Type 1. (b) Type 2. (c) Type 3.
(a)(b)(c)Figure 10
Failure modes for the specimens. (a) Type 1. (b) Type 2. (c) Type 3.
(a)(b)(c)For Type 2, when the load reaches about 50% of the ultimate load, the cracks first appear at the bottom of the wet joint. Then, the cracks in the lower part of the wet joint expand slowly, and some cracks appear in the upper part of the wet joint. When the load increases to about 73% of the ultimate load, the specimen squeaks, and interfaces of panels and wet joints appear debonding. Therein, cracks appear at the panels near the wet joint and expand with the increase of load. When the specimen is further crushed, the concrete of the wet joint moves down rapidly, and the concrete spalls locally. Figure10(b) shows the final state of the tested Type 2.For Type 3, when the applied load is around 45% of the ultimate load, the first crack is observed at the lower part of the wet joint. When the load increases to about 67% of the ultimate load, the specimen squeaks, but no crack propagation is observed. With the increase of load, the cracks in the wet joint increase gradually and connect with each other. When the load increases to about 80% of the ultimate load, the concrete-concrete interface appears with cracks. When the specimen is damaged, the wet joint moves down obviously, the concrete-concrete interface is staggered, and part of the concrete is separated from the main body. Figure10(c) shows the final state of tested Type 3.


### 3.2. Load-Displacement Response

Figure11 illustrates the load-displacement curves of three specimens. The ultimate shear capacity of the wet joint of the specimens can be analyzed. The curve of Type 1 changes linearly with the increase of load and decreases rapidly after the ultimate shear capacity is reached. The descending process of the curve of Type 1 is very short, which discloses the rapid fracture of the specimen.Figure 11
Load-displacement response.The curve of Type 2 is linear before the load reaches 219.1 kN (about 73% of ultimate shear capacity). Then, the displacement increases rapidly. Before the displacement reaches 0.2 mm, the curve continues to rise, which is attributed to the complete debonding of the concrete-concrete interface. At this moment, the bonding force generated by the interface almost disappears, the wet joint moves down, and the steel bars begin to bear the load. When the load reaches 300.2 kN, the test is terminated when the concrete around the steel bars completely fails.The curve of Type 3 changes linearly before the load reaches 350 kN. After that, the curve is still linear, but the slope of the load-displacement curve is clearly smaller, which may be caused by the crack propagation of the shear key. When the load reaches about 430 kN, the slope decreases drastically but remains roughly linear, which may be caused by the debonding of the concrete-concrete interface. When the load reaches 480 kN, the curve begins to change nonlinearly, which may be caused by complete shear failure and debonding of the interface. At this moment, the reinforcement bears most of the load. When the load reaches the ultimate shear capacity of 520 kN, the curve decreases gradually.Table3 shows the ultimate shear capacity of three types. It can be noticed that the plain concrete specimen of Type 1 has a certain shear capacity, which is about 33% of Type 2. The ultimate shear capacity of Type 3 is 73% higher than that of Type 2. Moreover, when the load for Type 2 reaches 219.1 kN, the interface has complete debonding. In Table 3, the ultimate shear strength of Type 3 improves greatly.Table 3
Ultimate shear strength of specimens (kN).
Specimen typeUltimate shear strengthfu/fu2 (%)Type 199.633.1Type 2300.2—Type 3520173.2Note.fu is the ultimate shear strength of Type 1 and Type 3, and fu2 is the ultimate shear strength of Type 2.


### 3.3. Strains

Figure12 shows the load-shear strain curves of the wet joints. The value of shear strain is represented by γ=2ε45°−ε0°−ε90°, where ε0° is the strain of CSG1, ε45° is the data of CSG2, ε90° is the data of CSG3, and γ is shear strain.Figure 12
Load-shear strain curves of wet joints.Note.γ is the shear strain.The shear strain of the specimens is compressive strain, so the value varies in the negative region. With the increase of load, the shear strain of Type 1 increases. The curve is roughly linear before the load reaches 60 kN and then nonlinear until the specimen is damaged. The shear strain of Type 1 increases greatly and approaches 3000 at failure. The curve slope of Type 2 changes when the load reaches 160 kN and changes again when it reaches 220 kN. This is the time when interfacial debonding occurs. The slope of the curve is gradually decreasing. The curve ends at 240 kN. This is due to the occurrence of cracks near the strain gauge, resulting in data interruption. The curve slope of Type 3 first changes when the load reaches 165 kN and then changes again at 240 kN. When the load reaches 350 kN, the curve has a sudden change. This is similar to the load-displacement curve. Then, the slope do not change until the specimen is destroyed.Figure13 shows the load-strain curve of reinforcements. The curves of Type 2 lower reinforcements, measured by RSG 2 and RSG 4, change when the load reaches 180 kN. The curves of the upper reinforcements, measured by RSG 2 and RSG 4, change when the load reaches 220 kN. At this time, it is time for the concrete-concrete interface debonding. It can be judged that the interfacial debonding develops from bottom to top. The curves of Type 3 change greatly when the load reaches 350 kN. At this time, although no debonding phenomenon is observed at the interface of the specimen, the reinforcement begin to bear the load.Figure 13
Load-strain curves of reinforcements. (a) Type 2. (b) Type 3.
(a)(b)


## 3.1. Crack Pattern and Failure Mode

Figure9 shows the crack pattern of specimens. For Type 1, when the load increases to the ultimate load, the specimen suddenly fails. The crack, through the whole specimen, appears at one of the interfaces of the panel and wet joint. After the failure, as shown in Figure 10(a), the shear key breaks.Figure 9
Crack pattern for specimens. (a) Type 1. (b) Type 2. (c) Type 3.
(a)(b)(c)Figure 10
Failure modes for the specimens. (a) Type 1. (b) Type 2. (c) Type 3.
(a)(b)(c)For Type 2, when the load reaches about 50% of the ultimate load, the cracks first appear at the bottom of the wet joint. Then, the cracks in the lower part of the wet joint expand slowly, and some cracks appear in the upper part of the wet joint. When the load increases to about 73% of the ultimate load, the specimen squeaks, and interfaces of panels and wet joints appear debonding. Therein, cracks appear at the panels near the wet joint and expand with the increase of load. When the specimen is further crushed, the concrete of the wet joint moves down rapidly, and the concrete spalls locally. Figure10(b) shows the final state of the tested Type 2.For Type 3, when the applied load is around 45% of the ultimate load, the first crack is observed at the lower part of the wet joint. When the load increases to about 67% of the ultimate load, the specimen squeaks, but no crack propagation is observed. With the increase of load, the cracks in the wet joint increase gradually and connect with each other. When the load increases to about 80% of the ultimate load, the concrete-concrete interface appears with cracks. When the specimen is damaged, the wet joint moves down obviously, the concrete-concrete interface is staggered, and part of the concrete is separated from the main body. Figure10(c) shows the final state of tested Type 3.


## 3.2. Load-Displacement Response

Figure11 illustrates the load-displacement curves of three specimens. The ultimate shear capacity of the wet joint of the specimens can be analyzed. The curve of Type 1 changes linearly with the increase of load and decreases rapidly after the ultimate shear capacity is reached. The descending process of the curve of Type 1 is very short, which discloses the rapid fracture of the specimen.Figure 11
Load-displacement response.The curve of Type 2 is linear before the load reaches 219.1 kN (about 73% of ultimate shear capacity). Then, the displacement increases rapidly. Before the displacement reaches 0.2 mm, the curve continues to rise, which is attributed to the complete debonding of the concrete-concrete interface. At this moment, the bonding force generated by the interface almost disappears, the wet joint moves down, and the steel bars begin to bear the load. When the load reaches 300.2 kN, the test is terminated when the concrete around the steel bars completely fails.The curve of Type 3 changes linearly before the load reaches 350 kN. After that, the curve is still linear, but the slope of the load-displacement curve is clearly smaller, which may be caused by the crack propagation of the shear key. When the load reaches about 430 kN, the slope decreases drastically but remains roughly linear, which may be caused by the debonding of the concrete-concrete interface. When the load reaches 480 kN, the curve begins to change nonlinearly, which may be caused by complete shear failure and debonding of the interface. At this moment, the reinforcement bears most of the load. When the load reaches the ultimate shear capacity of 520 kN, the curve decreases gradually.Table3 shows the ultimate shear capacity of three types. It can be noticed that the plain concrete specimen of Type 1 has a certain shear capacity, which is about 33% of Type 2. The ultimate shear capacity of Type 3 is 73% higher than that of Type 2. Moreover, when the load for Type 2 reaches 219.1 kN, the interface has complete debonding. In Table 3, the ultimate shear strength of Type 3 improves greatly.Table 3
Ultimate shear strength of specimens (kN).
Specimen typeUltimate shear strengthfu/fu2 (%)Type 199.633.1Type 2300.2—Type 3520173.2Note.fu is the ultimate shear strength of Type 1 and Type 3, and fu2 is the ultimate shear strength of Type 2.


## 3.3. Strains

Figure12 shows the load-shear strain curves of the wet joints. The value of shear strain is represented by γ=2ε45°−ε0°−ε90°, where ε0° is the strain of CSG1, ε45° is the data of CSG2, ε90° is the data of CSG3, and γ is shear strain.Figure 12
Load-shear strain curves of wet joints.Note.γ is the shear strain.The shear strain of the specimens is compressive strain, so the value varies in the negative region. With the increase of load, the shear strain of Type 1 increases. The curve is roughly linear before the load reaches 60 kN and then nonlinear until the specimen is damaged. The shear strain of Type 1 increases greatly and approaches 3000 at failure. The curve slope of Type 2 changes when the load reaches 160 kN and changes again when it reaches 220 kN. This is the time when interfacial debonding occurs. The slope of the curve is gradually decreasing. The curve ends at 240 kN. This is due to the occurrence of cracks near the strain gauge, resulting in data interruption. The curve slope of Type 3 first changes when the load reaches 165 kN and then changes again at 240 kN. When the load reaches 350 kN, the curve has a sudden change. This is similar to the load-displacement curve. Then, the slope do not change until the specimen is destroyed.Figure13 shows the load-strain curve of reinforcements. The curves of Type 2 lower reinforcements, measured by RSG 2 and RSG 4, change when the load reaches 180 kN. The curves of the upper reinforcements, measured by RSG 2 and RSG 4, change when the load reaches 220 kN. At this time, it is time for the concrete-concrete interface debonding. It can be judged that the interfacial debonding develops from bottom to top. The curves of Type 3 change greatly when the load reaches 350 kN. At this time, although no debonding phenomenon is observed at the interface of the specimen, the reinforcement begin to bear the load.Figure 13
Load-strain curves of reinforcements. (a) Type 2. (b) Type 3.
(a)(b)


## 4. Prediction of the Shear Capacity

To predict the ultimate shear capacity of three types of wet joints, a theoretical analysis is provided in this section.Figure14(a) shows the detailed configuration of Type 2, and l, h, and A1 are length, height, and area of the section, respectively. Figures 14(b)–14(d) illustrate the detailed dimensions of Type 1 and Type 3. In the figures, l1, l2, l3, h1, h2, h3, α, A2, A3, and A4 define the geometry of three specimens.Figure 14
Detailed configurations of three specimens. (a) Configuration of Type 2. (b) Configuration of Type 1 and Type 3. (c) The areaA3. (d) The area A4.
(a)(b)(c)(d)A1, A2, A3, and A4 can be calculated by the following formulas:(1)A1=l⋅h,A2=0.5⋅l1+l2⋅l3,A3=l⋅h−l2⋅h2+l1⋅h1,A4=3A2.Assume that the ultimate shear capacity of the wet joint with no shear key and reinforcement isF1 (see Figure 15(a)). There are a pair of cohesive forces of value FC between the wet joint and panels. The joint is about to slip when it is up to the ultimate shear capacity, and at this state, F1 is equal to FC. The cohesive stress of wet joints and panels is denoted by σC and can be calculated by σC=cd⋅fctd.Figure 15
The load schemes of three specimens. (a) Wet joint with no shear key and reinforcement. (b) Loads on Type 1. (c) Loads on Type 2. (d) Loads on Type 3.
(a)(b)(c)(d)The cohesive stress of wet joints and panels is denoted byσC which is determined by σC=cd⋅fctd [24–26], where cd is cohesion coefficient and is selected as cd = 0.492. fctd is the tensile strength of concrete. Then, FC can be easily obtained as FC=2A1σCAs shown in Figure15(b), the failure of Type 1 can be considered as the shear and sliding failure of interfaces of the wet joint and panels. Shear stress τmax, on the area A2 as shown in Figure 14(b), is obtained by the maximum shear stress theory as τmax=σ1−σ3/2=3Ft/2lh≤τ, where τmax is the ultimate shear stress of concrete, τ is calculated by the formula τ=0.3fc, and fc is the shear strength of concrete [27]. σ1 and σ3 are the principal stresses. In Figure 15(b), Ft is the reaction load acted on the area A2. The force balance equation for Type 1 is obtained as(2)F2=Ft+FC,where F2 is the ultimate shear capacity at the joint of Type 1, and a pair of cohesive forces FC are acted on A3 and A4. For Type 2 in Figure 15(c), as the shear force increases, the concrete first slides along the interfaces of the wet joint. Furthermore, when the cohesive stress attains its maximum, the concrete bonded with reinforcements is gradually crushed. At this state, the force on reinforcements, briefly denoted by FR, can be calculated by the following formula:(3)FR=∫0πRdθ⋅L⋅sinθ⋅fck=fck⋅2RL=fck⋅AR,where fck is the ultimate compressive strength of concrete. AR is the equivalent compression area of the reinforcement. R is the radius of the cross section of the reinforcements. L is the length of the wet joint. The angle θ is illustrated in Figure 16.Figure 16
The force on reinforcement.As shown in Figure15(c), the ultimate shear capacity of Type 2 is F3. FR′ is the reaction force of the FR. With force balance of the wet joint, F3 can be calculated by(4)F3=FC+4FR′.In Figure15(d), F4, the ultimate shear capacity of the wet joint of Type 3, can be calculated by(5)F4=FC+Ft+4FR′.Then, the ultimate shear capacityF of the specimen with reinforcement can be expressed as(6)F=FC+signsinα⋅Ft+FR′,where signsinα satisfies the following conditions:(7)α=0,signsinα=0,α>0,signsinα=1.


## 5. Numerical Analysis

In this section, the finite element analysis (FEA) is conducted to confirm the shear capability of three types of wet joints. A three-dimensional nonlinear finite element model is established, and the feasibility of FEA is verified by comparing the numerical results with the experimental results.The material parameters for the numerical model are provided in Section2.3. In this study, the mechanical behavior of concrete is modeled using the concrete damaged plasticity (CDP) constitutive model. This model is a continuum, plasticity-based, damage model for concrete; it is commonly used and adopted in ABAQUS. The CDP model defines that the two main failure mechanisms of the concrete are tensile cracking and compressive crushing. In this model, five variables or parameters are defined: ψ is the dilation angle, ε is the eccentricity, fb0/fc0 is the ratio of initial biaxial compressive yield stress to initial uniaxial compressive yield stress, K is the ratio of the concrete strength under biaxial compression to the concrete strength under triaxial compression, and μ is the viscosity parameter. Table 4 shows the value of these variables or parameters. Table 4 shows the value of the parameters. Uniaxial compressive stress-strain curve, tension-strain curve, and damage evolution of concrete are selected from the code [28]. The constitutive model of the steel is a bilinear model. Poisson’s ratio of concrete and steel is 0.2 and 0.3, respectively.Table 4
Parameter of the concrete damage plasticity.
Parameterψεfb0/fc0KμValue38°0.11.160.670.001In order to analyze the stress and failure of the shear key, the model of concrete in this study adopts solid elements (C3D8R). Truss element (T3D2) is used for reinforcements. The mesh sizes of concrete of Type 1 and Type 3 are 25 mm × 25 mm. The mesh sizes of panels of Type 2 are 30 mm × 30 mm and the wet joint is 20 mm × 20 mm. The mesh of reinforcements is 25 mm. The interface of the panel and wet joint, boundary conditions, and loading conditions are shown in Figure17. General contact is used for the interaction of the panels and wet joints. The contact with tangential, normal, and cohesive behavior is selected for the interaction property. The cohesive contact is used to simulate the interface of the concrete and concrete.Figure 17
Mesh, boundary condition, and loading condition.


### 5.1. Crack Patterns

In order to show the crack growth of the specimen, the constitutive model “DAMAGET,” assumed to be a plastic strain, is used to describe the tensile failure of concrete.Figure18(a) shows the crack distribution of Type 1 at failure. It can be seen from the figure that the failure of the specimen occurs on the upper part of the interaction of the wet joint and the bridge panel, and the predicted result is similar to the experimental result. Figure 18(b) shows one of the shear key cracks for the first time, and Figure 18(c) shows the crack distribution of the shear key when the specimen is damaged. When the load reaches 87 kN, the crack first appeared on the left and right sides of the shear key and gradually propagated. The failure of the shear key in the FE model is similar to that of the specimen in Figure 10(a). Thus, the crack patterns obtained from simulation and experiment have a good agreement. However, the crack development of the shear key cannot be easily observed in the experiment but can be clearly seen from numerical results.Figure 18
Crack patterns of Type 1. (a) Cracking patterns at failure. (b) Cracks at the first time. (c) Cracks at the failure of the shear key.
(a)(b)(c)Figure19(a) shows the state of Type 2 when the interface debonds, corresponding to the load at 232 kN. It can be seen that the concrete-concrete interface has a tensile failure, and the bridge panels also have local damage. Figure 19(b) shows the complete failure of the specimen at a load of 270 kN. As can be seen from the figure, the concrete-concrete interface is seriously damaged, the cracks in the middle of the wet joint and the small cracks at the bottom of the wet joint can be observed, while the bridge panels are further damaged. Compared with Figure 10(b), the simulation results are in desirable agreement with the experimental results.Figure 19
Cracking patterns of Type 2. (a) Initial interface cracking. (b) Cracking patterns at failure.
(a)(b)Figure20(a) shows the state of Type 3 when the interface debonds, corresponding to the load at 310 kN. It can be seen from the figure that the concrete-concrete interface has a tensile failure. The concrete on the upper of bridge panels near the wet joint has a local tensile failure. Figure 20(b) shows the complete failure of the specimen with a load at 520 kN. At this time, the concrete-concrete interface debonds, and the concrete tensile failure occurs at the bottom of the wet joint and the middle of the two loading points. Figure 20(c) shows the state of the shear key when the interface debonds. The shear key is not damaged, but the concrete at the top of the bridge panel has tension damage. Figure 20(d) shows the state of the shear key when the specimen fails. At this time, the concrete at the bottom of the shear key is damaged, and the interface is almost debonding.Figure 20
Cracking patterns of Type 3. (a) Initial interface cracking. (b) Cracking patterns at failure. (c) State of the shear key at initial interface cracking. (d) State of the shear key in failure of the specimen.
(a)(b)(c)(d)


### 5.2. Ultimate Shear Capacity

The experiment mainly tests the ultimate shear capacity of the wet joint. In the experiment, a displacement sensor is set at the lower part of the wet joint. The load data of the experiment is provided by the servohydraulic testing machine, and the displacement data comes from the displacement sensor. In Figure21(a), the finite element and experiment results of the ultimate shear capacity of Type 1 are illustrated. The trend of numerical and experimental results shows good consistency. After reaching the ultimate shear capacity, the deformation of the wet joint decreases. The predicted values of ultimate shear force are very close to the measured values, about 100 kN, with an error of less than 1%.Figure 21
Load-displacement curves of experiment and finite element results. (a) Type 1. (b) Type 2. (c) Type 3.
(a)(b)(c)In Figure21(b), the finite element and experiment results of the ultimate shear capacity of Type 2 are illustrated. The slopes of these two result curves are close before yielding. The experimental and finite element results show that the slopes alter when the load reaches 220 kN and 232 kN. The reason for this variation of the slope of the curve is due to the existence of cracks in the concrete-concrete interface. These two result curves end after reaching the ultimate shear capacity of 300 kN and 270 kN. The load difference of interface failure between two results curves is 5%, while the ultimate shear capacity difference is 10%.Figure21(c) shows the ultimate shear capacity comparison of Type 2 between the finite element results and the experimental results. The slope of the curve between the experimental and the finite element results alters when the load reaches around 310 kN. The ultimate shear capacity of the experimental and finite element results is, respectively, 520 kN and 519 kN.In Table5, the experimental results, predicted results, and finite element results of the ultimate shear capacity of the specimens are compared. Both the theoretical and numerical results are in acceptable agreement with the experimental results.Table 5
Comparison of experimental results, predicted results, and finite element results (unit: kN).
SpecimensExperimental resultFePredicted resultFtFt−Fe/Fe (%)Finite element resultFfFf−Fe/Fe (%)Type 199.696.03.699.60Type 2300.0245.918.0270.79.8Type 3520.0415.920.0519.30.1


## 5.1. Crack Patterns

In order to show the crack growth of the specimen, the constitutive model “DAMAGET,” assumed to be a plastic strain, is used to describe the tensile failure of concrete.Figure18(a) shows the crack distribution of Type 1 at failure. It can be seen from the figure that the failure of the specimen occurs on the upper part of the interaction of the wet joint and the bridge panel, and the predicted result is similar to the experimental result. Figure 18(b) shows one of the shear key cracks for the first time, and Figure 18(c) shows the crack distribution of the shear key when the specimen is damaged. When the load reaches 87 kN, the crack first appeared on the left and right sides of the shear key and gradually propagated. The failure of the shear key in the FE model is similar to that of the specimen in Figure 10(a). Thus, the crack patterns obtained from simulation and experiment have a good agreement. However, the crack development of the shear key cannot be easily observed in the experiment but can be clearly seen from numerical results.Figure 18
Crack patterns of Type 1. (a) Cracking patterns at failure. (b) Cracks at the first time. (c) Cracks at the failure of the shear key.
(a)(b)(c)Figure19(a) shows the state of Type 2 when the interface debonds, corresponding to the load at 232 kN. It can be seen that the concrete-concrete interface has a tensile failure, and the bridge panels also have local damage. Figure 19(b) shows the complete failure of the specimen at a load of 270 kN. As can be seen from the figure, the concrete-concrete interface is seriously damaged, the cracks in the middle of the wet joint and the small cracks at the bottom of the wet joint can be observed, while the bridge panels are further damaged. Compared with Figure 10(b), the simulation results are in desirable agreement with the experimental results.Figure 19
Cracking patterns of Type 2. (a) Initial interface cracking. (b) Cracking patterns at failure.
(a)(b)Figure20(a) shows the state of Type 3 when the interface debonds, corresponding to the load at 310 kN. It can be seen from the figure that the concrete-concrete interface has a tensile failure. The concrete on the upper of bridge panels near the wet joint has a local tensile failure. Figure 20(b) shows the complete failure of the specimen with a load at 520 kN. At this time, the concrete-concrete interface debonds, and the concrete tensile failure occurs at the bottom of the wet joint and the middle of the two loading points. Figure 20(c) shows the state of the shear key when the interface debonds. The shear key is not damaged, but the concrete at the top of the bridge panel has tension damage. Figure 20(d) shows the state of the shear key when the specimen fails. At this time, the concrete at the bottom of the shear key is damaged, and the interface is almost debonding.Figure 20
Cracking patterns of Type 3. (a) Initial interface cracking. (b) Cracking patterns at failure. (c) State of the shear key at initial interface cracking. (d) State of the shear key in failure of the specimen.
(a)(b)(c)(d)


## 5.2. Ultimate Shear Capacity

The experiment mainly tests the ultimate shear capacity of the wet joint. In the experiment, a displacement sensor is set at the lower part of the wet joint. The load data of the experiment is provided by the servohydraulic testing machine, and the displacement data comes from the displacement sensor. In Figure21(a), the finite element and experiment results of the ultimate shear capacity of Type 1 are illustrated. The trend of numerical and experimental results shows good consistency. After reaching the ultimate shear capacity, the deformation of the wet joint decreases. The predicted values of ultimate shear force are very close to the measured values, about 100 kN, with an error of less than 1%.Figure 21
Load-displacement curves of experiment and finite element results. (a) Type 1. (b) Type 2. (c) Type 3.
(a)(b)(c)In Figure21(b), the finite element and experiment results of the ultimate shear capacity of Type 2 are illustrated. The slopes of these two result curves are close before yielding. The experimental and finite element results show that the slopes alter when the load reaches 220 kN and 232 kN. The reason for this variation of the slope of the curve is due to the existence of cracks in the concrete-concrete interface. These two result curves end after reaching the ultimate shear capacity of 300 kN and 270 kN. The load difference of interface failure between two results curves is 5%, while the ultimate shear capacity difference is 10%.Figure21(c) shows the ultimate shear capacity comparison of Type 2 between the finite element results and the experimental results. The slope of the curve between the experimental and the finite element results alters when the load reaches around 310 kN. The ultimate shear capacity of the experimental and finite element results is, respectively, 520 kN and 519 kN.In Table5, the experimental results, predicted results, and finite element results of the ultimate shear capacity of the specimens are compared. Both the theoretical and numerical results are in acceptable agreement with the experimental results.Table 5
Comparison of experimental results, predicted results, and finite element results (unit: kN).
SpecimensExperimental resultFePredicted resultFtFt−Fe/Fe (%)Finite element resultFfFf−Fe/Fe (%)Type 199.696.03.699.60Type 2300.0245.918.0270.79.8Type 3520.0415.920.0519.30.1


## 6. Conclusions

A new type of concrete panel with a shear key is proposed, and specimens of this kind of bridge panel are fabricated. The shear capacity of the wet joint of the specimens is studied through experimental, theoretical, and numerical analysis. The mechanical properties of the specimens are discussed by analyzing ultimate shear stress, the displacement of the wet joint, the shear strain of the wet joint, and the strain of the reinforcement. The formulas of the shear strength are derived, and the finite element models of the specimens are considered for prediction. The main conclusions of this paper are as follows:(1)
In order to test the ultimate shear capacity of the wet joint, the experimental loading mode is designed. Through the experiment, under the same material characteristics, the ultimate shear capacity of the new wet joint structure is 73% higher than the conventional one(2)
Through numerical and experimental methods, the failure processes of three kinds of specimens are studied. The failure of Type 1 is illustrated, and the shear strain at the wet joint is very large. The failure of Type 2 is mainly caused by interfacial debonding. The interfacial debonding of Type 2 occurs from bottom to top along the concrete-concrete interface. The interfacial debonding of Type 3 occurs along the concrete-concrete interface. For Type 3, the shear key failure first occurs and then the interface debonds(3)
The formulas of the ultimate shear capacity of three specimens are derived, and the predicted results are in acceptable agreement with the experimental results



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*Source: 5783563-2021-08-19.xml*