Assessment of Reinforcement Effect of FRP-Strengthened Shield Segment Joint Based on the CZM Model

Kuang, Jianjun; Chen, Yuanqing; Li, Xiaofei; Guo, Wei; Li, Jia; Huang, Yiqun

doi:https://doi.org/10.1155/2024/8888139

Advances in Civil Engineering

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Research Article | Open Access

Volume 2024 | Article ID 8888139 | https://doi.org/10.1155/2024/8888139

Assessment of Reinforcement Effect of FRP-Strengthened Shield Segment Joint Based on the CZM Model

Jianjun Kuang,¹Yuanqing Chen,²Xiaofei Li,³Wei Guo,⁴Jia Li,⁵and Yiqun Huang⁶

Academic Editor: Tingting Zhang

Received06 Dec 2023

Revised18 Feb 2024

Accepted25 Apr 2024

Published09 May 2024

Abstract

As the weakest link in the shield segment, the reinforcement and repair technology of shield segment joint has received widespread attention. In this study, an finite element model utilizing a cohesive zone model (CZM) was constructed to simulate the mechanical behavior of the shield segment joint during the whole fracture process. The proposed modeling method of joint allows multiple layers of steel bars to be stacked without interference by applying cohesive elements. Cohesive elements were employed to represent the mechanical response of potential fracture surfaces in concrete, as well as the interfaces between steel–concrete and fiber-reinforced polymer (FRP)–concrete, by utilizing various constitutive models tailored for mixed-mode loading conditions. A group of experiments was chosen to assess the precision of the proposed model by comparing the mechanical response and the fracture patterns. Finally, parameter analyses were conducted to study the reinforcement effect of the FRP bonding length and width on the shield segment joint. The results indicate that external bonding of FRP can effectively enhance the bearing capacity and stiffness of shield segment joints. However, insufficient bonding length or width may significantly reduce the strengthening effect and potentially decrease the ductility of the joint.

1. Introduction

With the development of subway construction, the sealing and safety of shield tunnel segments have attracted widespread attention and research. Tunnels in service are subjected to a combination of factors during operation, including surrounding rock pressure, groundwater pressure, and surface and adjacent structure construction loads. The mechanical performance of tunnel structures deteriorates over time due to the prolonged influence of these combined loads, resulting in stress losses at the joints [1]. When the contact stress state at the pipe segment joints deteriorates to a certain extent, joint leakage can occur.

To investigate the mechanical behavior of the shield segment joint, in order to investigate the mechanical performance of shield tunnel segment joints, researchers have conducted a series of experiments and theoretical studies. For experimental studies, researchers typically utilize a four-point bending setup (or other experimental setup) to conduct load capacity tests on prototype pipe segment joints [2–7]. These approaches were employed to examine the stiffness, strength, and failure modes of the shield segment joints. For theoretical or numerical studies, researchers primarily analyze pipe segment joints using spring-based theoretical models or finite element (FE) models [8–13]. These analytical methods are effective in reflecting the macroscopic mechanical properties of the joints, such as the moment–rotation relationship. However, for detailed fracture behavior, existing models have certain limitations. Besides, researchers have conducted numerous studies on the reinforcement and repair of pipe segment joints. However, these studies predominantly utilize reinforcements, such as steel plates, steel fibers, or steel pipes [14–20]. In environments where there is water present, these steel reinforcements are susceptible to corrosion, which imposes certain limitations on their practical application. Therefore, there is a promising application potential in reinforcing segment joints using noncorrosive fiber-reinforced polymer (FRP) materials.

To enhance the simulation of the mechanical and fracture characteristics of the FRP-reinforced shield segment joint, an adequately detailed model is required to simultaneously simulate concrete cracking, the slip and debonding between steel reinforcement and concrete, as well as the interface mechanical properties between FRP and concrete. Traditional FE continuum element models are inadequate in accurately representing such problems. Hence, there is a pressing need to develop new models suitable for analyzing systems with a large number of interface issues. Therefore, the cohesive zone modeling (CZM) approach [21–28] is a preferable choice, since its primary advantage lies in its ability to accurately characterize the mechanical behavior of interfaces, such as the interaction between cracks in concrete before and after cracking, as well as the interface mechanical properties between different materials.

In this study, a numerical modeling approach for FRP-reinforced shield segment joints based on CZM is proposed. By using the zero-thickness cohesive elements, this model can simultaneously analyze the interfaces between FRP and concrete, steel reinforcement and concrete, concrete and concrete, and concrete and rubber. Additionally, through secondary development, the constitutive relationships applicable to different interfaces have been implemented in the model. Experimental data have been employed to confirm the precision of the proposed model, considering aspects such as load-bearing capacity, stiffness, ductility, and failure mode. Finally, the strengthening effect of CFRP plate on the shield segment joint is analyzed with different reinforcing parameters.

2. CZM Model of the Shield Segment Joint

2.1. Modeling Method of the Joint

The CZM was applied to simulate the FRP-strengthened shield segment joint. The joint of shield segment is essentially a reinforced concrete structure. Thus, the modeling method proposed previously [24, 27] was adopted to build up the FE model of joint. As shown in Figure 1, the procedure for constructing the FE model is outlined as follows:Step 1:Separate the concrete original mesh (solid elements), and insert concrete potential fracture surfaces (cohesive elements with zero thickness) to build up the CZM of concrete.Step 2:Insert the steel reinforcement (solid elements) and steel–concrete interface (zero-thickness cohesive elements) to establish the RC model.Step 3:Insert the FRP plate (beam elements) and FRP–concrete interface (zero-thickness cohesive elements) to model the FRP-strengthened RC.

(a)

(b)

(c)

It should be noticed that in step 2, the steel was inserted to the model by the connection of cohesive elements. Therefore, multilayer of steel reinforcement or bolt can be inserted together, and they will not interfere with each other.

2.2. Constitutive Models for FRP–Concrete Interface and Concrete Potential Fracture Surfaces

2.2.1. Damage Relation under Mixed-Mode Condition

The damage constitutive models proposed previously [24, 27] were employed to characterize the mechanical behavior of FRP–concrete interface and concrete potential fracture surfaces. As shown in Figure 2, the stress–displacement behavior for both interfaces under single-mode conditions can be described as follows:(1)Normal direction:where σ is the normal stress, k_n is stiffness in the normal direction, δ_n is the displacement in the normal direction, δ_n0 and δ_nf are the key parameters of damage state, as shown in Figure 2(a), and D is the damage coefficient (or damage factor), and it can be calculated by the following equation:(2)Tangential direction:where τ is the shear stress; k_s is stiffness in the tangential direction, it is a constant parameter for concrete potential fracture surfaces, for FRP–concrete interface, k_s = τ₀/(δ_s0ǀδ_sǀ)^0.5 (ǀδ_sǀ ≤ δ_s0ǀ); δ_s is the tangential displacement; δ_s0 and δ_sf are the key parameters of damage state, as shown in Figure 2(b).

(a)

(b)

In the tangential direction, the damage coefficient can be calculated by the following equation:

Defining the total displacements [24, 27] as follows:where δ is the total displacement; δ₀ is the displacement of the damaged initial state in the mixed-mode; δ_f is the displacement of the failure state in the mixed-mode; , , , and are the key parameters of damage state [24, 27], as shown in Figure 2.

Based on the total displacements defined above, in the mixed-mode condition, the damage coefficient D can be defined as follows:

2.2.2. Friction Effect

The friction effect [24, 27] was also considered into the calculation of stress. According to the different slip conditions, the friction stress can be calculated as follows:

(1) Interfacial nonsliding condition.

In the interfacial nonsliding condition, the shear stress can be transmitted normally. Thus, the friction stress T_f can be given as follows:where is the interfacial slip which has been generated during the fracture process, and T_fmax is the maximum friction stress, and it can be calculated by the following equation:where f is the friction coefficient.

(2) Interfacial sliding condition.

In the interfacial sliding condition, the friction stress can be calculated by the following equation:where is the slip displacement which has been updated.

2.2.3. Expression of Stresses

Finally, incorporating the damage relation and friction effect, the stress can be expressed as follows:

(1) Normal stress:

(2) Shear stress:

2.3. Constitutive Models of the Steel–Concrete Interface (Ribbed)

The mixed-mode constitutive model [24, 27] considering the influence of interfacial normal separation was adopted in this study. According to Figure 3, a weakening factor can be defined as follows:

Where h_rib is the height of the rib of reinforcement, as shown in Figure 3.

Based on the weakening factor , the modified bond-slip relation (recommended by CEB-FIP [29]) of the reinforcement–concrete interface can be given as follows:where τ_max is the bond strength, τ_res is the residual stress, δ_s1 and δ_s2 are the displacements in the tangential direction which corresponding to the bond strength and residual stress, and α is the constant parameter about stiffness. For ribbed rebar, τ_max = (f_ck)^0.5 ( is the concrete compression strength), τ_res = 0.15·τ_max, δ_s1 = 0.6 mm, δ_s2 = 2.5 mm, α = 0.4. As for plain rebar, τ_max = τ_res = 0.1 × (f_ck)^0.5, δ_s1 = 0.01 mm, α = 0.5.

3. Validation of the Numerical Model

To assess the precision of the FE model proposed in this study, a group of shield segment joint experiments [30] was chosen to be compared with the simulation results. Figure 4 shows the simplified load scheme and geometry of the segment joint. The outer diameter of the segment is 6.2 m, and the inner diameter of the segment is 5.5 m. The center angle of each segment is 22°, and the thickness of the segment is 1.2 m. Concrete with a design strength of 55 MPa and steel ribbed rebar with a yield strength of 400 MPa were used to cast the shield segment. Besides, two 30 mm-diameter bolts with 400 mm longitude and 400 MPa yield strength were used to connect two segments.

(a)

(b)

As shown in Figure 4, the shield segment is placed in two concave rigid frames, where the left rigid frame is hinged on the left and bottom sides, while the right rigid frame is supported by roller bearings at the bottom and subjected to horizontal thrust on the right side. The upper part of the specimen is subjected to a pair of vertical loads spaced 800 mm apart, resulting in the joint becoming a pure bending section. During the loading process, the ratio of bending moment to horizontal load is 300 mm.

The structure of the FE model is illustrated in Figure 5. The FE model consists of concrete, steel rebar, steel–concrete interface, rubber, bolt, and contact interface. The constitutive model applied to the contact interface is identical to that used for the potential fracture surfaces of concrete, with a very low normal and shear strength. There are about 20,000 nodes, 6,500 triangular elements (CPS3), and 12,000 cohesive elements (COH2D4) in a typical FE model. In this model, the concrete, steel rebar, bolt, and rubber are represented by solid elements. To ensure that the area of steel–concrete interface is consistent with the actual one, the width of the rebar is set to its radium R. Thus, the out-of-plane thickness of the steel–concrete interface can be set to . In addition, there is a 4 mm gap between the segments above the water-stop rubber. In the model, although there is no gap at this contact surface, it is set to have a contact stress after mutual penetration of 4 mm.

All the constitutive adopted in this study were implemented through ABAQUS subroutine VUMAT [31], the model was solved with the ABAQUS/EXPLICITE solver [31] by using a quasistatic method. The principle of this method is to solve static problems using dynamic solution methods. Its advantage lies in avoiding the convergence difficulties encountered in static solution.

According to the experimental results, repeat trials, and the relative references about CZM [21–27], the material parameters utilized in the cohesive elements are detailed in Table 1. Additionally, concrete has an elastic modulus E of 30 GPa and a Poisson’s ratio v of 0.2. Steel has an elastic modulus E of 30 GPa, a Poisson’s ratio v of 0.2, and a yield strength of 390 MPa. Rubber has an elastic modulus E of 20 MPa and a Poisson’s ratio v of 0.4.

Figure 6 shows the result of the simulation. By deleting cohesive elements with a damage factor reaching 1, the cracks in the model can be represented. The fracture process is as follows: At first, the bending moment increased linearly with the increment of midspan deflection; subsequently, the bolt entered the yield stage, which leaded that the slope of the bending moment–deflection curve undergoes a reduction. Finally, the concrete above the rubber makes contact, and the stiffness of the joint increases, causing the slope of the curve to recover until the upper concrete crushed, as shown in Figures 6(a) and 6(b). By comparing the bending moment–deflection curve and the fracture pattern between simulation and experiments, the simulation results closely match the experimental data, indicating that the proposed numerical model accurately captures the mechanical behavior of the shield segment joint.

(a)

(b)

(c)

4. Analysis of the FRP-Strengthened Shield Segment Joint

The strengthening effect of the FRP on the shield segment joint is assessed based on the proposed CZM model. Due to the varying dimensions of existing engineering shield segment, in order to facilitate the comparison of the mechanical performance of joints before and after reinforcement, the same joint form and material parameters as those in Section 3 were selected. The composition of the FRP-strengthened shield segment joint is as shown in Figure 7. The FRP plate is connected to the segment joint through FRP–concrete interface (zero-thickness cohesive elements).

According to the relative references [26, 27, 32], the CFRP plate was chosen as the external reinforcement. The CFRP plate is set to bond under the whole bottom of shield segments. The CFRP plate has a width of 1.2 m and a thickness of 1.2 mm. The material parameters of the FRP–concrete interface are listed in Table 2. It should be noted that due to the various types of epoxy resins, the parameters of the FRP–concrete interface also vary. Therefore, the parameters used in this paper mainly refer to those used in previous studies [26, 27, 32]. Besides, the CFRP plate has an elastic modulus E of 165 GPa.

Figure 8 shows enhancement provided by the externally bonded CFRP plate. Through the bending moment–deflection curve, as shown in Figure 8(a), the stiffness and the bearing capacity of the joint is significantly strengthened, the maximum bending moment and the stiffness are approximately 2.5 times and 1.7 times that of the original join. Besides, the fracture pattern of the joint is changed. Since the bottoms of the segments are connected by the CFRP plate (CFRP plate plays a role similar to steel rebar, as shown in Figures 8(c) and 8(d)), the joint is transformed into an integral RC structure. Thus, when the joint fails, several cracks will initiate at the bottom of segment concrete and propagate upward, with the crush of the top concrete. This fracture pattern is very similar to the traditional RC beam. However, it should be noticed the application of CFRP plate will reduce the ductility of the joint.

(a)

(b)

(c)

(d)

4.1. Influence of the Bonding Length

In this section, the effect of the CFRP bonding length on the segment joint is investigated. As shown in Figure 9, three types of segment joints with different bonding length (entire length, 2/3 length, and 1/3 length) were simulated. All the material parameters are the same to Sections 3 and 4.

Figure 10 shows the simulation results of the FRP-strengthened segment joint with different bonding lengths. The joint with the entire bonding length has the best strengthening effect. However, with the 2/3 and 1/3 bonding length, both the bearing capacity and ductility of the joint are substantially decreased, as shown in Figure 10(a). Besides, with the insufficient bonding length, the fracture pattern will also be changed. As shown in Figure 10(b), when the joint fails, the concrete cover will peel off, and this ultimately leads to the failure of the CFRP strengthening effect.

(a)

(b)

4.2. Influence of the Bonding Width

In this section, the effect of the CFRP bonding width on the segment joint is investigated. The CFRP-strengthened joint with different bonding width (1.2, 0.8, and 0.4 m corresponding to entire width, 2/3 width, 1/3 width) were simulated. Figure 11 shows the influence of the bonding width of CFRP plate. Reduced bonding width leads to a significant decrease in joint stiffness, bearing capacity, and ductility. Furthermore, as depicted in Figure 11(b), the fracture pattern with insufficient CFRP width appears similar to the one without an externally bonded CFRP plate. These results indicates that when the CFRP plate’s cross-sectional stiffness is insufficient, its reinforcement effectiveness is significantly compromised.

(a)

(b)

5. Conclusions

This study introduces a FE model for simulating the FRP-strengthened shield segment joint using the CZM. Cohesive elements were utilized to characterize the concrete potential fracture surfaces, as well as the interfaces between FRP and concrete, and between steel and concrete. The corresponding constitutive models were adopted to characterize these components. A group of experiments of segment joint was chosen to evaluate the simulation accuracy. The simulation results fit well with the experimental one.

Based on the proposed model, the efficacy of the externally bonded CFRP plate for reinforcement was studied. In summary:(1)By externally bonding the CFRP plate (with entire length and width), the stiffness and bearing capacity of the joint can be significantly increased (approximately 2.5 times and 1.7 times that of the original joint, respectively). Thus, the CFRP plate has a good potential for the application in segment joint reinforcement.(2)The bonding length and width have a great influence on the strengthening effect. The insufficient bonding length and bonding width will lead to a significant weakening of the strengthening effect. According to the analysis results, it is recommended to adhere the CFRP plate to the entire area at the bottom as much as possible.

Through this study, it has been demonstrated that CFRP plates have the capability to reinforce shield segment joints from a mechanical perspective. Additionally, due to the excellent corrosion resistance of CFRP compared to steel, it has great potential for engineering applications.

It should be noticed that this paper only studied the strengthening effect of CFRP plates on joints under positive bending moments. The reinforcing effect of CFRP under negative bending moments still needs to be further investigated in subsequent research.

Data Availability

The data are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This study was funded by the Natural Science Foundation of Fujian Province (2023J01938) and the Scientific Research Startup Foundation of Fujian University of Technology (GY-Z21026 and GY-Z21067).

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Copyright © 2024 Jianjun Kuang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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