# Ultimate Bearing Capacity Analysis of CFRP-Strengthened Shield Segments Using Bonding Slip Behavior Experiments

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure

#### 2.1. Experimental Design

#### 2.2. Mechanical Properties of Materials

^{3}, produced for C30 concrete as suggested by the China National Standard (GB 50010-2010). Portland cement (P.S.42.5) was used, and its loss-on-ignition and specific surface values were 4.46% and 325, respectively; these values have a strong effect on adhesive bonding. The aggregate was fine river sand, with a complete fineness modulus of 1.97. The gradation of the gravel was in the range of 5 mm–12 mm, where its maximum diameter did not exceed 20 mm.

#### 2.3. Experimental System and Method

#### 2.3.1. Slip Test of CFRP-Reinforced Concrete Arch Sections

#### 2.3.2. Confined Compression Strength Test of CFRP-Strengthened Tunnel Segmental Lining

## 3. Results and Discussion

#### 3.1. Slip Test Description

#### 3.2. Confined Compression Strength Test Description

## 4. Parameter Analysis

#### 4.1. Load Analysis on Bond-Slip Behavior

_{0}is the base value of temperature, A

_{1}is the coefficient of the first deflecting drop, and A

_{2}is the coefficient of the second deflecting drop. Table 4 lists the coefficients of fatigue. P

_{0}is the modified loaded parameter, H is expressed by humidity, i is the step counter, A is the humidity enlargement coefficient, and t is the degree of curve descent. The summary of coefficients, including the limit load, steps, and other parameters, is listed in Table 5.

#### 4.2. The Maximum Shearing Stress Analysis

_{e}and w are the effective length and width of the CFRP bonding, respectively, h is the specimen height.

#### 4.3. Maximum Strain Distribution in CFRP–Concrete Interface

#### 4.4. Relationship between Slip Distribution in CFRP–Concrete Interface

_{i+1/2}is the slip of the adhesive and the concrete located in the middle of the i th and i + 1-th electric resistance strain gauges (i = 1 in the center of the specimen), ${\mathsf{\epsilon}}_{\mathrm{i}}$ and $\Delta \mathrm{l}$ are the strain values of the i-th gauge and the space between two gauges, respectively, ${\mathrm{s}}_{0}$ is the slip at the center of the specimen as follows:

^{10}(N/m

^{2}) and 1.07 × 10

^{13}(N/m

^{2}), respectively. t

_{c}and t

_{a}are the failure thickness of the concrete and the adhesive, respectively. Moreover, t

_{c}is 0.25 mm and t

_{a}is 0.53 mm.

## 5. Ultimate Bearing Capacity of Strengthening Shield Segments on the Shear-Slip of CFRP-Reinforced Concrete Arch Sections

#### 5.1. Derivation of Ultimate Bearing Capacity Formulation

_{i}is the distance of the different structure, and i ranges from 1 to 5. In different tunnel environments, the effect of CFRP bonding has a great influence. Finally, ${\mathrm{u}}_{\mathrm{t}}$ is the result of Equation (10).

#### 5.2. Comparison of Analysis and Test Results

_{1}), ultimate load (P

_{2}), and the mechanical parameters of reinforced concrete, which are the tensile stress of CFRP (${\mathrm{f}}_{\mathrm{t}}{}_{\mathsf{\vartheta}}$), the tensile stress of steel (${\mathrm{f}}_{\mathrm{y}}{}_{\mathsf{\vartheta}}$), the compressive stress of concrete (${\mathsf{\sigma}}_{\mathsf{\vartheta}}$), and compressive stress of steel (${\mathrm{f}\u2019}_{\mathrm{y}}{}_{\mathsf{\vartheta}}$).

## 6. Conclusions

- The limit load as the length and layers increased showed a substantial effect on the flexural and sheared behavior of concrete arch sections reinforced with CFRP strengthening. However, the enhancement ratio of the limit load was more effective than the layers because of the increment in the CFRP length.
- The increment in the temperature caused a substantial reduction in the load limit of the strengthened specimens, and the limit load was similar to that of the specimens with an increase in humidity. The combined sustained humidity and temperature as a damaged factor considerably reduced the peak strength of the beams with CFRP strengthening.
- With regard to the maximum shear stress and strain, the slip relation under different factors was obtained. Adding layers and increasing the length caused the relation curve to create shear stress and increase the slope linearly; the load-slip curve changed from linear to nonlinear in the hygrothermal environment.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. The Maximum Shear Stress of CFRP-Reinforced Concrete Arch Sections

_{e}and w are the effective length and width of the CFRP bonding, respectively, ${\mathsf{\sigma}}_{2}$ and ${\mathsf{\tau}}_{2}$ are the stress–strain and maximum shear, respectively, and $\mathsf{\theta}$ is the slope of the two strengthened specimens during the loading process. Equation (A3) is solved by combining them; thus, the CFRP shear stress and adhesive can be written as

_{2}adhesive], the adhesive showed ductile shear deformation caused by the apparent shear stress. The maximum shear stress at the interface of the adhesive is related to the adhesive tensile strength, with a correction coefficient of 0.5 [30]. Consequently, the maximum shear stress ${\mathsf{\tau}}_{1}$ of the concrete and adhesive can be calculated as:

## Appendix B. The Maximum and Minimum Values of CFRP-Strengthened Tunnel Segmental Lining

**Figure A2.**Force analysis diagram of the shield segment strengthened by CFRP. (

**a**) Segment structure strengthened by CFRP, (

**b**) segment joint strengthened by CFRP.

_{2}outside of the shield tunnel. Assuming that the outer radius of the shield lining is R, r is equal to the outer radius, and the boundary conditions for the stress field should satisfy:

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**Figure 1.**Design of problem statement. (

**a**) Embedded methods, (

**b**) single-shear method, (

**c**) double-shear method, (

**d**) reinforced notched beam, (

**e**) bending and shear test, (

**f**) stress model of this study.

**Figure 2.**Location of strain gauge paste and rectangular CFRP. (

**a**) Resistance strain gauge, (

**b**) circular concrete pipe, (

**c**) sticking CFRP.

**Figure 3.**Accelerated loading of CFRP-strengthened tunnel segmental lining. (

**a**) Test loading diagram, (

**b**) schematic diagram.

**Figure 4.**Typical failure mode of CFRP arch concrete. (

**a**) The loading process, (

**b**) the loading failure.

**Figure 5.**Typical failure mode of a tunnel segmental lining. (

**a**) The failure of outer arch, (

**b**) the failure of inner arch.

**Figure 8.**Limit load of CFRP parameters. (

**a**) Temperature–load relationship under different humidity, (

**b**) humidity–load relationship under different temperature.

**Figure 10.**Relationship of shear stress and slope under different values of T and humidity. (

**a**) Relationship between T and θ, (

**b**) relationship between humidity and θ.

**Figure 15.**Interfacial shear stress and slip of CFRP bonding concrete arch. (

**a**) Shear stress and slip curves for different CFRP lengths, (

**b**) shear stress and slip curves for different, T.; (

**c**) shear stress and slip curves for different CFRP layers, (

**d**) shear stress and slip curves for different H, (

**e**) maximum interfacial shear stress and slip curves for hygrothermal coupling.

**Figure 18.**Comparison of the analytical and tested results. (

**a**) Prestrengthening CFRP, (

**b**) poststrengthening reinforced concrete.

CFRP | Elastic Modulus E _{f}(N/mm^{2}) | $\mathbf{Maximum}\mathbf{Strain}{\mathsf{\epsilon}}_{\mathbf{fu}}$ | Ultimate Strength ${\mathbf{f}}_{\mathbf{fu}}\left(\mathbf{MPa}\right)$ | ||
---|---|---|---|---|---|

JGN | 2.5 × 10^{5} | 1.5% | 3700 | ||

Adhesive | $\mathrm{Elastic}\mathrm{Modulus}{\mathrm{E}}_{\mathrm{e}}\xb7\mathrm{GPa}\xb7$ | Ultimate Strength${\mathrm{f}}_{e}\left(\mathrm{MPa}\right)$ | Elongation % | Bending Strength${\mathrm{f}}_{e}{}_{\mathrm{f}}\left(\mathrm{MPa}\right)$ | |

JGN-C | 26700 | 52 | 1.7 | 76 |

Model Number | CFRP | Environmental Parameter | Model Number | CFRP | Environmental Parameter | ||||
---|---|---|---|---|---|---|---|---|---|

Length | Layers | T/°C | H/% | Length | Layers | T/°C | H/% | ||

1-1 | 150 | 1 | 20 | 0% | 2-1 | 350 | 1 | 20 | 5% |

1-2 | 250 | 1 | 20 | 0% | 2-2 | 350 | 1 | 25 | 5% |

1-3 | 350 | 1 | 20 | 0% | 2-3 | 350 | 1 | 35 | 5% |

1-3-2 | 350 | 2 | 20 | 0% | 2-4 | 350 | 1 | 40 | 5% |

1-3-3 | 350 | 3 | 20 | 0% | 3-1 | 350 | 1 | 20 | 10% |

1-4-2 | 350 | 1 | 25 | 0% | 3-2 | 350 | 1 | 25 | 10% |

1-4-3 | 350 | 1 | 35 | 0% | 3-3 | 350 | 1 | 35 | 10% |

1-4-4 | 350 | 1 | 40 | 0% | 3-4 | 350 | 1 | 40 | 10% |

Model Number | CFRP | Environmental Parameter | Loading/kN | Model Number | CFRP | Environmental Parameter | Loading/kN | ||||
---|---|---|---|---|---|---|---|---|---|---|---|

Length | Layers | T/°C | H/% | Length | Layers | T/°C | H/% | ||||

1-1 | 150 | 1 | 20 | 0% | 15.0 | 2-1 | 350 | 1 | 20 | 5% | 26.2 |

1-2 | 250 | 1 | 20 | 0% | 17.1 | 2-2 | 350 | 1 | 25 | 5% | 25.7 |

1-3 | 350 | 1 | 20 | 0% | 30.1 | 2-3 | 350 | 1 | 35 | 5% | 20.6 |

1-3-2 | 350 | 2 | 20 | 0% | 34.2 | 2-4 | 350 | 1 | 40 | 5% | 20.0 |

1-3-3 | 350 | 3 | 20 | 0% | 40.2 | 3-1 | 350 | 1 | 20 | 10% | 19.2 |

1-4-2 | 350 | 1 | 25 | 0% | 28.7 | 3-2 | 350 | 1 | 20 | 10% | 17.3 |

1-4-3 | 350 | 1 | 35 | 0% | 20.9 | 3-3 | 350 | 1 | 35 | 10% | 12.1 |

1-4-4 | 350 | 1 | 40 | 0% | 19.9 | 3-4 | 350 | 1 | 40 | 10% | 11.6 |

Humidity/% | T_{0} | A_{1} | A_{2} | R^{2}/% |
---|---|---|---|---|

0 | 27.4 | 30.0 | 19.9 | 98.6 |

5 | 27.7 | 26.2 | 20.1 | 97.8 |

10 | 27.2 | 19.2 | 11.6 | 93.5 |

Temperature/T °C | L_{0} | i | A_{i} | t_{i} | R^{2}/% |
---|---|---|---|---|---|

20 | 30.0 | 2 | 2.03 | −8.29 | 99.7 |

25 | 28.7 | 2 | 0.56 | −4.19 | 96.7 |

30 | 20.9 | 2 | 0.01 | −1.49 | 97.8 |

40 | 19.9 | 2 | 1.16 × 10^{−6} | −0.78 | 92.8 |

T °C | A_{3} | A_{4} | p | l_{0} | R^{2}/% | l_{eT}/mm |
---|---|---|---|---|---|---|

20 | 8431 | 0 | 3 | 41.8 | 99.8 | 110 |

25 | 7542 | 12 | 3 | 42.5 | 96.2 | 363 |

30 | 6024 | 10 | 3 | 40.2 | 97.5 | 409 |

40 | 3421 | 5 | 3 | 50.2 | 98.5 | 563 |

Humidity | a | b | R^{2}/% | l_{eH}/mm |
---|---|---|---|---|

0% | 7169 | −58.1 | 87.7 | 110 |

5% | 4245 | −23.9 | 99.5 | 177 |

10% | 3972 | −17.6 | 98.1 | 226 |

Model Number | CFRP | T/°C | H/% | d/mm | $\mathsf{\theta}/{10}^{-1}\mathsf{\pi}$ | S_{0} 10^{−1} mm | ${\mathbf{l}}_{\mathbf{e}}\left(\mathbf{mm}\right)$ | ${\mathsf{\tau}}_{1\mathbf{max}}/\mathbf{MPa}$ | S 10^{−1} mm | |
---|---|---|---|---|---|---|---|---|---|---|

Length/mm | Layers | |||||||||

1-1 | 150 | 1 | 20 | 0 | 12.0 | 0.94 | 0.34 | 50 | 2.16 | 1.05 |

1-2 | 250 | 1 | 20 | 0 | 20.0 | 1.33 | 0.96 | 75 | 6.13 | 3.03 |

1-3 | 350 | 1 | 20 | 0 | 30.8 | 1.50 | 1.36 | 110 | 8.73 | 5.07 |

1-3-2 | 350 | 2 | 20 | 0 | 25.1 | 1.37 | 1.49 | 126 | 9.61 | 5.22 |

1-3-3 | 350 | 3 | 20 | 0 | 14.9 | 1.01 | 1.52 | 148 | 9.76 | 5.23 |

1-4-2 | 350 | 1 | 25 | 0 | 31.2 | 1.54 | 1.15 | 150 | 7.36 | 4.97 |

1-4-3 | 350 | 1 | 30 | 0 | 35.6 | 1.59 | 0.76 | 150 | 4.88 | 3.46 |

1-4-4 | 350 | 1 | 40 | 0 | 40.3 | 1.67 | 0.68 | 150 | 4.36 | 2.42 |

2-1 | 350 | 1 | 20 | 5 | 33.2 | 1.57 | 1.01 | 150 | 6.46 | 3.97 |

2-2 | 350 | 1 | 25 | 5 | 34.2 | 1.58 | 0.96 | 150 | 6.19 | 3.59 |

2-3 | 350 | 1 | 30 | 5 | 37.9 | 1.64 | 0.73 | 150 | 4.68 | 3.11 |

2-4 | 350 | 1 | 40 | 5 | 42.6 | 1.69 | 0.65 | 150 | 4.18 | 2.81 |

3-1 | 350 | 1 | 20 | 10 | 35.3 | 1.58 | 0.70 | 150 | 4.50 | 4.53 |

3-2 | 350 | 1 | 25 | 10 | 36.0 | 1.63 | 0.64 | 150 | 4.09 | 3.89 |

3-3 | 350 | 1 | 30 | 10 | 39.2 | 1.66 | 0.42 | 150 | 2.68 | 3.29 |

3-4 | 350 | 1 | 40 | 10 | 45.3 | 1.81 | 0.38 | 150 | 2.45 | 2.69 |

**Table 9.**Analytical and experimental results of the segment structure and joint under different humidity values.

Spe. | Pre-Load | Ultimate Load | Ratio | Analytical Results on Slope of CFRP/MPa | Test Results of Segment Strengthened by CFRP/MPa | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

P_{1} | P_{2} | P_{2}/P_{1} | ${\mathbf{f}}_{\mathbf{t}}{}_{\mathit{\vartheta}}$ | ${\mathbf{f}}_{\mathbf{y}}{}_{\mathit{\vartheta}}$ | ${\mathsf{\sigma}}_{\mathit{\vartheta}}$ | ${\mathbf{f}\u2019}_{\mathbf{y}}{}_{\mathit{\vartheta}}$ | ${\mathbf{f}}_{\mathbf{t}}{}_{\mathit{\vartheta}2}$ | ${\mathbf{f}}_{\mathbf{y}}{}_{\mathit{\vartheta}2}$ | ${\mathsf{\sigma}}_{\mathit{\vartheta}2}$ | ${\mathbf{f}\u2019}_{\mathbf{y}}{}_{\mathit{\vartheta}2}$ | |

A | 301 | 340 | 1.13 | 12.4 | 8.24 | 10.2 | 7.6 | 11.8 | 8.9 | 10.4 | 7.9 |

B | 301 | 327 | 1.09 | 8.7 | 6.24 | 6.6 | 5.2 | 8.2 | 5.9 | 6.7 | 5.3 |

C | 289 | 318 | 1.10 | 10.2 | 5.98 | 8.3 | 5.1 | 9.9 | 5.8 | 8.3 | 5.3 |

D | 289 | 309 | 1.07 | 7.2 | 4.89 | 5.3 | 2.3 | 6.9 | 4.8 | 5.4 | 2.9 |

E | 273 | 290 | 1.06 | 8.0 | 2.86 | 3.2 | 1.1 | 8.2 | 3.5 | 3.8 | 1.5 |

F | 273 | 283 | 1.04 | 5.2 | 2.01 | 1.9 | 0.9 | 5.5 | 2.6 | 1.8 | 0.6 |

Spe. | ${\mathbf{f}}_{\mathbf{t}}{}_{\mathit{\vartheta}}/{\mathbf{f}}_{\mathbf{t}}{}_{\mathit{\vartheta}2}$ | ${\mathbf{f}}_{\mathbf{y}}{}_{\mathit{\vartheta}}/{\mathbf{f}}_{\mathbf{y}}{}_{\mathit{\vartheta}2}$ | ${\mathsf{\sigma}}_{\mathit{\vartheta}}/{\mathsf{\sigma}}_{\mathit{\vartheta}2}$ | ${\mathbf{f}\u2019}_{\mathbf{y}}{}_{\mathit{\vartheta}}/{\mathbf{f}\u2019}_{\mathbf{y}}{}_{\mathit{\vartheta}2}$ |
---|---|---|---|---|

A | 1.05 | 0.92 | 0.99 | 0.96 |

B | 1.06 | 1.06 | 0.98 | 0.98 |

C | 1.04 | 1.03 | 1.00 | 0.97 |

D | 1.04 | 1.02 | 0.99 | 0.82 |

E | 0.97 | 0.81 | 0.83 | 0.70 |

F | 0.95 | 0.78 | 1.03 | 1.39 |

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## Share and Cite

**MDPI and ACS Style**

Nie, H.-b.; Gu, S.-c.
Ultimate Bearing Capacity Analysis of CFRP-Strengthened Shield Segments Using Bonding Slip Behavior Experiments. *Materials* **2020**, *13*, 4200.
https://doi.org/10.3390/ma13184200

**AMA Style**

Nie H-b, Gu S-c.
Ultimate Bearing Capacity Analysis of CFRP-Strengthened Shield Segments Using Bonding Slip Behavior Experiments. *Materials*. 2020; 13(18):4200.
https://doi.org/10.3390/ma13184200

**Chicago/Turabian Style**

Nie, Hong-bin, and Shuan-cheng Gu.
2020. "Ultimate Bearing Capacity Analysis of CFRP-Strengthened Shield Segments Using Bonding Slip Behavior Experiments" *Materials* 13, no. 18: 4200.
https://doi.org/10.3390/ma13184200