# Modelling of CFRP-Strengthened RC Shear Walls with a Focus on End-Anchor Effects

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## Abstract

**:**

## 1. Introduction

## 2. Development of Tube Anchor System

#### 2.1. Phases 1 and 2: Angle Anchor System vs. Tube Anchor System

#### 2.2. Phase 3: Application of Tube Anchor System to Shear-Critical Walls

## 3. Proposed Modelling Method

#### 3.1. Modelling of an RC Shear Wall

#### 3.2. Modeling of CFRP Sheets

#### 3.2.1. Bond–Slip Behaviour

_{max}is the maximum shear stress and ${s}_{0}$ is the interfacial slip corresponding to τ

_{max}. These two parameters can be determined from Equations (2) and (3).

_{t}is the tensile strength of concrete and β

_{w}is a factor representing the FRP-to-concrete width ratio as expressed in Equation (4).

_{f}and b

_{c}are the width of the FRP strip and the concrete member, respectively. The last parameter in Equation (1) is the α factor, which is a function of the interfacial fracture energy (G

_{f}) and can be determined using Equations (5) and (6).

_{max}) was calculated to be 3.69 MPa and 1.73 MPa for the strengthened shear walls tested in Phase 2 and Phase 3, respectively. The corresponding slip (${s}_{0}$) at the maximum bond shear stress was found to be 0.050 mm and 0.022 mm for these two phases.

#### 3.2.2. Confinement Effect

_{l}) proposed by Kupfer et al. [46] and expressed in Equation (7). The β

_{l}factor is a function of the triaxial stress state in concrete, which depends on the ratio and properties of the OOP reinforcement.

_{cl}is the lateral confining stress and f

_{cn}is the difference in normal lateral stresses acting on the concrete, both determined from the in-plane and OOP stresses in concrete. The in-plane stresses are calculated from the two-dimensional analysis, while the OOP stress (f

_{cz}) can be estimated from the OOP strain (ε

_{cz}) based on the following equation.

_{l}enhancement factor using Equations (7) and (8) and increases their strength and ductility to account for the confinement effect. The 0.9% ratio is only appropriate for walls with design parameters within the range investigated in this study. Future work is needed to develop relationships to predict OOP compressive stress in concrete for other wall geometries and CFRP strengthening schemes.

#### 3.3. Modeling of Tube Anchor Effects

## 4. Verification Study

## 5. Summary and Conclusions

- The proposed FE modelling methods were able to accurately compute the key structural response parameters of CFRP-strengthened shear walls including the initial stiffness, peak strength, and ductility under cyclic loads. The FE models were also able to predict the damage sequence and crack patterns of the walls reasonably well.
- It was shown that oversimplifying the effect of development length and anchor system, using assumptions such as uniform perfect or imperfect bond between CFRP and concrete at the base of the wall, can lead to significant overestimation or underestimation of the peak strength. Consideration of the effects of the anchor system in the analytical model was found to be critical for a reliable prediction of the nonlinear performance of shear walls reinforced with CFRP sheets.
- The analysis results showed that the confining effect of CFRP sheets near the anchor region was more significant for walls with smaller aspect ratios. Modelling the confining effect played an important role in capturing the ductility capacity of the walls.
- It was also found that accounting for the effect of anchor system was essential for capturing the nonlinear stress distribution in CFRP sheets near the base specially the stress concentration at bolt locations. This stress concentration ultimately led to debonding and rupture of CFRP sheets after the CFRP has developed its full tensile capacity.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Failure mechanism of steel angle anchor system; (

**a**) Prying action; (

**b**) Debonding and premature rupture of FRP [19].

**Figure 5.**Envelopes of hysteretic responses for control (CW), repaired (RW) and strengthened (SW) walls tested in Phase 3 [33]; (

**a**) Aspect ratio: 1.2; (

**b**) Aspect ratio: 0.85; (

**c**) Aspect ratio: 0.65.

**Figure 7.**Modelling of bond–slip behaviour and confinement effect of CFRP sheets; (

**a**) bond–slip model; (

**b**) confinement effect.

**Figure 8.**(

**a**) Finite element model of CFRP-strengthened wall and (

**b**) sources of flexibility in CFRP sheets near the tube anchor.

**Figure 9.**Two modelling approaches proposed to consider flexibility of CFRP sheets due to pulley mechanism of anchor system.

**Figure 10.**Comparison of the measured and calculated responses of control and strengthened shear walls in Phase 2 using the two proposed modelling approaches.

**Figure 11.**The effect of tube anchor on the analysis results of SW1-2: (

**a**) envelopes of hysteretic responses for positive cycles and (

**b**) stress distribution in CFRP trusses at the peak load at the anchor location.

**Figure 12.**Comparison of the measured and calculated responses of control and strengthened shear walls in Phase 3.

**Figure 13.**Comparison of observed and computed damage modes of control and strengthened walls of Phase 3.

Phase | Wall ID | Anchor Type | Aspect Ratio | Type of Specimen | Repair/Strengthening Scheme ^{1} |
---|---|---|---|---|---|

1 | CW1 | Angle | 1.2 | Control | --- |

RW1 | 1.2 | Repaired | 1V | ||

SW1-1 | 1.2 | Strengthened | 1V | ||

SW2-1 | 1.2 | Strengthened | 2V + 1H | ||

2 | CW2 | Tube | 1.2 | Control | --- |

RW2 | 1.2 | Repaired | 1V | ||

SW1-2 | 1.2 | Strengthened | 1V | ||

SW2-2 | 1.2 | Strengthened | 2V | ||

SW3-2 | 1.2 | Strengthened | 3V + 1H |

^{1}“V” and “H” stand for vertically and horizontally oriented CFRP sheets, respectively.

**Table 2.**Characteristics of shear wall specimens in Phase 3 [33].

Series | Specimen | Wall ID | Specimen Type | Length × Thickness (mm ^{2}) | Aspect Ratio | Vertical CFRP Sheets ^{1} | Horiz. CFRP Sheets ^{1} |
---|---|---|---|---|---|---|---|

1 | 1 | CW1 | Control | 1500 × 100 | 1.20 | - | - |

1 | RW1 | Repaired | 1500 × 100 | 1.20 | 2 | 6 | |

2 | SW1 | Strengthened | 1500 × 100 | 1.20 | 2 | 6 | |

2 | 3 | CW2 | Control | 2100 × 140 | 0.85 | - | - |

3 | RW2 | Repaired | 2100 × 140 | 0.85 | 2 | 6 | |

4 | SW2a | Strengthened | 2100 × 140 | 0.85 | 2 | 6 | |

5 | SW2b ^{2} | Strengthened | 2100 × 140 | 0.85 | 2 | 6 | |

3 | 6 | CW3 | Control | 2750 × 180 | 0.65 | - | - |

6 | RW3 | Repaired | 2750 × 180 | 0.65 | 0 | 8 | |

7 | SW3 | Strengthened | 2750 × 180 | 0.65 | 0 | 8 |

^{1}Total number of vertical and horizontal CFRP layers on both sides of the specimen;

^{2}Specimen SW2b has all of the layers of CFRP applied to a single side of the wall.

Wall ID | Observed Damage Sequence | Calculated Damage Sequence | |||||||
---|---|---|---|---|---|---|---|---|---|

Disp. (mm), Force (kN) | Model Type | Disp. (mm), Force (kN) | |||||||

Reinf. Yielding | CFRP Debonding | Concrete Crushing | CFRP Rupture | Reinf. Yielding | CFRP Debonding | Concrete Crushing | CFRP Rupture | ||

CW2 | 4 mm, 121 kN | N/A | 15 mm, 184 kN | N/A | --- | 4 mm, 164 kN | N/A | 19 mm, 195 kN | N/A |

SW1-2 | 2 mm, 150 kN | 5 mm, 217 kN | 14 mm, 223 kN | 19 mm, 313 kN | Model A | 3 mm, 177 kN | 12 mm, 297 kN | 16 mm, 315 kN | 38 mm, 328 kN |

Model B | 3 mm, 169 kN | 8 mm, 272 kN | 17 mm, 307 kN | 30 mm, 294 kN | |||||

SW2-2 | 3 mm, 227 kN | 9 mm, 360 kN | 12 mm, 415 kN | 15 mm, 426 kN | Model A | 3 mm, 232 kN | 13 mm, 377 kN | 16 mm, 413 kN | 36 mm, 230 kN |

Model B | 3 mm, 237 kN | 12 mm, 404 kN | 15 mm, 329 kN | 19 mm, 367 kN | |||||

SW3-2 | 3 mm, 247 kN | 13 mm, 414 kN | 20 mm, 426 kN | 26 mm, 413 kN | Model A | 3 mm, 226 kN | 9 mm, 418 kN | 17 mm, 534 kN | 43 mm, 318 kN |

Model B | 4 mm, 289 kN | 11 mm, 469 kN | 20 mm, 457 kN | 38 mm, 295 kN |

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**MDPI and ACS Style**

Sadeghian, V.; Said, S.A.; Lau, D.
Modelling of CFRP-Strengthened RC Shear Walls with a Focus on End-Anchor Effects. *Buildings* **2023**, *13*, 747.
https://doi.org/10.3390/buildings13030747

**AMA Style**

Sadeghian V, Said SA, Lau D.
Modelling of CFRP-Strengthened RC Shear Walls with a Focus on End-Anchor Effects. *Buildings*. 2023; 13(3):747.
https://doi.org/10.3390/buildings13030747

**Chicago/Turabian Style**

Sadeghian, Vahid, Said Ali Said, and David Lau.
2023. "Modelling of CFRP-Strengthened RC Shear Walls with a Focus on End-Anchor Effects" *Buildings* 13, no. 3: 747.
https://doi.org/10.3390/buildings13030747