# Experimental and Analytical Modeling of GFRP Strengthened Grouted Mortarless Masonry Prisms

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Research

#### 2.1. Material and Specimen Fabrication

^{3}air-cured cubes following GB50081-2002 [31]. The average strength of the three grout types (i.e., GN1, GN2, and GN3) were 23.9 MPa, 34.7 MPa, and 45.0 MPa, respectively, and their standard deviations were 1.37 MPa, 0.54 MPa, and 1.03 MPa, respectively. For GFRP strengthened GMM specimens, the mechanical properties of GFRP and epoxy are listed in Table 1 and Table 2, respectively. E-glass unidirectional fibers were selected as the confinement and the properties of glass fibers are provided in Table 1 from the producer, where the nominal thickness was for the dry fibers, with a density of 414 g/m

^{2}.

#### 2.2. Test Setup and Method

_{cr}. Then, the test machine was reloaded until failure of the specimen.

## 3. Results and Discussion

#### 3.1. Failure Modes

#### 3.2. Tested Results and Analysis

_{g,m}of grouted masonry prisms is calculated as Equation (1) according to GB50003-2011 [30]:

#### 3.3. Axial Compressive Stress–Strain Behavior

#### 3.4. Confinement Mechanism of GFRP Strengthened Mortarless Masonry

#### 3.5. Effective Restraint Area of GFRP Strengthened Masonry

#### 3.6. Carrying Capacity of GFRP Strengthened Masonry

## 4. Conclusions

- Like the FRP-confined concrete, the GFRP confinement has improved the initial cracking load and ultimate carrying capacity of grouted mortarless masonry, which indicated that the GFRP confinement has restrained the crack development of masonry efficiently and increased the ultimate strain to improve the ductility of masonry system.
- The strength of grouted concrete has a parabolic influence on the ultimate carrying capacity of plain masonry strength but a positive effect on the ultimate carrying capacity of GFRP strengthened masonry. Unstrengthened masonry with different strengths of grouted concrete performed the same failure mode and stress–strain behaviour.
- The general compressive behaviour of GFRP strengthened grouted mortarless masonry was bilinear with an initial PSEUDO-elastic stage and an elastic-linear stage, while the slopes of the second stage at the stress–strain curves exhibit the trend of degression.
- The mechanism properties of GFRP strengthened grouted mortarless masonry was analyzed by homogenization according to FRP-confined concrete, which indicated that the stress concentration phenomenon existing at the corner of the masonry caused GFRP jackets to rupture mostly at the corner of masonry.
- One compressive stress–strain model was developed for the GFRP strengthened grouted mortarless masonry, which performed well to predict the experimental results.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Typical compressive failure modes of the unstrengthened specimens: (

**a**) failure mode 1 (Specimen B-3); (

**b**) failure mode 2 (Specimen C-3).

**Figure 5.**Compressive failure modes of the G-GMM specimen: (

**a**) failure mode of the masonry; (

**b**) failure mode of glass fiber-reinforced polymer (GFRP).

**Figure 7.**Compressive stress–strain curves of the specimens with grouting strengths of (

**a**) 23.9 MPa; (

**b**) 34.7 MPa; (

**c**) 45.0 MPa.

**Figure 8.**Compressive stress–strain curves fitting that uses the logarithmic constitutive relation presented by Zeng et al. [33] with grouted concrete strengths of (

**a**) 23.9 MPa; (

**b**) 34.7 MPa; (

**c**) 45.0 MPa.

**Figure 9.**Comparison of the experimental values (listed in Table 5) and the predicted values based on fitting.

Nominal Thickness (mm) | Tensile Strength (MPa) | Modulus of Elasticity (GPa) | The Volume Fractions | Weight Density (g/m^{2}) | Ultimate Elongation (%) | Fiber Direction |
---|---|---|---|---|---|---|

0.436 | 660 | 83 | 29.5% | 414 | 4.3 | Uni- directional |

Resin Type | Density (g/cm^{3}) | Tensile Strength (MPa) | Tensile Modulus (GPa) | Thermal Expansion Coefficient (10^{−6}/°C) | Solidification Shrinkage (%) |
---|---|---|---|---|---|

Epoxy | 1.2–1.3 | 35–130 | 1.75–4.1 | 40 | 1–5 |

Specimen | Grouted Concrete Standard Strength (MPa) | Grouted Concrete Tested Strength (MPa) | Strengthened |
---|---|---|---|

AG-1,2,3 | C20 | 23.9 | GFRP |

A-1,2,3 | C20 | 23.9 | – |

BG-1,2,3 | C30 | 34.7 | GFRP |

B-1,2,3 | C30 | 34.7 | – |

CG-1,2,3 | C45 | 45.0 | GFRP |

C-1,2,3 | C45 | 45.0 | – |

Group | Sample | Grout | ${\mathit{f}}_{\mathit{c}\mathit{r}}$ (MPa) | ${\mathit{f}}_{\mathit{u}}$ (MPa) | ${\mathit{f}}_{\mathit{g},\mathit{m}}$ (MPa) | N_{cr}/N_{u} | Failure Mode | |
---|---|---|---|---|---|---|---|---|

Type | f_{cu,m} (MPa) | |||||||

G. 1 | AG-1 | GN1 | 23.9 | 19.66 | 24.63 | 11.6 | 0.80 | Z |

AG-2 | GN2 | 23.9 | 17.37 | 22.79 | 0.76 | X | ||

AG-3 | GN3 | 23.9 | 18.11 | 23.64 | 0.77 | X | ||

Average | – | 23.9 | 18.38 | 23.69 | 0.78 | — | ||

A-1 | GN1 | 23.9 | 12.51 | 19.65 | 0.64 | Y | ||

A-2 | GN2 | 23.9 | 12.23 | 18.08 | 0.68 | Y | ||

A-3 | GN3 | 23.9 | 12.66 | 20.11 | 0.63 | Y | ||

Average | – | 23.9 | 12.47 | 19.28 | 0.65 | — | ||

G. 2 | BG-1 | GN1 | 34.7 | 19.23 | 32.71 | 14.7 | 0.59 | Z |

BG-2 | GN2 | 34.7 | 18.87 | 30.57 | 0.62 | Y | ||

BG-3 | GN3 | 34.7 | 19.10 | 32.09 | 0.60 | Z | ||

Average | – | 34.7 | 19.06 | 31.79 | 0.60 | — | ||

B-1 | GN1 | 34.7 | 16.13 | 29.81 | 0.54 | Y | ||

B-2 | GN2 | 34.7 | 16.29 | 29.87 | 0.55 | Y | ||

B-3 | GN3 | 34.7 | 16.05 | 29.60 | 0.54 | Y | ||

Average | – | 34.7 | 16.15 | 29.76 | 0.54 | — | ||

G. 3 | CG-1 | GN1 | 45.0 | 23.08 | 43.70 | 17.7 | 0.53 | X |

CG-2 | GN2 | 45.0 | 25.24 | 44.53 | 0.57 | Z | ||

CG-3 | GN3 | 45.0 | 23.75 | 44.24 | 0.54 | Z | ||

Average | – | 45.0 | 24.02 | 44.16 | 0.54 | — | ||

C-1 | GN1 | 45.0 | 14.82 | 33.41 | 0.44 | Y | ||

C-2 | GN2 | 45.0 | 14.47 | 34.67 | 0.42 | Y | ||

C-3 | GN3 | 45.0 | 15.21 | 35.72 | 0.43 | Y | ||

Average | – | 45.0 | 14.83 | 34.60 | 0.43 | — |

Sample | ${\mathit{f}}_{\mathit{m}\mathbf{0}}$ (MPa) | ${\mathit{f}}_{\mathit{m}\mathit{m}}$ (MPa) | ${\mathit{f}}_{\mathit{l}}^{\mathit{\prime}}$ (MPa) | ${\mathit{f}}_{\mathit{l}}^{\mathit{\prime}}$/${\mathit{f}}_{\mathit{m}\mathbf{0}}$ | ${\mathit{f}}_{\mathit{m}\mathit{m}}$/${\mathit{f}}_{\mathit{m}\mathbf{0}}$ |
---|---|---|---|---|---|

AG-1 | 19.28 | 24.63 | 0.829 | 0.043 | 1.277 |

AG-2 | 19.28 | 22.79 | 0.330 | 0.017 | 1.182 |

AG-3 | 19.28 | 23.64 | 0.792 | 0.041 | 1.226 |

BG-1 | 29.76 | 32.71 | 0.659 | 0.022 | 1.099 |

BG-2 | 29.76 | 30.57 | 0.132 | 0.004 | 1.027 |

BG-3 | 29.76 | 32.09 | 0.734 | 0.025 | 1.078 |

CG-1 | 34.60 | 43.70 | 1.020 | 0.029 | 1.263 |

CG-2 | 34.60 | 44.53 | 1.103 | 0.032 | 1.287 |

CG-3 | 34.60 | 44.24 | 1.108 | 0.032 | 1.279 |

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**MDPI and ACS Style**

Huang, L.; Gao, C.; Yan, L.; Li, X.; Ma, G.; Wang, T.
Experimental and Analytical Modeling of GFRP Strengthened Grouted Mortarless Masonry Prisms. *Fibers* **2017**, *5*, 18.
https://doi.org/10.3390/fib5020018

**AMA Style**

Huang L, Gao C, Yan L, Li X, Ma G, Wang T.
Experimental and Analytical Modeling of GFRP Strengthened Grouted Mortarless Masonry Prisms. *Fibers*. 2017; 5(2):18.
https://doi.org/10.3390/fib5020018

**Chicago/Turabian Style**

Huang, Liang, Chang Gao, Libo Yan, Xiaoxi Li, Gao Ma, and Tianfeng Wang.
2017. "Experimental and Analytical Modeling of GFRP Strengthened Grouted Mortarless Masonry Prisms" *Fibers* 5, no. 2: 18.
https://doi.org/10.3390/fib5020018