# The Effects of Hybrid Steel/Basalt Fibers on the Durability of Concrete Pavement against Freeze–Thaw Cycles

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure

#### 2.1. Raw Materials

#### 2.2. Mix Proportion and Experimental Design

#### 2.3. Test Procedures

#### 2.3.1. Mass Loss Tests

_{n}is the mass loss rate of the specimen that underwent F-T cycles, W

_{n}is the mass of the specimen after F-T cycles (g), and W

_{0}is the initial mass of the specimen (g).

#### 2.3.2. Abrasion Resistance Tests

_{n}is the abrasion loss of the specimen that underwent F-T cycles, M

_{0}is the mass of the specimen before abrasion (g), M

_{n}is the mass of the specimen after abrasion (g), and A is the specimen abrasion area (m

^{2}).

#### 2.3.3. Compressive Strength Tests

_{c}is the compressive strength loss ratio of the specimen that underwent F-T cycles, R

_{c}

_{0}is the initial compressive strength of the specimen (MPa), and R

_{cn}is the compressive strength of the specimen after F-T cycles (MPa).

#### 2.3.4. Flexural Strength Tests

_{f}is the flexural strength loss ratio of the specimen that underwent F-T cycles, R

_{f}

_{0}is the initial flexural strength of the specimen (MPa), and R

_{fn}is the flexural strength of the specimen after F-T cycles (MPa).

#### 2.3.5. Thickness of the Damaged Layer and Relative Dynamic Modulus of Elasticity Tests

_{n}is the RDME value of the specimen subject to n times cyclic F-T, V

_{n}is the UPV value after n times cyclic F-T (m/s), and V

_{0}is the UPV value without any F-T cycle (m/s).

#### 2.3.6. Micro-Hardness Tests

#### 2.3.7. SEM Tests

## 3. Results and Discussion

#### 3.1. Macroscopic Results

#### 3.1.1. Surface Deterioration and Mass Loss

#### 3.1.2. Abrasion Resistance

^{2}to 1.45 kg/m

^{2}. As the F-T cycles progressed, Group A witnessed a sharp increase in abrasion loss, whereas the abrasion loss rate for the three fiber-reinforced groups notably remained lower than that of the control group. Finally, after 200 F-T cycles, Group A exhibited an abrasion loss of 4.13 kg/m

^{2}under a 200 N load. In contrast, the wear values for Groups B, C, and D ranged from 2.07 kg/m

^{2}to 2.75 kg/m

^{2}, significantly lower than Group A. Notably, Group D displayed the most substantial divergence in abrasion loss when compared to the control group, with a difference of 2.06 kg/m

^{2}. This observation underscores that, when abrasion resistance serves as a reference criterion, HFRC exhibits at least twice the F-T resistance of conventional concrete.

#### 3.1.3. Compressive Strength Loss

#### 3.1.4. Flexural Strength Loss

_{f}values for Groups B to D ranged between 19.38% and 24.18%. Notably, Group D displayed the lowest flexural strength loss rate, indicating that the interwoven SF/BF within the concrete forms a “chaotic supportive system,” effectively impeding crack propagation induced by F-T damage and enhancing the concrete’s toughness [24].

#### 3.1.5. Damaged Layer Thickness

#### 3.1.6. Relative Dynamic Modulus of Elasticity

#### 3.2. Microscopic Results

#### 3.2.1. Micro-Hardness Test Results

#### 3.2.2. SEM Observations

## 4. Grey–Markov Model of F-T Damage

#### 4.1. Grey Theory

^{(0)}(t) = {X

^{(0)}(1), X

^{(0)}(2), …, X

^{(0)}(n)} represents the irregularly distributed raw data sequence, the application of an Accumulated Generation Operation (AGO) yields X

^{(1)}(t) as follows:

^{(1)}(t) pertains to the background value concerning X

^{(1)}(t).

^{(1)}(t) can be calculated using the following equation:

#### 4.2. Markov Chain Correction of Grey Model Errors

^{(0)}(t) was obtained.

^{(0)}(t) yields the residual prediction model and residual prediction values.

#### 4.3. Analysis of Prediction Results

^{2}) lie within the range of 0.9791 to 0.9942, thereby attesting to a commendable concurrence between the projected values and experimental outcomes. Hence, it can be inferred that the utilization of the Grey–Markov model contributes to the anticipation and assessment of the detrimental ramifications inflicted upon HFRC pavement in F-T environments. The corresponding predictive curve is depicted in Figure 16.

## 5. Conclusions

- (1)
- F-T cycling exerts detrimental effects on the durability characteristics of concrete. Compressive strength, flexural strength, abrasion resistance, and RDME typically exhibit a declining trend with increasing F-T cycles, while the mass loss and damage layer thickness increase with the augmentation of F-T cycles. A copious assembly of randomly dispersed hybrid SFs/BFs within the concrete matrix engenders a three-dimensional constraining framework, thereby efficaciously enhancing the F-T durability of the concrete.
- (2)
- The SEM analysis reveals that the fibers dissipate the energy required for crack propagation by means of friction with the cementitious matrix, as well as the pull-out energy and fracture energy of the fibers, thereby serving to toughen and impede crack propagation, consequently enhancing F-T resistance. The microhardness test results indicate that the ITZ strength is lowest in the control group, whereas in the HFRC, the impact of F-T cycles on the ITZ is relatively minimal due to the robust bonding between fibers and the surrounding matrix.
- (3)
- A Grey–Markov model, built upon the results obtained from the RDME test, is formulated to predict the service life of each group of specimens. The hybrid method affects the concrete’s service life. Under F-T cycles, the predicted life of each group in the sequence is Group D > Group B > Group C > Group A.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**Illustration of the micro-hardness test: (

**a**) Micro-hardnedd tester, (

**b**) Micro-hardness test sample, (

**c**) Typical shape of indentation and (

**d**) Selection scheme of test points.

**Figure 9.**The compressive strength results of specimens after different F-T cycles: (

**a**) compressive strength and (

**b**) compressive strength loss rate.

**Figure 10.**The flexural strength results of specimens after different F-T cycles: (

**a**) flexural strength and (

**b**) flexural strength loss rate.

**Figure 13.**Micro-hardness values in the ITZ and typical micro-hardness trend curves of the fiber edge–matrix interfacial zone in concrete specimens: (

**a**) micro-hardness around fibers and (

**b**) typical micro-hardness trend curves.

Chemical Composition | SiO_{2} | Al_{2}O_{3} | CaO | Fe_{2}O_{3} | MgO | MnO | K_{2}O | IL | TiO_{2} |
---|---|---|---|---|---|---|---|---|---|

Cement | 26.7 | 11.5 | 48.9 | 4.9 | 3.0 | 0.4 | 1.6 | 1.8 | 1.2 |

Fly ash | 46.4 | 29.9 | 9.4 | 6.9 | 1.9 | 0.2 | 1.5 | 2.4 | 1.4 |

Types | Length (mm) | Diameter (μm) | Density (g/cm ^{3}) | Elastic Modulus (GPa) | Tensile Modulus (GPa) |
---|---|---|---|---|---|

SF | 30 | 50 | 7.8 | 200 | 1.2 |

BF | 12 | 20 | 2.7 | 100 | 4.5 |

Samples | A | B | C | D |
---|---|---|---|---|

Cement/(kg·m^{−3}) | 400 | 400 | 400 | 400 |

Fly ash/(kg·m^{−3}) | 100 | 100 | 100 | 100 |

Coarse aggregate/(kg·m^{−3}) | 1165 | 1165 | 1165 | 1165 |

Fine aggregate/(kg·m^{−3}) | 635 | 635 | 635 | 635 |

Water /(kg·m^{−3}) | 200 | 200 | 200 | 200 |

Water reducer/(kg·m^{−3}) | 4.5 | 4.5 | 4.5 | 4.5 |

SF/% (by volume fraction) | / | 2.0 | / | 2.0 |

BF/%(by volume fraction) | / | / | 0.1 | 0.1 |

Test Project | Specimen Dimension/mm |
---|---|

Mass loss | 100 × 100 × 100 |

Abrasion resistance | 150 × 150 × 150 |

Compressive strength test | 100 × 100 × 100 |

Flexural strength test | 400 × 100 × 100 |

Damaged layer thickness | 400 × 100 × 100 |

Relative dynamic modulus of elasticity | 400 × 100 × 100 |

Samples | a | b | R^{2} | Expected Service Life (Time) |
---|---|---|---|---|

A | 0.077 | 109.810 | 0.9791 | 175 |

B | 0.048 | 105.972 | 0.9932 | 280 |

C | 0.068 | 110.108 | 0.9889 | 205 |

D | 0.039 | 105.395 | 0.9942 | 350 |

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## Share and Cite

**MDPI and ACS Style**

Yu, J.; Yi, Z.; Zhang, Z.; Liu, D.; Ran, J.
The Effects of Hybrid Steel/Basalt Fibers on the Durability of Concrete Pavement against Freeze–Thaw Cycles. *Materials* **2023**, *16*, 7137.
https://doi.org/10.3390/ma16227137

**AMA Style**

Yu J, Yi Z, Zhang Z, Liu D, Ran J.
The Effects of Hybrid Steel/Basalt Fibers on the Durability of Concrete Pavement against Freeze–Thaw Cycles. *Materials*. 2023; 16(22):7137.
https://doi.org/10.3390/ma16227137

**Chicago/Turabian Style**

Yu, Jianqiao, Zijing Yi, Zhigang Zhang, Dawei Liu, and Junxin Ran.
2023. "The Effects of Hybrid Steel/Basalt Fibers on the Durability of Concrete Pavement against Freeze–Thaw Cycles" *Materials* 16, no. 22: 7137.
https://doi.org/10.3390/ma16227137