# The Freeze-Thaw Strength Evolution of Fiber-Reinforced Cement Mortar Based on NMR and Fractal Theory: Considering Porosity and Pore Distribution

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## Abstract

**:**

_{2}spectrum curve and porosity cumulative distribution curve showed that the freeze-thaw resistance of cement mortar increased first and then decreased with the fiber content. The optimal fiber content was approximately 0.5%. By conducting mechanical experiments, it is found that the uniaxial compressive strength (UCS) of the samples exhibited the ‘upward convex’ evolution trends with freeze-thaw cycles due to cement hydration, and based on fractal theory, the negative correlation between UCS and D

_{min}was established. Eventually, a freeze-thaw strength prediction model considering both porosity and pore distribution was proposed, which could accurately predict the strength deterioration law of cement-based materials under freeze-thaw conditions.

## 1. Introduction

## 2. Experimental Materials and Procedures

#### 2.1. Material Selection and Sample Preparation

^{3}, bulk density of 1430 kg/m

^{3}, mud content of 0.8%, and fineness modulus of 2.91. The sand passed through 4.75 mm sieve, and its particle distribution is shown in Figure 2. Water reducing agent was polycarboxylate superplasticizer, water reduction rate of 35%, gas content of 3.4%. Polyester fiber is bundle monofilament, length approximately 10 mm, diameter 13–21 mm, specific gravity 1180 kg/m

^{3}, tensile strength ≥900 MPa, fracture elongation 10–20%, elastic modulus ≥17,000 MPa.

#### 2.2. Freeze-Thaw Treatment

#### 2.3. NMR Analysis

_{2}spectrum distribution of saturated samples were obtained by using AniMR-150 NMR analysis system. The magnetic field intensity of the system is 0.3 ± 0.05 T, and the RF pulse frequency range is 2~49.9 MHz.

#### 2.4. Uniaxial Compression Tests

## 3. Experimental Results and Analysis

#### 3.1. NMR Microscopic Pore Distribution Characteristics

#### 3.1.1. T_{2} Spectrum and Porosity Cumulative Distribution Curve

_{2}spectrum by collecting the magnetic resonance signals released by hydrogen nuclei in the water medium. Finally, the porosity can be obtained by appropriate calibration of the T

_{2}spectrum [31]. Figure 3a shows the T

_{2}spectrum curve obtained in the experiment. The abscissa T

_{2}is the transverse relaxation time, which is directly related to the pore size [32], namely:

_{2}value, the larger the pore size. The ordinate is the porosity corresponding to each relaxation time point T

_{2}, and the larger the value, the larger the porosity occupied by the corresponding pore size. As can be seen from the figure, the T

_{2}spectrum curve can be roughly divided into two parts. The area with T

_{2}< 10 is classified as micropores, and the area with T

_{2}≥ 10 is classified as macropores. The area enclosed by the T

_{2}spectrum curve and the coordinate axis is proportional to the total amount of hydrogen atoms, that is, the integral sum of the curve can represent the total amount of fluid in porous media. Therefore, the porosity cumulative distribution curve shown in Figure 3b can be obtained by integral transformation of the curve in Figure 3a.

#### 3.1.2. Changes of NMR Curves under Freeze-Thaw Cycles

_{2}spectral distribution curves of cement mortars with different fiber contents after 100 freeze-thaw cycles. As the fiber content increases from 0 to 0.5% (A1–A3), the curves corresponding to macropores and micropores both drop, indicating that the fibers dispersed in the cement mortar can effectively fill the gaps between particles. When the fiber content reaches 0.75% (A4), the increased content causes the fibers to tangle more easily, and the appearance of voids in the fiber clusters leads to the increase of macropores. In addition, since fiber and cement particles belong to two kinds of substances, the interface cannot be completely contacted. The tiny pores between the interface lead to the increase of micropores. Therefore, the curve of A4 is generally higher than that of A2 and A3.

_{2}spectrum curve in Figure 4 more intuitively shows the freeze-thaw response characteristics of the internal structure and the influence of fiber on the frost resistance of cement mortar. In Figure 4a, with the increase of freeze-thaw cycles, the peak value of the micropore part roughly presents an increasing trend, indicating that the number of micropores keeps increasing. However, the number of macropores decreases first and then increases, which is attributed to cement hydration. Before 25 cycles, the cement hydration is still in progress, and the generated hydration products fill or separate a part of macropores into micropores, resulting in the decrease of macropores and the increase of micropores. After 25 cycles, the hydration is almost completed and the freeze-thaw effect is continuously enhanced, so the number of macropores increases significantly. In comparison, the change amplitude of the T

_{2}spectrum curve with freeze-thaw cycles is A3 < A2 < A4 < A1, which once again confirms that the freeze-thaw resistance of cement mortar increases first and then decreases with the fiber content. The optimal content is approximately 0.5%.

#### 3.2. UCS of Cement Mortar under Freeze-Thaw Cycles

## 4. Discussion

#### 4.1. Relationship between UCS and Porosity

#### 4.2. NMR Fractal Characteristics

_{2}spectrum curve, it can be found that the number of micropores is much larger than that of macropores. Too small of a number leads to extremely uneven distribution of macropores, so its distribution law is more difficult to characterize.

_{2}spectrum distribution curve, it can be found that after 100 freeze-thaw cycles, the curve of macropore part rises significantly, that is, the number of macropores increases, and its distribution law is easier to characterize, so ${D}_{\mathrm{max}}$ decreases. In general, the evolution law of ${D}_{\mathrm{min}}$ is more relevant to that of UCS, so the deterioration model considering the distribution state of micropores will better reflect the freeze-thaw strength evolution law of cement mortar.

## 5. Freeze-Thaw Strength Degradation Prediction Model

#### 5.1. Proposal of the Model

#### 5.2. Validation of the Model

## 6. Conclusions

- (1)
- Fiber dispersed in cement mortar can fill the gaps between particles, so the addition of fiber can effectively improve the frost resistance of cement mortar. When the fiber content exceeds 0.5%, the fibers are easily entangled into clusters. The macropores inside the fiber clusters and the micropores at the interface between fiber and cement increase, resulting in the weakening of freeze-thaw resistance of cement mortar;
- (2)
- Cement hydration causes the UCS evolution curve of cement mortar to present the ‘upward convex’ shape under freeze-thaw conditions. Hydration reaction leads to the increase of UCS, while freeze-thaw leads to the decrease of UCS. The substances produced by the chemical reaction between fibers and clinker will prolong the hydration reaction time, resulting in UCS of samples with fiber content less than 0.5% starting to decrease after 25 freeze-thaw cycles, while that of samples with fiber content more than 0.5% starting to decrease after 50 freeze-thaw cycles;
- (3)
- Based on fractal theory, it is found that the fractal dimension of micropores D
_{min}has a negative correlation with UCS under freeze-thaw conditions. The freeze-thaw strength prediction model considering both porosity and pore distribution can accurately reflect the strength evolution law of cement mortar under freeze-thaw cycles.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**T

_{2}spectrum and porosity cumulative distribution curve. (

**a**) T

_{2}spectrum curve, (

**b**) Porosity cumulative distribution curve.

**Figure 5.**T

_{2}spectral distribution curves of cement mortars with different fiber contents after 100 freeze-thaw cycles.

**Figure 9.**Changes of ${D}_{\mathrm{min}}$ and ${D}_{\mathrm{max}}$ under freeze-thaw cycles. (

**a**) ${D}_{\mathrm{min}}$ (

**b**) ${D}_{\mathrm{max}}$.

Group | Cement (kg/m ^{3}) | Sand (kg/m ^{3}) | Water (kg/m ^{3}) | Water Reducing Agent (%) | Polyester Fiber (%) |
---|---|---|---|---|---|

A1 | 360 | 760 | 162 | 0.5 | 0 |

A2 | 360 | 760 | 162 | 0.5 | 0.25 |

A3 | 360 | 760 | 162 | 0.5 | 0.5 |

A4 | 360 | 760 | 162 | 0.5 | 0.75 |

Group | Porosity Change Rate | Standard Deviation | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

0 | 25 | 50 | 75 | 100 | 0 | 25 | 50 | 75 | 100 | |

A1 | 0 | 6.826 | 20.408 | 66.106 | 97.085 | 0 | 1.767 | 0.306 | 0.447 | 3.896 |

A2 | 0 | 5.243 | 13.738 | 25.989 | 47.391 | 0 | 0.587 | 0.954 | 0.435 | 1.132 |

A3 | 0 | 5.290 | 11.696 | 21.214 | 28.268 | 0 | 1.324 | 1.496 | 0.768 | 0.952 |

A4 | 0 | 12.111 | 23.658 | 59.083 | 93.528 | 0 | 0.943 | 1.996 | 2.357 | 1.413 |

Fractal Dimension | Freeze-Thaw Cycles | ||||
---|---|---|---|---|---|

0 | 25 | 50 | 75 | 100 | |

D_{min} | 1.249 | 1.189 | 1.197 | 1.252 | 1.284 |

D_{max} | 2.979 | 2.977 | 2.977 | 2.985 | 2.949 |

Freeze-Thaw Cycles | |||||
---|---|---|---|---|---|

0 | 25 | 50 | 75 | 100 | |

W | 0 | −5.03 | −4.31 | 0.23 | 2.61 |

UCS (MPa) | 24.91 | 29.57 | 28.59 | 24.27 | 20.44 |

Model | Formula | Note |
---|---|---|

This study | $\frac{F(N)}{{F}_{0}}=\eta \cdot \mathrm{exp}[\delta \cdot \frac{1-P(N)}{1-{P}_{0}}\cdot \frac{{D}_{N,\mathrm{min}}-{D}_{0,\mathrm{min}}}{{D}_{N,\mathrm{min}}}]$ | Related to total porosity $P$ and micropore fractal dimension ${D}_{\mathrm{min}}$ |

Gao et al. [35] | $F(N)/{F}_{0}=\beta \cdot \mathrm{exp}\left[-\lambda (\Delta P)\right]$ | Related to the change in porosity $\Delta P$ |

Deng et al. [29] | $F={\beta}_{0}+{\beta}_{1}{D}_{\mathrm{max}}+{\beta}_{2}{P}_{\mathrm{max}}+{\beta}_{3}{D}_{\mathrm{max}}\times {P}_{\mathrm{max}}$ | Related to macropore porosity ${P}_{\mathrm{max}}$ and macropore fractal dimension ${D}_{\mathrm{max}}$ |

**Table 6.**The research data of Hu et al. [17].

Sample | UCS(MPa) | Porosity (%) | D_{min} |
---|---|---|---|

A | 1.427 | 15.245 | 1.637 |

B | 1.247 | 14.431 | 1.718 |

C | 1.122 | 16.634 | 1.829 |

D | 1.090 | 14.187 | 1.943 |

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**MDPI and ACS Style**

Zhang, C.; Liu, T.; Jiang, C.; Chen, Z.; Zhou, K.; Chen, L. The Freeze-Thaw Strength Evolution of Fiber-Reinforced Cement Mortar Based on NMR and Fractal Theory: Considering Porosity and Pore Distribution. *Materials* **2022**, *15*, 7316.
https://doi.org/10.3390/ma15207316

**AMA Style**

Zhang C, Liu T, Jiang C, Chen Z, Zhou K, Chen L. The Freeze-Thaw Strength Evolution of Fiber-Reinforced Cement Mortar Based on NMR and Fractal Theory: Considering Porosity and Pore Distribution. *Materials*. 2022; 15(20):7316.
https://doi.org/10.3390/ma15207316

**Chicago/Turabian Style**

Zhang, Chaoyang, Taoying Liu, Chong Jiang, Zhao Chen, Keping Zhou, and Lujie Chen. 2022. "The Freeze-Thaw Strength Evolution of Fiber-Reinforced Cement Mortar Based on NMR and Fractal Theory: Considering Porosity and Pore Distribution" *Materials* 15, no. 20: 7316.
https://doi.org/10.3390/ma15207316