# The Effects of Corrugated Steel Fiber on the Properties of Ultra-High Performance Concrete of Different Strength Levels

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Raw Materials

#### 2.2. Mix Design

#### 2.3. Mix Preparation

#### 2.4. Experimental Methods

#### 2.4.1. Compressive Strength

- F—maximum force, N;
- A—cross-sectional area, ${\mathrm{m}\mathrm{m}}^{2}$.

#### 2.4.2. Splitting Tensile Strength

- F—maximum force, N;
- A—cross-sectional area, ${\mathrm{m}\mathrm{m}}^{2}$.

#### 2.4.3. Flexural Strength

- F—maximum force, N;
- L is the distance between supports, mm;
- b, h is the width and height of cross-section, mm.

#### 2.4.4. Modulus of Elasticity and Poisson’s Coefficient

- ${\sigma}_{c}$ is the compressive stress equal to 30% of the prismatic compressive strength, MPa;
- ${\epsilon}_{1,m}$ и ${\epsilon}_{2,m}$ is the average longitudinal and transverse deformation at a stress level of 30% of the prismatic compressive strength.

#### 2.4.5. Critical Stress Intensity Factor

- $F$ is the force at cracking, MN;
- L is the distance between supports, m;
- b, t is the height and width of cross-section, m;
- ${a}_{0}$ is the notch depth, m;
- $\lambda $=${a}_{0}/b$.

#### 2.4.6. Axial Tensile Strength

## 3. Results and Discussion

#### 3.1. Compressive Strength

#### 3.2. Indirect Tensile Strength

#### 3.3. Modulus of Elasticity and Poisson’s Coefficient

#### 3.4. Critical Stress Intensity Factor

#### 3.5. Direct Tensile Test

- ${\alpha}_{0}$ is the fiber orientation factor;
- ${\alpha}_{1}$ is the fiber efficiency factor;
- ${\tau}_{f}$ is the fiber-to-matrix bond strength, MPa;
- ${V}_{f}$ is the fiber volume fraction;
- ${l}_{f}$, ${d}_{f}$ is the length and diameter of fiber, mm.

## 4. Practical Recommendations

- ${R}_{c}$ is the 28 days compressive strength of Portland cement, MPa;
- ${W/C}_{eff}$ is the effective water–cement ratio.

- ${R}_{rel}$ is the relative compressive strength of silica fume and control mixture;
- p is the percentage cement replacement by silica fume in fractions of a unit.

**a**in the equation practically does not change, resulting in a series of parallel straight lines. This fact allows us to determine the properties of UHPC/UHPFRC with any other volume content of corrugated steel fiber by the following equation:

- Y is the one of mechanical property of UHPC/UHPFRC from Figure 15;
- ${b}_{0}$ is the empirical coefficient for UHPC without steel fiber;
- ${b}_{1}$ is the increment value of coefficient ${b}_{0}$ per 1% of steel fiber.

- ${b}_{{v}_{f=2\%}}$ is the value of the coefficient b of the linear equation for the composition with 2% steel fiber;
- ${b}_{{v}_{f=0\%}}$ is the value of the coefficient b of the linear equation for the composition with 0% steel fiber.

## 5. Conclusions

- The introduction of steel fiber slightly increases compressive strength;
- There is a sharp increase in flexural strength, splitting tensile strength and critical stress intensity factor with the introduction of steel fiber. This is due to the fact that the fiber takes up the load after the formation of a crack in the concrete matrix;
- A slight increase in elastic modulus with the introduction of steel fiber is observed, which is consistent with the well-known “rule of mixtures”;
- It is found that the Poisson’s ratio is independent of the strength of UHPC and the presence of steel fiber. The average value obtained in this work is 0.2;
- From the axial tensile tests carried out, it is found that an increase in UHPC compressive strength leads to a proportional increase in cracking stress and tensile strength of UHPFRC. The fracture energy during strain-hardening and during softening also increases with the increasing strength of the UHPC matrix.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Critical stress intensity factor determination scheme. Dimensions are expressed in millimeters.

**Figure 6.**(

**a**) Shape and dimensions (in millimeters) of test specimens; (

**b**) Specimen in the testing machine.

**Figure 9.**Effect of steel fiber addition on indirect tensile strength of different UHPC mixes: (

**a**) splitting tensile strength; (

**b**) flexural strength.

**Figure 10.**Effect of steel fiber addition deformability of different UHPC mixes: (

**a**) modulus of elasticity; (

**b**) Poisson’s coefficient.

**Figure 11.**Relationship between modulus elasticity and compressive strength of UHPC with and without steel fiber.

**Figure 12.**Effect of steel fiber addition on critical stress intensity factor of different UHPC mixes.

**Figure 13.**Direct tensile test results: (

**a**,

**b**) stress–strain and stress–crack opening for mix I-F; (

**c**,

**d**) stress–strain and stress–crack opening for mix II-F; (

**e**,

**f**) stress–strain and stress–crack opening for mix III-F.

**Figure 17.**Properties of UHPC and UHPFRC depending on $\phi $: (

**a**) compressive strength; (

**b**) splitting tensile strength; (

**c**) flexural strength; (

**d**) modulus of elasticity; (

**e**) Poisson’s coefficient; (

**f**) critical stress intensity factor; (

**g**) direct tensile strength.

**Figure 18.**Comparison of experimental data with those obtained from the Equation (16): (

**a**) compressive strength; (

**b**) splitting tensile strength; (

**c**) flexural strength; (

**d**) modulus of elasticity; (

**e**) critical stress intensity factor.

Cement ID | $\mathbf{Density},\mathbf{k}\mathbf{g}/{\mathbf{m}}^{3}$ | $\mathbf{Fineness},{\mathbf{m}}^{2}/\mathbf{k}\mathbf{g}$ | 28 Days Compressive Strength, MPa | ${\mathit{C}}_{3}\mathit{S}$, % | ${\mathit{C}}_{2}\mathit{S}$, % | ${\mathit{C}}_{3}\mathit{A}$, % | ${\mathit{C}}_{4}\mathit{A}\mathit{F}$, % |
---|---|---|---|---|---|---|---|

${C}_{1}$ | 2960 | 468.2 | 48.3 | 69.9 | 8.4 | 4.9 | 12.5 |

${C}_{2}$ | 3110 | 409.3 | 56.0 | 60.4 | 8.07 | 4.9 | 11.7 |

${C}_{3}$ | 3100 | 497.1 | 66.5 | 70.8 | 19.5 | 6.0 | 1.0 |

Fraction | $\mathbf{Density},\mathbf{k}\mathbf{g}/{\mathbf{m}}^{3}$ | $\mathbf{Bulk}\mathbf{Density},\mathbf{k}\mathbf{g}/{\mathbf{m}}^{3}$ | Mean Particle Size, mm | Packing Density, - |
---|---|---|---|---|

0.1–0.4 | 2637 | 1403 | 0.25 | 0.532 |

0.4–0.8 | 2632 | 1524 | 0.60 | 0.579 |

Powder | $\mathbf{Density},\mathbf{k}\mathbf{g}/{\mathbf{m}}^{3}$ | $\mathbf{Fineness},{\mathbf{m}}^{2}/\mathbf{k}\mathbf{g}$ |
---|---|---|

Limestone powder (LP) | 2715 | 281.2 |

Quartz powder (QP) | 2650 | 429.6 |

Silica fume (SF) | 2200 | 17000 |

Component | I | II | III | I-F | II-F | III-F |
---|---|---|---|---|---|---|

${C}_{1}$ | 850 | - | - | 832 | - | - |

${C}_{2}$ | - | 796 | - | - | 780 | - |

${C}_{3}$ | - | - | 803 | - | - | 787 |

LP | 213 | - | - | 208 | - | - |

QP | - | 200 | 200 | - | 195 | 197 |

SF | 128 | 200 | 200 | 125 | 195 | 197 |

Sand 0.1–0.4 | 295 | 285 | 290 | 287 | 280 | 283 |

Sand 0.4–0.8 | 685 | 670 | 675 | 670 | 655 | 661 |

Water | 195 | 191 | 177 | 191 | 187 | 173 |

SP | 26 | 29 | 36 | 29 | 31 | 39 |

Steel fiber | - | - | - | 156 | 156 | 156 |

W/C | 0.23 | 0.24 | 0.22 | 0.23 | 0.24 | 0.22 |

SP/C | 0.031 | 0.036 | 0.045 | 0.035 | 0.040 | 0.050 |

SF/C | 0.15 | 0.15 | 0.25 | 0.15 | 0.25 | 0.25 |

Property | I | I-F | II | II-F | III | III-F |
---|---|---|---|---|---|---|

${f}_{c}$, MPa | 143.4 | 152.1 | 152.3 | 163.6 | 177.0 | 189.8 |

${f}_{ct,sp}$, MPa | 6.52 | 11.44 | 6.72 | 12.45 | 8.79 | 14.20 |

${f}_{ct,fl}$, MPa | 9.13 | 24.04 | 10.68 | 25.51 | 15.26 | 28.43 |

${f}_{ct,cr}$, MPa | - | 7.43 | - | 8.51 | - | 9.03 |

${f}_{ct,loc}$, MPa | - | 8.49 | - | 9.87 | - | 11.55 |

${g}_{f,A}$, $\mathrm{k}\mathrm{J}/{\mathrm{m}}^{3}$ | - | 8.06 | - | 23.81 | - | 28.12 |

${G}_{f,B}$, $\mathrm{k}\mathrm{J}/{\mathrm{m}}^{2}$ | - | 9.02 | - | 11.63 | - | 14.10 |

${E}_{c}$, GPa | 44.4 | 47.4 | 43.3 | 46.2 | 47.1 | 49.6 |

${\nu}_{c}$, - | 0.22 | 0.21 | 0.19 | 0.19 | 0.20 | 0.19 |

${K}_{I,c}$, $\mathrm{M}\mathrm{P}\mathrm{a}\xb7\sqrt{\mathrm{m}}$ | 0.929 | 2.856 | 1.001 | 3.122 | 1.164 | 3.353 |

Compressive Strength Range, MPa | Equation | References | |
---|---|---|---|

38–235 | ${E}_{c}=(9\xb7{\left({f}_{c}\right)}^{1.45}+\mathrm{35,120})/1000$ | (8) | [59] |

120–256 | ${E}_{c}=3.565\xb7{\left({f}_{c}\right)}^{0.5}$ | (9) | [60] |

127–200 | ${E}_{c}=(9100\xb7{\left({f}_{c}\right)}^{0.33})/1000$ | (10) | [61] |

№ | Percentage Cement Replacement | Compressive Strength Range, MPa | ${\mathit{K}}_{\mathit{e}\mathit{f}\mathit{f}}$ | References |
---|---|---|---|---|

1 | 0.15 | 110–160 | 1.37 | Author’s results |

2 | 0.25 | 0.94 | ||

3 | 0.15 | 1.53 | ||

4 | 0.25 | 1.18 | ||

5 | 0.25 | 0.88 | ||

6 | 0.30 | 0.80 | ||

7 | 0.10 | 89–115 | 2.91 | [67] |

8 | 0.20 | 2.46 | ||

9 | 0.25 | 1.99 | ||

10 | 0.05 | 81–92 | 3.72 | [70] |

11 | 0.08 | 124–138 | 2.40 | [71] |

12 | 0.16 | 89–96 | 0.87 | [72] |

13 | 0.25 | 0.98 | ||

14 | 0.16 | 0.99 | ||

15 | 0.25 | 0.81 | ||

16 | 0.05 | 96–109 | 2.34 | [73] |

17 | 0.10 | 2.31 | ||

18 | 0.15 | 1.89 | ||

19 | 0.20 | 1.71 | ||

20 | 0.25 | 1.56 | ||

21 | 0.05 | 71–72 | 3.35 | [74] |

22 | 0.075 | 2.32 | ||

23 | 0.10 | 82–105 | 2.95 | [75] |

24 | 0.20 | 2.40 | ||

25 | 0.30 | 1.73 | ||

26 | 0.05 | 101–129 | 2.58 | [76] |

27 | 0.10 | 2.19 | ||

28 | 0.15 | 2.19 | ||

29 | 0.20 | 2.39 | ||

30 | 0.25 | 2.03 |

Mix | p, - | ${\mathit{K}}_{\mathit{e}\mathit{f}\mathit{f}}$.- | $\mathit{\phi}$, MPa |
---|---|---|---|

I | 0.13 | 2.05 | 266 |

II | 0.20 | 1.63 | 309 |

III | 0.20 | 1.63 | 401 |

Parameter | a | ${\mathit{b}}_{0}$ | ${\mathit{b}}_{1}$ |
---|---|---|---|

${f}_{c}$ | 0.265 | 75 | 1.0 |

${f}_{ct,sp}$ | 0.019 | 1.6 | 2.3 |

${f}_{ct,fl}$ | 0.040 | −3.4 | 9.4 |

${\nu}_{c}$ | - | - | - |

${E}_{c}$ | 0.022 | 37.3 | 2.1 |

${K}_{I,c}$ | 0.0027 | 0.46 | 0.8 |

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## Share and Cite

**MDPI and ACS Style**

Soloviev, V.; Matiushin, E.
The Effects of Corrugated Steel Fiber on the Properties of Ultra-High Performance Concrete of Different Strength Levels. *Buildings* **2023**, *13*, 2591.
https://doi.org/10.3390/buildings13102591

**AMA Style**

Soloviev V, Matiushin E.
The Effects of Corrugated Steel Fiber on the Properties of Ultra-High Performance Concrete of Different Strength Levels. *Buildings*. 2023; 13(10):2591.
https://doi.org/10.3390/buildings13102591

**Chicago/Turabian Style**

Soloviev, Vadim, and Evgenii Matiushin.
2023. "The Effects of Corrugated Steel Fiber on the Properties of Ultra-High Performance Concrete of Different Strength Levels" *Buildings* 13, no. 10: 2591.
https://doi.org/10.3390/buildings13102591