# The Prediction of Compressive Strength and Compressive Stress–Strain of Basalt Fiber Reinforced High-Performance Concrete Using Classical Programming and Logistic Map Algorithm

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### Experimental Materials and Mixing Method

^{3}. The initial setting time of the cement was 60 min, and the final setting time was 600 min. Table 1 shows the chemical compounds of Cement M500 manufactured by Novoroscement factory, Novorossiysk, Russia. The crushed granite with a particle size range of 20 mm to 5 mm with specific gravity (2853 Kg/m

^{3}), and the granulometric curves of the coarse aggregates is shown in Figure 2. Quartz sands with a particle size range of 0.8 mm to 2.0 mm were mixed with concrete, and they were collected from the Ryazan region. The specific gravity of the fine aggregates was 2384 Kg/m

^{3}, and the granulometric curves are illustrated in Figure 3. Two kinds of aggregates were produced by the SUKHOGRUZ Company. SILVERBOND 50 quartz flour manufactured by SIBELCO in the Antwerp, Belgiumwas used. Micro-silica-type MK85 from the Novolipetsk steel company (NLMK) in Lipetsk, Russia was added to the concrete type to cover the holes between the aggregate and cement paste (Table 2, the properties of micro silica). The addition of silica to concrete can provide concrete properties with a high density. Moreover, the smaller silica grain size causes the higher density of the concrete, which is beneficial for the preparation of BFHPC [17]. Kamenny Vek’s chopped BF was used as the additional fibers (Figure 4 and Table 3).

#### 2.2. Mathematical Modeling

#### 2.3. Research Methodology

#### 2.4. OtherPrediction Compressive Stress-Strength Models

## 3. Results

#### 3.1. Experimental Material Results

#### 3.2. Compressive Strength Prediction

#### 3.3. The Stress–Strain Curve Prediction

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The Algorithm of different programming types: (

**a**) the CP method; (

**b**) the AI programming method.

**Figure 5.**Mixing design devices: (

**a**) Pan Mixer; (

**b**) Concrete formwork; (

**c**) Moist Cabinet; (

**d**) cleaning method.

**Figure 7.**The similarity between (

**a**) Logistic Map; and (

**b**) the ideological compressive stress–strain curve.

**Figure 8.**The conception of ideological compressive strength of the stress–strain curve is considered by the Logic Map.

**Figure 10.**The relationship between BF percentages and compressive strength through Polynomial Function.

**Figure 13.**Compression Strength Failure Shapes: (

**a**) Basalt Fiber reinforced High-Performance Concrete PC; (

**b**) High-Performance Concrete.

**Figure 16.**Flexural Strength Failure Shapes: (

**a**) Basalt Fiber reinforced High-Performance Concrete; (

**b**) High-Performance Concrete.

Oxide (%) | Fineness (m^{2}/kg) | Relative Density | |||||||
---|---|---|---|---|---|---|---|---|---|

SiO_{2} | Fe_{2}O_{3} | MgO | SO_{3} | Al_{2}O_{3} | CaO | K_{2}O | LOI | ||

19.52 | 4.04 | 4.36 | 2.89 | 4.81 | 62.18 | 0.6 | 1.62 | 387 | 3.14 |

Index | Value (%) |
---|---|

Appearance | Approximate Value |

Mass fraction of micro silica in the cross.dryprod.,% | not less than 99.6 |

Mass fraction of water,% | no more than 0.36 |

Mass fraction of losses on ignition (pp),% | no more than 0.80 |

Bulk density, kg/m^{3} | 152.2 |

Chemical Composition | Percentage |

Mass fraction of silicon dioxide (SiO_{2}) | 90–92 |

Mass fraction of alumina (Al_{2}O_{3}) | 0.68 |

Mass fraction of iron oxide (Fe_{2}O_{3}) | 0.69 |

Mass fraction of calcium oxide (CaO) | 1.58 |

Mass fraction of Magnesium oxide (MgO) | 1.01 |

Mass fraction of Sodium oxide (Na_{2}O) | 0.61 |

Mass fraction of potassium oxide (K_{2}O) | 1.23 |

Mass fraction of Carbon (C) | 0.98 |

Mass fraction of Sulfur (S) | 0.26 |

Length (mm) | Diameter (µm) | Tensile Strength (MPa) | Young’s Modulus (GPa) | Elongation (%) | Specific Gravity |
---|---|---|---|---|---|

18 | 17.9 | 4100–4840 | 93.1–110 | 3.1 | 2.63–2.8 |

Specimens | Cement (Kg/m ^{3}) | Water (Kg/m ^{3}) | Granit (Gravel/Couse Aggregate) (Kg/m ^{3}) | Quartz Sand (Fine Aggregate) (Kg/m ^{3}) | Micro Silica (Kg/m ^{3}) | Quartz Flour (Kg/m ^{3}) | Plasticizing (Kg/m ^{3}) | Basalt Fiber (%) |
---|---|---|---|---|---|---|---|---|

BFHPC | 500 | 187.5 | 1005 | 585 | 125 | 100 | 12.5 | _ |

BFHPC-6 | 500 | 187.5 | 1005 | 585 | 125 | 100 | 12.5 | 0.6 |

BFHPC-9 | 500 | 187.5 | 1005 | 585 | 125 | 100 | 12.5 | 0.9 |

BFHPC-1.2 | 500 | 187.5 | 1005 | 585 | 125 | 100 | 12.5 | 1.2 |

BFHPC-1.5 | 500 | 187.5 | 1005 | 585 | 125 | 100 | 12.5 | 1.5 |

BFHPC-1.8 | 500 | 187.5 | 1005 | 585 | 125 | 100 | 12.5 | 1.8 |

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**MDPI and ACS Style**

Hematibahar, M.; Vatin, N.I.; Ashour Alaraza, H.A.; Khalilavi, A.; Kharun, M.
The Prediction of Compressive Strength and Compressive Stress–Strain of Basalt Fiber Reinforced High-Performance Concrete Using Classical Programming and Logistic Map Algorithm. *Materials* **2022**, *15*, 6975.
https://doi.org/10.3390/ma15196975

**AMA Style**

Hematibahar M, Vatin NI, Ashour Alaraza HA, Khalilavi A, Kharun M.
The Prediction of Compressive Strength and Compressive Stress–Strain of Basalt Fiber Reinforced High-Performance Concrete Using Classical Programming and Logistic Map Algorithm. *Materials*. 2022; 15(19):6975.
https://doi.org/10.3390/ma15196975

**Chicago/Turabian Style**

Hematibahar, Mohammad, Nikolai Ivanovich Vatin, Hayder Abbas Ashour Alaraza, Aghil Khalilavi, and Makhmud Kharun.
2022. "The Prediction of Compressive Strength and Compressive Stress–Strain of Basalt Fiber Reinforced High-Performance Concrete Using Classical Programming and Logistic Map Algorithm" *Materials* 15, no. 19: 6975.
https://doi.org/10.3390/ma15196975