# Relationship of Time-Dependent Parameters from Destructive and Non-Destructive Tests of Structural Concrete

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Properties of Concrete

#### 2.2. Destructive Testing Methods

#### 2.3. Non-Destructive Testing Methods

#### 2.4. Correlation and Regression Analysis

^{2}are varied. For example, a value of 0.82 to 1 is reported to indicate a very strong fit, a value of 0.5 to 0.81 is a strong fit, and lower values are moderate or weak fits [39]. Therefore, the value of 0.8 was chosen as the boundary where linear correlation is sufficient, and there is no need to look for a quadratic equation.

## 3. Results

^{2}. Further analysis of the results was performed at the level of application of linear regression and best-fit analysis using the coefficient of determination. In case of low agreement, quadratic regression was applied.

#### 3.1. Time-Dependent Results

#### 3.2. Bulk and Surface Electrical Resistivity

#### 3.3. Compressive Strength vs. Electrical Resistivity

#### 3.4. Compressive Strength vs. Modulus of Elasticity

#### 3.5. Dynamic Modulus of Elasticity vs. Electrical Resistivity

#### 3.6. Static Modulus of Elasticity vs. Electrical Resistivity

#### 3.7. Summary of Results

## 4. Discussion

## 5. Conclusions

- NDT methods generally correlate well linearly with compressive strength;
- In case of further comparisons, a quadratic curve had to be applied;
- The quadratic regression between the dynamic modulus and the electrical resistivity showed a highly significant agreement;
- The worst values were observed between static modulus and both non-destructive methods.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Linear regression analysis of the relationship between surface and bulk electrical resistivity on large and small cylindrical samples (LC = Large Cylinders, SC = Small Cylinders).

**Figure 6.**Linear regression analysis of the relationship between bulk electrical resistivity and compressive strength (LC = Large Cylinders, SC = Small Cylinders).

**Figure 7.**Linear regression analysis of the relationship between modulus of elasticity and compressive strength (D = Dynamic, S = Static).

**Figure 8.**Quadratic regression analysis of the relationship between modulus of elasticity and compressive strength (D = Dynamic, S = Static).

**Figure 9.**Linear regression analysis of the relationship between bulk electrical resistivity and dynamic modulus of elasticity (LC = Large Cylinders, SC = Small Cylinders).

**Figure 10.**Quadratic regression analysis of the relationship between bulk electrical resistivity and dynamic modulus of elasticity (LC = Large Cylinders, SC = Small Cylinders).

**Figure 11.**Linear regression analysis of the relationship between bulk electrical resistivity and dynamic modulus of elasticity (LC = Large Cylinders, SC = Small Cylinders).

**Figure 12.**Quadratic regression analysis of the relationship between bulk electrical resistivity and dynamic modulus of elasticity (LC = Large Cylinders, SC = Small Cylinders).

First Parameter | Second Parameter | PCC |
---|---|---|

Small cylinder surface electrical resistivity | Small cylinder bulk electrical resistivity | 0.99 |

Large cylinder surface electrical resistivity | Large cylinder bulk electrical resistivity | 0.99 |

Compressive strength | Small cylinder bulk electrical resistivity | 0.96 |

Compressive strength | Large cylinder bulk electrical resistivity | 0.94 |

Compressive strength | Dynamic modulus of elasticity | 0.85 |

Compressive strength | Static modulus of elasticity | 0.78 |

Dynamic modulus of elasticity | Small cylinder bulk electrical resistivity | 0.77 |

Dynamic modulus of elasticity | Large cylinder bulk electrical resistivity | 0.68 |

Static modulus of elasticity | Small cylinder bulk electrical resistivity | 0.75 |

Static modulus of elasticity | Large cylinder bulk electrical resistivity | 0.65 |

**Table 2.**The value of the regression analysis results (not app. means that quadratic regression was not necessary).

First Parameter | Second Parameter | R^{2} from Linear Regression | R^{2} from Quadratic Regression |
---|---|---|---|

Small cylinder surface electrical resistivity | Small cylinder bulk electrical resistivity | 0.983 | not app. |

Large cylinder surface electrical resistivity | Large cylinder bulk electrical resistivity | 0.977 | not app. |

Compressive strength | Small cylinder bulk electrical resistivity | 0.928 | not app. |

Compressive strength | Large cylinder bulk electrical resistivity | 0.892 | not app. |

Compressive strength | Dynamic modulus of elasticity | 0.716 | 0.857 |

Compressive strength | Static modulus of elasticity | 0.602 | 0.606 |

Dynamic modulus of elasticity | Small cylinder bulk electrical resistivity | 0.595 | 0.981 |

Dynamic modulus of elasticity | Large cylinder bulk electrical resistivity | 0.453 | 1.000 |

Static modulus of elasticity | Small cylinder bulk electrical resistivity | 0.728 | 0.867 |

Static modulus of elasticity | Large cylinder bulk electrical resistivity | 0.595 | 0.780 |

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Lehner, P.; Hrabová, K. Relationship of Time-Dependent Parameters from Destructive and Non-Destructive Tests of Structural Concrete. *Mathematics* **2022**, *10*, 460.
https://doi.org/10.3390/math10030460

**AMA Style**

Lehner P, Hrabová K. Relationship of Time-Dependent Parameters from Destructive and Non-Destructive Tests of Structural Concrete. *Mathematics*. 2022; 10(3):460.
https://doi.org/10.3390/math10030460

**Chicago/Turabian Style**

Lehner, Petr, and Kristýna Hrabová. 2022. "Relationship of Time-Dependent Parameters from Destructive and Non-Destructive Tests of Structural Concrete" *Mathematics* 10, no. 3: 460.
https://doi.org/10.3390/math10030460