# The Influence of the Rebound Hammer Test Location on the Estimation of Compressive Strength of a Historical Solid Clay Brick

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Materials

#### 2.2. Testing Methods

- (a)
- from all locations of the specimen on original and cut faces,
- (b)
- from all locations of the specimen on original face only,
- (c)
- from all locations of the specimen on cut face only,
- (d)
- from middle face of the specimen on original and cut faces,
- (e)
- from middle face of the specimen on original face only,
- (f)
- from middle face of the specimen on cut face only.

_{max}) achieved is recorded. The compressive strength of masonry is calculated to the nearest 0.1 MPa using the following formula:

_{i}is the loaded cross-section of an individual masonry specimen.

_{b}, the compressive strength of masonry units is multiplied by a shape factor (δ), given in Annex A of EN 772-1 [2], wherein the width and height should be determined in accordance with EN 772-16 [14]. The purpose of this test is to validate the rebound hammer test results and check if it is within the confidence limit of ±25% [12].

## 3. Results and Discussion

#### 3.1. Rebound Hammer Test

#### 3.2. Standard Compression Test

#### 3.3. Comparative Study of the Test Results

^{2}), which are found in Figure 10 and Figure 11.

## 4. Conclusions

- The average rebound value obtained from all locations varies with face type except in specimen 4A.
- The rebound value from cut face is lesser than original face value except at specimen 6A.
- In the case of average rebound value obtained from middle points, the influence of face type is not significant due to the closeness of the results except for specimen 4A.
- The estimated compressive strength from all points of original face is the least convergent to the normalized mean compressive strength.
- The compressive strength obtained from case (d) is the closest one to the normalized mean compressive strength.
- The estimation error of compressive strength at the middle face is within and around the confidence limits of ±25%.
- An accurate estimation of the compressive strength can be achieved by taking the rebound hammer test at the middle points of the specimen regardless of the face type.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Characteristic curve for concrete and rebound hammer model: N/NR [11].

**Figure 10.**Relationship between estimated compressive strength from middle points. (

**A**) The correlation of compressive strength at middle points (d) and (e); (

**B**) The correlation of compressive strength at middle points (d) and (f).

**Figure 11.**Estimated versus normalized mean compressive strength. (

**A**) Compressive strength at middle points (d); (

**B**) Compressive strength at middle points (f).

**Figure 12.**Error in compressive strength estimation. (

**A**) Closeness of estimation error between middle points (d) and (f); (

**B**) Closeness of estimation error between middle points (d) and (e).

Brick from 2018 | Brick from ca. 1780 | ||||||||
---|---|---|---|---|---|---|---|---|---|

Element Number | Element Symbol | Element Name | Atomic Conc. | Weight Conc. | Element Number | Element Symbol | Element Name | Atomic Conc. | Weight Conc. |

8 | O | Oxygen | 70.38 | 46.95 | 8 | O | Oxygen | 75.97 | 55.52 |

14 | Si | Silicon | 13.89 | 16.27 | 14 | Si | Silicon | 14.46 | 18.56 |

35 | Br | Bromine | 4.73 | 15.77 | 35 | Br | Bromine | 3.88 | 14.18 |

20 | Ca | Calcium | 4.60 | 7.68 | 38 | Sr | Strontium | 1.12 | 4.49 |

26 | Fe | Iron | 2.15 | 5.01 | 19 | K | Potassium | 1.67 | 2.99 |

12 | Mg | Magnesium | 2.01 | 2.03 | 20 | Ca | Calcium | 1.47 | 2.70 |

38 | Sr | Strontium | 1.31 | 4.78 | 12 | Mg | Magnesium | 1.42 | 1.58 |

19 | K | Potassium | 0.93 | 1.52 |

Specimen | Dimension [mm] | Dry Mass, m_{d} [kg] | Dry Density ρ_{d} [kg/m^{3}] | Wet Mass, m_{w} [kg] | Water Absorption, % [10] ${\mathit{w}}_{\mathit{m}}=\frac{{\mathit{m}}_{\mathit{w}}-{\mathit{m}}_{\mathit{d}}}{{\mathit{m}}_{\mathit{d}}}\times 100\mathit{\%}$ | |||
---|---|---|---|---|---|---|---|---|

L | W | H | ||||||

1A | 250 | 120 | 65 | 3.243 | 1663 | 3.925 | 21 | Average = 20.5 |

2A | 250 | 120 | 65 | 3.187 | 1634 | 3.844 | 21 | |

3A | 250 | 120 | 65 | 3.290 | 1687 | 3.947 | 20 | |

4A | 250 | 120 | 65 | 3.122 | 1601 | 3.758 | 20 | |

5A | 295 | 145 | 65 | 4.142 | 1490 | 5.059 | 22 | Average = 21.5 |

6A | 295 | 145 | 65 | 4.199 | 1540 | 5.114 | 22 | |

7A | 295 | 145 | 65 | 4.001 | 1439 | 4.798 | 20 | |

8A | 295 | 145 | 65 | 4.172 | 1500 | 5.076 | 22 |

Specimen | Dimension [mm] | Specimen | Dimension [mm] | ||||
---|---|---|---|---|---|---|---|

L | W | H | L | W | H | ||

1A | 124.2 | 102.4 | 78.7 | 5A | 142.0 | 102.8 | 78.5 |

2A | 123.4 | 101.5 | 81.95 | 6A | 137.1 | 102.5 | 83.3 |

3A | 119.2 | 103.7 | 79.9 | 7A | 144.9 | 103.7 | 82.1 |

4A | 124.0 | 101.8 | 75.6 | 8A | 141.5 | 102.6 | 68.9 |

Specimen | Rebound Hammer Values | Tested Surface Type | ||
---|---|---|---|---|

Middle Face | Right Edge | Left Edge | ||

1A | 39 | 26 | 26 | Cut face |

40 | 30 | 37 | Original face | |

40 | 34 | 25 | Cut face | |

42 | 40 | 32 | Original face | |

2A | 37 | 25 | 23 | Cut face |

42 | 43 | 26 | Original face | |

46 | 30 | 32 | Cut face | |

34 | 28 | 35 | Original face | |

3A | 33 | 26 | 27 | Cut face |

40 | 32 | 30 | Original face | |

46 | 33 | 30 | Cut face | |

44 | 33 | 33 | Original face | |

4A | 36 | 31 | 36 | Cut face |

48 | 34 | 31 | Original face | |

39 | 37 | 36 | Cut face | |

42 | 29 | 36 | Original face | |

5A | 38 | 30 | 25 | Cut face |

38 | 42 | 34 | Original face | |

42 | 33 | 35 | Cut face | |

40 | 38 | 34 | Original face | |

6A | 42 | 30 | - | Cut face |

40 | 32 | 28 | Original face | |

40 | 28 | 26 | Cut face | |

40 | 33 | 25 | Original face | |

7A | 42 | 27 | - | Cut face |

38 | 36 | 32 | Original face | |

42 | 37 | 33 | Cut face | |

39 | - | - | Original face | |

8A | 34 | 30 | 26 | Cut face |

41 | 42 | 34 | Original face | |

40 | 33 | 31 | Cut face | |

42 | 39 | 40 | Original face |

Specimen | Average Rebound Value [R] | |||||
---|---|---|---|---|---|---|

Original and Cut Faces | Original Face Only | Cut Face Only | ||||

All Points (a) | Middle Points (d) | All Points (b) | Middle Points (e) | All Points (c) | Middle Points (f) | |

1A | 34 | 40 | 37 | 41 | 31 | 40 |

2A | 33 | 40 | 35 | 38 | 31 | 42 |

3A | 34 | 41 | 35 | 42 | 31 | 40 |

4A | 36 | 41 | 36 | 45 | 36 | 38 |

5A | 36 | 40 | 39 | 39 | 34 | 40 |

6A | 33 | 41 | 31 | 40 | 33 | 41 |

7A | 36 | 40 | 37 | 39 | 35 | 42 |

8A | 36 | 39 | 40 | 42 | 32 | 37 |

Specimen | Correlation between Rebound Value and Compressive Strength | |||||||
---|---|---|---|---|---|---|---|---|

Original and Cut Faces | Original Face Only | Cut Face Only | ||||||

Middle Points (d) | All Points (b) | Middle Points (e) | Middle Points (f) | |||||

R | ${\mathit{f}}_{\mathit{c}\mathit{k}}{}_{\mathit{B}\mathit{i}\mathit{r}\mathit{c}\mathit{k}}\left[\mathit{M}\mathit{P}\mathit{a}\right]$ | R | ${\mathit{f}}_{\mathit{c}\mathit{k}}{}_{\mathit{B}\mathit{i}\mathit{r}\mathit{c}\mathit{k}}\left[\mathit{M}\mathit{P}\mathit{a}\right]$ | R | ${\mathit{f}}_{\mathit{c}\mathit{k}}{}_{\mathit{B}\mathit{i}\mathit{r}\mathit{c}\mathit{k}}\left[\mathit{M}\mathit{P}\mathit{a}\right]$ | R | ||

1A | 40 | 12.7 | 37 | 11.1 | 41 | 13.1 | 40 | 12.7 |

2A | 40 | 13.0 | 35 | 10.1 | 38 | 11.8 | 42 | 14.0 |

3A | 41 | 12.9 | 35 | 9.8 | 42 | 13.5 | 40 | 12.6 |

4A | 41 | 12.5 | 36 | 10.0 | 45 | 14.7 | 38 | 11.0 |

5A | 40 | 14.6 | 39 | 13.9 | 39 | 13.9 | 40 | 14.6 |

6A | 41 | 15.3 | 31 | 9.4 | 40 | 14.9 | 41 | 15.3 |

7A | 40 | 15.7 | 37 | 13.6 | 39 | 15.0 | 42 | 16.8 |

8A | 39 | 12.2 | 40 | 12.7 | 42 | 13.7 | 37 | 11.0 |

Specimen | Dimension [mm] | Shape Factor, δ | Compressive Strength, fc [MPa] | $\mathbf{Normalized}\mathbf{Mean}\mathbf{Compressive}\mathbf{Strength},{\mathbf{f}}_{\mathbf{b}}\left[\mathbf{MPa}\right]{\mathit{f}}_{\mathit{b}}=\mathit{\delta}{\mathit{f}}_{\mathit{c}}$ | |
---|---|---|---|---|---|

W | H | ||||

1A | 124.2 | 78.7 | 0.861 | 15.5 | 13.3 |

2A | 123.4 | 81.95 | 0.876 | 15.4 | 13.5 |

3A | 119.2 | 79.9 | 0.876 | 17.3 | 15.2 |

4A | 124 | 75.6 | 0.847 | 16.7 | 14.2 |

5A | 142 | 78.5 | 0.824 | 17.3 | 14.2 |

6A | 137.1 | 83.3 | 0.854 | 18.8 | 16.0 |

7A | 144.9 | 82.1 | 0.834 | 24.5 | 20.4 |

8A | 141.5 | 68.9 | 0.784 | 16.3 | 12.8 |

Specimen | Estimated Compressive Strength [MPa] | Normalized Mean Compressive Strength [MPa] | |||
---|---|---|---|---|---|

Original and Cut Faces | Original Face Only | Cut Face Only | |||

Middle Points (d) | All Points (b) | Middle Points (e) | Middle Points (f) | ||

1A | 12.7 | 11.1 | 13.1 | 12.7 | 13.3 |

2A | 13.0 | 10.1 | 11.8 | 14.0 | 13.5 |

3A | 12.9 | 9.8 | 13.5 | 12.6 | 15.2 |

4A | 12.5 | 10.0 | 14.7 | 11.0 | 14.2 |

5A | 14.6 | 13.9 | 13.9 | 14.6 | 14.2 |

6A | 15.3 | 9.4 | 14.9 | 15.3 | 16.0 |

7A | 15.7 | 13.6 | 15.0 | 16.8 | 20.4 |

8A | 12.2 | 12.7 | 13.7 | 11.0 | 12.8 |

Specimen | Error in Estimation of Compressive Strength [%] | |||
---|---|---|---|---|

Original and Cut Faces | Original Face Only | Cut Face Only | ||

Middle Point (d) | All Points (b) | Middle Points (e) | Middle Points (f) | |

1A | −5 | −17 | −2 | −5 |

2A | −3 | −25 | −12 | 4 |

3A | −15 | −36 | −11 | −17 |

4A | −12 | −29 | 4 | −22 |

5A | 2 | −2 | −2 | 2 |

6A | −5 | −41 | −7 | −5 |

7A | −23 | −33 | −27 | −17 |

8A | −7 | −1 | 7 | −14 |

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**MDPI and ACS Style**

Mengistu, G.M.; Gyurkó, Z.; Nemes, R.
The Influence of the Rebound Hammer Test Location on the Estimation of Compressive Strength of a Historical Solid Clay Brick. *Solids* **2023**, *4*, 71-86.
https://doi.org/10.3390/solids4010005

**AMA Style**

Mengistu GM, Gyurkó Z, Nemes R.
The Influence of the Rebound Hammer Test Location on the Estimation of Compressive Strength of a Historical Solid Clay Brick. *Solids*. 2023; 4(1):71-86.
https://doi.org/10.3390/solids4010005

**Chicago/Turabian Style**

Mengistu, Girum Mindaye, Zoltán Gyurkó, and Rita Nemes.
2023. "The Influence of the Rebound Hammer Test Location on the Estimation of Compressive Strength of a Historical Solid Clay Brick" *Solids* 4, no. 1: 71-86.
https://doi.org/10.3390/solids4010005