# Probabilistic Conversion of the Compressive Strength of Cubes to Cylinders of Natural and Recycled Aggregate Concrete Specimens

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## Abstract

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## 1. Introduction

## 2. Research Significance and Goals

- Evaluate the suitability of the cubic to cylindrical NAC conversion factors of Eurocode 2 and EN-206 for RAC with recycled aggregates (RA) sourced from concrete waste;
- Propose a conservative deterministic factor for RAC cube to cylinder strength conversions;
- Propose a probability distribution suitable for RAC strength conversions allowing the use of data from RAC cubic specimens for reliability analyses, including RAC code calibrations.

## 3. Background

## 4. RAC Size Effects

- The higher heterogeneity of the RA may contribute to higher fracture energies in low to medium strength concrete (when compared to NAC with the same compressive strength), since aggregate heterogeneity is related to tortuous fracture surfaces [16];
- The lower stiffness of the RA results in higher strains at peak stress [28], changing stress-strain relationships, stress paths, and damage pattern;
- The lower stiffness of the RA also results in lower E of RAC, increasing the friction between the test plates and the specimen (the reason for the higher confinement of cubes in comparison to cylinders) [29];
- For the same compressive strength of NAC, the relative strength of the ITZ of RAC is higher, since the hydration products of the ITZ tend to be denser and “nailed” to the attached mortar of the RA [11,30], as long as the RA are not soaked prior to mixing—a two-stage mixing approach [31] is recommended to offset workability losses without compromising this beneficial effect.

## 5. Appraisal and Statistical Analysis of Data

- Comparing datasets having concrete mixes with different mix design, materials, and execution conditions (in this study all NAC compositions are paired with analogue RAC compositions);
- Including NAC tests that would not be paired with RAC experiments performed with the same testing equipment and protocols, such factors such as different roughness of test plates (which influences specimen/plate friction), cylinder capping method, and mould material.

- ${f}_{c,cyl\text{\hspace{0.17em}}\varnothing 150}$ is the compressive strength tested in Փ 150 mm × 300 mm cylinders;
- ${f}_{c,cub\text{\hspace{0.17em}}150}$ is the compressive strength tested in 150 mm cubes.

## 6. Suitability of EN206/Eurocode 2 Specimen Strength Conversion

- The premature micro cracking of CRAC [27] limits stress-paths and the development of the fracture process zone, increasing fracture mechanics size effects;
- Since RA are more heterogeneous than NA [47], statistical size effects on RAC specimens may be more meaningful. This results in a lower K because the region of the specimen under uniaxial compression on Փ 150 cylinders is higher than on 150 mm cubes (multiaxial stress-states caused by Poisson effects are more relevant near the ends of the specimens and the height of standard cylinders is twice their width).

## 7. Definition of K for NAC and CRAC

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Research | Number of NAC Mixes | Number of CRAC Mixes | NA Type | Dmax (mm) | Number of Cubes | Number of Cylinders | Test Standard |
---|---|---|---|---|---|---|---|

Pedro et al. [35] | 6 | 12 | Limestone | 22.4 | 5 | 2 | [36] |

Paul [37] | 2 | 3 | Greywacke | 19 | 5 | 5 | [38] |

Gull [39] | 3 | 6 | Undisclosed | 20 | 3 | 3 | [40] |

Santos et al. [41] | 2 | 2 | Limestone | 20 | 3 | 2 | [36] |

Kheder & Al-Windaw [29] | 10 | 10 | Gravel | 20 | 3 | 3 | [40] |

Rao & Desai [42] | 3 | 3 | Granite | 20 | 3 | 3 | [43] |

Muhammad & Sankaranarayanan [44] | 2 | 2 | Undisclosed | 20 | 3 | 3 | [43] |

Total | 28 | 38 | - | - | - | - |

Relative Percentage of: | w/b Ratio | Binder Content (kg/m^{3}) | Cubic Compressive Strength (MPa) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Range | 0.32–0.45 | 0.45–0.65 | 0.65–0.86 | 0.32–0.45 | 0.45–0.65 | 0.65–0.86 | 0.32–0.45 | 0.45–0.65 | 0.65–0.86 | 0.32–0.45 |

NAC | 25% | 61% | 14% | 11% | 44% | 38% | 11% | 14% | 53% | 32% |

CRAC | 24% | 58% | 18% | 11% | 48% | 33% | 5% | 26% | 47% | 26% |

Parameter | NAC | CRAC |
---|---|---|

Sample | 28 | 38 |

Average (MPa) | 0.81 | 0.77 |

Standard deviation (MPa) | 0.065 | 0.055 |

CoV | 8.0% | 7.1% |

Strength Class | ||||||||
---|---|---|---|---|---|---|---|---|

Statistic | C12/16 + C16/20 | C20/25 + C25/30 | C30/37 + C35/45 | ≥C45 | ||||

NAC | CRAC | NAC | CRAC | NAC | CRAC | NAC | CRAC | |

Count | 3 | 13 | 8 | 10 | 12 | 9 | 5 | 6 |

Average | 0.81 | 0.76 | 0.77 | 0.74 | 0.82 | 0.78 | 0.88 | 0.84 |

Standard deviation | 0.031 | 0.046 | 0.048 | 0.035 | 0.064 | 0.063 | 0.057 | 0.030 |

CoV | 3.9% | 6.1% | 6.3% | 4.7% | 7.8% | 8.1% | 6.5% | 3.5% |

Model | Parameter | NAC | CRAC |
---|---|---|---|

Deterministic factor | Average | 0.81 | 0.77 |

Conservative factor | 0.79 | 0.76 | |

Probabilistic model (Normal) | Average | 0.81 | 0.77 |

Standard deviation | 0.065 | 0.055 |

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**MDPI and ACS Style**

Pacheco, J.N.; de Brito, J.; Chastre, C.; Evangelista, L.
Probabilistic Conversion of the Compressive Strength of Cubes to Cylinders of Natural and Recycled Aggregate Concrete Specimens. *Materials* **2019**, *12*, 280.
https://doi.org/10.3390/ma12020280

**AMA Style**

Pacheco JN, de Brito J, Chastre C, Evangelista L.
Probabilistic Conversion of the Compressive Strength of Cubes to Cylinders of Natural and Recycled Aggregate Concrete Specimens. *Materials*. 2019; 12(2):280.
https://doi.org/10.3390/ma12020280

**Chicago/Turabian Style**

Pacheco, João Nuno, Jorge de Brito, Carlos Chastre, and Luís Evangelista.
2019. "Probabilistic Conversion of the Compressive Strength of Cubes to Cylinders of Natural and Recycled Aggregate Concrete Specimens" *Materials* 12, no. 2: 280.
https://doi.org/10.3390/ma12020280