# Can We Truly Predict the Compressive Strength of Concrete without Knowing the Properties of Aggregates?

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## Abstract

**:**

## 1. Introduction

#### 1.1. General Facts on Compressive Strength Estimation

_{P}). For that purpose, researchers have proposed several formulas to calculate the strength of concrete [1,2].

^{−}that is absorbed by the aggregates and that releases Si

^{4+}at the same time depends on the geological nature of the aggregates, and this process significantly affects the pore structure of the hydration product and the ITZ as a result.

#### 1.2. Background of the Compressive Strength Estimation Models

## 2. Methodology

_{cm, cube 100 mm}→ f

_{cm, cube 150 mm}→ f

_{cm, cylinder 150 × 300}← f

_{cm, cylinder 100 × 200}) in order to compare them with the calculated strength. Thus, according to the state-of-the-art method described in FIB Bulletin 42 [118], the “f

_{cm, cube 150 mm}to f

_{cm, cube 100 mm}” ratio is equal to 0.97. Similar results can be seen in other studies [119,120]. After that, f

_{cm, cube 150 mm}was converted to f

_{cm, cylinder 150 × 300}, according to EN 1992-1-1:2004 (E). Regarding f

_{cm, cylinder 100 × 200}, the majority of the researchers agree that, up to 33 MPa, the difference between f

_{cm, cylinder 150 × 300}and f

_{cm, cylinder 100 × 200}is insignificant. The average difference between them is 2%, according to previous studies [121,122,123]. For higher strength values (over 33 MPa), the average “f

_{cm, cylinder 150 × 300}to f

_{cm, cylinder 100 × 200}” ratio is 0.90 (Table 5).

## 3. Results

#### 3.1. Effect of the Geological Nature of Natural Aggregates on the Compressive Strength of Concrete

^{2}was −0.31, −0.14 and 0.15 in the Abrams, Slater, and ACI models, respectively) when only w/c was considered to be an influencing factor. This is because the compressive strength of concretes with the same w/c may vary with cement content [23] and cement class [24], which respectively influence the aggregate: cement volume ratio and void index and the quality of the hydration product. The other reason is that the original formulas ignore the quality (e.g., geological nature) of the aggregates. Thus, the relationship between the calculated and actual strength of concrete mixes improved when the original formulas also considered the geological nature of the aggregates (R

^{2}was −0.23, 0.03, −0.58, −0.05, 0.52 and 0.46 with Abram’s model, and 0.27, 0.20, −0.57, 0.20, 0.85 and 0 with Slater’s model, and 0.25, 0.40, −0.03, 0.23, 0.81, 0.84 with the ACI model when the aggregates were classified as basalt, granite, limestone, NA (geological nature not given), quartz, and sandstone, respectively. The negative R

^{2}is due to the fact that the linear trendline was set to intercept the origin of the axes [130,131]). This behaviour is further discussed in the next paragraphs. Furthermore, for the 95% confidence intervals (red dashed lines in each graph), there is a big scatter between w/c and compressive strength of concrete, and the lower and upper k (f

_{cm, calculated}/f

_{cm, experimental}) values in all original models were 0.67 ± 0.02 and 1.67 ± 0.01, respectively.

^{2}was up 0.15) that only considered the w/c as a main factor, the relationship between the calculated and actual compressive strength significantly improved (R

^{2}≈ 0.50), as seen in Figure 3a. This is due to the additional factors considered in Bolomey’s model, namely the strength class of cement and the way that aggregates are produced (Table 2). However, this model neglected the effect of the cement content (volume of aggregates to cement ratio) which significantly affects the results due to its influence on the strength of concrete (for the same w/c, the strength may vary with the cement content [23]). As shown in Figure 3b, by using Feret’s model, the relationship between the calculated and experimental strength of concrete significantly improved (R

^{2}≈ 0.60) relative to the original models. This is because of the factors considered in the model, namely, the cement strength and content. However, this model neglected the aggregates’ production methods.

_{cm, calculated}/f

_{cm, experimental}) varied between 1.20–0.60 and 1.63–0.83 when the strength was calculated based on the Bolomey and Feret models, respectively. This may be related to the fact that both models neglected the properties of the aggregates as a factor to calculate the strength. To validate this assumption, the mixes were classified according to the geological nature of their aggregates, and the k value was found for each of them according to a 95% confidence interval (Figure 4). As a consequence, the relationship between calculated and actual strengths considerably improved in most cases. For example, the R

^{2}of concrete mixes made with basalt, granite, limestone, and quartz was about 0.60, 0.80, 0.40, and 0.80 when Bolomey’s model was used to calculate the strength, and 0.40, 0.90, 0.60, 0.90 for Feret’s model, respectively. Additionally, for both the Bolomey (Figure 4a) and Feret models (Figure 4b), the difference between upper (k1) and lower (k2) boundaries (k value = f

_{cm, calculated}/f

_{cm, experimental}) for a 95% confidence interval of the concrete mixes significantly decreased when the classification was based on the geological nature of the aggregates, except for concrete with limestone aggregates. This is because limestone has a large scatter of characteristics (Table 4), and it is classified in various generic categories, e.g., carboniferous, dolomitic, and calcareous, or it may be a composite (e.g., limestone–quartzitic, limestone–siliceous).

#### 3.2. Effect of the Quality of Natural Aggregates on the Compressive Strength of Concrete

^{2}values for the linear trends were 0.50 and 0.60 for the Bolomey and Feret formulas, respectively) improved when the mixes were classified based on their quality (classes A, B, C, and D). Thus, the R

^{2}values for the linear trends were 0.72 and 0.62 for the Bolomey model and 0.60 and 0.74 for the Feret model when the mix’s aggregates were from classes AI and AII (specified in Table 1), respectively (Figure 7). This shows that the quality of the aggregates may significantly affect the ultimate strength of concrete. Therefore, it is important to identify the quality of the aggregates simultaneously with the other factors shown in Figure 6. According to both models, the scatter between the results (the k values of the all mixes were 0.6–1.30 and 0.80–1.50 when the strength was calculated according to the Bolomey and Feret models, respectively) decreases when the mixes are classified in terms of the quality of their aggregates (Figure 7).

## 4. Conclusions

_{cm, calculated}/f

_{cm, experimental}) for a 95% confidence interval significantly decreased when they were split based on the geological nature of the aggregates used. The same occurred when the mixes were split based on the quality of their aggregates.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Relationship between the compressive strength “f

_{cm, cylinder 150 mm x 300 mm length}” and w/c ratio of concrete.

**Figure 2.**Relationship between the actual and calculated compressive strength of concrete mixes made with NA sourced from different geological natures. The strength values were calculated according to the (

**a**) Abrams, (

**b**) Slater and (

**c**) ACI formulas. k = (f

_{cm, calculated}/f

_{cm, experimental}).

**Figure 3.**Relationship between the actual and calculated compressive strength of concrete mixes made with NA sourced from different geological natures. The strength values were calculated according to the (

**a**) Bolomey and (

**b**) Feret formulas. k = (f

_{cm, calculated}/f

_{cm, experimental}).

**Figure 4.**Relationship between the actual and calculated compressive strength of concrete mixes made with NA sourced from different geological natures. k1 and k2 are the upper and lower boundaries for a 95% confidence interval, respectively, according to the (

**a**) Bolomey and (

**b**) Feret models.

**Figure 5.**Relationship between the actual and calculated compressive strength of concrete mixes made with NA sourced from different geological natures. The average k value is the average of k1 and k2 from Figure 4, according to the (

**a**) Bolomey and (

**b**) Feret models. The standard deviation for the k values was ≈0.20 in both models.

**Figure 7.**Relationship between the actual and calculated compressive strength of the concrete mixes made with NA, classified in terms of their quality. The physical quality of A-I aggregates is better than that of A-II aggregates, followed by B-I aggregates. k1 and k2 are the upper and lower boundaries for the 95% confidence intervals, respectively, according to the (

**a**) Bolomey and (

**b**) Feret models.

**Figure 8.**Relationship between the actual and calculated compressive strength of concrete mixes made with NA, classified in terms of their quality. The physical quality of the A-I aggregates is better than that of A-II, then followed by B-I. The average k value is the average of k1 and k2 from Figure 7, according to the (

**a**) Bolomey and (

**b**) Feret models. The standard deviation for the k values was ≈0.25 in both models.

**Figure 9.**Relationship between the actual and calculated compressive strength of concrete mixes made with 100% NA and RA classified in terms of their quality. The strength was calculated according to Bolomey’s model. The physical quality of A aggregates is better than B, followed by C and D. (

**a**) k values for NA and RA concrete mixes, (

**b**) k1 and k2 are the upper and lower boundaries for the 95% confidence intervals, and (

**c**) the average k value is the average of k1 and k2 from Figure 9b. The standard deviation for the k values was ≈0.51 in (

**c**).

**Table 1.**Physical boundaries for each proposed class of aggregates [7].

Aggregate Class | A | B | C | D | ||||||
---|---|---|---|---|---|---|---|---|---|---|

I | II | III | I | II | III | I | II | III | ||

Minimum oven-dried density (kg/m^{3}) | 2600 | 2500 | 2400 | 2300 | 2200 | 2100 | 2000 | 1900 | 1800 | No limit |

Maximum water absorption (%) | 1.5 | 2.5 | 3.5 | 5 | 6.5 | 8.5 | 10.5 | 13 | 15 | |

Maximum LA abrasion mass loss (%) | 40 | 45 | 50 |

Model | Formula ^{a,b} | Notes/Limitations |
---|---|---|

Abram | $\mathit{f}\mathbf{cm}=\frac{\mathit{A}}{{\mathit{B}}^{\mathit{w}/\mathit{c}}}$ | The constants A and B are 96 MPa and 7, respectively. The w/c ratio should be between 0.3 and 1.2 |

Slater | $\mathit{f}\mathbf{cm}=\mathbf{0.007}\xb7\left(\mathbf{2700}\xb7\frac{\mathit{C}}{\mathit{w}}-\mathbf{760}\right)$ | This formula can be used only for mixes without S_{P} |

American Concrete Institute Manual of Concrete Practice (ACI2000-I) | $\mathit{f}\mathbf{cm}=\mathbf{117.07}\xb7{\mathit{e}}^{-\mathbf{2.572}\xb7\mathit{w}/\mathit{c}}$ | The w/c ratio and cement content of the concrete mixes are limited to 0.41–0.82 and 300–360 kg/m^{3}, respectively. The equation was adapted from the results of the table given in the specification with R^{2} = 0.996 |

Bolomey | $\mathit{f}\mathbf{cm}=\mathit{A}\mathbf{1}\xb7\left(\frac{\mathbf{1}}{\mathit{w}/\mathit{c}}-\mathbf{0.5}\right)$ if w/c > 0.4 $\mathit{f}\mathbf{cm}=\mathit{A}\mathbf{2}\xb7\left(\frac{\mathbf{1}}{\mathit{w}/\mathit{c}}+\mathbf{0.5}\right)$ if w/c ≤ 0.4 | The constants (A1 and A2) depend on the way aggregates are produced and on the strength class of cement (Table 3) |

Feret | $\mathit{f}\mathbf{cm}=\mathit{k}\xb7{\left(\frac{\mathit{v}}{\mathit{v}+\mathit{I}}\right)}^{2}$ | The constant, k, depends on the strength class of cement. It is 265–290 and 315–350 for cement class CEM I 32.5 and 42.5, respectively; v is the absolute volume of cement paste and I is the volume index (air and water contents) |

^{a}c and w are the cement and water contents, respectively. In other words, w/c is the water to cement ratio;

^{b}f

_{cm}is the average compressive strength of the concrete in cylinders (150 mm diameter × 300 mm length) at 28 days (MPa).

Aggregate | w/c | Constants ^{a} | Strength Class of Cement (MPa) | |||||
---|---|---|---|---|---|---|---|---|

25 | 35 | 40 | 45 | 52.5 | 55 | |||

Natural (rolled) | >0.40 | A1 | 13.73 | 17.65 | 19.61 | 20.59 | 22.0675 | 22.56 |

Natural (rolled) | ≤0.40 | A2 | 9.32 | 11.7 | 12.75 | 14.22 | 14.5875 | 14.71 |

Natural (crushed) | >0.40 | A1 | 15.2 | 19.61 | 21.57 | 23.54 | 25.01 | 25.5 |

Natural (crushed) | ≤0.40 | A2 | 10.3 | 13.24 | 14.22 | 15.69 | 16.7925 | 17.16 |

^{a}The constant between the presented strength class was determined by interpolation and the average value of the rolled and crushed aggregates was considered if information on the way the aggregates were produced was not provided.

References ^{a} | Aggregates | Cement | Mix Composition | Strength | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Geological Nature | Physical Properties | Oven-Dried Particle Density (kg/m^{3}) | WA-24h (%) | Properties | Max. Aggregate Size (mm) | Los Angeles (LA) Abrasion (%) | Cement Type/Strength | Cement Content (kg/m^{3}) | w/c | Water Content (L/m^{3}) | f_{cm, cyl 150 × 300 (MPa)} | |

[26,27,28,29,30,31,32,33,34,35] | Basalt | AI | 2716–2915 | 0.68–1.60 | Crushed | 14–20 | 17–24 | CEM I 42.5–52.5 | 300–500 | 0.24–0.70 | 108–210 | 20–62 |

[26,27,31,33,34,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80] | Limestone | AI-BI | 2277–2739 | 0.20–5.00 | Crushed/ rounded | 10–32 | 10–42 | CEM I 32.5–52.5 | 210–677 | 0.28–0.86 | 126–266 | 10–69 |

[26,81,82,83,84] | Quartz | AI | 2624–2780 | 0.17–1.5 | Crushed/ rounded | 16–32 | 24–36 | CEM I 42.5 | 300–500 | 0.36–0.61 | 148–214 | 22–59 |

[85,86,87] | Sandstone | AI | 2625–2660 | 0.50–0.94 | Crushed | 19–20 | - | CEM I 42.5 | 250–463 | 0.40–0.60 | 153–185 | 23–56 |

[34,50,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109] | Natural gravel (N.G.) ^{b} | AI-AII | 2511–2719 | 0.05–2.5 | Crushed/ rounded | 15–25 | 20–30 | CEM I 42.5 | 214–635 | 0.32–0.84 | 148–259 | 15–52 |

^{a}The following studies [34,35,36,42,46,47,48,50,52,53,54,57,66,67,70,71,76,77,78,81,85,87,90,93,94,95,100,102,103,104,105,107,110,111,112,113,114,115,116,117] were considered to study the effects of quality of aggregates on the compressive strength of concrete made with 100% coarse recycled aggregates (RA);

^{b}N.G.—the geological nature of the natural aggregates (NA) is not given.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

De Brito, J.; Kurda, R.; Raposeiro da Silva, P.
Can We Truly Predict the Compressive Strength of Concrete without Knowing the Properties of Aggregates? *Appl. Sci.* **2018**, *8*, 1095.
https://doi.org/10.3390/app8071095

**AMA Style**

De Brito J, Kurda R, Raposeiro da Silva P.
Can We Truly Predict the Compressive Strength of Concrete without Knowing the Properties of Aggregates? *Applied Sciences*. 2018; 8(7):1095.
https://doi.org/10.3390/app8071095

**Chicago/Turabian Style**

De Brito, Jorge, Rawaz Kurda, and Pedro Raposeiro da Silva.
2018. "Can We Truly Predict the Compressive Strength of Concrete without Knowing the Properties of Aggregates?" *Applied Sciences* 8, no. 7: 1095.
https://doi.org/10.3390/app8071095