# Crack Width and Propagation in Recycled Coarse Aggregate Concrete Beams Reinforced with Steel Fibres

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}), respectively. Furthermore, ${k}_{1}$ refers to the participation rate and boundary condition coefficients for rebars, which are considered equal to 0.4 and 0.8 for smooth and conventional rebars, respectively; ${k}_{2}$ is the strain coefficient, which is equal to $0.25\left({\epsilon}_{1}+{\epsilon}_{2}\right)/2{\epsilon}_{1}$, where ${\epsilon}_{1}$ and ${\epsilon}_{2}$ are the highest and lowest effective strains in the tensioned area, respectively. Moreover, ${h}_{eff}$ is the effective tensioned depth (mm) and is considered equal to the largest amount of either ${a}_{1}+7.5{d}_{b}$ or ${a}_{2}+7.5{d}_{b}$. Furthermore, it should not be much larger than the tensioned area or half the height of the section, according to CSA S474 [53]. Furthermore, it should not be much larger than the area of the tension or half the thickness as shown in Figure 1.

^{2}). ${\beta}_{ACI}$ is a ratio equal to 1.2 times the space between the horizontal axis and the concrete’s outer tensile layer divided by the distance between the horizontal axis and the longitudinal rebars in the RC beam, as shown in Figure 4.

## 2. Research Significance

## 3. Materials and Methods

#### 3.1. Specimens’ Specifications

#### 3.2. Test Setup and Loading Condition

## 4. Results and Discussion

^{2}values were determined in order to predict the stress and strain of the RCARC. As per Figure 13, the maximum error between the experimental outcomes and presented formulas was 6%, which indicates a high accuracy. Table 4 presents the obtained formulas for different specimens.

## 5. Flexural Capacity and the Load–Displacement Relationship

## 6. Conclusions

- RCA is an appropriate material that can be used instead of natural materials in concrete for buildings.
- The bending capability increased by increasing the RCA content. Additionally, using 100% RCA decreased the load drop after the maximum bearing capability point, while in the specimen without RCA, the bending resistance abruptly dropped after the maximum load.
- SFs enhanced the maximum bearing capability and using this material with RCA enhanced the flexural resistance of the RCARC beams compared to the control specimens.
- Enough shear rebars must be provided over the beams to control the crack width and propagation but SFs can enhance the bending performance of RCARC beams without shear rebars.
- In addition to increasing the bonding between the rebars and concrete, cracks developed less when SFs were used. Therefore, specimens with a 2% SF content deformed with more ductility and did not collapse quickly.
- Adding SFs to concrete improved the bending performance of the specimens. A minimum number of shear rebars should be provided but SFs should be used in the specimens.
- In specimens with no shear rebars, CSA properly predicted the crack width, unlike CEB. On the other hand, all codes presented an appropriate equation to predict crack width in specimens with different SF and RCA contents.
- In cylindrical specimens under pressure, by adding SFs, cracking occurred only in the concrete surface. Furthermore, due to RCA’s higher and more angulated specific surface compared to NCA, RCA was better impregnated with cement paste, which prevented the complete disintegration of the sample.
- In cylindrical specimens under indirect tensile stresses, a specimen with no SFs broke into two parts but using SFs prevented them from separating. The use of RCA increased the tensile strength of the specimen.
- SFs had a significant effect on reducing the initial crack’s width but there was no significant difference when 1% and 2% SFs were used. On the other hand, using 1% SFs did not have a considerable effect on reducing the initial crack’s width when 100% RCA were used.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Data Availability

## Notation

${A}_{ct}$ | effective concrete cross-sectional area |

${A}_{st}$ | outer area of the tension rebars layer |

b | cross-sectional width |

C | concrete cover |

d | effective depth |

${d}_{b}$ | diameter of the rebars |

${E}_{S}$ | elasticity modulus of the steel rebars |

${f}_{c}^{\prime}$ | concrete compressive resistance |

${f}_{y}$ | yield strength of the steel rebars |

${k}_{2}$ | strain coefficient |

${l}_{s\u060cmax}$ | length of the tension rebars’ slip |

NCA | natural coarse aggregate |

RC | reinforced concrete |

RCA | recycled coarse aggregate; |

RCARC | recycled coarse aggregate reinforced concrete; |

S | depth of the outer reinforcement layer |

SFs | steel fibres |

${S}_{m}$ | average distance between the cracks |

${S}_{m\u060cCSA}$ | average crack distance according to CSA S474 2004; |

TD | shear rebars’ spacing |

${W}_{k\u060cEC2}$ | design crack spacing |

${\epsilon}_{1}$ | highest effective strain in the tensioned area |

${\epsilon}_{2}$ | lowest effective strain in the tensioned area |

${\epsilon}_{cs}$ | free shrinkage strain of concrete |

${\epsilon}_{sr2}$ | rebars’ stress in the cracks under equivalent load ${f}_{ctm}$ |

${\rho}_{{t}_{NS}}$ | effective reinforcement ratio. |

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**Figure 1.**Thickness of the buried area according to CSA-S474-2044 [53].

**Figure 2.**Calculation of the effective area to determine the flexural crack spacing, according to NS 3473E 2003 [54].

**Figure 3.**The effective area [55].

**Figure 4.**Determination of A, ${d}_{c}$ and S to calculate the flexural crack spacing according to ACI 224R-01 [57].

**Figure 9.**Geometry of the beams and arrangement of the rebars: (

**a**) boundary condition, (

**b**) specimen without transverse reinforcement, (

**c**) specimens with a 200 mm transverse reinforcement spacing and (

**d**) specimens with a 100 mm transverse reinforcement spacing. (Note: LVDT: Linear variable differential transformer).

**Figure 10.**Test setup: (

**a**) four-point bending test of the beams and the (

**b**) compressive stress–strain setup.

**Figure 14.**Bending behaviour of the specimens with various SF and RCA contents and no shear rebars. WTD: without transverse reinforcement.

**Figure 16.**Bending behaviour of specimens with various SF and RA contents and 200 mm shear rebars’ spacing. 20TD: transverse reinforcement spacing 200 mm.

**Figure 18.**Bending behaviour of specimens with various S values and RCA contents and a 100 mm shear rebar spacing.

**Figure 21.**Applied load–crack width performance of specimens with various SF and RA contents (

**a**) specimens without SF with different RCA contents, (

**b**) specimens with different SF contents and 100% RCA, (

**c**) specimens without SF and stirrup, (

**d**) specimens without SF and with 100% RCA, (

**e**) specimens with different SF contents, 100 RCA and different stirrup spacing and (

**f**) specimens without fibres and stirrup with different RCA contents.

**Figure 23.**Observed versus predicted ultimate crack widths of specimens with a 200 mm shear rebar spacing.

**Figure 24.**Observed versus predicted ultimate crack width of specimens with a 100 mm shear rebar spacing.

Physical Properties | Aggregate Type | |
---|---|---|

NCA | RCA | |

Apparent density (g/cm^{3}) | 2.8 | 2.7 |

Bulk density (g/cm^{3}) | 2.7 | 2.6 |

Water absorption (wt%) | 1.44 | 1.19 |

Crush index (%) | 30.00 | 48.9 |

Porosity (%) | 3.9 | 3.88 |

Specimens | 0SF-0RCA | 0SF-50RCA | 0SF-100RCA | 1SF-0RCA | 1SF-50RCA | 1SF-100RCA | 2SF-0RCA | 2SF-50RCA | 2SF-100RCA |
---|---|---|---|---|---|---|---|---|---|

Water (kg/m^{3}) | 165 | 165 | 165 | 165 | 165 | 165 | 165 | 165 | 165 |

Cement (kg/m^{3}) | 400 | 400 | 400 | 400 | 400 | 400 | 400 | 400 | 400 |

SFs (kg/m^{3}) | 0 | 0 | 0 | 78 | 78 | 78 | 156 | 156 | 156 |

RCA (kg/m^{3}) | 0 | 420 | 840 | 0 | 385 | 765 | 0 | 345 | 685 |

NCA (kg/m^{3}) | 840 | 420 | 0 | 765 | 385 | 0 | 685 | 345 | 0 |

NFA (kg/m^{3}) | 950 | 950 | 950 | 950 | 950 | 950 | 950 | 950 | 950 |

Average tensile stress (MPa) | 3.78 | 4.29 | 4.04 | 5.00 | 6.12 | 4.10 | 5.01 | 4.68 | 4.99 |

Tensile stress coefficient of variation | 0.17 | 0.04 | 0.09 | 0.01 | 0.27 | 0.04 | 0.27 | 0.09 | 0.13 |

Average compressive resistance (MPa) | 38.4 | 35.0 | 37.1 | 36.8 | 35.7 | 35.7 | 36.9 | 35.7 | 35.6 |

Compressive strength coefficient of variation | 1.56 | 1.08 | 1.65 | 1.33 | 1.19 | 0.85 | 1.38 | 1.00 | 0.78 |

Properties | Results | ||
---|---|---|---|

Rebar diameter (mm) | 8 | 10 | 20 |

Yield stress (MPa) | 370 | 410 | 370 |

Ultimate stress (MPa) | 560 | 680 | 560 |

Yield strain (%) | 13.0 | 13.0 | 15.3 |

Ultimate strain (%) | 25.0 | 25.4 | 25.9 |

Modulus of elasticity (GPa) | 209.3 | 210.10 | 213.2 |

Specimens | Formula | ${\mathit{R}}^{2}$ |
---|---|---|

0SF-0RCA | $y=-1\times {10}^{7}{x}^{2}+40269x-0.37$ | 0.9838 |

1SF-0RCA | $y=-9\times {10}^{6}{x}^{2}+35670x-0.19$ | 0.9959 |

2SF-0RCA | $y=-2\times {10}^{6}{x}^{2}+18183x+2.85$ | 0.9429 |

0SF-50RCA | $y=-3\times {10}^{7}{x}^{2}+22481x+5.28$ | 0.8862 |

1SF-50RCA | $y=-1\times {10}^{7}{x}^{2}+47581x-0.28$ | 0.9839 |

2SF-50RCA | $y=-3\times {10}^{6}{x}^{2}+20805x+2.63$ | 0.9574 |

0SF-100RCA | $y=-3\times {10}^{7}{x}^{2}+69316x+1.75$ | 0.9921 |

1SF-100RCA | $y=-2\times {10}^{7}{x}^{2}+47953x+1.75$ | 0.9921 |

2SF-100RCA | $y=-4\times {10}^{6}{x}^{2}+25425x+4.88$ | 0.9492 |

Specimens | Loading of First Crack Occurrence (kN) | Specimen’s Failure Load (kN) | Crack Widths at the Peak Load (mm) | Mode of Failure |
---|---|---|---|---|

0SF-0RCA-WTD | 20.0 | 70.0 | 12.0 | Shear |

0SF-0RCA-20TD | 20.2 | 80.1 | 12.0 | Shear |

0SF-0RCA-10TD | 20.6 | 90.5 | 5.0 | Flexural |

0SF-50RCA-WTD | 20.1 | 70.2 | 7.0 | Shear |

0SF-50RCA-20TD | 20.2 | 90.1 | 6.5 | Shear |

0SF-50RCA-10TD | 20.6 | 90.7 | 2.0 | Flexural |

0SF-100RCA-WTD | 20.1 | 80.0 | 11.0 | Shear |

0SF-100RCA-20TD | 30.4 | 90.0 | 4.0 | Flexural |

0SF-100RCA-10TD | 20.8 | 90.5 | 3.0 | Flexural |

1SF-0RCA-WTD | 20.2 | 80.1 | 8.0 | Shear |

1SF-0RCA-20TD | 20.8 | 100.0 | 9.0 | Flexural |

1SF-0RCA-10TD | 30.2 | 100.6 | 3.5 | Flexural |

1SF-50RCA-WTD | 10.1 | 80.2 | 5.0 | Shear |

1SF-50RCA-20TD | 20.0 | 90.6 | 3.0 | Flexural |

1SF-50RCA-10TD | 20.6 | 95.4 | 2.5 | Flexural |

1SF-100RCA-WTD | 20.0 | 80.1 | 9.0 | Shear |

1SF-100RCA-20TD | 20.6 | 100.2 | 3.5 | Flexural |

1SF-100RCA-10TD | 40.4 | 100.9 | 3.2 | Flexural |

2SF-0RCA-WTD | 20.2 | 80.0 | 3.6 | Shear |

2SF-0RCA-20TD | 40.4 | 90.0 | 3.4 | Shear |

2SF-0RCA-10TD | 40.8 | 100.5 | 3.5 | Flexural |

2SF-50RCA-WTD | 20.0 | 90.1 | 4.0 | Shear |

2SF-50RCA-20TD | 20.1 | 90.7 | 3.5 | Flexural |

2SF-50RCA-10TD | 20.6 | 100.3 | 3.5 | Flexural |

2SF-100RCA-WTD | 30.0 | 90.1 | 5.0 | Shear |

2SF-100RCA-20TD | 40.2 | 100.5 | 3.5 | Shear |

2SF-100RCA-10TD | 50.5 | 110.2 | 2.5 | Flexural |

Series Number | Beams | Dimensions (mm) | Tensile Reinforcement (mm) | Stirrups (mm) | Volume Fraction (%) |
---|---|---|---|---|---|

1 | B1 | 150 × 200 × 1500 | 2#8 | #6@125 | --- |

BF1 | 150 × 200 × 1500 | 2#8 | #6@125 | 1 | |

BF1a | 150 × 200 × 1500 | 2#8 | --- | 1 | |

2 | B2 | 150 × 200 × 1500 | 2#12 | #6@125 | --- |

BF2 | 150 × 200 × 1500 | 2#12 | #6@125 | 1 | |

BF2a | 150 × 200 × 1500 | 2#12 | --- | 1 | |

3 | B3 | 150 × 200 × 1500 | 2#16 | #6@125 | --- |

BF3 | 150 × 200 × 1500 | 2#16 | #6@125 | 1 | |

BF3a | 150 × 200 × 1500 | 2#16 | --- | 1 | |

4 | B1-0.0F | 150 × 200 × 1500 | #3 | #3@127 | --- |

Specimens | $\frac{{\mathit{W}}_{\mathit{A}\mathit{C}\mathit{I}}}{{\mathit{W}}_{\mathit{e}\mathit{x}\mathit{p}}}$ | $\frac{{\mathit{W}}_{\mathit{C}\mathit{E}\mathit{B}-\mathit{F}\mathit{I}\mathit{P}}}{{\mathit{W}}_{\mathit{e}\mathit{x}\mathit{p}}}$ | $\frac{{\mathit{W}}_{\mathit{E}\mathit{u}\mathit{r}\mathit{o}}}{{\mathit{W}}_{\mathit{e}\mathit{x}\mathit{p}}}$ | $\frac{{\mathit{W}}_{\mathit{N}\mathit{S}}}{{\mathit{W}}_{\mathit{e}\mathit{x}\mathit{p}}}$ | $\frac{{\mathit{W}}_{\mathit{C}\mathit{S}\mathit{A}}}{{\mathit{W}}_{\mathit{e}\mathit{x}\mathit{p}}}$ |
---|---|---|---|---|---|

1SF-100RCA-10TD | 2.220815 | 1.61263 | 2.43332 | 2.584992 | 2.911027 |

1SF-0RCA-20TD | 2.090179 | 1.517769 | 2.290184 | 2.432934 | 2.73979 |

1SF-0RCA-WTD | 1.974058 | 1.433449 | 2.162951 | 2.297771 | 2.58758 |

1SF-100RCA-20TD | 2.030459 | 1.474404 | 2.22475 | 2.363421 | 2.66151 |

2SF-0RCA-10TD | 2.368869 | 1.720138 | 2.595541 | 2.757325 | 3.105096 |

2SF-50RCA-WTD | 2.030459 | 1.474404 | 2.22475 | 2.363421 | 2.66151 |

1SF-0RCA-10TD | 2.030459 | 1.474404 | 2.22475 | 2.363421 | 2.66151 |

0SF-100RCA-WTD | 0.646055 | 0.469129 | 0.707875 | 0.751998 | 0.846844 |

2SF-50RCA-10TD | 1.776652 | 1.290104 | 1.946656 | 2.067994 | 2.328822 |

0SF-100RCA-20TD | 1.776652 | 1.290104 | 1.946656 | 2.067994 | 2.328822 |

2SF-50RCA-20TD | 2.030459 | 1.474404 | 2.22475 | 2.363421 | 2.66151 |

0SF-100RCA-10TD | 2.368869 | 1.720138 | 2.595541 | 2.757325 | 3.105096 |

0SF-0RCA-WTD | 0.592217 | 0.430035 | 0.648885 | 0.689331 | 0.776274 |

2SF-0RCA-20TD | 0.789623 | 0.573379 | 0.86518 | 0.919108 | 1.035032 |

0SF-0RCA-20TD | 1.421322 | 1.032083 | 1.557325 | 1.654395 | 1.863057 |

1SF-50RCA-10TD | 2.842643 | 2.064166 | 3.11465 | 3.30879 | 3.726115 |

2SF-100RCA-WTD | 2.842643 | 2.064166 | 3.11465 | 3.30879 | 3.726115 |

0SF-50RCA-20TD | 3.553304 | 2.580208 | 3.893312 | 4.135987 | 4.657643 |

1SF-50RCA-20TD | 2.368869 | 1.720138 | 2.595541 | 2.757325 | 3.105096 |

1SF-50RCA-WTD | 1.421322 | 1.032083 | 1.557325 | 1.654395 | 1.863057 |

1SF-100RCA-WTD | 0.789623 | 0.573379 | 0.86518 | 0.919108 | 1.035032 |

0A-50RCA-WTD | 1.01523 | 0.737202 | 1.112375 | 1.181711 | 1.330755 |

2SF-100RCA-10TD | 2.030459 | 1.474404 | 2.22475 | 2.363421 | 2.66151 |

2SF-0RCA-WTD | 0.888326 | 0.645052 | 0.973328 | 1.033997 | 1.164411 |

2SF-100RCA-20TD | 1.421322 | 1.032083 | 1.557325 | 1.654395 | 1.863057 |

0SF-0RCA-10TD | 0.592217 | 0.430035 | 0.648885 | 0.689331 | 0.776274 |

0SF-50RCA-10TD | 1.093324 | 0.79391 | 1.197942 | 1.272611 | 1.433121 |

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## Share and Cite

**MDPI and ACS Style**

Ghalehnovi, M.; Karimipour, A.; de Brito, J.; Chaboki, H.R.
Crack Width and Propagation in Recycled Coarse Aggregate Concrete Beams Reinforced with Steel Fibres. *Appl. Sci.* **2020**, *10*, 7587.
https://doi.org/10.3390/app10217587

**AMA Style**

Ghalehnovi M, Karimipour A, de Brito J, Chaboki HR.
Crack Width and Propagation in Recycled Coarse Aggregate Concrete Beams Reinforced with Steel Fibres. *Applied Sciences*. 2020; 10(21):7587.
https://doi.org/10.3390/app10217587

**Chicago/Turabian Style**

Ghalehnovi, Mansour, Arash Karimipour, Jorge de Brito, and Hamid Reza Chaboki.
2020. "Crack Width and Propagation in Recycled Coarse Aggregate Concrete Beams Reinforced with Steel Fibres" *Applied Sciences* 10, no. 21: 7587.
https://doi.org/10.3390/app10217587