# Discrete Element Simulation Analysis of Biaxial Mechanical Properties of Concrete with Large-Size Recycled Aggregate

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Building

#### 2.1. Generating the Random Aggregate Model

_{c}is used, it is difficult to solve D

_{0}. Therefore, a gradation curve is drawn in the gradation interval of 5~25 mm and then a polynomial is used to fit the method, and the curve is shown in Figure 4. The inverse function of the curve is

_{c}, then we get

#### 2.2. Building a Discrete Element Model

#### 2.3. Discrete Element Parameter Determination

## 3. Model Validation

## 4. Results and Analysis

#### 4.1. Influence of Different Incorporation Ratios under 10 MPa Confining Pressure

#### 4.2. Stress–Strain Curve under 10 MPa Confining Pressure

#### 4.3. Stress–Strain Curve under 10 MPa Confining Pressure

#### 4.4. Strength under Different Confining Pressures

## 5. Conclusions

- (1)
- In this research, the biaxial mechanical characteristics of concrete with large-size recycled aggregate were analyzed using a two-stage random aggregate creation and distribution approach. This model can more accurately describe the effect of the complex composition of large-size recycled aggregates on the cracking and strength variations of recycled concrete under confining pressure.
- (2)
- When restricting pressure was applied, the strength of concrete containing large-sized recycled aggregate was not significantly diminished compared to tha of conventional concrete. When both new and old concrete had high strength, the recycled concrete’s strength diminished proportionately more. When new concrete had a lesser strength than the existing concrete, the strength fell less. Under a confining pressure of 10 MPa, the strength of recycled concrete deteriorated the most, falling 15% below that of unrecycled concrete. The strength of recycled concrete was only 0.6 percent less than that of unrecycled concrete.
- (3)
- When restricting pressure was applied, the fracture morphology of recycled concrete was significantly altered following the addition of large-size recycled aggregate. Cracks in standard concrete were square and had an angle of around 45 degrees with a horizontal direction. As the proportion of large recycled aggregates rose, the model’s crack count climbed. The model’s cracks eventually transitioned from the ITZ to a diagonal crack that penetrated two opposing corners.
- (4)
- When confining pressure was applied, the addition of large-size recycled aggregate had a bigger effect on the rising region of the stress–strain curve but a relatively lower effect on the falling section. When the age of the concrete was greater than the age of the new concrete, adding large-size recycled aggregate did not affect the stress–strain curve. When the old and new concrete strengths were equal, the stress–strain curve’s rising portion had a higher reduction.
- (5)
- When the stress–strain curve was fitted using Guo’s equation and the coefficients of Xiao’s equation were compared, it was observed that as confining pressure is increased, the rising section coefficient of the stress–strain curve of large-size recycled aggregate concrete gradually increased. When the strength of the old concrete was low and the new concrete was strong, the influence of confining forces was more visible.
- (6)
- When confining pressure was applied, the following elements affected the strength of recycled concrete: confining pressure, new concrete strength, incorporation ratio of recycled coarse aggregate, and strength of old concrete. The Pearson correlation coefficients calculated using this study’s simulation results were 0.96, 0.197, −0.07, and 0.006, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Notation

${E}_{c}$ | Interparticle contact modulus |

${k}_{n}/{k}_{s}$ | Ratio of particle normal and tangential stiffness |

$\overline{\mu}$ | Particle friction coefficient |

$\overline{\lambda}$ | Parallel bonding radius multiplier |

${\overline{E}}_{c}$ | Parallel bonding modulus |

${\overline{k}}_{n}/{\overline{k}}_{s}$ | Ratio of parallel bonding normal and tangential stiffness |

${\overline{\sigma}}_{c}(mean)$ | Average normal strength of parallel bonding |

${\overline{\sigma}}_{c}(std.dev)$ | Standard deviation of normal strength of parallel bonding |

${\overline{\tau}}_{c}(mean)$ | Average tangential strength of parallel bonding |

${\overline{\tau}}_{c}(std.dev)$ | Standard deviation of tangential strength of parallel bonding |

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Gravel | C30 Mortar | C40 Mortar | Old ITZ 1 | Old ITZ 2 | New ITZ 1 | New ITZ 2 | New ITZ 3 | |
---|---|---|---|---|---|---|---|---|

${\overline{E}}_{c}/\mathrm{Pa}$ | 55.15 | 27.76 | 35.11 | 22.83 | 29.31 | 22.82 | 27.76 | 23.46 |

${k}_{\mathrm{n}}/{k}_{\mathrm{s}}$ | 2.69 | 2.34 | 2.53 | 2.26 | 2.38 | 2.21 | 2.34 | 2.29 |

$\overline{\mu}$ | 0.43 | 0.17 | 0.20 | 0.18 | 0.18 | 0.17 | 0.17 | 0.19 |

$\overline{\lambda}$ | 0.23 | 0.24 | 0.23 | 0.23 | 0.24 | 0.24 | 0.24 | 0.23 |

${\overline{E}}_{\mathrm{c}}/\mathrm{Pa}$ | 135.27 | 47.09 | 67.55 | 40.25 | 54.79 | 43.23 | 47.09 | 43.69 |

${\overline{k}}_{n}/{\overline{k}}_{s}$ | 0.51 | 0.58 | 0.60 | 0.53 | 0.57 | 0.54 | 0.58 | 0.52 |

${\overline{\sigma}}_{\mathrm{c}}(\mathrm{mean})/\mathrm{Pa}$ | 338.12 | 246.10 | 348.15 | 199.43 | 267.51 | 174.69 | 246.10 | 213.84 |

${\overline{\sigma}}_{\mathrm{c}}(\mathrm{std}.\mathrm{dev})$ | 41.52 | 73.05 | 68.09 | 72.28 | 70.90 | 73.37 | 73.05 | 70.81 |

${\overline{\tau}}_{\mathrm{c}}(\mathrm{mean})/\mathrm{Pa}$ | 240.88 | 104.43 | 132.60 | 101.32 | 113.97 | 95.05 | 104.43 | 107.74 |

${\overline{\tau}}_{c}(std.dev)$ ${\overline{\tau}}_{\mathrm{c}}(\mathrm{std}.\mathrm{dev})$ | 51.90 | 49.38 | 42.65 | 53.71 | 48.47 | 55.52 | 49.38 | 53.07 |

Grade | Incorporation % | Cement kg | Water kg | Sand kg | NCA kg | LRCA kg | Superplasticizer kg |
---|---|---|---|---|---|---|---|

C30 | 0 | 286 | 175 | 924 | 1068 | 0 | 3.70 |

20 | 270 | 165 | 871 | 636 | 480 | 3.49 | |

30 | 261 | 160 | 844 | 420 | 720 | 3.38 | |

40 | 253 | 155 | 818 | 204 | 960 | 3.28 | |

C40 | 0 | 360 | 170 | 893 | 1057 | 0 | 7.00 |

20 | 339 | 160 | 842 | 625 | 480 | 6.60 | |

30 | 329 | 155 | 817 | 409 | 720 | 6.40 | |

40 | 319 | 151 | 791 | 193 | 960 | 6.20 |

Label | C300030 | C302030 | C303030 | C304030 | C400040 | C402040 | C403040 | C404040 |
---|---|---|---|---|---|---|---|---|

Test | 25.76 | 26.43 | 26.87 | 24.47 | 33.25 | 34.83 | 33.37 | 28.51 |

Simulation | 29.78 | 25.15 | 25.57 | 24.37 | 37.02 | 29.84 | 31.02 | 30.17 |

Number | Incorporation Ratio | Confining Pressure/MPa | Old Concrete Strength/MPa | New Concrete Strength/MPa | Recycled Concrete Strength/MPa |
---|---|---|---|---|---|

P00300030 | 0.00 | 0.00 | 30.00 | 30.00 | 30.73 |

P00300040 | 0.00 | 0.00 | 30.00 | 40.00 | 38.07 |

P00400030 | 0.00 | 0.00 | 40.00 | 30.00 | 30.73 |

P00400040 | 0.00 | 0.00 | 40.00 | 40.00 | 38.07 |

P10300030 | 0.00 | 10.00 | 30.00 | 30.00 | 47.66 |

P10300040 | 0.00 | 10.00 | 30.00 | 40.00 | 54.63 |

P10400030 | 0.00 | 10.00 | 40.00 | 30.00 | 47.66 |

P10400040 | 0.00 | 10.00 | 40.00 | 40.00 | 54.63 |

P20300030 | 0.00 | 20.00 | 30.00 | 30.00 | 61.90 |

P20300040 | 0.00 | 20.00 | 30.00 | 40.00 | 70.23 |

P20400030 | 0.00 | 20.00 | 40.00 | 30.00 | 61.90 |

P20400040 | 0.00 | 20.00 | 40.00 | 40.00 | 70.23 |

P00301030 | 0.10 | 0.00 | 30.00 | 30.00 | 25.17 |

P00301040 | 0.10 | 0.00 | 30.00 | 40.00 | 31.75 |

P00401030 | 0.10 | 0.00 | 40.00 | 30.00 | 28.70 |

P00401040 | 0.10 | 0.00 | 40.00 | 40.00 | 30.72 |

P10301030 | 0.10 | 10.00 | 30.00 | 30.00 | 41.42 |

P10301040 | 0.10 | 10.00 | 30.00 | 40.00 | 48.47 |

P10401030 | 0.10 | 10.00 | 40.00 | 30.00 | 44.57 |

P10401040 | 0.10 | 10.00 | 40.00 | 40.00 | 46.69 |

P20301030 | 0.10 | 20.00 | 30.00 | 30.00 | 57.95 |

P20301040 | 0.10 | 20.00 | 30.00 | 40.00 | 65.76 |

P20401030 | 0.10 | 20.00 | 40.00 | 30.00 | 60.20 |

P20401040 | 0.10 | 20.00 | 40.00 | 40.00 | 61.74 |

P00302030 | 0.20 | 0.00 | 30.00 | 30.00 | 25.43 |

P00302040 | 0.20 | 0.00 | 30.00 | 40.00 | 32.82 |

P00402030 | 0.20 | 0.00 | 40.00 | 30.00 | 28.97 |

P00402040 | 0.20 | 0.00 | 40.00 | 40.00 | 29.72 |

P10302030 | 0.20 | 10.00 | 30.00 | 30.00 | 41.92 |

P10302040 | 0.20 | 10.00 | 30.00 | 40.00 | 49.81 |

P10402030 | 0.20 | 10.00 | 40.00 | 30.00 | 46.34 |

P10402040 | 0.20 | 10.00 | 40.00 | 40.00 | 47.33 |

P20302030 | 0.20 | 20.00 | 30.00 | 30.00 | 58.12 |

P20302040 | 0.20 | 20.00 | 30.00 | 40.00 | 65.18 |

P20402030 | 0.20 | 20.00 | 40.00 | 30.00 | 61.24 |

P20402040 | 0.20 | 20.00 | 40.00 | 40.00 | 63.52 |

P00303030 | 0.30 | 0.00 | 30.00 | 30.00 | 25.73 |

P00303040 | 0.30 | 0.00 | 30.00 | 40.00 | 35.42 |

P00403030 | 0.30 | 0.00 | 40.00 | 30.00 | 29.57 |

P00403040 | 0.30 | 0.00 | 40.00 | 40.00 | 31.54 |

P10303030 | 0.30 | 10.00 | 30.00 | 30.00 | 43.08 |

P10303040 | 0.30 | 10.00 | 30.00 | 40.00 | 51.56 |

P10403030 | 0.30 | 10.00 | 40.00 | 30.00 | 45.89 |

P10403040 | 0.30 | 10.00 | 40.00 | 40.00 | 47.55 |

P20303030 | 0.30 | 20.00 | 30.00 | 30.00 | 59.04 |

P20303040 | 0.30 | 20.00 | 30.00 | 40.00 | 67.52 |

P20403030 | 0.30 | 20.00 | 40.00 | 30.00 | 62.23 |

P20403040 | 0.30 | 20.00 | 40.00 | 40.00 | 64.44 |

P00304030 | 0.40 | 0.00 | 30.00 | 30.00 | 26.72 |

P00304040 | 0.40 | 0.00 | 30.00 | 40.00 | 34.29 |

P00404030 | 0.40 | 0.00 | 40.00 | 30.00 | 29.34 |

P00404040 | 0.40 | 0.00 | 40.00 | 40.00 | 31.27 |

P10304030 | 0.40 | 10.00 | 30.00 | 30.00 | 42.50 |

P10304040 | 0.40 | 10.00 | 30.00 | 40.00 | 51.16 |

P10404030 | 0.40 | 10.00 | 40.00 | 30.00 | 46.69 |

P10404040 | 0.40 | 10.00 | 40.00 | 40.00 | 47.41 |

P20304030 | 0.40 | 20.00 | 30.00 | 30.00 | 58.42 |

P20304040 | 0.40 | 20.00 | 30.00 | 40.00 | 66.51 |

P20404030 | 0.40 | 20.00 | 40.00 | 30.00 | 60.69 |

P20404040 | 0.40 | 20.00 | 40.00 | 40.00 | 64.03 |

Number | Confining Pressure/MPa | Rising Section Coefficient | Falling Section Coefficient | ${\mathit{R}}_{\mathit{a}}^{2}$ | ${\mathit{R}}_{\mathit{f}}^{2}$ |
---|---|---|---|---|---|

P00300030 | 0 | 1.45E+00 | 6.65E+00 | 1.00E+00 | 9.38E−01 |

P10300030 | 10 | 2.11E+00 | 1.66E+00 | 1.00E+00 | 9.96E−01 |

P20300030 | 20 | 2.32E+00 | 4.54E−01 | 1.00E+00 | 8.61E−01 |

P00303030 | 0 | 2.01E+00 | 1.43E+01 | 9.95E−01 | 9.51E−01 |

P10303030 | 10 | 2.08E+00 | 5.65E−01 | 1.00E+00 | 9.46E−01 |

P20303030 | 20 | 2.47E+00 | 3.85E−01 | 9.99E−01 | 8.08E−01 |

P00303040 | 0 | 1.74E+00 | 4.60E+01 | 9.98E−01 | 6.06E−01 |

P10303040 | 10 | 2.07E+00 | 5.56E−01 | 9.99E−01 | 9.57E−01 |

P20303040 | 20 | 2.71E+00 | 5.32E−01 | 9.99E−01 | 9.30E−01 |

P00403030 | 0 | 1.82E+00 | 1.25E+01 | 9.99E−01 | 9.78E−01 |

P10403030 | 10 | 2.37E+00 | 7.08E−01 | 9.98E−01 | 8.53E−01 |

P20403030 | 20 | 2.32E+00 | 4.66E−01 | 9.98E−01 | 9.73E−01 |

Incorporation Ratio | Confining Pressure/MPa | Old Concrete Strength/MPa | New Concrete Strength/MPa | |
---|---|---|---|---|

Pearson correlation | −0.07 | 0.96 | 0.006 | 0.197 |

Significance (bilateral) | 0.58 | 0.00 | 0.966 | 0.132 |

N | 60 | 60 | 60 | 60 |

Control Variable | Incorporation Ratio | Old Concrete Strength/MPa | New Concrete Strength/MPa | |
---|---|---|---|---|

Confining pressure | Correlation | −0.24 | 0.021 | 0.743 |

Significance (bilateral) | Significance (bilateral) | 0.06 | 0.873 | 0.000 |

N | df | 57 | 57 | 57 |

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## Share and Cite

**MDPI and ACS Style**

Li, T.; Xiao, J.
Discrete Element Simulation Analysis of Biaxial Mechanical Properties of Concrete with Large-Size Recycled Aggregate. *Sustainability* **2021**, *13*, 7498.
https://doi.org/10.3390/su13137498

**AMA Style**

Li T, Xiao J.
Discrete Element Simulation Analysis of Biaxial Mechanical Properties of Concrete with Large-Size Recycled Aggregate. *Sustainability*. 2021; 13(13):7498.
https://doi.org/10.3390/su13137498

**Chicago/Turabian Style**

Li, Tan, and Jianzhuang Xiao.
2021. "Discrete Element Simulation Analysis of Biaxial Mechanical Properties of Concrete with Large-Size Recycled Aggregate" *Sustainability* 13, no. 13: 7498.
https://doi.org/10.3390/su13137498