# Simulation and Validation of Discrete Element Parameter Calibration for Fine-Grained Iron Tailings

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}, Al

_{2}O

_{3}, Fe

_{2}O

_{3}, CaO, MgO, etc., as well as a small amount of K

_{2}O, Na

_{2}O and S, P, etc. [5]. The mineral composition of iron tailings varies greatly due to the different origins and processing processes, except for the main mineral composition of quartz, hematite, dolomite and feldspar, and other minerals such as hornblende and chlorite have unequal contents [6].

## 2. Experiments to Calibrate Parameters

#### 2.1. JKR Contact Discrete Element Model

_{JKR}stands for the normal elastic contact force, N; E* for the equivalent Young’s modulus, Pa; R* for the equivalent radius, m; a

_{2}for the contact radius, m; W for the equivalent surface energy of the contact particle, J/m

^{2}; and u for the normal overlap, m.

_{1}and r

_{2}, respectively. The border energy between particle 1 and particle 2 is represented by the number r

_{12}.

_{12}= 0 and r

_{1}= r

_{2}= r. As a result, W = 2r is the equation for the cohesion between similar particle types [17]. In (2) and (3), respectively, the normal elastic contact force JKR and the normal overlap u of the particles are displayed:

_{JKR}normal to the overlap u can be written as follows

_{2}is the radius of the contact surface following the collision of the two particles, r is the surface energy of the contacting particles, E* is the modulus of elasticity and R* is the equivalent contact radius.

#### 2.2. Sizing for Discrete Element Models

_{a}is the particle size, mm; T is the device volume, L; $\overline{\rho}$ is the original particle average size, mm; X

_{n}is the enlarged large particle size, mm; and a

_{n}is the particle radius with different occupancy ratio, mm.

_{a}of the amplified particles is first calculated while performing particle size analysis

_{a}is introduced into Equation (8):

_{n}are finally made:

#### 2.3. Determination of the Angle of Repose

#### 2.4. Particle Modeling with Discrete Elements

## 3. Designing and Analyzing Studies for Parameter Calibration

#### 3.1. Plackett-Burman Experimental Design Importance

^{2}= 0.9922, demonstrating that the regression equation model suited the data well, and was a representative regression equation [30]. Where R

_{adj}= 0.9829, this indicated that the model applies to 98.29% of the effect values. The ANOVA results showed that the results for JKR surface energy coefficient (C), particle-particle static friction coefficient (E) and particle-particle dynamic friction coefficient (F) had a significant effect (p < 0.05) on the particle resting angle (R), while the other factors were not significant.

#### 3.2. Box-Behnken Response Surface Analysis

^{2}= 0.9884; and the corrected coefficient of determination R

^{2}

_{adj}= 0.9736. The predictive coefficient of determination R

^{2}

_{pre}= 0.9064, indicating that the model is a true representation of the actual situation [33]. The test precision Adep Precision = 24.6778, indicating that the model has good accuracy.

^{2}− 698.85000E

^{2}− 7583.75000F

^{2}

#### 3.3. Regression Model Interaction Effect Analysis

^{2}to 0.60 J/m

^{2}. According to the JKR contact model, an increase in the surface energy coefficient causes an increase in the cohesive forces that exist between particles. These forces can cause particles to adhere to one another and form new particle clusters, which causes the angle of repose to increase, as the particles at the top of the angle of repose are adsorbed and difficult to slide off when stacking is done. A strong interaction between the JKR surface energy coefficient C and the static friction coefficient E between the particles can be taken into account in the contour plot of Figure 10b.

## 4. Determination of the Optimal Combination of Parameters and Validation of the Simulation

## 5. Conclusions

- (1)
- The computational performance of the numerical simulation was improved by increasing the discrete element of fine-grained iron tailings’ particle size by 1.959708 mm, with an average particle size of 24.15 um, and using 500,000 particles as the maximum.
- (2)
- The contact characteristics of the amplified particles were calibrated using the JKR contact model in discrete elements. The Plackett-Burman tests were used to determine the factors that significantly affect the resting angle of the amplified particles of microfine-grained iron tailings. These factors included the surface energy JKR coefficient, particle-particle static friction coefficient and particle-particle dynamic friction coefficient.
- (3)
- The Box-Behnken test revealed that, in contrast to the simulated particle rest angle of 44.81° for fine-grained iron tailings particles at 0.459, 0.393 and 0.106, respectively, the relative error of the surface energy JKR coefficient, particle-particle static friction coefficient and particle-particle kinetic friction coefficient in the EDEM discrete element software was only 2.18%; this proves the viability of response surface experiments for the discrete element particle system. It was shown that it was possible to calibrate the particle coefficients for discrete elements.
- (4)
- The best experimentally obtained parameters were entered into discrete element software, where the mean resting angle was calculated to be 45.823°. This was compared to the mean angle from physical experiments, which was 45.119°, and the error was calculated to be 1.56%, which was not significantly different. This proves that the contact parameters obtained from the particle size scaling coefficient calibration trials satisfy the numerical simulation’s requirements, and serve as a reference for the discrete element model used to simulate the numerical behavior of fine-grained iron tailings particles.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Theoretical diagram of original particle size distribution (

**a**) and amplified particle size distribution (

**b**).

**Figure 10.**Response surface diagram (

**a**) and contour diagram (

**b**) of the influence of JKR surface energy coefficient and static friction coefficient on repose angle.

**Figure 11.**Influence of JKR surface energy and rolling friction coefficient on angle of repose surface diagram (

**a**) and contour diagram (

**b**).

**Figure 12.**Surface diagram (

**a**) and contour diagram (

**b**) of the influence of JKR surface energy and rolling friction coefficient on repose angle.

Simulation Parameters | Level | ||
---|---|---|---|

Low Level | High Level | ||

Particle Poisson’s ratio | A | 0.3 | 0.5 |

Coefficient of shear elasticity (pa) | B | 2.40 × 10^{9} | 2.40 × 10^{10} |

JKR surface energy coefficient (J/m^{2}) | C | 0.3 | 0.6 |

Collision recovery factor (particles) | D | 0.1 | 0.3 |

Coefficient of static friction (particles) | E | 0.3 | 0.5 |

Coefficient of dynamic friction (particles) | F | 0.08 | 0.12 |

Serial Number | A | B (pa) | C (J/m^{3}) | D | E | F | Repose Angle (°) |
---|---|---|---|---|---|---|---|

1 | 0.50 | 2.40 × 10^{10} | 0.3 | 0.3 | 0.50 | 0.12 | 35.41 |

2 | 0.30 | 2.40 × 10^{10} | 0.6 | 0.1 | 0.50 | 0.12 | 40.29 |

3 | 0.50 | 2.40 × 10^{9} | 0.6 | 0.3 | 0.30 | 0.12 | 35.53 |

4 | 0.30 | 2.40 × 10^{10} | 0.3 | 0.3 | 0.50 | 0.08 | 30.12 |

5 | 0.30 | 2.40 × 10^{9} | 0.6 | 0.1 | 0.50 | 0.12 | 40.25 |

6 | 0.30 | 2.40 × 10^{9} | 0.3 | 0.3 | 0.30 | 0.12 | 30.94 |

7 | 0.50 | 2.40 × 10^{9} | 0.3 | 0.1 | 0.50 | 0.08 | 29.18 |

8 | 0.50 | 2.40 × 10^{10} | 0.3 | 0.1 | 0.30 | 0.12 | 27.03 |

9 | 0.50 | 2.40 × 10^{10} | 0.6 | 0.1 | 0.30 | 0.08 | 29.18 |

10 | 0.30 | 2.40 × 10^{10} | 0.6 | 0.3 | 0.30 | 0.08 | 30.96 |

11 | 0.50 | 2.40 × 10^{9} | 0.6 | 0.3 | 0.50 | 0.08 | 37.85 |

12 | 0.30 | 2.40 × 10^{9} | 0.3 | 0.1 | 0.30 | 0.08 | 24.35 |

Factors | Sum of Squares | F-Value | p-Value | Effect |
---|---|---|---|---|

Models | 293.48 | 106.54 | <0.0001 | |

A | 0.6211 | 1.35 | 0.2973 | −0.2275 |

B | 2.18 | 4.74 | 0.0814 | −0.425833 |

C | 114.27 | 248.88 | <0.0001 | 3.08583 |

D | 9.24 | 20.13 | 0.0065 | 0.8775 |

E | 102.73 | 223.74 | <0.0001 | 2.92583 |

F | 64.45 | 140.37 | <0.0001 | 2.3175 |

Residual | 2.30 | |||

Total deviation | 295.78 |

Serial Number | C (J/m^{2}) | E | F | Repose Angle (°) |
---|---|---|---|---|

1 | 0.30 | 0.40 | 0.08 | 34.36 |

2 | 0.45 | 0.40 | 0.10 | 45.88 |

3 | 0.30 | 0.40 | 0.12 | 34.11 |

4 | 0.45 | 0.30 | 0.08 | 33.32 |

5 | 0.45 | 0.40 | 0.10 | 44.13 |

6 | 0.60 | 0.40 | 0.08 | 29.19 |

7 | 0.45 | 0.40 | 0.10 | 44.12 |

8 | 0.45 | 0.40 | 0.10 | 45.34 |

9 | 0.45 | 0.30 | 0.12 | 39.45 |

10 | 0.30 | 0.30 | 0.10 | 28.13 |

11 | 0.30 | 0.50 | 0.10 | 30.13 |

12 | 0.60 | 0.40 | 0.12 | 35.13 |

13 | 0.45 | 0.40 | 0.10 | 46.34 |

14 | 0.60 | 0.30 | 0.10 | 29.23 |

15 | 0.45 | 0.50 | 0.12 | 34.45 |

16 | 0.60 | 0.50 | 0.10 | 25.19 |

17 | 0.45 | 0.50 | 0.08 | 33.34 |

Source of Variance | Sum of Squares | Freedom | Mean Square | F-Value | p-Value |
---|---|---|---|---|---|

Models | 637.64 | 9 | 70.85 | 66.47 | <0.0001 |

C | 272.84 | 1 | 272.84 | 255.99 | <0.0001 |

E | 13.47 | 1 | 13.47 | 12.64 | 0.0093 |

F | 18.30 | 1 | 18.30 | 17.17 | 0.0043 |

C × E | 22.09 | 1 | 22.09 | 20.73 | 0.0026 |

C × F | 7.18 | 1 | 7.18 | 6.74 | 0.0356 |

E × F | 6.30 | 1 | 6.30 | 5.91 | 0.0453 |

C^{2} | 29.09 | 1 | 29.09 | 27.29 | 0.0012 |

E^{2} | 205.64 | 1 | 205.64 | 192.94 | <0.0001 |

F^{2} | 38.75 | 1 | 38.75 | 36.35 | 0.0005 |

Residual | 7.46 | 7 | 1.07 | ||

Lack of fit | 3.38 | 3 | 1.13 | 1.10 | 0.4458 |

Pure error | 4.09 | 4 | 1.02 | ||

Sum | 645.10 | 16 | |||

R^{2} = 0.9884 | R^{2}_{adj} = 0.9736 | R^{2}_{pre} = 0.9064 | Adep Precision = 24.6778 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, J.; Chang, Z.; Niu, F.; Chen, Y.; Wu, J.; Zhang, H.
Simulation and Validation of Discrete Element Parameter Calibration for Fine-Grained Iron Tailings. *Minerals* **2023**, *13*, 58.
https://doi.org/10.3390/min13010058

**AMA Style**

Zhang J, Chang Z, Niu F, Chen Y, Wu J, Zhang H.
Simulation and Validation of Discrete Element Parameter Calibration for Fine-Grained Iron Tailings. *Minerals*. 2023; 13(1):58.
https://doi.org/10.3390/min13010058

**Chicago/Turabian Style**

Zhang, Jinxia, Zhenjia Chang, Fusheng Niu, Yuying Chen, Jiahui Wu, and Hongmei Zhang.
2023. "Simulation and Validation of Discrete Element Parameter Calibration for Fine-Grained Iron Tailings" *Minerals* 13, no. 1: 58.
https://doi.org/10.3390/min13010058