# Study on Macro-Meso Deformation Law and Acoustic Emission Characteristics of Granular Gangue under Different Loading Rates

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Design and the Establishment of Particle Flow Numerical Model

#### 2.1. Material Preparation

_{2}, which is the skeleton composition of the gangue. Moreover, gangue specimens also contain different contents of Al

_{2}O

_{3}and CaO and other substances.

#### 2.2. Experiment Design

#### 2.3. Construction of Particle Flow Numerical Model

^{−3}. The particles inside the particle contour generated before were divided into groups, and the particles in the contour were not deleted [15,16,17]. The rigid cluster units with different gradations were obtained, as shown in Figure 2. At the same time, the flexible cluster particle flow model of broken gangue specimens was generated by the FISH function. In the simulation process, the wall stiffness was 1.0 × 10

^{9}N/m, the wall friction coefficient was 0, and the particle density and porosity of the gangue specimen were 2800 kg/m and 0.3. The stress, strain, force chain, and fracture evolution during compaction were recorded in real time by the FISH function [18,19].

## 3. Result and Analysis

#### 3.1. Confined Compression Deformation of Gangue at Different Loading Rates

- (1)
- Stress-strain relationship

- (1)
- The overall trend of stress–strain curves of gangue specimens under six different loading rates is consistent. With the increase of stress, the strain presents three stages of fast growth, slow growth, and stable deformation. The growth rate of the strain is larger in the early loading stage, and the strain amount at this stage accounts for about 50% of the total strain. This is because the pores among gangue blocks are compacted in this stage, and the gangue block with large grain size is gradually broken. In the middle loading stage, the growth rate of the gangue strain decreases. At this stage, pores have been compacted, and the gangue deformation is mainly caused by fragmentation. In the later loading stage, the strain of the gangue remains stable. This is because the gangue cannot be broken, and has reached a relatively stable state.
- (2)
- The maximum strain of the gangue is directly proportional to the loading rate, that is, the greater the loading rate, the greater the maximum strain. With the increase of loading rate, the maximum strain of the gangue increases from 0.321 to 0.353, indicating that the loading rate has a great impact on the mechanical properties and deformation characteristics of crushed gangue. The main reason is that under the low loading rate, the gangue fragmentation and compaction process are relatively slow, and a stable bonding of the gangue can be formed. At this time, the gangue cannot be further broken. Under the high loading rate, pores between the gangue are quickly compacted, and then the gangue with large particle size is quickly broken. At this time, the gangue is incapable of forming a stable bonding state. Finally, the gangue is crushed and compacted again, leading to a further increase of the strain.
- (3)
- With the increase of loading rate, the maximum strain increases continuously. When the loading rate is greater than 2 kN/s, the growth rate of the strain decreases, indicating that 2 kN/s is the optimal loading rate under this condition. Therefore, when the backfill body is compacted, the optimal compacting force should be maintained at about 2 kN/s. Moreover, after the backfill body is backfilled into the goaf, the loading rate generated by the overlying surrounding rock is in a dynamic change under the disturbance of mining activities, which will have a greater impact on the bearing capacity of the backfill body. Consequently, the influence of mining activities should be minimized to reduce the disturbance to the backfill body.
- (2)
- Porosity–strain relationship

_{0}is the absolute volume of the gangue in the absolute dense state, mL; r is the radius of the steel tube; h is the residual height of the gangue after compression, m is the mass of the gangue before and after compression; h

_{0}is the initial backfill height of the gangue; ${\rho}_{0}$ is the strain in the compression process and the absolute density of the gangue.

_{0}, the porosity decreases with the increase of strain. If ε = 0, the initial porosity is positively correlated with the initial backfill height.

- (3)
- Porosity-stress relationship

#### 3.2. AE Energy Characteristics of Gangue at Different Loading Rates

- (1)
- The changing trend of the cumulative energy curves and strain curves are consistent. With the increase of loading rate, the cumulative AE energy of the gangue also increases. Through the AE monitoring technology, the dynamic monitoring of AE energy in the process of gangue fragmentation can reflect the damage process inside the specimen. It shows that AE energy can effectively characterize the mechanical properties of the gangue.
- (2)
- When the loading rate is less than 1.0 kN/s, the AE energy and strain curve of the specimen can be clearly divided into three stages: early loading stage, middle loading stage, and later loading stage. In the early loading stage (Stage 1), strain and AE energy increase slowly. This is because the pores between the gangues are compacted, and the gangues are not broken under the low loading rate, and AE energy mainly stems from the friction between the gangues. In the middle loading stage (Stage 2), the crushing of gangue results in the release of a large amount of energy, which increases the accumulated energy rapidly. Due to the low loading rate, a stable structure can be easily formed by the gangue. Thus, the duration of the AE signal is short. In the later loading stage (Stage 3), the AE signal intensity is low, and the accumulated energy gradually tends to be stable.
- (3)
- When the loading rate is more than 1.5 kN/s, the changing trend of AE signal energy at the early loading stage is the same as that under the low loading rate. However, at the middle loading stage, the gangue cannot adjust each other to form a stable carrier under the higher loading rate, some gangue is further crushed and accompanied by the energy release. This process lasts so long that the late stage of stress loading does not appear. The deformation process of gangue and the generation process of the AE phenomenon last for a long time, and the later loading stage (the accumulated AE energy tends to stable state) is not significant.
- (4)
- As shown in Figure 6, the maximum AE energy of gangue specimens under six different loading rates during the whole compaction process are 1.1 × 10
^{3}, 9.6 × 10^{3}, 10.8 × 10^{3}, 13.3 × 10^{3}, 14.3 × 10^{3}, and 14.4 × 10^{3}, respectively. Meanwhile, the cumulative energy of gangue specimens are 2.11 × 10^{6}, 14.32 × 10^{6}, 20.79 × 10^{6}, 24.18 × 10^{6}, 23.28 × 10^{6}, and 24.33 × 10^{6}, respectively. It is found that under the low loading rate, the damage of the gangue is smoother and the energy cycle is short, and the cumulative energy is also smaller; under the high loading rate, the gangue is broken, and the compaction process is more violent and the energy cycle is longer, the accumulated energy is greater.

#### 3.3. Relationship Model of Macroscopic Deformation and AE Energy at Different Loading Rates

- (1)
- The variation trend of maximum strain, maximum energy, and accumulated energy of gangue under different loading rates is consistent. With the increase of loading rate, the maximum strain, AE energy, and cumulative energy rapidly increase first and then become stable, but the fragmentation rate decreases. Other than that, when the loading rate is less than 1.5 kN/s, the change of the loading rate has a large impact on specimens; when the loading rate is more than 1.5 kN/s, the influence of the loading rate change on specimens is decreased.
- (2)
- At the low loading rate, the relationship between the macroscopic deformation and energy change of gangue shows three stages, and the linear correlation coefficients at different stages are higher than 0.96. However, at the high loading rate, the relationship between macroscopic deformation of the specimens and AE energy is mainly reflected in the first two stages while the third stage is not obvious. It implies that the macroscopic deformation of gangue specimens is closely related to the change of energy, so the fragmentation process of gangue can be analyzed through the change of AE energy.

#### 3.4. Distribution Characteristics of Force Chain of Gangue Model under Different Loading Rates

#### 3.5. Fracture Evolution Characteristics of Gangue Model under Different Loading Rates

## 4. Conclusions

- (1)
- Direct compression of pores under low stress is the main factor affecting macroscopic deformation of the gangue. The porosity of the gangue decreases with the decrease of residual height, and increases with the decrease of strain. The porosity is inversely proportional to the stress, and the decreasing rate decreases gradually.
- (2)
- With the increase of loading rate, the maximum energy and cumulative energy of AE increase continuously, which is consistent with the macroscopic deformation characteristics of gangue. In the early loading, there is less gangue fragmentation and low AE signal; in the later loading stage, the gangue fragmentation is intensified, and the AE signal strength and cumulative energy increase significantly.
- (3)
- With the increase of loading rate, the influence of loading rate on deformation, fragmentation and AE signals of gangue is gradually weakened.
- (4)
- In the early loading stage, the distribution of the force chain and the fracture development of the gangue model are deepened. In the later loading stage, there is almost no difference in the state distribution of each model. The macroscopic deformation and failure mechanism of gangue under different loading rates is revealed from the mesoscopic point of view.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Stress-strain curve of gangue specimens at different loading rates under the confined compression.

**Figure 5.**AE energy-cumulative energy-strain-time curve of gangue at different loading rates: (

**a**) 0.25 kN/s. (

**b**) 0.5 kN/s. (

**c**) 1.0 kN/s. (

**d**) t 1.5 kN/s. (

**e**) 2.0 kN/s (

**f**) 5.0 kN/s.

**Figure 9.**Distribution of force chain of gangue model at different loading rates under the axial pressure of 4 MPa.

**Figure 10.**Force chain distribution of gangue model at different loading rates under the axial pressure of 16 MPa.

**Figure 11.**Step-coordination number curve in the compression process of gangue with different loading rates.

**Figure 12.**Fracture evolution of gangue models with different loading rates under the axial pressure of 4 MPa.

**Figure 13.**Fracture evolution of gangue models with different loading rates under the axial pressure of 16 MPa.

Ingredients | SiO_{2} | Fe_{2}O_{3} | Al_{2}O_{3} | CaO | MgO | TiO_{2} | Burning Loss |
---|---|---|---|---|---|---|---|

% | 49.34 | 5.11 | 16.79 | 5.8 | 0.93 | 0.92 | 14.96 |

Loading Rate/(kN/s) | Stage 1 | Stage 2 | Stage 3 |
---|---|---|---|

0.25 | y = 9.288 x + 0.009 | y = 13.209 x − 0.141 | y = 2.639 x + 1.260 |

0.5 | y = 4.747 x + 0.044 | y = 94.252 x − 11.141 | y = 25.233 x + 6.622 |

1.0 | y = 11.592 x − 0.009 | y = 50.115 x − 1.801 | y = 6.128 x + 8.752 |

1.5 | y = 11.881 x − 0.015 | y = 75.086 x − 1.445 | |

2.0 | y = 22.670 x − 0.044 | y = 72.071 x − 1.923 | |

5.0 | y = 12.298 x − 0.023 | y = 75.696 x − 2.553 |

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**MDPI and ACS Style**

Qin, T.; Guo, X.; Huang, Y.; Wu, Z.; Qi, W.; Wang, H.
Study on Macro-Meso Deformation Law and Acoustic Emission Characteristics of Granular Gangue under Different Loading Rates. *Minerals* **2022**, *12*, 1422.
https://doi.org/10.3390/min12111422

**AMA Style**

Qin T, Guo X, Huang Y, Wu Z, Qi W, Wang H.
Study on Macro-Meso Deformation Law and Acoustic Emission Characteristics of Granular Gangue under Different Loading Rates. *Minerals*. 2022; 12(11):1422.
https://doi.org/10.3390/min12111422

**Chicago/Turabian Style**

Qin, Tao, Xin Guo, Yanli Huang, Zhixiong Wu, Wenyue Qi, and Heng Wang.
2022. "Study on Macro-Meso Deformation Law and Acoustic Emission Characteristics of Granular Gangue under Different Loading Rates" *Minerals* 12, no. 11: 1422.
https://doi.org/10.3390/min12111422