# Wavelet Energy Evolution Characteristics of Acoustic Emission Signal under True-Triaxial Loading during the Rockburst Test

^{1}

^{2}

^{*}

*Appl. Sci.*

**2022**,

*12*(15), 7786; https://doi.org/10.3390/app12157786 (registering DOI)

## Abstract

**:**

## 1. Introduction

## 2. Specimen and Methods

#### 2.1. Specimen

#### 2.2. Methods

_{x}, σ

_{y}, and σ

_{z}, which were simultaneously loaded at a rate of 2.5 KN/s, and the horizontal stress σ

_{y}was applied with a binding force of 9.8 KN (about 1 MPa). The stress σ

_{x}and σ

_{z}were loaded to 147 KN (σ

_{x}was 15 MPa, σ

_{z}was 30 MPa), for simulating the original ground stress state of the rock mass in the deep-buried underworkings. The loading state was maintained for 5 min, then stopped loading to simulate the situation of stress redistribution after excavation. The vertical stress σ

_{z}was then loaded at a certain rate of 2.5 KN/s until the rockburst happened. Figure 3 indicates the sample loading way, while Figure 4 represents the test loading path.

## 3. Phenomenon and Results

#### 3.1. Phenomenon

#### 3.2. Results

## 4. Wavelet Energy Evolution Characteristics

#### 4.1. Wavelet Transform

^{2}(R) contains several functions. One of the functions or signal Ψ(x) is the wavelet that satisfies the following conditions:

^{2}(R) that satisfies the following conditions:

#### 4.2. Remove Zero Data Processing

#### 4.3. Wavelet Energy Analysis

^{0}= (f

_{0}, f

_{1}, …, f

_{n}).

_{5}represents the low-frequency sub-signal of wavelet decomposition in layer 5, and CD

_{5}represents the high-frequency sub-signal of wavelet decomposition in layer 5.

_{i}with different frequency ranges. The energy values of the reconstructed signal were quantified as per Formula (8) and the signal energy distribution coefficients were calculated for each frequency band. Meanwhile, the dominant frequency band was defined.

_{ik}is the amplitude of the k sampling point of the layer i signal; m is the number of the signal discrete sampling points; E

_{i}is the corresponding energy of S

_{i}; K

_{i}is the AE signal energy distribution coefficients of each frequency band and the dominant frequency band is established as the highest energy distribution coefficient’s frequency band.

_{2}(125~250 kHz) and its energy value is 0.2812. The energy distribution coefficient is 0.3990, which accounts for the largest proportion.

#### 4.4. Characteristics of the Wavelet Energy Evolution

_{ti}) are counted in each period.

_{ti}is the number of dominant frequency bands of the i-type frequency band sub-signal in the t-the period; l is the total number of divided periods, and t is the number of 1 to l.

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Rockburst test phenomenon. (

**a**) Before rockburst; (

**b**) Small rock fragments ejecting; (

**c**) Rock plate splitting and peeling; (

**d**) Rock plate buckling ejection; (

**e**) Rockburst violence occurring; (

**f**) After rockburst.

**Figure 8.**Removing zero processing to the original waveform. (

**a**) Before processing; (

**b**) After processing.

**Figure 10.**The 3546th effective acoustic emission signal. (

**a**) The original AE signal waveform; (

**b**) AE signal reconstructed waveform of each frequency band.

Number i | Wavelet Sub-Signal | Frequency Range/kHz |
---|---|---|

1 | CA_{5} | 0~15.625 |

2 | CD_{5} | 15.625~31.250 |

3 | CD_{4} | 31.25~62.50 |

4 | CD_{3} | 62.5~125.0 |

5 | CD_{2} | 125~250 |

6 | CD_{1} | 250~500 |

CD_{1} | CD_{2} | CD_{3} | CD_{4} | CD_{5} | CA_{5} | |
---|---|---|---|---|---|---|

E | 0.1983 | 0.2812 | 0.1352 | 0.0830 | 0.0046 | 0.0025 |

K | 0.2813 | 0.3990 | 0.1918 | 0.1177 | 0.0066 | 0.0036 |

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**MDPI and ACS Style**

Hu, C.; Mei, F.; Hussain, W.
Wavelet Energy Evolution Characteristics of Acoustic Emission Signal under True-Triaxial Loading during the Rockburst Test. *Appl. Sci.* **2022**, *12*, 7786.
https://doi.org/10.3390/app12157786

**AMA Style**

Hu C, Mei F, Hussain W.
Wavelet Energy Evolution Characteristics of Acoustic Emission Signal under True-Triaxial Loading during the Rockburst Test. *Applied Sciences*. 2022; 12(15):7786.
https://doi.org/10.3390/app12157786

**Chicago/Turabian Style**

Hu, Chuanyu, Fuding Mei, and Wakeel Hussain.
2022. "Wavelet Energy Evolution Characteristics of Acoustic Emission Signal under True-Triaxial Loading during the Rockburst Test" *Applied Sciences* 12, no. 15: 7786.
https://doi.org/10.3390/app12157786