# Study on Crack Classification Criterion and Failure Evaluation Index of Red Sandstone Based on Acoustic Emission Parameter Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Experimental Methods

#### 2.1. Specimen Preparation

^{3}, respectively. All specimens used in the lab tests came from the same rock block and were cut in the same direction to avoid specimen dispersion. In this testing, nine specimens were prepared in three sizes. The side of the cube specimen used in DST was 100 mm, the size of disc specimen used in BITT was $\mathsf{\Phi}50\times \mathrm{H}25$mm, and the size of the cylindrical specimens used in UCT was $\mathsf{\Phi}50\times \mathrm{H}100\mathrm{m}$m. The geometry and dimensions of the specimens in the three test types are shown in Figure 2. The accuracy of each specimen is within the range specified by ISRM.

#### 2.2. Experimental Equipment and Setup

- (1)
- Loading equipment

- (2)
- AE monitoring system

_{t}, σ

_{s}and σ

_{c}denote the tensile strength (Mpa), the shear strength (Mpa), and the uniaxial compressive strength (Mpa), respectively.

## 3. AE Data Processing Methods

#### 3.1. Inter-Event Time Function F(τ) Theory

_{i}is the time of the i-th AE event, and t

_{i−}

_{1}is the time of the previous AE event.

#### 3.2. RA and AF Values Method

#### 3.3. Kernel Density Estimation (KDE) Method

_{i}represents the i-th data point. K(x) is a kernel function. In this paper, the multivariate Gaussian function is taken as the kernel function, and its formula is as follows:

## 4. Experimental Results

#### 4.1. AE Event Rate Monitoring

_{t}, and F

_{t}is the corresponding load at T

_{t}. F

_{t}is expressed as F

_{t}= kF

_{p}, where F

_{p}is the peak load and k is the ratio of F

_{t}to F

_{p}. In addition, the proportion of AE events in phase-1 and phase-2 to the total number of events in each test type is shown in Figure 7.

_{t}, indicating that the rock has been damaged to a certain extent in the microcrack generation phase. However, in DST and UCT, the number of AE events is less before loading F

_{t}, which indicates that the rock damage mainly occurs in the macrocrack generation phase. In addition, the F

_{t}in BITT, DST, and UCT are 94.16% F

_{p}, 69.02% F

_{p}and 71.81% F

_{p}, respectively. It can be seen that the macrocrack generation phase in BITT is significantly shorter than that in DST and UCT. The above results are due to the different fracture modes of rocks under different loading conditions. In BITT, tensile fracture mainly occurs; in DST, shear fracture mainly occurs; and in UCT, tensile and shear fracture always occur together.

#### 4.2. Evolution of RA and AF Values

_{t}; however, they show obvious trends after T

_{t}. When the loading time is in the interval between T

_{t}and the final failure time (T

_{f}), there is an obvious downward trend in RA value and an obvious upward trend in AF value. In addition, when rock failure occurs, the RA value will suddenly decrease, and the AF value will suddenly increase in the three test types.

#### 4.3. The Kernel Density Distribution of RA–AF Values

_{t}is selected as the dividing point to divide the loading process of each test into two phases, in which the RA–AF distribution is compared. Here, t represents the actual time, and T

_{f}represents the moment when the sample failure occurs.

#### 4.4. Classification of Tensile and Shear Cracks

#### 4.5. Statistics of Tension and Shear Fracture, and Analysis of Failure Mechanism

## 5. Discussion

#### 5.1. Evolution Characteristics of Tensile and Shear Sources in UCT

_{t}, 57.22%σ

_{t}and 70.25%σ

_{t}, respectively (σ

_{t}is the peak stress). The rapid growth point of the tensile source of the U-1 specimen is at the critical point of phase II and phase III, and the rapid growth points of the tensile sources of the U-2 and U-3 samples are all at phase II. However, in phase I, the shear source increases rapidly; in phase II, the growth of the shear source is slow, and its cumulative curve is roughly “horizontal”. The rapid growth point of the shear source appears in phase III, which is close to rock failure. The stress corresponding to the rapid growth points of the shear sources of the U-1, U-2, and U-3 specimens is 99.49%σ

_{t}, 95.46%σt, and 95.93%σ

_{t}, respectively. Owing to the strength of the U-2 specimen being lower than that of the U-1 and U-3 specimens, the rapid growth point of the U-2 specimen occurs earlier, and especially the rapid growth point of the tensile source.

#### 5.2. Failure Precursor Index of Rock Based on k Value

## 6. Conclusions

- (1)
- AE event rate can reflect the transformation of rock samples from microcracks to macrocracks. The macrocrack generation phase in UCT was the longest, that in DST was the second longest, and that in BITT was the shortest;
- (2)
- The KDE method can effectively identify and visualize the high-density areas of RA and AF values. In the failure mode dominated by tensile fracture, the RA value was low and the AF value was high. On the contrary, in the failure mode dominated by shear fracture, the RA value was high and the AF value was low. When rock failure occurred, the RA and AF values both developed in opposite directions;
- (3)
- It was determined that the dividing line for classifying tensile and shear cracks in the RA and AF value data is AF = 93RA + 75. The reliability of the dividing line has been verified by analyzing the failure mode and fracture mechanism of the sample;
- (4)
- Under uniaxial compression loading, the fracture source of red sandstone was mainly the shear source in the initial phase of loading, and the tensile source in the critical failure phase, and the number of the latter was far greater than that of the shear source;
- (5)
- K = AF/(93RA + 75) was proposed as an AE parameter index to reflect the internal fracture of the red sandstone specimen. Further, the corresponding reference judgment value CV (k) = 1 was proposed. It can be considered that the test sample entered the instability failure phase when CV (k) < 1.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AE | Acoustic emission |

BITT | Brazilian indirect tensile test |

DST | Direct shear test |

UCT | Uniaxial compression test |

KDE | Kernel density estimation |

RA | RA = rise time/amplitude |

AF | Average frequency |

σ_{s} | Shear strength |

σ_{c} | Uniaxial compressive strength |

F(τ) | The inter-event time function/AE event rate |

Tt | Time at the beginning of drastic increase in AE events |

Ft | Load at the beginning of drastic increase in AE events |

F_{p} | Peak load during the test |

CV | The coefficient of variation |

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**Figure 1.**Typical AE waveform and micro fracture (crack) classification. (

**a**) AE parameter in a hit; (

**b**) crack classification based on RA/AF value.

**Figure 2.**The geometry and dimensions of the specimens in the three types. (

**a**) DST; (

**b**) BITT; (

**c**) UCT.

**Figure 3.**Testing systems used in this study: (

**a**) DSZ-1000 stress–strain controlled testing system; (

**b**) WDAJ-600 rock shear testing machine; (

**c**) PCI-2 AE monitoring.

**Figure 4.**Types of test, the distribution of AE sensors and damaged rock specimens. (

**a**) BITT; (

**b**) DST; (

**c**) UCT.

**Figure 5.**The stress–displacement curve or stress–strain curve of the specimen in three test types. (

**a**) DST; (

**b**) BITT; (

**c**) UCT.

**Figure 6.**Variations of stress, cumulative AE events and corresponding AE event rate with time. (

**a**) BITT; (

**b**) DST; (

**c**) UCT.

**Figure 7.**The proportion of AE events in phase-1 and phase-2 to the total number of events. (

**a**) BITT; (

**b**) DST; (

**c**) UCT.

**Figure 14.**The statistics of tensile and shear cracks of the U-1, U-2 and U-3 specimens. (

**a**) U-1; (

**b**) U-2; (

**c**) U-3.

**Figure 17.**Spatial distribution of AE sources: (

**a**) U-1; (

**b**) U-2; (

**c**) U-3.

**Note:**The size of the scatter diagram indicates the source amplitude.

Number | Type of Test | Loading Rate (mm/min) | σ_{t}/σ_{s}/σ_{c} (MPa) |
---|---|---|---|

B-1 | BITT | 0.05 | 7.06 |

B-2 | 8.50 | ||

B-3 | 8.80 | ||

D-1 | DST | 0.1 | 12.48 |

D-2 | 11.79 | ||

D-3 | 13.68 | ||

U-1 | UCT | 0.1 | 115.27 |

U-2 | 108.79 | ||

U-3 | 118.10 |

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## Share and Cite

**MDPI and ACS Style**

Li, J.; Lian, S.; Huang, Y.; Wang, C.
Study on Crack Classification Criterion and Failure Evaluation Index of Red Sandstone Based on Acoustic Emission Parameter Analysis. *Sustainability* **2022**, *14*, 5143.
https://doi.org/10.3390/su14095143

**AMA Style**

Li J, Lian S, Huang Y, Wang C.
Study on Crack Classification Criterion and Failure Evaluation Index of Red Sandstone Based on Acoustic Emission Parameter Analysis. *Sustainability*. 2022; 14(9):5143.
https://doi.org/10.3390/su14095143

**Chicago/Turabian Style**

Li, Jiashen, Shuailong Lian, Yansen Huang, and Chaolin Wang.
2022. "Study on Crack Classification Criterion and Failure Evaluation Index of Red Sandstone Based on Acoustic Emission Parameter Analysis" *Sustainability* 14, no. 9: 5143.
https://doi.org/10.3390/su14095143