# Mechanical Properties and Acoustic Emission Characteristics of Anchored Structure Plane with Different JRC under Direct Shear Test

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experiment

_{y}= 205 MPa and elastic modulus E = 199 GPa.

_{u}, y

_{u}) of points on the JRC profile could be output every 1 mm interval length through MATLAB, and a 3D model was drawn by 3D modeling software according to the extracted coordinate point data. Finally, a 3D printer was used to print it as resin plates recorded with different JRC (the center of the resin plate contains a prefabricated hole with a diameter of 3 mm for placing the bolt). The size of the resin plate was 100 mm × 100 mm × 30 mm. The realization process of the resin plate is shown in Figure 2

## 3. Mechanical Properties

^{2}after linearly fitting were all greater than 0.95, indicating that the imitative effect is good and performs a reliable law. Cohesion-like stress and friction angle of the structural plane were calculated by using the Mohr–Coulomb criterion, as shown in Table 2. From Figure 7, under the same normal stress, the peak shear strength of unanchored structural plane increased with the increase of JRC, and the cohesion-like stress of unanchored structural planes with different JRC were 0.34 Mpa, 0.82 Mpa, 0.14 MPa, and 1.73 MPa, respectively. Based on the linear fitting parameters in Figure 7, friction angle of structural planes with different JRC could be inverted, which were 36.2°, 34.0°, 47.7°, and 44.2°, respectively. Except for the structural plane with JRC of 12–14, the larger the joint roughness, the larger the cohesion of unanchored structural plane. The roughness of the structural plane with JRC of 12–14 was large, but the cohesion-like stress was the smallest. This is because there existed a relatively large and smooth sawtooth on the structural plane with JRC of 12–14, and sliding is the main cause of specimen failure. The shear strength of the specimen is determined by cohesion and friction angle, which may explain why the cohesion-like stress of the structural plane with JRC of 12–14 was the minimum, but its friction angle was the maximum.

## 4. AE Characteristics

#### 4.1. Ring-Down Count

#### 4.2. B-value

_{dB}is the amplitude in dB, a is a constant, and b represents b-value. b-value can indicate the degree of fracture in the rock mass. The increase of b-value means that the rock fracture is mainly caused by small cracks, and the decrease of b-value represents that the rock fracture is mainly caused by large cracks.

#### 4.3. Analysis of RA-AF

#### 4.3.1. Variation of Cumulative Proportion of Shear-Tensile Cracks

#### 4.3.2. Variation of Real-Time Proportion of Shear Cracks

## 5. Conclusions

- (1)
- The larger the normal stress, the larger the peak shear strength of the anchored structural plane. Under the same normal stress, compared with the peak shear strength, the residual strength of structural planes with JRC of 6–8 and 18–20 decreased more, and that of structural planes with JRC of 0–2 and 12–14 decreased less. The peak shear strength of the anchored structural plane increased and then decreased with the variation of anchorage angle, and always reached the maximum value at 45° or 60°, which means the optimal installation angle of the bolt is in the range of [45°, 60°].
- (2)
- According to the AE monitoring results, the ring-down count rises first, then decreases and finally flattens, showing an obvious correlation with the shear stress curve. The ring-down count still kept a certain degree in the residual stage, which was about 60. The cumulative ring-down count curve was characterized by three-stage and the increase of normal stress accelerated the curve entering the rapid growth stage. The b-value curve was dense at the initial loading stage and tended to be sparse in the residual stage. Its variation trend mainly depended on the topography of structural plane, not only affected by the value of JRC. The influence of anchorage angle on b-value variation characteristics mainly depended on whether the bolt would be deformed during shearing.
- (3)
- Through AE experiments, the cumulative ratio of shear cracks could reach 85%, which is much higher than that of tensile cracks. The cumulative proportion curve of tensile cracks showed a three-stage pattern and the correlation with the shear stress curve was more significant. Besides, the higher the normal stress, the easier the signal cumulative proportion curve appearing in three-stage form. The proportion of shear cracks and tensile cracks in the experiment changed dynamically. For unanchored structural planes, the proportion of shear cracks was more than 50% in the whole experiment. For anchored structural planes, the proportion of tensile cracks may exceed that of shear cracks, sometimes even up to 80%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Extraction process of JRC profile coordinates. (

**a**) standard JRC profile with value of 12-14 (

**b**) basic gray image (

**c**) gray matrix and intensity matrix.

**Figure 5.**The arrangement of experimental devices. (

**a**) AE monitoring system (

**b**) Loading platform (

**c**) Data acquisition system.

**Figure 7.**Fitting curves of shear strength parameters of unanchored structural planes with different JRC.

**Figure 8.**Shear stress-displacement curves of anchored structural planes under different normal stress: (

**a**) σ = 2 MPa, (

**b**) σ = 3 MPa, (

**c**) σ = 4 MPa, (

**d**) σ = 5 Mpa (specimen ID: DS-ab-α-σ, where DS represents direct shear experiment, ab represents the range of JRC, α means the anchorage angle, and σ means the normal stress).

**Figure 9.**Shear stress-displacement curves of anchored structural planes with different JRC: (

**a**) JRC = 0–2, (

**b**) JRC = 6–8, (

**c**) JRC = 12–14, (

**d**) JRC = 18–20 (Specimen ID: DS-ab-α-σ, where DS represents direct shear experiment, ab represents the range of JRC, α means the anchorage angle, and σ means the normal stress).

**Figure 10.**Relationship between shear strength and anchorage angle: (

**a**) σ = 2 MPa, (

**b**) σ = 3 MPa, (

**c**) σ = 4 MPa, (

**d**) σ = 5 Mpa.

**Figure 11.**The variation trend of ring-down count and shear stress with time: (

**a**) DS-02-30-2, (

**b**) DS-02-60-5.

**Figure 12.**b-value curves of unanchored structural planes with different JRC under shearing: (

**a**) DS-02-0-2, (

**b**) DS-68-0-2, (

**c**) DS-1214-0-2, (

**d**) DS-1820-0-2, (

**e**) DS-02-0-5, (

**f**) DS-68-0-5, (

**g**) DS-1214-0-5, and (

**h**) DS-1820-0-5 (specimen ID: DS-ab-α-σ, where DS represents direct shear experiment, ab represents the range of JRC, α means the anchorage angle, and σ means the normal stress).

**Figure 13.**b-value curves of anchored structural planes with different JRC under shearing: (

**a**) DS-02-60-2, (

**b**) DS-68-60-2, (

**c**) DS-1214-60-2, and (

**d**) DS-1820-60-2 (specimen ID: DS-ab-α-σ, where DS represents direct shear experiment, ab represents the range of JRC, α means the anchorage angle, and σ means the normal stress).

**Figure 14.**b-value curves of anchored structural planes with different anchorage angles under shearing: (

**a**) DS-02-30-2, (

**b**) DS-02-45-2, (

**c**) DS-02-60-2, and (

**d**) DS-02-90-2 (specimen ID: DS-ab-α-σ, where DS represents direct shear experiment, ab represents the range of JRC, α means the anchorage angle, and σ means the normal stress).

**Figure 15.**RA-AF distribution of unanchored structural planes. (

**a**) DS-02-0-2 (

**b**) DS-68-0-2 (

**c**) DS-1214-0-2 (

**d**) DS-1820-0-2 (

**e**) DS-02-0-5 (

**f**) DS-68-0-5 (

**g**) DS-1214-0-5 (

**h**) DS-1820-0-5.

**Figure 16.**Variation trend of cumulative proportion of shear cracks and tensile cracks with time. ((

**A**) (

**a**) DS-02-0-2 (

**b**) DS-68-0-2 (

**c**) DS-1214-0-2 (

**d**) DS-1820-0-2 (

**e**) DS-02-0-5 (

**f**) DS-68-0-5 (

**g**) DS-1214-0-5 (

**h**) DS-1820-0-5); ((

**B**) (

**a**) DS-02-30-2 (

**b**) DS-68-30-2 (

**c**) DS-1214-30-2 (

**d**) DS-1820-30-2 (

**e**) DS-02-30-5 (

**f**) DS-68-30-5 (

**g**) DS-1214-30-5 (

**h**) DS-1820-30-5); ((

**C**) (

**a**) DS-02-90-2 (

**b**) DS-68-90-2 (

**c**) DS-1214-90-2 (

**d**) DS-1820-90-2 (

**e**) DS-02-90-5 (

**f**) DS-68-90-5 (

**g**) DS-1214-90-5 (

**h**) DS-1820-90-5).

**Figure 17.**Variation trend of real-time shear cracks’ proportion curves of unanchored structural planes. (

**a**) Ds-02-0-2 (

**b**) Ds-68-0-2 (

**c**) Ds-1214-0-2 (

**d**) Ds-1820-0-2 (

**e**) Ds-02-0-5 (

**f**) Ds-68-0-5 (

**g**) Ds-1214-0-5 (

**h**) Ds-1820-0-5.

**Figure 18.**Variation trend of real-time shear cracks’ proportion of anchored structural planes with anchorage angle of 30°. (

**a**) DS-02-30-2 (

**b**) DS-68-30-2 (

**c**) DS-1214-30-2 (

**d**) DS-1820-30-2 (

**e**) DS-02-30-5 (

**f**) DS-68-30-5 (

**g**) DS-1214-30-5 (

**h**) DS-1820-30-5.

**Figure 19.**Variation trend of real-time shear cracks’ proportion curves of anchored structural planes with anchorage angle of 90°. (

**a**) DS-02-90-2 (

**b**) DS-68-90-2 (

**c**) DS-1214-90-2 (

**d**) DS-1618-90-2 (

**e**) DS-02-90-5 (

**f**) DS-68-90-5 (

**g**) DS-1214-90-5 (

**h**) DS-1820-90-5.

Mechanical Parameters | Value |
---|---|

Unconfined compression strength (MPa) | 34.13 |

Elastic modulus (GPa) | 5.27 |

Tensile strength (MPa) | 2.98 |

Cohesion (MPa) | 13.79 |

Friction angle (°) | 27.92 |

Poisson’s ratio | 0.21 |

Parameters | JRC = 0–2 | JRC = 6–8 | JRC = 12–14 | JRC = 18–20 |
---|---|---|---|---|

Cohesion-like stress (Mpa) | 0.34 | 0.82 | 0.14 | 1.73 |

Friction angle (°) | 36.2 | 34.0 | 47.7 | 44.2 |

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**MDPI and ACS Style**

Li, S.; Lin, H.; Feng, J.; Cao, R.; Hu, H. Mechanical Properties and Acoustic Emission Characteristics of Anchored Structure Plane with Different JRC under Direct Shear Test. *Materials* **2022**, *15*, 4169.
https://doi.org/10.3390/ma15124169

**AMA Style**

Li S, Lin H, Feng J, Cao R, Hu H. Mechanical Properties and Acoustic Emission Characteristics of Anchored Structure Plane with Different JRC under Direct Shear Test. *Materials*. 2022; 15(12):4169.
https://doi.org/10.3390/ma15124169

**Chicago/Turabian Style**

Li, Su, Hang Lin, Jingjing Feng, Rihong Cao, and Huihua Hu. 2022. "Mechanical Properties and Acoustic Emission Characteristics of Anchored Structure Plane with Different JRC under Direct Shear Test" *Materials* 15, no. 12: 4169.
https://doi.org/10.3390/ma15124169