# Energy Evolution and Damage Mechanism of Fractured Sandstone with Different Angles

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## Abstract

**:**

## 1. Introduction

## 2. Test Scheme and Equipment

#### 2.1. Test Preparation

#### 2.2. Test Scheme and Results

## 3. Analysis of Mechanical Properties

#### 3.1. Influence of Crack Angle on Strength and Deformation Characteristics

_{50}, E

_{t}, the slope of the approximate straight line portion of the elastic segment, and the secant modulus of the unloading curve. The evaluation method of Poisson’s ratio is similar. In this study, the slope of the elastic segment of the stress–axial strain curve was used as the deformation modulus; the slope of the elastic segment of the lateral strain–axial strain curve was used as the Poisson ratio.

#### 3.2. Failure Mode

## 4. Analysis of Energy Evolution of Fractured Sandstone

#### 4.1. Energy Conversion Theory under Cyclic Loading

#### 4.2. Energy Evolution Laws and Stage Divisions of Fractured Sandstone

#### 4.3. Influence of Crack Angle on Energy at Peak Point

## 5. Damage Mechanism Based on Energy Dissipation

#### 5.1. Damage Model Based on Energy Dissipation Theory and Initial Damage

#### 5.2. Damage Evolution and Energy Damage Mechanism

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 10.**Energy evolution curve of fractured sandstone. (

**a**) intact, (

**b**) θ = 0°, (

**c**) θ = 30°, (

**d**) θ = 45°, (

**e**) θ = 60°, (

**f**) θ = 90°.

**Figure 11.**Stage division and curves of the energy storage ratio and energy consumption ratio. (

**a**) intact, (

**b**) θ = 0°, (

**c**) θ = 30°, (

**d**) θ = 45°, (

**e**) θ = 60°, (

**f**) θ = 90°.

Samples | Crack Angle/ ° | Crack Length/ mm | Horizontal Projection Area/ mm ^{2} | Peak Stress/ MPa | Peak Strain | Elastic Modulus/ GPa | Poisson’s Ratio |
---|---|---|---|---|---|---|---|

D–0° | 0° | 16 | 786.2 | 24.7 | 0.00875 | 5400 | 0.56 |

D–30° | 30° | 16 | 683.8 | 28.8 | 0.0088 | 6300 | 0.443 |

D–45° | 45° | 16 | 560.9 | 35.6 | 0.00803 | 7000 | 0.39 |

D–60° | 60° | 16 | 398.3 | 36. 9 | 0.00857 | 7200 | 0.33 |

D–90° | 90° | 16 | 100.0 | 44.3 | 0.01041 | 7300 | 0.252 |

D–intact | / | 16 | 0 | 47.3 | 0.0097 | 8300 | 0.229 |

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**MDPI and ACS Style**

Li, X.; Yao, Z.; Liu, X.; Huang, X.
Energy Evolution and Damage Mechanism of Fractured Sandstone with Different Angles. *Energies* **2022**, *15*, 1518.
https://doi.org/10.3390/en15041518

**AMA Style**

Li X, Yao Z, Liu X, Huang X.
Energy Evolution and Damage Mechanism of Fractured Sandstone with Different Angles. *Energies*. 2022; 15(4):1518.
https://doi.org/10.3390/en15041518

**Chicago/Turabian Style**

Li, Xinwei, Zhishu Yao, Xiaohu Liu, and Xianwen Huang.
2022. "Energy Evolution and Damage Mechanism of Fractured Sandstone with Different Angles" *Energies* 15, no. 4: 1518.
https://doi.org/10.3390/en15041518