# Meso-Damage Mechanism of Strength and Deformation Characteristics of Typical Sandstone in Xinwen Coalfield

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Typical Sandstone and Sample Preparation

#### 2.1. Typical Sandstone Geological Conditions

#### 2.2. Rock Sample Preparation

## 3. Meso Structural Characteristics of Rock Mass

#### 3.1. Micropores and Distribution Characteristics of Sandstone

#### 3.2. Microfractures Characteristics of Sandstone

#### 3.3. Fractal Characteristics of Sandstone Micropores

^{n}, and ${N}_{\delta}\left(F\right)$ is the minimum number of sets whose diameter is the largest δ and can cover F, then the box dimension of F is defined as

## 4. Relationship between Fractal Dimension and Mechanical Properties of Sandstone

#### 4.1. Strength Characteristics of Sandstone

#### 4.2. Damage Mechanics Analysis of Sandstone

_{c}and peak strain ε

_{c}, the critical damage value is defined

## 5. Conclusions

- (1)
- The study of micro-damage to sandstone can analyze its macro mechanical characteristics in depth. According to the observation of SEM, there are many micropores and microcracks in the three kinds of sandstones, the overall structure is undulating, and there are many particles on the surface, which are typical materials with original damage. The macroscopic mechanical properties of sandstone can be analyzed according to its meso-structure;
- (2)
- Matlab is used to calculate the fractal dimension. In order to exclude the particularity, the average value of fractal dimension is selected as the final fractal dimension value. The average fractal dimensions of the three kinds of sandstones are 1.6678, 1.9756 and 2.0974, the micro-morphology of different sandstones varies greatly. The more obvious the micro-fractures and micropores are, the larger the fractal dimension is. Therefore, it is appropriate to use the fractal dimension to describe the characteristics of sandstone. The fractal dimension decreases with the increase in magnification;
- (3)
- According to the results of uniaxial compression test, the compressive strength of the three sandstones are 63.25, 40.93 and 29.54 Mpa, and the elastic modulus are 9.97, 8.46 and 7.06 GPa. The strength characteristics of sandstone are inversely proportional to the fractal dimension. The larger the uniaxial compressive strength and elastic modulus are, the smaller the fractal dimension is;
- (4)
- Based on the damage mechanics theory, the relationship between the critical damage value, compressive strength and fractal dimension is studied. It is found that the critical damage values of the three sandstones are in direct proportion to their fractal dimensions. The larger the fractal dimension of sandstone is, the more micropores and microcracks there are, and the more serious the damage is, the lower the compressive strength is. This shows that the strength and deformation characteristics of sandstone are directly related to its meso-damage, which is consistent with the actual situation.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Development of micro-pores in the first type of sandstone. (

**a**) Meso-image with magnification of 200; (

**b**) Meso-image with magnification of 500; (

**c**) Meso-image with magnification of 1000; (

**d**) Meso-image with magnification of 2000.

**Figure 3.**Development of micro-pores in the second type of sandstone. (

**a**) Meso-image with magnification of 200; (

**b**) Meso-image with magnification of 500; (

**c**) Meso-image with magnification of 1000; (

**d**) Meso-image with magnification of 2000.

**Figure 4.**Development of micro-pores in the third type of sandstone. (

**a**) Meso-image with magnification of 200; (

**b**) Meso-image with magnification of 500; (

**c**) Meso-image with magnification of 1000; (

**d**) Meso-image with magnification of 2000.

**Figure 5.**Micro-fracture development of the first type sandstone. (

**a**) Meso-image with magnification of 200; (

**b**) Meso-image with magnification of 500; (

**c**) Meso-image with magnification of 1000; (

**d**) Meso-image with magnification of 2000.

**Figure 6.**Micro-fracture development of the second type sandstone. (

**a**) Meso-image with magnification of 200; (

**b**) Meso-image with magnification of 500; (

**c**) Meso-image with magnification of 1000; (

**d**) Meso-image with magnification of 2000.

**Figure 7.**Micro-fracture development of the third type sandstone. (

**a**) Meso-image with magnification of 200; (

**b**) Meso-image with magnification of 500; (

**c**) Meso-image with magnification of 1000; (

**d**) Meso-image with magnification of 2000.

**Figure 8.**The binary diagram of the first kind of sandstone. (

**a**) Binary graph at 200 magnification; (

**b**) Binary graph at 500 magnification; (

**c**) Binary graph at 1000 magnification; (

**d**) Binary graph at 2000 magnification.

**Figure 9.**The binary diagram of the second kind of sandstone. (

**a**) Binary graph at 200 magnification; (

**b**) Binary graph at 500 magnification; (

**c**) Binary graph at 1000 magnification; (

**d**) Binary graph at 2000 magnification.

**Figure 10.**The binary diagram of the third kinds of sandstone. (

**a**) Binary graph at 200 magnification; (

**b**) Binary graph at 500 magnification; (

**c**) Binary graph at 1000 magnification; (

**d**) Binary graph at 2000 magnification.

**Figure 11.**Fractal dimension fitting diagram of the first type sandstone. (

**a**) Fitting diagram at 200 magnification; (

**b**) Fitting diagram at 500 magnification; (

**c**) Fitting diagram at 1000 magnification; (

**d**) Fitting diagram at 2000 magnification.

**Figure 12.**Fractal dimension fitting diagram of the second type sandstone. (

**a**) Fitting diagram at 200 magnification; (

**b**) Fitting diagram at 500 magnification; (

**c**) Fitting diagram at1000 magnification; (

**d**) Fitting diagram at 2000 magnification.

**Figure 13.**Fractal dimension fitting diagram of the third type sandstone. (

**a**) Fitting diagram at 200 magnification; (

**b**) Fitting diagram at 500 magnification; (

**c**) Fitting diagram at 1000 magnification; (

**d**) Fitting diagram at 2000 magnification.

**Figure 15.**Stress–strain curves of three types of sandstone. (

**a**) The stress-strain curve of the first kind of sandstone; (

**b**) The stress–strain curve of the second kind of sandstone; (

**c**) The stress–strain curve of the third kind of sandstone.

Sandstone Type | Fractal Dimension Values Under Different Magnification | Average Fractal Dimension | |||
---|---|---|---|---|---|

×200 | ×500 | ×1000 | ×2000 | ||

1 | 1.7051 | 1.7236 | 1.6386 | 1.6037 | 1.6678 |

2 | 1.9902 | 1.9784 | 1.9615 | 1.9722 | 1.9756 |

3 | 2.1235 | 2.1178 | 2.1237 | 2.0247 | 2.0974 |

Sandstone Type | Compressive Strength Rc/MPa | Elastic Modulus E/GPa | Poisson’s Ratio μ | Fractal Dimension Value D_{f} |
---|---|---|---|---|

1 | 63.25 | 9.97 | 0.04 | 1.6678 |

2 | 40.93 | 8.46 | 0.16 | 1.9756 |

3 | 29.54 | 7.06 | 0.18 | 2.0974 |

Sandstone Type | Critical Damage Value Dr | Compressive Strength Rc/MPa | Fractal Dimension Value D_{f} |
---|---|---|---|

1 | 25.35% | 63.25 | 1.6678 |

2 | 35.50% | 40.93 | 1.9756 |

3 | 40.18% | 29.54 | 2.0974 |

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**MDPI and ACS Style**

Gao, C.; Huang, D.; Chang, X.; Xi, H.
Meso-Damage Mechanism of Strength and Deformation Characteristics of Typical Sandstone in Xinwen Coalfield. *Symmetry* **2020**, *12*, 1815.
https://doi.org/10.3390/sym12111815

**AMA Style**

Gao C, Huang D, Chang X, Xi H.
Meso-Damage Mechanism of Strength and Deformation Characteristics of Typical Sandstone in Xinwen Coalfield. *Symmetry*. 2020; 12(11):1815.
https://doi.org/10.3390/sym12111815

**Chicago/Turabian Style**

Gao, Chunjing, Dongmei Huang, Xikun Chang, and Han Xi.
2020. "Meso-Damage Mechanism of Strength and Deformation Characteristics of Typical Sandstone in Xinwen Coalfield" *Symmetry* 12, no. 11: 1815.
https://doi.org/10.3390/sym12111815