# Seepage and Damage Evolution Characteristics of Gas-Bearing Coal under Different Cyclic Loading–Unloading Stress Paths

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Equipment and Test Scheme

#### 2.1. Experimental Equipment

#### 2.2. Coal Sample Preparation

^{3}/t. The main characteristics related to the coal’s quality are shown in Table 1. The coal field where the mine is located is affected by the Huaxia tectonic system and the construction line is dominated by North-northeast (NNE), which is shown in Figure 3. These coal samples were cored, cut, and ground to form standard cylindrical coal samples that were 50 mm in diameter and 100 mm in length.

#### 2.3. Experimental Scheme

## 3. Methods and Data

#### 3.1. Permeability Calculation

^{2}), q

_{v}is the seepage velocity (m

^{3}/s) of gas in coal masses, P

_{a}is the atmospheric pressure (Pa), A is the cross-sectional area (m

^{2}) of the specimen, L is the length (m) of the specimens, P

_{1}is the gas pressure at the air inlet (Pa), P

_{2}is the gas pressure at the air outlet (MPa), and μ is the gas viscosity (Pa·s).

_{1}and ε

_{2}) on the raw coal were monitored in real-time. Through the formula ε

_{v}= ε

_{1}+ 2ε

_{2}, the volumetric strain (ε

_{v}) in the raw coal was calculated. Based on the drawing, the axial stress–axial strain curve (σ

_{1}–ε

_{1}), axial stress–lateral strain curve (σ

_{1}–ε

_{2}), axial stress–volumetric strain curve (σ

_{1}–ε

_{v}), and permeability–axial strain curve (K–ε

_{1}) of raw coal under different cyclic loading–unloading paths were obtained.

#### 3.2. Permeability Ratio

_{a}and K

_{i}refer to the absolute recovery rates of the permeability and the permeability (mD) when the axial stress applied to coal samples was unloaded to 2 MPa during the ith cycle, respectively. Additionally, K

_{1}denotes the permeability (mD) of coal samples when the axial stress was loaded from 2 MPa during the first loading–unloading cycle.

_{r}and K

_{i}

_{+1}represent the relative recovery rates of the permeability and the permeability (mD) when the axial stress was unloaded to 2 MPa during the (i + 1)th loading–unloading cycle, respectively.

#### 3.3. Mining-Enhanced Permeability

_{p}) is defined as the variation in permeability under the change per unit volume of coal masses.

_{v}represent the permeability (mD) of coal masses and the volumetric strain of damaged and fractured coal masses, respectively. The mining-enhanced permeability describes the permeability increase due to the fracturing of coal masses under the impact of mining and can allow the quantitative evaluation of the effect of permeability by increasing measures in coal seams.

#### 3.4. Stress Sensitivity Coefficient of Permeability

_{0}refer to the permeability (mD) under different effective stresses and that under the initial effective stress, respectively.

_{e}, σ

_{e}, and b separately denote the stress sensitivity coefficient (MPa

^{−1}) of the permeability, the effective stress (MPa), and the dimensionless coefficient influenced by the initial permeability. Additionally, the stress sensitivity coefficient of the permeability of coal samples can be defined by the equation below.

_{e}refer to the variation in the permeability of coal samples and the variation in the effective stress, respectively.

#### 3.5. Damage Variable of Coal

_{+}and X

_{−}separately refer to the responses during loading and unloading, respectively. $\Delta P$ and $\Delta R$ denote the increments corresponding to the stress load variable (P) and the strain response variable (R), respectively, which can be acquired according to the stress–strain curve under the effect of experimental cyclic loading. When the load (P) is low, rocks are in an elastic stage and a linear or quasi-linear relationship arises between P and R with X

_{+}= X

_{−}and LURR Y = 1. When the load gradually increases, the damage increases, which shows that X

_{+}> X

_{−}and, correspondingly, Y > 1. Moreover, with increased damage, Y also rises. When media are close to becoming damaged, Y reaches a maximum. Therefore, the damage to coal samples during cyclic loading can be characterized by using LURR Y.

_{E}and damage variable (D) based on the fact that the fracture limit of materials conforms to a Weibull distribution on a mesoscopic scale was established by Zhang et al. [34].

## 4. Results

#### 4.1. Characteristics of Deformation–Permeability of Gas-Containing Coal under Stress Path 1

#### 4.2. Characteristics of the Deformation–Permeability Curve of Gas-Containing Coal under Stress Path 2

#### 4.3. Characteristics of the Deformation–Permeability Curve of Gas-Containing Coal under Stress Path 3

## 5. Discussion

#### 5.1. Effects of the Loading–Unloading Processes on the Permeability of Gas-Containing Coal

#### 5.2. Changes in the Relative and Absolute Recovery Rates of Permeability under Different Cyclic Loading–Unloading Paths

#### 5.3. Evolution of Mining-Enhanced Permeability of Gas-Containing Coal under Different Cyclic Loading–Unloading Paths

#### 5.4. Stress Sensitivity of the Permeability of Gas-Containing Coal under Different Cyclic Loading–Unloading Paths

#### 5.5. Damage Evolution Characteristics of Gas-Containing Coal under Different Cyclic Loading–Unloading Paths

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Triaxial seepage experimental device for the measurement of the heat–fluid–solid coupling property of gas-containing coal and the experimental chamber: (

**a**) The whole experimental device and (

**b**) the experimental chamber.

**Figure 4.**Similarity model for real-time monitoring of the stress state of the protected seam during the mining of multiple protective seams.

**Figure 6.**Three cyclic loading–unloading stress paths. (

**a**) Stress path 1: stepped-loading and unloading. (

**b**) Stress path 2: stepped-increasing-loading and unloading. (

**c**) Stress path 3: crossed-cyclic-loading and unloading.

**Figure 7.**The relationships among the stress, strain, and permeability of raw coal under stress path 1. (

**a**) Stress–strain and permeability–strain curves. (

**b**) Partial enlargement of the axial stress–strain curve and the permeability–axial strain curve.

**Figure 8.**The relationships among the stress, strain, and permeability of raw coal under stress path 2.

**Figure 9.**The axial stress–axial strain and permeability–axial strain curves of raw coal during each cycle under stress path 2. (

**a**) The first cycle. (

**b**) The second cycle. (

**c**) The third cycle. (

**d**) The fourth cycle. (

**e**) The fifth cycle. (

**f**) The sixth cycle. (

**g**) The seventh cycle.

**Figure 10.**The relationships among stress, strain, and permeability of raw coal under stress path 3. (

**a**) Stress–strain and permeability–strain curves. (

**b**) Partial enlargement.

**Figure 11.**The axial stress–axial strain and permeability–axial strain curves of raw coal during each cycle under stress path 3. (

**a**) The first cycle. (

**b**) The second cycle. (

**c**) The third cycle. (

**d**) The fourth cycle. (

**e**) The fifth cycle. (

**f**) The sixth cycle. (

**g**) The seventh cycle.

**Figure 13.**Changes in permeability of raw coal and its recovery rate at different stress levels under stress path 1.

**Figure 14.**Changes in the absolute and relative recovery rates of the permeability of raw coal under cyclic loading–unloading paths 2 and 3. (

**a**) Stress path 2. (

**b**) Stress path 3.

**Figure 15.**Changes in the mining-enhanced permeability of coal samples under different cyclic loading–unloading paths. (

**a**) Stress path 1. (

**b**) Stress path 2. (

**c**) Stress path 3.

**Figure 16.**The changes in the stress sensitivity coefficient of the permeability of coal samples under different cyclic loading–unloading paths. (

**a**) Stress path 1. (

**b**) Stress path 2. (

**c**) Stress path 3.

**Figure 17.**The changes in LURR and D of raw coal with stress under different cyclic loading–unloading paths. (

**a**) Stress path 1. (

**b**) Stress path 2. (

**c**) Stress path 3.

Item | Fixed Carbon | Ash Content | Sulfur Content | Phosphorus Content | Volatile Content | Calorific Value | Bulk Density |
---|---|---|---|---|---|---|---|

3-1 Coal seam | 60% | 6% | 0.40% | 0.0004% | 32% | 27.86 MJ/kg | 1350 Kg/m^{3} |

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**MDPI and ACS Style**

Li, Q.; Liang, Y.; Zou, Q.
Seepage and Damage Evolution Characteristics of Gas-Bearing Coal under Different Cyclic Loading–Unloading Stress Paths. *Processes* **2018**, *6*, 190.
https://doi.org/10.3390/pr6100190

**AMA Style**

Li Q, Liang Y, Zou Q.
Seepage and Damage Evolution Characteristics of Gas-Bearing Coal under Different Cyclic Loading–Unloading Stress Paths. *Processes*. 2018; 6(10):190.
https://doi.org/10.3390/pr6100190

**Chicago/Turabian Style**

Li, Qingmiao, Yunpei Liang, and Quanle Zou.
2018. "Seepage and Damage Evolution Characteristics of Gas-Bearing Coal under Different Cyclic Loading–Unloading Stress Paths" *Processes* 6, no. 10: 190.
https://doi.org/10.3390/pr6100190