# Mechanical and Acoustic Response of Low-Permeability Sandstone under Multilevel Cyclic Loading-Unloading Stress Paths

^{1}

^{2}

^{3}

^{4}

^{*}

_{2}Transformation and Storage in Deep Formations)

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Low-Permeability Sandstone Samples and Test Equipment

^{3}. The porosity and permeability were 9.3% and 2.7 mD, respectively. The sandstone was composed mainly of quartz (83%), while clay minerals (e.g., chlorite, illite, kaolinite) accounted for 12.6% and carbonate minerals (calcite and iron dolomite) accounted for 4.4%. The microstructure of the low-permeability sandstone, observed by SEM imaging, is shown in Figure 1.

#### 2.2. Experimental Schemes

#### 2.2.1. Experimental Parameters

^{3}[35].

_{m}were designed based on the results of Martin et al. [37], considering crack initiation and expansion.

#### 2.2.2. Experimental Procedures

## 3. Results and Discussion

#### 3.1. Stress-Strain Curves under Different Confining Stresses

#### 3.1.1. Stress-Strain Curves after Conventional Triaxial Compression Tests

#### 3.1.2. Stress-Strain Curves after Cyclic Loading-Unloading Triaxial Compression Tests

#### 3.2. Evolution of Deformation Parameters after Cyclic Loading-Unloading Tests

#### 3.2.1. Evolution of the Elastic Modulus

#### 3.2.2. Evolution of Irreversible Strain

#### 3.3. Acoustic Emission (AE) Characteristics during Cyclic Loading-Unloading on Low-Permeability Sandstone

#### 3.3.1. AE Count Characteristic Analysis

#### 3.3.2. Frequency–Amplitude Characteristics Analysis

#### 3.3.3. b-Value Analysis

^{2}) are 0.97, 0.85, 0.82, 0.96, 0.91 and 0.92 under confining pressures from 5 MPa to 40 MPa (Figure 13).

#### 3.3.4. RA–AF Distribution Analysis

## 4. Conclusions

- Compared with conventional triaxial compression experiments, the peak strength of the low-permeability sandstone increased slightly (less than 10%) after multi-stage constant-amplitude cyclic loading and unloading processes. Based on the variation characteristics of the elastic modulus, the mechanical behavior of low-permeability sandstone under cyclic loading is divided into three stages: the cyclic hardening stage, the mechanical stability stage and the cyclic softening stage.
- The evolution of AE counts implies that microcracks in rocks develop actively and then gradually stabilize at the initial stage of each level of stress. The evolution of the AE cumulative count shows that the internal cracks of low-permeability sandstone develop obviously with an increase in confining pressure and stress level.
- The AE frequency signals show a zonal distribution, and they present the same trends under different confining pressures. The intermediate-frequency signals are the dominant type, and the low-frequency and high-frequency signals only appear under high stress, indicating that large cracks appeared under high-stress conditions.
- The variation of the AE b-value reflects that the internal cracks of rocks initiate faster under low confining pressure than under high confining pressure. The decrease in the b-value in the cyclic loading and unloading stage indicates that damage occurs in the rocks, while the increase in the b-value in the monotonic compression stage indicates that larger cracks initiate in the rocks. The distribution of the RA–AF value shows that the mixed tensile–shear cracks are continuously generated in low-permeability sandstone during the cyclic loading process, and the development of shear cracks is more obvious.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Microstructure of low-permeability sandstone observed by scanning electron microscopy (

**a**), and partial enlarged view of clay minerals (

**b**).

**Figure 3.**Schematic diagram of multilevel and multicycle loading paths (I–VI represent six maximum axial stress levels 0.4σ

_{c}, 0.6σ

_{c}, 0.7σ

_{c}, 0.8σ

_{c}, 0.9σ

_{c}, σ

_{c}).

**Figure 4.**Stress-strain curve of low-permeability sandstone under different confining pressures (The dotted line represents the radial strain curve, and the solid line represent the axial strain curve).

**Figure 5.**Deviatoric stress-axial strain curves after cyclic loading-unloading experiments with different confining pressures. ((

**a**–

**f**): 5 MPa, 10 MPa, 15 MPa, 20 MPa, 30 MPa and 40 MPa).

**Figure 6.**Evolution of the elastic modulus: (

**a**) under different confining pressures (I–VI represent six maximum axial stress levels 0.4σ

_{c}, 0.6σ

_{c}, 0.7σ

_{c}, 0.8σ

_{c}, 0.9σ

_{c}, σ

_{c}); (

**b**–

**d**) under confining pressures of 5, 20 and 40 MPa, respectively.

**Figure 7.**Variation in the axial irreversible strain with the number of cycles under the cyclic loading process: (

**a**) with confining pressures of 5, 10 and 15 MPa; (

**b**) with confining pressures of 20, 30 and 40 MPa.

**Figure 8.**Relationship between axial stress, AE count (cumulative count) and time under different confining pressures: (

**a**–

**f**) represent 5 MPa, 10 MPa, 15 MPa, 20 MPa, 30 MPa and 40 MPa, respectively. (Red: AE count; Blue: AE Cumulative Count; Black: Axial Stress).

**Figure 9.**The evolution of AE counts with time in the first 5 cycles of axial stress loading and unloading process under a confining pressure of 10 MPa. (stage 1~stage 6 represent six different maximum axial stress levels 0.4σ

_{c}, 0.6σ

_{c}, 0.7σ

_{c}, 0.8σ

_{c}, 0.9σ

_{c}, σ

_{c}).

**Figure 10.**Variations in peak frequency with time during cyclic loading: (

**a**–

**f**) represent 5, 10, 15, 20, 30 and 40 MPa confining pressure. (Blue part is low frequency, green part is intermediate frequency and yellow part is high frequency).

**Figure 11.**Relationship between peak frequency and normalized amplitude under different confining pressures ((

**a**–

**f**): 5 MPa, 10 MPa, 15 MPa, 20 MPa, 30 MPa and 40 MPa; the red line is the median after normalization of the amplitude).

**Figure 12.**Variations in peak frequency, amplitude and axial stress with time under different confining pressures ((

**a**–

**f**): 5 MPa, 10 MPa, 15 MPa, 20 MPa, 30 MPa and 40 MPa).

**Figure 13.**Statistical distribution of macroscopic AE counts under cyclic loading ((

**a**–

**f**) represent the confining pressures of 5 MPa, 10 MPa, 15 MPa, 20 MPa, 30 MPa and 40 MPa; blue line is the cumulative curve of macroscopic AE counts, and the red line is the fitting curve of amplitude and macroscopic AE counts).

**Figure 14.**Changes in the b-value in the process of cyclic loading: (

**a**) equation fitting to obtain the b-value; (

**b**) the relationship between the b-value and loading stages. A–F refer to the first to sixth stages, respectively, and G–J refer to 1/4, 1/2, 3/4 and 1 of the monotonous loading stage, respectively.

**Figure 15.**Variation in RA and AF during cyclic loading under different confining pressures (red and blue lines represent RA and AF, respectively, and brown lines represent stress paths).

Confining Pressure (MPa) | Length (mm) | Diameter (mm) | Peak Strength (MPa) | Peak Strength under Cyclic Load (MPa) | Increment (%) | Elastic Modulus (GPa) | Poisson’s Ratio (-) |
---|---|---|---|---|---|---|---|

5 | 100.44 | 49.77 | 83.14 | 87.51 | 5.26 | 16.39 | 0.29 |

10 | 100.45 | 49.80 | 104.51 | 108.27 | 3.64 | 18.31 | 0.32 |

15 | 100.65 | 49.86 | 116.99 | 125.38 | 7.17 | 17.86 | 0.29 |

20 | 100.56 | 49.80 | 132.24 | 138.31 | 4.59 | 19.74 | 0.24 |

30 | 100.57 | 49.83 | 155.87 | 163.63 | 4.98 | 19.63 | 0.24 |

40 | 100.42 | 49.97 | 173.43 | 178.16 | 2.73 | 22.07 | 0.29 |

Samples | HAHF | LAHF | HALF | LALF |
---|---|---|---|---|

TS-5 | Failure | -- | Stage4-No.2 | Stage6-No.1 |

TS-10 | Stage1-No.1 | -- | -- | Stage4-No.17 |

TS-15 | Stage4-No.2 | Failure | Stage1-No.1 | Stage1-No.1 |

TS-20 | Stage2-No.1 | Stage6-No.1 (More at Failure) | Failure | Stage1-No.3 (More at Failure) |

TS-30 | Stage5-No.1 | Failure | -- | Failure |

TS-40 | Stage1-No.1 | Stage1-No.1 | -- | Stage6-No.6 |

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**MDPI and ACS Style**

Tan, H.; Liu, H.; Shi, X.; Ma, H.; Qiu, X.; Guo, Y.; Ban, S.
Mechanical and Acoustic Response of Low-Permeability Sandstone under Multilevel Cyclic Loading-Unloading Stress Paths. *Energies* **2023**, *16*, 6821.
https://doi.org/10.3390/en16196821

**AMA Style**

Tan H, Liu H, Shi X, Ma H, Qiu X, Guo Y, Ban S.
Mechanical and Acoustic Response of Low-Permeability Sandstone under Multilevel Cyclic Loading-Unloading Stress Paths. *Energies*. 2023; 16(19):6821.
https://doi.org/10.3390/en16196821

**Chicago/Turabian Style**

Tan, Hongying, Hejuan Liu, Xilin Shi, Hongling Ma, Xiaosong Qiu, Yintong Guo, and Shengnan Ban.
2023. "Mechanical and Acoustic Response of Low-Permeability Sandstone under Multilevel Cyclic Loading-Unloading Stress Paths" *Energies* 16, no. 19: 6821.
https://doi.org/10.3390/en16196821