# Study on Creep Characteristics and Long-Term Strength of Mud-Calcareous Conglomerates in the Three Gorges Reservoir Area

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Conventional Long-Term Strength Determination Method

#### 2.1. Transitional Creep Method

#### 2.2. Isochronous Stress–Strain Curve Method

#### 2.3. Volume Expansion Method

#### 2.4. Stress Relaxation Method

#### 2.5. Comparison of Different Long-Term Strength Determination Methods

## 3. Creep and Stress Relaxation Characteristics Test

#### 3.1. Test Scheme

#### 3.2. Test Results

#### 3.2.1. Creep Test Results

#### 3.2.2. Stress Relaxation Test Results

#### 3.3. Long-Term Strength Determination Based on Conventional Methods

## 4. Steady-State Creep Rate Method Based on Stress Interval

#### 4.1. Principle of Steady-State Creep Rate Method Based on Stress Interval

#### 4.2. Analysis of the Test Results of the Steady-State Creep Rate Method Based on the Stress Interval

_{a}on the curve represents the end of the compression stage of crack closure and the beginning of the line elastic deformation stage; σ

_{b}represents the initial crack extension stress, which marks the start of the stress–strain curve’s divergence from the linear elastic trajectory (this illustrates the steady progression of internal fissures in the rock); and σ

_{c}represents the start of unstable crack growth, and the volume strain appears inverted at this point, indicating the onset of rock volume expansion. The stress value corresponding to the point σ

_{b}is taken as the lower limit of the interval where the long-term strength value is located, and the stress level of the creep failure of the rock is taken as the upper limit of the interval where the long-term strength value is located, so that the stress interval range of the long-term strength value of the rock can be initially estimated. In accordance with the above method, the stress interval range of the long-term strength value of the rock was initially determined to be 30~55 mPa from the stress–strain curve of the creep test.

^{2}was 0.962.

## 5. Conclusions

- (1)
- The creep and stress relaxation tests were conducted on a slightly weathered mud-calcareous conglomerate in the Three Gorges Reservoir Area. The creep test results show that the creep characteristics of the rock samples over time are very obvious and show the typical characteristics of the three stages of rocks changing over time. The relaxation test results show that the stress relaxation effect of the mud-calcareous conglomerate was significant, which was manifested in the two stages of decay relaxation and stable relaxation, and the relaxation rate gradually tended toward 0 after entering the stable relaxation stage. Under the conditions of constant strain levels in the latter three stages, the residual stress level after relaxation basically remained close to the same value;
- (2)
- Different methods were used to determine the long-term strength values of the conglomerate specimens. Through comparative analysis, the transition creep method requires a more stringent accuracy of the creep test curve, it is suitable for rocks with distinct characteristics in the decaying creep phase and stable creep phase, and it can only estimate the interval of long-term strength; in addition, the process of determining the inflection point using the isokinetic stress–strain curve method contains a certain number of subjective factors. The volumetric expansion method is simple and easy to implement, but its accuracy depends on the accuracy of the specific values of axial and transverse strains measured during the test. The stress relaxation method is able to directly obtain the residual stress value after stabilization, but the test procedure is relatively complicated, the test period is long, and the rock effect is poor. It is suitable for determining the long-term strength of rocks with obvious relaxation characteristics;
- (3)
- A method is proposed here to rapidly determine the long-term strength of rocks based on the steady-state creep rate in the stress interval. The method first estimates the range of stress levels for the long-term strength of rocks based on the characteristics of stress–strain curves during the deformation and fracture of rocks, and it assumes an exponential nonlinear relationship between the steady-state creep rate and the increase in stress in terms of the long-term strength. As the steady-state creep rate gradually approaches 0, the stress gradually decreases and approaches the long-term strength value.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Table 1.**Characteristics and applicable conditions of different long-term strength determination methods.

Name | The Physical Meaning of the Long-Term Intensity Value | Required Test | Features | Scope of Application |
---|---|---|---|---|

Transition creep method | The point where the steady-state creep rate tends to 0 | Creep characteristic test | Only long-term intensity intervals can be estimated, and it is difficult to determine specific values | Rocks with prominent characteristics in the decay creep stage and steady-state creep stage |

Isochronous stress–strain curve method | The critical point of stable expansion and unstable expansion | The accuracy of the test curve is very demanding, and the determination of the inflection point is influenced by subjective factors | Rocks with significant creep characteristics and large long-term deformations | |

Volume expansion method | The inflection point where the volumetric strain changes from a negative increase to a positive increase | High requirements for instrument accuracy and high cost | Rocks with significant changes in volumetric strain | |

Stress relaxation method | Stress relaxation under viscous deformation is induced to the point corresponding to a creep rate of 0. | Stress relaxation test | The test procedure is relatively cumbersome, the test period is long, and the effect on rocks with insignificant stress relaxation characteristics is poor | Rocks with remarkable relaxation characteristics |

Level | $({\mathit{\sigma}}_{1}-{\mathit{\sigma}}_{3})$/mPa | ${\mathit{\sigma}}_{3}$/mPa | Loading Rate/(mPa/s) |
---|---|---|---|

1 | 10 | 5 | 0.05 |

2 | 15 | 5 | 0.05 |

3 | 20 | 5 | 0.05 |

… | … | 5 | 0.05 |

10 | 55 (failure) | 5 | 0.05 |

Level | ${\mathit{\epsilon}}_{1}$/% (Corresponding force/mPa) | ${\mathit{\sigma}}_{3}$/mPa | Loading Rate/(mPa/s) |
---|---|---|---|

1 | 0.517 (25) | 5 | 0.05 |

2 | 0.601 (30) | 5 | 0.05 |

3 | 0.699 (35) | 5 | 0.05 |

… | … | 5 | 0.05 |

10 | 1.23 (52.5) | 5 | 0.05 |

${\mathit{\sigma}}_{\mathit{\infty}}$/mPa | q/10^{−4} | P/10^{−2} | K | R^{2} |
---|---|---|---|---|

38.6 | 1.67 | 8.85 | 1.33 | 0.962 |

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**MDPI and ACS Style**

Wang, R.; Luo, H.; Yang, C.; Wang, F.
Study on Creep Characteristics and Long-Term Strength of Mud-Calcareous Conglomerates in the Three Gorges Reservoir Area. *Sustainability* **2023**, *15*, 9684.
https://doi.org/10.3390/su15129684

**AMA Style**

Wang R, Luo H, Yang C, Wang F.
Study on Creep Characteristics and Long-Term Strength of Mud-Calcareous Conglomerates in the Three Gorges Reservoir Area. *Sustainability*. 2023; 15(12):9684.
https://doi.org/10.3390/su15129684

**Chicago/Turabian Style**

Wang, Ruihong, Hao Luo, Chao Yang, and Fang Wang.
2023. "Study on Creep Characteristics and Long-Term Strength of Mud-Calcareous Conglomerates in the Three Gorges Reservoir Area" *Sustainability* 15, no. 12: 9684.
https://doi.org/10.3390/su15129684