journal article·2024-07-25Open access

Quantitative Calculation of Crack Stress Thresholds Based on Volumetric Strain Decomposition for Siltstone and Granite

Mingchun Liang, Shengjun Miao, Meifeng Cai, Fei Li, Zejing Liu

Applied Sciences· Volume 14· Issue 15

Abstract

Crack stress thresholds in rocks have long been a popular subject in rock mechanics and engineering research. In this study, the applicability of existing methods for determining the crack stress thresholds of granite and weakly cemented porous siltstone is investigated using step loading and unloading tests. In addition, a novel method for decomposing the volumetric strain into solid-phase linear elastic strain, gas-phase nonlinear elastic strain, and plastic volumetric strain is presented. A quantitative calculation method for determining these thresholds is proposed based on the evolution law of the gas-phase volumetric strain and the physical significance of crack stress thresholds. The initiation and termination points of the stationary stage of the gas-phase volumetric strain are determined as σcc and σci; the point at which the gas-phase strain changes from positive to negative is determined as σcd. To validate the proposed method, statistical results of the existing methods after screening are compared with the results of the proposed method. The results show that the proposed method provides reasonable crack stress thresholds for siltstone and granite and is applicable to rocks with similar stress–strain behaviors. The proposed method offers the advantages of independence from other methods, suitability across high and low confining pressures, and the capability for the quantitative calculation and processing of numerous samples.
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Research context

OpenAlex topics: Rock Mechanics and Modeling · Landslides and related hazards · Drilling and Well Engineering

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China

Key Laboratory of High-Efficient Mining and Safety of Metal Mines (Ministry of Education of China), University of Science and Technology Beijing, Beijing 100083, China

Funding

National Natural Science Foundation of China · National Key Research and Development Program of China

References (49)

Show source-provided references
1. Challenges in the Mining and Utilization of Deep Mineral Resources10.1016/J.ENG.2017.04.027 ↗
2. Plastic and Damage Energy Dissipation Characteristics and Damage Evolution of Beishan Granite under Triaxial Cyclic Loading10.1016/j.ijrmms.2024.105644 ↗
3. Some Observations Concerning the Microscopic and Mechanical Behaviour of Quartzite Specimens in Stiff, Triaxial Compression Tests10.1016/0148-9062(73)90015-6 ↗
4. Mapping the State of Fracture around Cavities10.1016/0013-7952(1)90012-A ↗
5. Mechanical Damage of an Anisotropic Porous Rock in Cyclic Triaxial Tests10.1016/S1365-1609(02)00029-1 ↗
6. Cracking Processes in Barre Granite: Fracture Process Zones and Crack Coalescence10.1007/s10704-013-9810-y ↗
7. A Novel Method for Determining the Crack Closure Stress of Brittle Rocks Subjected to Compression10.1007/s00603-020-02156-6 ↗
8. Damage Initiation and Propagation in Hard Rock during Tunnelling and the Influence of Near-Face Stress Rotation10.1016/j.ijrmms.2004.02.003 ↗
9. Kaiser, P.K., Diederichs, M.S., Martin, C.D., Sharp, J., and Steiner, W. (2000, January 19). Underground Works in Hard Rock Tunnelling and Mining. Proceedings of the ISRM International Symposium 2000, Melbourne, Australia.
10. The Progressive Fracture of Lac Du Bonnet Granite10.1016/0148-9062(94)90005-1 ↗
11. Manuel Rocha Medal Recipient Rock Fracture and Collapse under Low Confinement Conditions10.1007/s00603-003-0015-y ↗
12. Long Experimental Study on Rock Strength and Deformation Characteristics under Triaxial Cyclic Loading and Unloading Conditions10.1007/s00603-020-02289-8 ↗
13. Crack Initiation and Crack Propagation in Heterogeneous Sulfate-Rich Clay Rocks10.1007/s00603-013-0495-3 ↗
14. Objective Determination of Crack Initiation Stress of Brittle Rocks under Compression Using AE Measurement10.1007/s00603-014-0703-9 ↗
15. Identifying Crack Initiation and Propagation Thresholds in Brittle Rock10.1139/t97-091 ↗
16. A Novel Observation Method for Determining the Crack Stress Thresholds of Rock Based on Hooke’s Law10.1111/ffe.13306 ↗
17. Experimental Study on the Determination Method of Σcc,Σci and Σcd for Granite under Different Confining Pressures
18. Identifying Crack Compaction and Crack Damage Stress Thresholds of Rock Using Load–Unload Response Ratio (LURR)Theory10.1007/s00603-019-01936-z ↗
19. Estimation of Crack Initiation and Propagation Thresholds of Confined Brittle Coal Specimens Based on Energy Dissipation Theory10.1007/s00603-017-1317-9 ↗
20. Stresses for Crack Closure and Its Application to Assessing Stress-Induced Microcrack Damage
21. Determination of Crack Closure Stress under Constant-Fatigue Loading Based on Damage Variable Evolution10.1016/j.tafmec.2022.103526 ↗
22. Brittle Fracture in Compression10.1007/BF00155255 ↗
23. The 2003 Canadian Geotechnical Colloquium: Mechanistic Interpretation and Practical Application of Damage and Spalling Prediction Criteria for Deep Tunnelling10.1139/T07-033 ↗
24. Evaluation of Methods for Determining Crack Initiation in Compression Tests on Low-Porosity Rocks10.1007/s00603-012-0221-6 ↗
25. Evaluation of Methods for Determining Crack Initiation Stress under Compression10.1016/j.enggeo.2018.01.018 ↗
26. An Objective Crack Initiation Stress Identification Method for Brittle Rock under Compression Using a Reference Line10.1007/s00603-021-02479-y ↗
27. Dilatancy in the Fracture of Crystalline Rocks10.1029/JZ071i016p03939 ↗
28. Mechanism of Brittle Fracture of Rock. Part I-Theory of the Fracture Process10.1016/0148-9062(67)90030-7 ↗
29. Acoustic Emission in Host-Rock Material for Radioactive Waste Disposal: Comparison between Clay and Rock Salt10.1007/s10064-002-0160-7 ↗
30. Performance of Rock Crack Stress Thresholds Determination Criteria and Investigating Strength and Confining Pressure Effects10.1016/j.conbuildmat.2020.118263 ↗
31. Compaction Localization in Porous Sandstones: Spatial Evolution of Damage and Acoustic Emission Activity10.1016/j.jsg.2003.09.002 ↗
32. Multiscale Analyses of Failure Pattern Transition in High-Porosity Sandstones
33. Experimental and Theoretical Study on the Creep Behavior of a Clayey Rock10.1007/s00603-022-03146-6 ↗
34. Rodríguez, C.A., Rodríguez-Pérez, Á.M., López, R., Hernández-Torres, J.A., and Caparrós-Mancera, J.J. (2023). A Finite Element Method Integrated with Terzaghi’s Principle to Estimate Settlement of a Building Due to Tunnel Construction. Buildings, 13.10.3390/buildings13051343 ↗
35. Elastic–Plastic Response of a Deep Tunnel Excavated in 3D Hoek–Brown Rock Mass Considering Different Approaches for Obtaining the out-of-Plane Stress10.1016/j.ijrmms.2023.105425 ↗
36. Hoek, E., Carranza, C., and Corkum, B. (2024, July 19). Hoek-Brown Failure Criterion—2002 Edition. Available online: https://www.researchgate.net/publication/282250802_Hoek-Brown_failure_criterion_-_2002_Edition.
37. Thermal-Mechanical Modelling on Cumulative Freeze-Thaw Deformation of Porous Rock in Elastoplastic State Based on Drucker-Prager Criterion Considering Dilatancy10.1016/j.ijrmms.2024.105815 ↗
38. Suggested Methods for Determining the Strength of Rock Materials in Triaxial Compression: Revised Version10.1016/0148-9062(83)90598-3 ↗
39. Suggested Methods for Determining the Uniaxial Compressive Strength and Deformability of Rock Materials10.1016/0148-9062(79)91451-7 ↗
40. Permeability Evolution of Deep Coal Samples Subjected to Energy-Based Damage Variable10.1016/j.jngse.2019.103070 ↗
41. Experimental and Numerical Modelling of the Mechanical Behaviour of Low-Permeability Sandstone Considering Hydromechanics10.1016/j.mechmat.2020.103454 ↗
42. Multi-Dimensional Non-Uniform Deformation and Failure of Siltstone Determined Using Acoustic, 3D-Digital Image Correlation, and Computed Tomography10.1016/j.tafmec.2023.103800 ↗
43. Coupled Modeling of Sedimentary Basin and Geomechanics: A Modified Drucker–Prager Cap Model to Describe Rock Compaction in Tectonic Context10.1007/s00603-019-01783-y ↗
44. A Modified Drucker-Prager Cap Model for Die Compaction Simulation of Pharmaceutical Powders10.1016/j.ijsolstr.2008.01.024 ↗
45. An Empirical Dilatancy Index for the Dilatant Deformation of Rock10.1016/j.ijrmms.2003.11.001 ↗
46. A Study on Crack Damage Stress Thresholds of Different Rock Types Based on Uniaxial Compression Tests10.1007/s00603-013-0479-3 ↗
47. Miao, S., Liu, Z., Yang, P., Liang, M., Wang, H., Xia, D., and Zhao, Z. (2024). Mechanical Properties, Instability Precursors, and Fatigue Life Prediction of Siltstone under Bivariate Fatigue Damage-Controlled Tests. Rock Mech. Rock Eng.10.1007/s00603-024-04043-w ↗
48. A Potential Strain Indicator for Brittle Failure Prediction of Low-Porosity Rock: Part I-Experimental Studies Based on the Uniaxial Compression Test10.1007/s00603-014-0675-9 ↗
49. A Quantitative Strain Energy Indicator for Predicting the Failure of Laboratory-Scale Rock Samples: Application to Shale Rock10.1007/s00603-018-1480-7 ↗