Damage Evolution Constitutive Behavior of Rock in Thermo-Mechanical Coupling Processes
Abstract
:1. Introduction
2. Thermomechanical Unified Constitutive Model
2.1. Definition of Damage Variable
2.2. Definition of Thermal Damage Variable
2.3. Thermomechanical (TM) Damage Evolution Equation
3. Example Verification of the Thermomechanical Damage Evolution Model
4. Conclusions
- (1)
- After heat treatment, rock is given a thermal load first, and thermal damage appears inside the rock specimen. Based on this condition, the stress load is the second load coupled with the thermal load. The process is not the mechanical superposition of thermal damage and stress damage but, rather, the coupling effect. Meanwhile, the coupling effect of stress damage and thermal damage is lower compared with the mechanical superposition of them;
- (2)
- The TM unified constitutive model can describe the whole process, including the compaction stage and post-failure stage. The experimental results of uniaxial compression testing are used for verification of the theoretical model. The results show that the theoretical curves match the experimental curves accurately;
- (3)
- The relationship between the total damage evolution ratio and the axial strain of granite subjected to heat treatment at different temperatures can be calculated by the total damage evolution equation. The results show that the peak of the total damage evolution ratio occurs later with increasing temperature. In addition, the peak value of the total damage evolution ratio also decreases with increasing temperature.
Author Contributions
Funding
Conflicts of Interest
References
- Sygała, A.; Bukowska, M.; Janoszek, T. High temperature versus geomechanical parameters of selected rocks—The present state of research. J. Min. Sci. 2013, 12, 45–51. [Google Scholar] [CrossRef] [Green Version]
- Rao, Q.H.; Xie, H.F.; Xie, Q. In-plane shear (Mode II) crack sub-critical propagation of rock at high temperature. J. Cent. South Univ. 2008, 15, 402–405. [Google Scholar] [CrossRef]
- Zhang, P.; Mishra, B.; Heasley, K.A. Experimental Investigation on the Influence of High Pressure and High Temperature on the Mechanical Properties of Deep Reservoir Rocks. Rock Mech. Rock Eng. 2015, 48, 2197–2211. [Google Scholar] [CrossRef]
- Roy, D.G.; Singh, T.N. Effect of Heat Treatment and Layer Orientation on the Tensile Strength of a Crystalline Rock under Brazilian Test Condition. Rock Mech. Rock Eng. 2016, 49, 1663–1677. [Google Scholar]
- Liang, W.G.; Xu, S.G.; Zhao, Y.S. Experimental study of temperature effects on physical and mechanical characteristics of salt rock. Rock Mech. Rock Eng. 2006, 39, 469–482. [Google Scholar] [CrossRef]
- Chen, Y.L.; Wang, S.R.; Ni, J.; Azzam, R.; Fernández-Steeger, T.M. An experimental study of the mechanical properties of granite after high temperature exposure based on mineral characteristics. Eng. Geol. 2017, 220, 234–242. [Google Scholar] [CrossRef]
- Zuo, J.P.; Xie, H.P.; Zhou, H.W. Investigation of meso-failure behavior of rock under thermal mechanical coupled effects based on high temperature SEM. Sci. China Phys. Mech. 2012, 55, 1855–1862. [Google Scholar] [CrossRef]
- Stephen, J.B.; John, H. Thermal expansion and cracking of three confined water-saturated igneous rocks to 800 °C. Rock Mech. Rock Eng. 1983, 16, 181–198. [Google Scholar]
- Rao, Q.H.; Wang, Z.; Xie, H.F.; Xie, Q. Experimental study of mechanical properties of sandstone at high temperature. J. Cent. South Univ. 2007, 14, 478–483. [Google Scholar] [CrossRef]
- Tiskatine, R.; Eddemani, A.; Gourdo, L.; Abnay, B.; Ihlal, A.; Aharoune, A.; Bouirden, L. Experimental evaluation of thermo-mechanical performances of andidate rocks for use in high temperature thermal storage. Appl. Energy 2016, 171, 243–255. [Google Scholar] [CrossRef]
- Liu, X.F.; Yuan, S.Y.; Sieffert, Y.; Fityus, S.; Buzzi, L. Changes in Mineralogy Microstructure Compressive Strength and Intrinsic Permeability of Two Sedimentary Rocks Subjected to High-Temperature Heating. Rock Mech. Rock Eng. 2016, 49, 1–14. [Google Scholar] [CrossRef]
- Dougill, J.W.; Lau, J.C.; Burtn, J. Toward a theoretical model for progressive failure and softening in rock concrete and similar materials. Mech. Eng. Am. Soc. Civ. Eng.-Eng. Mech. Div. 1976, 102, 333–355. [Google Scholar]
- Liu, Q.S.; Xu, X.C. Damage analysis of brittle rock at high temperature. Chin. J. Rock Mech. Eng. 2000, 19, 408–411. (In Chinese) [Google Scholar]
- Voyiadjis, G.Z.; Kattan, P.I. Mechanics of damage healing damageability and integrity of materials: A conceptual framework. Int. J. Damage Mech. 2017, 26, 50–103. [Google Scholar] [CrossRef]
- Zhang, Q.S.; Yang, G.S.; Ren, J.X. New study of damage variable and constitutive equation of rock. Chin. J. Rock Mech. Eng. 2003, 22, 31–34. (In Chinese) [Google Scholar]
- Pensée, V.; Morin, L.; Kondo, D. A damage model for ductile porous materials with a spherically anisotropic matrix. Int. J. Damage Mech. 2015, 25, 315–335. [Google Scholar] [CrossRef]
- Brünig, M.A. Thermodynamically consistent continuum damage model taking into account the ideas of CL Chow. Int. J. Damage Mech. 2016, 25, 1130–1141. [Google Scholar] [CrossRef]
- Xu, X.L.; Karakus, M. A coupled thermo-mechanical damage model for granite. Int. J. Rock Mech. Min. Sci. 2018, 104, 195–204. [Google Scholar] [CrossRef]
- Xu, X.L.; Gao, F.; Zhang, Z.Z. Thermo-mechanical coupling damage constitutive model of rock based on the Hoek-Brown strength criterion. Int. J. Damage Mech. 2017, 27, 1213–1230. [Google Scholar] [CrossRef]
- Gao, M.B.; Li, T.B.; Wei, T.; Meng, L.B. A Statistical Constitutive Model considering Deterioration for Brittle Rocks UNDER A Coupled Thermal-Mechanical Condition. Geofluids 2018, 2018, 3269423. [Google Scholar] [CrossRef]
- Liu, X.S.; Ning, J.G.; Tan, Y.L.; Gu, Q.H. Damage constitutive model based on energy dissipation for intact rock subjected to cyclic loading. Int. J. Rock Mech. Min. Sci. 2016, 85, 27–32. [Google Scholar] [CrossRef]
- Loland, K.E. Continuum damage model for load response estimation of concrete. Cement Concr. Res. 1980, 10, 395–402. [Google Scholar] [CrossRef]
- Wu, Z.; Zhang, C.J. Investigation of rock damage model and its mechanical behavior. Chin. J. Rock Mech. Eng. 1996, 15, 55–61. (In Chinese) [Google Scholar]
Initial Young’s Modulus (MPa) | Poisson’s Ratio μ |
Triple-Shear Constant |
Damage Shape Parameter |
Damage Scale Parameter | Experimental Constant n |
---|---|---|---|---|---|
24.3 | 0.25 | 0.52167 | 3.82 | 3.72 × 108 | 3.0 |
Temperature (°C) | 200 | 400 | 600 | 800 | 1000 |
---|---|---|---|---|---|
Initial Young’s Modulus E0 (MPa) | 24.3 | 24.3 | 24.3 | 24.3 | 24.3 |
Thermal Young’s Modulus ET (MPa) | 20.4 | 17.3 | 11.6 | 8.09 | 7.69 |
Possion’s ratio m | 0.25 | 0.25 | 0.25 | 0.25 | 0.25 |
Triple shear constant α0 | 0.52167 | 0.52167 | 0.52167 | 0.52167 | 0.52167 |
Damage shape parameter m0 | 3.82 | 3.82 | 3.82 | 3.82 | 3.82 |
Damage scale parameter F0 | 3.72 × 108 | 3.95 × 108 | 4.15 × 108 | 4.73 × 108 | 5.51 × 108 |
Experimental constant n | 0.3 | 0.3 | 0.2 | 0.1 | 0.11 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Wang, S.; Liao, H.; Chen, Y.; Fernández-Steeger, T.M.; Du, X.; Xiong, M.; Liao, S. Damage Evolution Constitutive Behavior of Rock in Thermo-Mechanical Coupling Processes. Materials 2021, 14, 7840. https://0-doi-org.brum.beds.ac.uk/10.3390/ma14247840
Wang S, Liao H, Chen Y, Fernández-Steeger TM, Du X, Xiong M, Liao S. Damage Evolution Constitutive Behavior of Rock in Thermo-Mechanical Coupling Processes. Materials. 2021; 14(24):7840. https://0-doi-org.brum.beds.ac.uk/10.3390/ma14247840
Chicago/Turabian StyleWang, Suran, Haohao Liao, Youliang Chen, Tomás Manuel Fernández-Steeger, Xi Du, Min Xiong, and Shaoming Liao. 2021. "Damage Evolution Constitutive Behavior of Rock in Thermo-Mechanical Coupling Processes" Materials 14, no. 24: 7840. https://0-doi-org.brum.beds.ac.uk/10.3390/ma14247840