Abstract
Coal mining can pose safety risks as mining stress and adsorption-desorption damage the coal in front of the working face. To address this, a damage model under the coupled influence of mining stress and adsorption-desorption was proposed by incorporating statistical damage mechanics and the effective stress principle. The method for determining model parameters was provided, and the model was validated through triaxial compression tests on coal containing methane. The model parameters were qualitatively analyzed, and the impact of parameters on the deformation and damage evolution of coal was also examined. The residual strengths of coal determined by previous classical models and the proposed damage model under various confining pressures were compared. The results mainly show that coal containing methane has distinct stages during triaxial compression, including compaction, elastic deformation, yield, strain softening, and residual deformation. The proposed damage model accurately tracks deformation and damage in a coal containing methane at varying confining pressures. An increase in Weibull distribution parameters causes peak stress and damage accumulation to start at a higher strain. Furthermore, a higher correction coefficient of residual strength results in a faster stress drop rate but lower residual strength of coal after peak stress. The proposed damage model accurately predicts the residual strength of coal under various confining pressures.
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Abbreviations
- \(A\) :
-
Area
- \(D\) :
-
Damage variable
- \(E\) :
-
Elastic modulus of coal (MPa)
- \(F\) :
-
The strength of coal micro-elements
- \(I'_{1}\) :
-
The first stress invariant
- \(J'_{2}\) :
-
The second deviatoric stress invariant
- \(K\) :
-
Bulk modulus of porous soil (MPa)
- \(K_{s}\) :
-
Bulk modulus of skeleton of soil (MPa)
- \(Q\) :
-
Adsorption capacity (\(\text{cm}^{3}\boldsymbol{\cdot}\text{g}^{-1}\))
- \(R\) :
-
The disturbance factor
- GSI:
-
Geological Strength Index
- RVE:
-
Representative Volume Element
- \(m_{i}\) :
-
Dimensionless empirical parameter
- \(c\) :
-
Cohesion (MPa)
- \(f\) :
-
Degradation rate (%)
- \(p\) :
-
Gas pressure (MPa)
- \(p_{w}\) :
-
Pore pressure (MPa)
- \(m_{\mathrm{b}}\), \(s\), \(a\) :
-
H–B model parameter
- \(\alpha \), \(k\), \(k_{1}\), \(k'\), \(B\), \(N\) :
-
Simplified calculation notation
- \(w_{e}\), \(w_{p}\) :
-
Boundary widths of the damaged entity and the damaged pore in the coal RVE
- \(\alpha _{b}\) :
-
Biot coefficient
- \(\beta \) :
-
The material constant
- \(\delta \) :
-
Correction coefficient of residual strength
- \(\varepsilon _{1}\) :
-
Axial strain (%)
- \(\varepsilon _{10}\) :
-
Axial initial strain (%)
- \(\varepsilon _{1t}\) :
-
Deviatoric strain (%)
- \(\varepsilon '_{i}\) :
-
Effective strain (%)
- \(\varphi \) :
-
The internal friction angle (°)
- \(\gamma \) :
-
Damaged pore factor
- \(\lambda \) :
-
Adsorption degradation coefficient of modulus
- \(\nu \) :
-
Poisson’s ratio
- \(\sigma _{1}\) :
-
Axial stress (MPa)
- \(\sigma _{1t}\) :
-
Deviatoric stress (MPa)
- \(\sigma _{3}\) :
-
Confining pressure (MPa)
- \(\sigma _{c}\) :
-
Uniaxial compressive strength (MPa)
- \(\sigma _{i}\) :
-
Macroscopic total stress (MPa)
- \(\sigma '_{i}\) :
-
Effective stress (MPa)
- \(\sigma ''_{i}\) :
-
Microscopic stress (MPa)
- 0:
-
Initial state
- \(c\) :
-
Mining stress
- \(cx\) :
-
Coupling of mining stress and adsorption-desorption
- \(d\) :
-
Damaged zone
- \(e\) :
-
Damaged entity
- \(m\) :
-
Matrix
- \(p\) :
-
Damaged pore
- \(r\) :
-
Residual
- \(t\) :
-
Total part of RVE in coal
- \(u\) :
-
Undamaged zone
- \(x\) :
-
Adsorption-desorption
- \(i\), \(j\), \(k\) :
-
Principal stress direction
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Funding
This work was supported by the National Natural Science Foundation of China (No. 52004081), the Key Scientific Research Project of Higher Education Institutions of Henan Province (No. 21A440005), the research fund of Henan Key Laboratory for Green and Efficient Mining & Comprehensive Utilization of Mineral Resources (Henan Polytechnic University), the opening project of Henan Key Laboratory of Underground Engineering and Disaster Prevention (Henan Polytechnic University), the Science and Technology Development Fund Project of China Coal Research Institute (No. 2021CX-II-12), the Natural Science Foundation of Henan Polytechnic University (No. B2020-34), the research fund of Jiaozuo Road Traffic and Transportation Engineering and Technology Research Center (No. JRTT2023008). The financial supports are gratefully acknowledged.
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Tenglong Rong and Keliu Liu contributed to the conception, design and writing of the manuscript; Sheng Zhang revised the manuscript; Yang Zhao participated in the material preparation and data collection; Pengju Liu and Ming Wang plotted the figures.
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Rong, T., Liu, K., Zhang, S. et al. A damage constitutive model for coal under mining stress and adsorption-desorption. Mech Time-Depend Mater (2023). https://doi.org/10.1007/s11043-023-09627-7
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DOI: https://doi.org/10.1007/s11043-023-09627-7