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An Original Coupled Damage–Permeability Model Based on the Elastoplastic Mechanics in Coal

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Abstract

Coal and gas outburst have always been one of the principal gas energy disasters in coal mines. Pre-extraction of coal-bed methane (CBM) is an effective method to reduce the outburst risk. However, during coal mining and drilling for CBM extraction, coal will inevitably undergo plastic deformation or even failure. This will result in a change in gas’s migration behavior, bringing severe challenges to coal mine gas disaster prevention and effective CBM extraction. Therefore, it was considered necessary to study the evolutionary law of permeability characteristics, and the mechanical property response of coal under engineering disturbance. Based on generalized plastic theory, the plastic strain in coal is calculated by using the non-associated flow rule. The damage variable was modified with reference to the stress–strain constitutive relationship, that was introduced into a simplified permeability model to successfully construct an original coupled damage–permeability model based on the elastoplastic mechanics in coal (D–P coupling model). The proposed model has been verified by carrying out a tri-axial compression-seepage experiment (mining simulations) under different confining pressures and a tri-axial seepage experiment (extraction simulations) under different effective stresses and under different pore pressures. The results showed that during the whole stress–strain process, the new model could well reflect the seepage behavior of CBM on whether coal permeability decreased before the yield point or increased sharply after peak failure. Coal permeability decreased with an increase of effective stress and pore pressure, and the new model corresponded well with the experimental results. Finally, the relationships between plastic strain, damage variables and mechanical properties in coal were discussed. The proposed model has provided a theoretical basis for coal mine gas disaster prevention and CBM extraction.

Highlights

  • Tri-axial compression-seepage experiments under different confining pressures (mining simulations) were conducted.

  • Based on the generalized plastic theory, the plastic deformation of coal was quantified.

  • The mathematical model from elastoplastic deformation to damage and seepage of coal was established.

  • The relationships between plastic strain, the damage variable, and mechanical properties of coal were analyzed.

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Abbreviations

K :

Coal bulk modulus (MPa)

K s :

Coal matrix modulus (MPa)

p :

Pore pressure (MPa)

a :

Cleat spacing (cm)

b :

Cleat aperture (cm)

Δb :

Cleat aperture change (cm)

G :

Shear modulus (MPa)

E :

Elastic modulus of coal (MPa)

E 0 :

Initial elastic modulus of coal (MPa)

E cd :

Elastic modulus of coal at the yield point (MPa)

E c0 :

Elastic modulus of coal at the peak point (MPa)

ν :

Poisson’s ratio

L :

Length of the duct (cm)

k f :

Fracture permeability (10–3 um3)

k f 0 :

Initial fracture permeability (10–3 um3)

X, B :

Langmuir constant (MPa−1)

R :

Ideal gas constant

T :

Temperature (K)

R m :

Elastic modulus reduction ratio

Q k :

Plastic potential function

q :

Generalized shear stress (MPa)

f t 0 :

Uniaxial tensile strength (MPa)

f c 0 :

Uniaxial compressive strength (MPa)

D m :

Mechanical damage variable

n :

Constitutive coefficient

I d :

Damage coefficient

p eff :

Effective confining pressure (MPa)

σ ij :

Total stress tensor

σ ij ' :

Effective stress tensor

σ 1 :

Axial stress (MPa)

σ 3 :

Confining pressure (MPa)

σ m :

Mean stress (MPa)

σ cd :

Yield stress (MPa)

σ c 0 :

Peak stress (MPa)

Δσ :

Deviatoric stress (MPa)

Δσ et :

Total effective stress change (MPa)

α :

Biot’s coefficient

ε 1 :

Axial strain

ε cd :

Yield strain

ε c 0 :

Peak strain

ε cr :

Residual strain

ε cu :

Maximum residual strain

ε 1 e :

Axial elastic strain

ε v e :

Volumetric elastic strain

ε ij :

Strain tensor

ε s :

Sorption-induced volumetric strain

ε si :

Adsorption line strain in direction i

ε v p :

Plastic volume strain

γ p :

Generalized plastic shear strain

θ σ :

Lade angle (°)

dλ k :

Plastic factor

dε ij :

Total strain increment

dε ij e :

Elastic strain increment

dε ij p :

Plastic strain increment

dε v p :

Plastic volume strain increment

dγ p :

Plastic shear strain increment

dε 1 p :

Axial plastic strain increment

δ ij :

Kronecker delta

ϕ f :

Fracture porosity

ϕ f 0 :

Initial fracture porosity

φ :

Internal friction angle (°)

λ c :

Residual strength coefficient

γ d :

Damage–permeability coefficient

ρ s :

Solid body density (g/cm3

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Acknowledgements

This study was financially supported by the National Natural Science Foundation of China (Grants No. 52064007, 51804085 and 51911530203). Supported by Guizhou Provincial Science and Technology Projects (Qianke Combination Foundation -ZK[2021]Key 052). Supported by Project of Guizhou Postgraduate Scientific Research Fund (Guizhou Education Cooperation YJSCXJH [2020] 062).

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Authors and Affiliations

  1. College of Mining, Guizhou University, Guiyang, 550025, China

    Xuehai Wu, Bobo Li, Chonghong Ren, Zheng Gao, Yao Zhang & Chunhong Yao

  2. National & Local Joint Laboratory of Engineering for Effective Utilization of Regional Mineral Resources From Karst Areas, Guizhou University, Guiyang, 550025, China

    Bobo Li

  3. State Key Laboratory of Mining Disaster Prevention and Control Co-Founded By Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao, 266590, China

    Bobo Li

  4. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, China

    Jiang Xu

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  1. Xuehai Wu
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  2. Bobo Li
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Contributions

Xuehai Wu: Conceptualization, Validation, Data curation, Writing—original draft, Writing—review and editing; Bobo Li: Idea guidance, Funding acquisition, Investigation, Methodology; Chonghong Ren: Data processing, Language modification; Zheng Gao: Validation, Paper revision; Jiang Xu: Data collection; Yao Zhang: Draw schematics; Chunhong Yao: Draw concept map.

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Correspondence to Bobo Li.

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Wu, X., Li, B., Ren, C. et al. An Original Coupled Damage–Permeability Model Based on the Elastoplastic Mechanics in Coal. Rock Mech Rock Eng 55, 2353–2370 (2022). https://doi.org/10.1007/s00603-022-02771-5

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