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Energy Dissipation and Release During Coal Failure Under Conventional Triaxial Compression

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Abstract

Theoretical and experimental studies have revealed that energy dissipation and release play an important role in the deformation and failure of coal rocks. To determine the relationship between energy transformation and coal failure, the mechanical behaviors of coal specimens taken from a 600-m deep mine were investigated by conventional triaxial compression tests using five different confining pressures. Each coal specimen was scanned by microfocus computed tomography before and after testing to examine the crack patterns. Sieve analysis was used to measure the post-failure coal fragments, and a fractal model was developed for describing the size distribution of the fragments. Based on the test results, a damage evolution model of the rigidity degeneration of coal before the peak strength was also developed and used to determine the initial damage and critical damage variables. It was found that the peak strength increased with increasing confining pressure, but the critical damage variable was almost invariant. More new cracks were initiated in the coal specimens when there was no confining pressure or the pressure was too high. The parameters of failure energy ratio β and stress drop coefficient α are further proposed to describe the failure mode of coal under different confining pressures. The test results revealed that β was approximately linearly related to the fractal dimension of the coal fragments and that a higher failure energy ratio corresponded to a larger fractal dimension and more severe failure. The stress drop coefficient α decreased approximately exponentially with increasing confining pressure, and could be used to appropriately describe the evolution of the coal failure mode from brittle to ductile with increasing confining pressure. A large β and small α under a high confining pressure were noticed during the tests, which implied that the failure of the coal was a kind of pseudo-ductile failure. Brittle failure occurred when the confining pressure was unloaded—an observation that is important for the safety assessment of deep mines, where a high in situ stress might result in brittle failure of the coal seam, or sudden outburst.

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Abbreviations

A :

A constant related to the fractal characteristic of the fragments

C :

Cohesion

D :

Fractal dimension

E :

Elastic (tangential) modulus

E 0 :

Initial elastic modulus without damage

M R :

Mass of fragments of size less than R

M T :

Total mass of fragments

N :

Number of fragments of size greater than R

R :

Characteristic size of fragments

U d1 :

Energy dissipation before peak strength

U d2 :

Energy dissipation during stress drop

U d3 :

Energy dissipation during residual deformation

U e :

Elastic energy

U ec :

Elastic energy at the peak strength

U ed :

Elastic energy at the drop stress

U f :

Failure energy

W :

Work done by axial load

W c :

Total work done by axial load before peak strength

W d :

Total work before the drop stress

a, k, c, σ 0 :

Parameters for fitting the elastic modulus

b :

Mass-size frequency parameter

α :

Stress drop coefficient

β :

Failure energy ratio

β d1 :

Energy dissipation ratio before the peak strength

β d2 :

Energy dissipation ratio after the peak strength

β r :

Energy release ratio

ε a :

Vertical or axial strain

ε d :

Axial strain at the drop stress

ε r :

Axial strain at the eventual residual stress

ε tc :

Axial strain at the peak stress

Δε a :

Increment of the vertical strain

σ 1, σ 2, σ 3 :

Principal stress

σ a :

Vertical or axial stress

σ cf :

Confining pressure

σ d :

Drop stress

σ tc :

Peak axial stress or triaxial compression strength

σ r :

Eventual residual stress

Δσ a :

Increment of the vertical stress

ν :

Poisson’s ratio

ν 0 :

Poisson’s ratio without damage

φ :

Friction angle

χ :

Parameter related to the average fragment size

ω :

Damage variable

ω 0 :

Initial damage variable

ω c :

Maximum damage variable (i.e., critical damage variable)

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Acknowledgments

This study was financially supported by the National Basic Research Program of China (Nos. 2010CB226804 and 2011CB201201), the National Natural Science Funds for Distinguished Young Scholar of China (Grant No. 51125017), the National Natural Science Foundation of China (No. 10802092), the Program for New Century Excellent Talents in University (No. NCET-12-0966), and the Fundamental Research Funds for the Central Universities (No. 2009QM03).

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Authors and Affiliations

  1. State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing, 100083, People’s Republic of China

    Ruidong Peng, Yang Ju & Lingtao Mao

  2. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, People’s Republic of China

    Yang Ju, J. G. Wang & Feng Gao

  3. School of Mechanical and Chemical Engineering, The University of Western Australia, Crawley, WA, 6009, Australia

    J. G. Wang

  4. College of Hydraulic and Hydroelectric Engineering, Sichuan University, Chengdu, 610065, People’s Republic of China

    Heping Xie

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  1. Ruidong Peng
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  2. Yang Ju
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Correspondence to Ruidong Peng or Yang Ju.

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Peng, R., Ju, Y., Wang, J.G. et al. Energy Dissipation and Release During Coal Failure Under Conventional Triaxial Compression. Rock Mech Rock Eng 48, 509–526 (2015). https://doi.org/10.1007/s00603-014-0602-0

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