Rock Mechanics and Rock Engineering

, Volume 51, Issue 1, pp 119–134 | Cite as

Estimation of Crack Initiation and Propagation Thresholds of Confined Brittle Coal Specimens Based on Energy Dissipation Theory

  • Jianguo Ning
  • Jun Wang
  • Jinquan Jiang
  • Shanchao Hu
  • Lishuai Jiang
  • Xuesheng Liu
Original Paper


A new energy-dissipation method to identify crack initiation and propagation thresholds is introduced. Conventional and cyclic loading–unloading triaxial compression tests and acoustic emission experiments were performed for coal specimens from a 980-m deep mine with different confining pressures of 10, 15, 20, 25, 30, and 35 MPa. Stress–strain relations, acoustic emission patterns, and energy evolution characteristics obtained during the triaxial compression tests were analyzed. The majority of the input energy stored in the coal specimens took the form of elastic strain energy. After the elastic-deformation stage, part of the input energy was consumed by stable crack propagation. However, with an increase in stress levels, unstable crack propagation commenced, and the energy dissipation and coal damage were accelerated. The variation in the pre-peak energy-dissipation ratio was consistent with the coal damage. This new method demonstrates that the crack initiation threshold was proportional to the peak stress (σ p) for ratios that ranged from 0.4351 to 0.4753σ p, and the crack damage threshold ranged from 0.8087 to 0.8677σ p.


Acoustic emission Coal damage Energy accumulation and dissipation Crack damage initiation Crack damage stress 

List of symbols


Crack initiation threshold


Crack damage stress


Peak stress


Total stored energy


Elastic strain energy


Dissipated energy


Absorbed strain energy by axial compression


Consumed strain energy for radial dilation


Axial strain


Radial strain


Unloading module of elasticity


Unloading Poisson’s ratio


Axial stress


Confining pressure



The research described in this paper was financially supported by the National Natural Science Foundation of China (No. 51574154, 51574155, 51704182), the Qingdao Postdoctoral Applied Research Project (No. 2015198), and the Taishan Scholar Talent Team Support Plan for Advantaged & Unique Discipline Areas.


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Copyright information

© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Mining Disaster Prevention and ControlCo-Founded By Shandong Province and the Ministry of Science and Technology, Shandong University of Science and TechnologyQingdaoChina

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