Pure and Applied Geophysics

, Volume 174, Issue 6, pp 2199–2215 | Cite as

Scaling law of average failure rate and steady-state rate in rocks

  • Shengwang Hao
  • Chao Liu
  • Yingchong Wang
  • Fuqing Chang


The evolution properties in the steady stage of a rock specimen are reflective of the damage or weakening growth within and thus are used to determine whether an unstable transition occurs. In this paper, we report the experimental results for rock (granite and marble) specimens tested at room temperature and room humidity under three typical loading modes: quasi-static monotonic loading, brittle creep, and brittle creep relaxation. Deformed rock specimens in current experiments exhibit an apparent steady stage characterized by a nearly constant evolution rate, which dominates the lifetime of the rock specimens. The average failure rate presents a common power–law relationship with the evolution rate in the steady stage, although the exponent is different for different loading modes. The results indicate that a lower ratio of the slope of the secondary stage with respect to the average rate of the entire lifetime implies a more brittle failure.


Steady stage time-to-failure failure mode rock 



This work is supported by National Natural Science Foundation of China (Grant 11672258), National Basic Research Program of China (Grant 2013CB834100) and Natural Science Foundation of Hebei Province (Grant D2015203398). We acknowledge useful comments of two anonymous reviewers.


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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • Shengwang Hao
    • 1
    • 2
  • Chao Liu
    • 1
  • Yingchong Wang
    • 1
  • Fuqing Chang
    • 1
  1. 1.School of Civil Engineering and MechanicsYanshan UniversityQinhuangdaoChina
  2. 2.The State Key Laboratory of Nonlinear Mechanics, Institute of MechanicsChinese Academy of ScienceBeijingChina

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