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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao, China

    Shengwang Hao, Chao Liu, Yingchong Wang & Fuqing Chang

  2. The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Science, Beijing, China

    Shengwang Hao

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Correspondence to Shengwang Hao.

Appendix: results for specimens that failed immediately and did not fail after a long time loading

Appendix: results for specimens that failed immediately and did not fail after a long time loading

See Figs. 15 and 16.

Fig. 15
figure 15

Results of the brittle creep tests: one specimen failed immediately while trying to hold the stress and one did not fail after a long load time. a The results of a specimen that did not fail after a long load time. After approximately 12.16 h of testing, the data are too large to be stored. b The curves of stress vs. time of a specimen that failed immediately while trying to hold the stress

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Fig. 16
figure 16

Results in creep relaxation tests: one specimen failed immediately when trying to hold the displacement and one that did not fail after a long time loading. a The results of a specimen that did not fail after a long time loading. After about 5.1 h in the tests, the data is too large to be stored. b The results of a specimen that failed immediately when try to hold the displacement

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Hao, S., Liu, C., Wang, Y. et al. Scaling law of average failure rate and steady-state rate in rocks. Pure Appl. Geophys. 174, 2199–2215 (2017). https://doi.org/10.1007/s00024-017-1523-0

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