Scaling law of average failure rate and steady-state rate in rocks
- 177 Downloads
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.
KeywordsSteady 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.
- Amitrano, D., Grasso, J. R., & Senfaute, G. (2005). Seismic precursory patterns before a cliff collapse and critical point phenomena. Geophysical Research Letters, 32(5), L08314. doi: 10.1029/2004GL022270.
- Amitrano, D., & Helmstetter, A. (2006). Brittle creep, damage and time to failure in rocks. Journal of Geophysical Research, 111, 1–17, B11201. doi: 10.1029/2005JB004252.
- Andrade E. N. da C. (1910). On the viscous flow in metals and allied phenomena. Proceedings of the Royal Society of London. Series A, 84, 1.Google Scholar
- Atkinson, B., Meredith, P. (1987) The theory of subcritical crack growth with applications to minerals and rocks. In: Fracture mechanics of rocks (pp. 111–166). New York: Academic Press.Google Scholar
- Baud, P., & Meredith, P. (1997). Damage accumulation during triaxial creep of darley dale sandstone from pore volumetry and acoustic emission. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 34(3–4), 1–8.Google Scholar
- Benioff, H. (1951). Earthquake and rock creep. Bulletin of the Seismological Society of America, 41(1), 31–62.Google Scholar
- Guarino, A., Ciliberto, S., Garcimartin, A., Zei, M., & Scoretti, R. (2002). Failure time and critical behavior of fracture precursors in heterogeneous materials. European Physical Journal B: Condensed Matter and Complex Systems, 26, 141–151.Google Scholar
- Heap, M. J., Baud, P., Meredith, P. G., Bell, A. F., & Main, I. G. (2009). Time-dependent brittle creep in Darley Dale sandstone. Journal of Geophysical Research Solid Earth, 114, B07203. doi: 10.1029/2008JB006212.
- Jeager, J. C., Cook, N. G. W., & Zimmerman, R. (2007). Fundamentals of rock mechanics (4th ed.). London: Wiley-Blackwell.Google Scholar
- Lockner, D. A., & Byerlee, J. D. (1980). Development of fracture planes during creep in granite. In H. R. Hardy, F. W. Leiton, (Eds.) Proceedings of 2nd conference on acoustic emission/microseismic activity in geological structures and materials (pp 11–25). Clausthal-Zellerfeld, Germany: Trans Tech Publications.Google Scholar
- Omori, F. (1894). On the aftershocks of eathquakes. Journal of the College of Science, Imperial University of Tokyo, 7, 111–120.Google Scholar
- Perfettin, H., & Avouac, J. P. (2004). Postseismic relaxation driven by brittle creep: A possible mechanism to reconcile geodetic measurements and the decay rate of aftershocks, application to the Chi-Chi earthquake, Taiwan. Journal of Geophysical Research, 109, B02304. doi: 10.1029/2003JB002488.Google Scholar
- Saito, M. (1969). Forecasting time of slope failure by tertiary creep. In Proc. 7th Int. Conf. Soil Mechanics and Foundation Engineering, Mexico City (Vol. 2, pp. 677–683).Google Scholar
- Saito, M., Uezawa, H. (1961) Failure of soil due to creep. In Proc. 5th Int. Conf. Soil Mechanics and Foundation Engineering, Montreal (Vol. 1, pp. 315–318).Google Scholar
- Utsu, T. (1961). Statistical study on the occurrence of aftershocks. Geophysical Magazine, 30, 521–605.Google Scholar