Abstract
High-sensitivity detection of acoustic emission from granite under uniaxial stress, together with advanced statistical analysis, shows changing collapse mechanisms when a sample is pre-heated. Massive microstructural changes occur at temperatures >500 °C while low-temperature (<<500 °C) treatment leads to scale invariant crackling noise with a mixed fix-point behavior. After treatment at higher temperatures, the collapse occurs via acoustic signals that show energy distributions with systematic deviations from the Gutenberg-Richter law while the Omori’s and Båth’s laws are not influenced by the thermal treatment. The granite samples stem from the site in the Beishan mountains where a new burial site for nuclear waste will be constructed. According to the 13th Five-Year Plan of the P.R. China, Chinese nuclear power installed capacity will reach 58 million kilowatts in 2020 and produce about 3200 tons of high-level nuclear waste every year. Monitoring the stability of the host rock at high temperatures becomes hence a key issue. Our analysis can serve as a blueprint for a protocol for continuous monitoring of the burial site.
Funding
K. Xie, D. Jiang, and X. Jiang acknowledge financial support from the National Science and Technology Major Project (Grant No. 2016ZX05045001-005), and graduate research and innovation foundation of Chongqing (CYB18031). E.K.H. Salje is grateful to EPSRC (EP/P024904/1) for support. E. Vives and A. Planes acknowledge financial support from CICyT (Spain) project MAT2016-75823-R.
References cited
Bak, P., Christensen, K., Danon, L., and Scanlon, T. (2002) Unified scaling law for earthquakes. Physical Review Letters, 88, 178501.10.1103/PhysRevLett.88.178501Search in Google Scholar
Baró, J., Corral, A., Illa, X., Planes, A., Salje, E.K.H., Schranz, W., Soto-Parra, D.E., and Vives, E. (2013) Statistical similarity between the compression of a porous material and earthquakes. Physical Review Letters, 110, 088702.10.1103/PhysRevLett.110.088702Search in Google Scholar
Båth, M. (1965) Lateral inhomogeneities of the upper mantle. Tectonophysics, 2, 483–514.10.1016/0040-1951(65)90003-XSearch in Google Scholar
Bredehoeft, J.D., England, A.W., Stewart, D.B., Trask, N.J., and Winograd, I.J. (1978) Geologic disposal of high-level radioactive wastes—Earth science perspectives. Department of Interior, Geological Survey Circular, No. 779.10.3133/cir779Search in Google Scholar
Byerlee, J. (1978) A review of rock mechanics studies in the United States pertinent to earthquake prediction. Pure and Applied Geophysics, 116, 586–602.10.1007/978-3-0348-7182-2_2Search in Google Scholar
Carpenter, M.A., Salje, E.K.H., Graeme-Barber, A., Wruck, B., Dove, M.T., and Knight, K.S. (1998) Calibration of excess thermodynamic properties and elastic constant variations associated with the alpha-beta phase transition in quartz. American Mineralogist, 83, 2–22.10.2138/am-1998-1-201Search in Google Scholar
Castillo-Villa, P.O., Baró, J., Planes, A., Salje, E.H.K., Sellappan, P., Kriven, W.M., and Vives, E. (2013) Crackling noise during failure of alumina under compression: The effect of porosity. Journal of Physics: Condensed Matter, 25, 292202.10.1088/0953-8984/25/29/292202Search in Google Scholar PubMed
Chen, S., Yang, C., and Wang, G. (2017) Evolution of thermal damage and permeability of Beishan granite. Applied Thermal Engineering, 110, 1533–1542.10.1016/j.applthermaleng.2016.09.075Search in Google Scholar
Clauset, A., Shalizi, C.R., and Newman, M.E. (2009) Power-law distributions in empirical data. Society for Industrial and Applied Mathematics Review, 51, 661–703.10.1137/070710111Search in Google Scholar
Console, R., Lombardi, A.M., Murru, M., and Rhoades, D. (2003) Båth’s law and the self-similarity of earthquakes. Journal of Geophysical Research: Solid Earth, 108, B22128.10.1029/2001JB001651Search in Google Scholar
Corral, A. (2003) Local distributions and rate fluctuations in a unified scaling law for earthquakes. Physical Review E, 68, 035102(R).10.1103/PhysRevE.68.035102Search in Google Scholar PubMed
Dahmen, K.A., Ben-Zion, Y., and Uhl, J.T. (2011) A simple analytic theory for the statistics of avalanches in sheared granular materials. Nature Physics, 7, 554–557.10.1038/nphys1957Search in Google Scholar
Davidsen, J., Grassberger, P., and Paczuski, M. (2006) Earthquake recurrence as a record breaking process. Geophysical Research Letters, 33, l11304.10.1029/2006GL026122Search in Google Scholar
Davidsen, J., Stanchits, S., and Dresen, G. (2007) Scaling and universality in rock fracture. Physical Review Letters, 98, 125502.10.1103/PhysRevLett.98.125502Search in Google Scholar PubMed
Davidsen, J., Grassberger, P., and Paczuski, M. (2008) Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity. Physical Review E, 77, 066104.10.1103/PhysRevE.77.066104Search in Google Scholar PubMed
Eshelby, J.D. (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society A, 241, 376–396.10.1007/1-4020-4499-2_18Search in Google Scholar
Falk, M.L., and Langer, J. S. (1998) Dynamics of viscoplastic deformation in amorphous solids. Physical Review E, 57, 7192–7205.10.1103/PhysRevE.57.7192Search in Google Scholar
Fan, L.F., Gao, J.W., Wu, Z.J., Yang, S.Q., and Ma, G.W. (2018) An investigation of thermal effects on micro-properties of granite by X‑ray CT technique. Applied Thermal Engineering, 140, 505–519.10.1016/j.applthermaleng.2018.05.074Search in Google Scholar
Fergus, G.F.G., and Philip, G.A. (2003) Granite recrystallization: The key to the nuclear waste problem? Geology, 31, 657–660.10.1130/G19410.1Search in Google Scholar
Fredrich, J.T., and Wong, T.F. (1986) Micromechanics of thermally induced cracking in three crustal rocks. Journal of Geophysical Research, 91, 12743–12764.10.1029/JB091iB12p12743Search in Google Scholar
Glover, P.W.J., Baud, P., Darot, M., Meredith, P.G., Boon, S.A., LeRavaleq, M., Zoussi, S., and Reusche, T. (1995) a/b phase transition in quartz monitored using acoustic emissions. Geophysical Journal International, 120, 775–782.10.1111/j.1365-246X.1995.tb01852.xSearch in Google Scholar
Godbeer, W.C., and Wilkins, R.W.T. (1967) The water content of a synthetic quartz. American Mineralogist, 62, 831–832.Search in Google Scholar
Hall, L., and Bodnar, R.J. (1989) Comparison of fluid inclusion decrepitation and acoustic emission profiles of Westerly granites and quartzite. Tectonophysics, 168, 283–296.10.1016/0040-1951(89)90223-0Search in Google Scholar
Helmstetter, A., and Sornette, D. (2003) Båth’s law derived from the Gutenberg-Richter law and from aftershock properties. Geophysical Research Letters, 30, 20, 2069.10.1029/2003GL018186Search in Google Scholar
Jansen, D.P., Carlson, S.R., Young, R.P., and Hutchins, D.A. (1993) Ultra-sonic imaging and acoustic emission monitoring of thermally induced microcracks in Lacdu Bonnet granite. Journal of Geophysical Research, 98, 22,231–22,243.10.1029/93JB01816Search in Google Scholar
Jiang, X., Jiang, D., Chen, J., and Salje, E.K.H. (2016) Collapsing minerals: Crackling noise of sandstone and coal, and the predictability of mining accidents. American Mineralogist, 101, 2751–2758.10.2138/am-2016-5809CCBYSearch in Google Scholar
Jiang, X., Liu, H., Main, I.G., and Salje, E.K.H. (2017) Predicting mining collapse: Superjerks and the appearance of record-breaking events in coal as collapse precursors. Physical Review E, 96, 023004.10.1103/PhysRevE.96.023004Search in Google Scholar
Karmakar, S., Lerner, E., Procaccia, I., and Zylberg, J. (2010) Statistical physics of elastoplastic steady states in amorphous solids: finite temperatures and strain rates. Physical Review E, 82, 031301.10.1103/PhysRevE.82.031301Search in Google Scholar
Kendrick, M.A., Phillips, D., and Miller, J. M., (2006) Part I. Decrepitation and degassing behaviour of quartz up to 1560 °C: analysis of noble gases and halogens in complex fluid inclusion assemblages. Geochimica et Cosmochimica Acta, 70, 2540–2561.10.1016/j.gca.2005.12.023Search in Google Scholar
Kranz, R.L. (1983) Microcracks in rocks: a review. Tectonophysics, 100, 449–480.10.1016/0040-1951(83)90198-1Search in Google Scholar
Kun, F., Varga, I., Lennartz-Sassinek, S., and Main, I.G. (2013) Approach to failure in porous granular materials under compression. Physical Review E, 88, 062207.10.1103/PhysRevE.88.062207Search in Google Scholar PubMed
Kun, F., Varga, I., Lennartz-Sassinek, S., and Main, I.G. (2014) Rupture cascades in a discrete element model of a porous sedimentary rock. Physical Review Letters, 112, 065501.10.1103/PhysRevLett.112.065501Search in Google Scholar PubMed
Lin, W. (2002) Permanent strain of thermal expansion and thermally induced microcracking in Inada granite. Journal of Geophysical Research: Atmospheres, 107, 3–16.10.1029/2001JB000648Search in Google Scholar
Mansurov, V.A. (1994) Acoustic emission from failing rock behavior. Rock Mechanics and Rock Engineering, 27, 173–182.10.1007/BF01020309Search in Google Scholar
Martens, K., Bocquet, L., and Barrat, J.L. (2012) Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter. Soft Matter, 8, 4197–4205.10.1039/c2sm07090aSearch in Google Scholar
Nataf, G.F., Castillo-Villa, P.O., Baró, J., Illa, X., Vives, E., Planes, A., and Salje, E.K.H. (2014a) Avalanches in compressed porous SiO2-based materials. Physical Review E, 90, 022405.10.1103/PhysRevE.90.022405Search in Google Scholar PubMed
Nataf, G.F., Castillo-Villa, P.O., Sellappan, P., Kriven, W.M., Vives, E., Planes, A., and Salje, E.K.H. (2014b) Predicting failure: acoustic emission of berlinite under compression. Journal of Physics: Condensed Matter, 26, 275401.10.1088/0953-8984/26/27/275401Search in Google Scholar PubMed
Neudecker, M., and Mayr, S.G. (2009) Dynamics of shear localization and stress relaxation in amorphous. Acta Materialia, 57, 1437–1441.10.1016/j.actamat.2008.11.032Search in Google Scholar
Pál, G., Raischel, F., Lennartz-Sassinek, S., Kun, F., and Main, I.G. (2016) Record-breaking events during the compressive failure of porous materials. Physical Review E, 93, 033006.10.1103/PhysRevE.93.033006Search in Google Scholar PubMed
Picard, G., Ajdari, A., Lequeux, F.M.C., and Bocquet, L. (2005) Slow flows of yield stress fluids: complex spatiotemporal behaviour within a simple elastoplastic model. Physical Review E, 71, 010501.10.1103/PhysRevE.71.010501Search in Google Scholar PubMed
Pradhan, S., Hansen, A., and Hemmer, P.C. (2005) Crossover behavior in burst avalanches: Signature of imminent failure. Physical Review Letters, 95, 125501.10.1103/PhysRevLett.95.125501Search in Google Scholar PubMed
Reuschlé, T. (1989) Les fluides et I’evolution des proprieties, mechaniques des roches, Ph.D. Thesis, Louis Pasteur University, Strasbourg.Search in Google Scholar
Ribeiro, H.V., Costa, L.S., Alves, L.G.A., Santoro, P.A., Picoli, S., Lenzi, E.K., and Mendes, R.S. (2015) Analogies between the cracking noise of ethanol-dampened charcoal and earthquakes. Physical Review Letters, 115, 025503.10.1103/PhysRevLett.115.025503Search in Google Scholar
Richter, D., and Simmons, G. (1974) Thermal expansion behavior of igneous rocks. International Journal of Rock Mechanics and Mining Science, 11, 403–411.10.1016/0148-9062(74)91111-5Search in Google Scholar
Salje, E.K.H., Soto-Parra, D.E., Planes, A., Vives, E., Reineckerc, M., and Schranz, W. (2011) Failure mechanism in porous materials under compression: Crackling noise in mesoporous SiO2 Philosophical Magazine Letters, 91, 554–560.10.1080/09500839.2011.596491Search in Google Scholar
Salje, E.K.H., Lampronti, G.I., Soto-Parra, D.E., Baró, J., Planes, A., and Vives, E. (2013) Noise of collapsing minerals: Predictability of the compressional failure in goethite mines. American Mineralogist, 98, 609–615.10.2138/am.2013.4319Search in Google Scholar
Salje, E.K.H., and Dahmen, K.A. (2014) Crackling noise in disordered materials. Annual Review of Condensed Matter Physics, 5, 233–254.10.1146/annurev-conmatphys-031113-133838Search in Google Scholar
Salje, E.K.H., Planes, A., and Vives, E. (2017) Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping. Physical Review E, 96, 042122.10.1103/PhysRevE.96.042122Search in Google Scholar PubMed
Sethna, J.P., Dahmen, K.A., and Myers, C.R. (2001) Crackling noise. Nature, 410, 242–250.10.1038/35065675Search in Google Scholar PubMed
Soprunyuk, V., Puchberger, S., Tröster, A., Vives, E., Salje, E.K.H., and Schranz, W. (2017) Strain intermittency due to avalanches in ferroelastic and porous materials Journal of Physics: Condensed Matter, 29, 224002.10.1088/1361-648X/aa6bd2Search in Google Scholar PubMed
Soto-Parra, D., Zhang, X., Cao, S., Vives, E., Salje, E.K.H., and Planes, A. (2015) Avalanches in compressed Ti-Ni shape-memory porous alloys: An acoustic emission study. Physical Review E, 91, 060401.10.1103/PhysRevE.91.060401Search in Google Scholar PubMed
Utsu, T., Ogata, Y., and Matsu’ura, R.S. (1995) The centenary of the omori formula for a decay law of aftershock activity. Journal of Physics of the Earth, 43, 1–33.10.4294/jpe1952.43.1Search in Google Scholar
Wang, H.F., Bonner, B.P., Carlson, S.R., Kowallis, B.J., and Heard, H.C. (1989) Thermal stress cracking in granite. Journal of Geophysical Research, 94, 1745–1758.10.1029/JB094iB02p01745Search in Google Scholar
Wergen, G., and Krug, J. (2010) Record-breaking temperatures reveal a warming climate. Europhysics Letters, 92, 30008.10.1209/0295-5075/92/30008Search in Google Scholar
Xu, Y., Angeles, G.B., Planes, A., Ding, X., and Vives, E. (2019) Criticality in failure under compression: acoustic emission study of coal and charcoal with different microstructures. Physical Review E, 99, 033001.10.1103/PhysRevE.99.033001Search in Google Scholar PubMed
Yoder, M.R., Turcotte, D.L., and Rundle, J.B. (2010) Record-breaking earthquake intervals in a global catalogue and an aftershock sequence. Nonlinear Processes in Geophysics, 17, 169–176.10.5194/npg-17-169-2010Search in Google Scholar
Zhao, X.G., Zhao, Z., Guo, Z., Cai, M., Li, X., Li, P.F., Chen, L., and Wang, J. (2018) Influence of thermal treatment on the thermal conductivity of Beishan Granite. Rock Mechanics and Rock Engineering, 51, 2055–2074.10.1007/s00603-018-1479-0Search in Google Scholar
Zink, M., Samwer, K., Johnson, W.L., and Mayr, S.G. (2006) Plastic deformation of metallic glasses: size of shear transformation zones from molecular dynamics simulations. Physical Review B, 73, 172203.10.1103/PhysRevB.73.172203Search in Google Scholar
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