Modeling acoustic emissions in heterogeneous rocks during tensile fracture with the Discrete Element Method
Open Geomechanics, Volume 2 (2020) , article no. 2, 19 p.

A computationally efficient and open sourced methodology designed for the investigation of rock matrix heterogeneities and their effect on pre- and post- fracture Acoustic Emission (AE) distributions is presented. First, an image analysis method is proposed for building a statistical model representing rock heterogeneity. The statistical model is generalized and implemented into a discrete element contact model where it efficiently simulates the presence of defects and locally tough regions. The coupling of the heterogeneity model, discrete element model, and acoustic emission model is demonstrated using a numerical three point bending test. The shape parameter of the statistical model, which controls heterogeneity magnitude, is found to control the spatial width of the acoustic emission distribution generated during failure. The same acoustic emission distribution trend is observed in literature for rocks containing various magnitudes of heterogeneity. Further analysis of the numerical AE activity reveals that larger AE events are located directly along the fracture and they are linearly related to their number of constituent interactions. As such, an AE interaction count threshold is identified to distinguish between fracture and damage AE activity. These results demonstrate the ability of the presented methodology to investigate the location and energy release associated with large fracture events for various levels of heterogeneity.

Supplementary Materials:
Supplementary material for this article is supplied as a separate file: Caulk-opengeomechanics-suppl.zip

Received: 2019-08-16
Accepted: 2020-04-14
Published online: 2020-05-05
DOI: https://doi.org/10.5802/ogeo.5
Keywords: Discrete Element Method; rock heterogeneity modeling; acoustic emission; tensile fracture; intrinsic process zone
@article{OGEO_2020__2__A2_0,
     author = {Caulk, Robert A.},
     title = {Modeling acoustic emissions in heterogeneous rocks during tensile fracture with the Discrete Element Method},
     journal = {Open Geomechanics},
     publisher = {Alert Geomaterials},
     volume = {2},
     year = {2020},
     doi = {10.5802/ogeo.5},
     language = {en},
     url = {opengeomechanics.centre-mersenne.org/item/OGEO_2020__2__A2_0/}
}
Caulk, Robert A. Modeling acoustic emissions in heterogeneous rocks during tensile fracture with the Discrete Element Method. Open Geomechanics, Volume 2 (2020) , article  no. 2, 19 p. doi : 10.5802/ogeo.5. https://opengeomechanics.centre-mersenne.org/item/OGEO_2020__2__A2_0/

[1] Ahrens, James; Geveci, Berk; Law, Charles ParaView: An end-user tool for large-data visualization, Visualization Handbook, 2005 | Article

[2] Alava, Mikko J.; Nukala, Phani K.V.V.; Zapperi, Stefano Statistical models of fracture, Advances in Physics, Volume 55 (2006) no. 3-4, pp. 349-476 | arXiv:0609650 | Article

[3] Buxton, Gavin A; Care, Christopher M; Cleaver, Douglas J A lattice spring model of heterogeneous materials with plasticity, Modelling and Simulation in Materials Science and Engineering, Volume 9 (2001), pp. 485-497 | Article

[4] Berkovits, Avraham; Fang, Daining Study of fatigue crack characteristics by acoustic emission, Engineering Fracture Mechanics, Volume 51 (1995) no. 3 | Article

[5] Boyce, G M; Mccabe, W M; Koerner, R M Acoustic Emission Signatures of Various Rock Types in Unconfined Compression, Geotechnical Engineering Practice (1981), pp. 142-154

[6] Birck, Gabriel; Riera, Jorge D.; Iturrioz, Ignacio Numerical DEM simulation of AE in plate fracture and analogy with the frequency of seismic events in SCRs, Engineering Failure Analysis, Volume 93 (2018) no. December 2017, pp. 214-223 | Article

[7] Bai, Qing Sheng; Tu, Shi Hao; Zhang, Cun DEM investigation of the fracture mechanism of rock disc containing hole(s) and its influence on tensile strength, Theoretical and Applied Fracture Mechanics, Volume 86 (2016) no. July, pp. 197-216 | Article

[8] Chun’an Tang Numerical simulation of progressive rock failure and associated seismicity, International journal of rock mechanics and mining sciences & geomechanics abstracts (1997) | Article

[9] Caulk, R.A. Stochastic augmentation of a discrete element model for the investigation of tensile rupture in heterogeneous rock, Yade Technical Archive (2018) | Article

[10] Cai, M; Kaiser, P.K. Numerical simulation of the Brazilian test and the tensile strength of anisotropic rock and rocks with pre-existing cracks, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr, Volume 41 (2004) no. 3, pp. 1-6

[11] Da Cruz, Frédéric; Emam, Sacha; Prochnow, Michaël; Roux, Jean Noël; Chevoir, François Rheophysics of dense granular materials: Discrete simulation of plane shear flows, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Volume 72 (2005) no. 2 | arXiv:0503682 | Article

[12] Eisenblatter, J; Grosse, Christian U.; Koppel, S.; Kurz, J.; Landis, E.; Linzer, L.; Manthei, G.; Ohstu, M.; Schechinger, B.; Shigeishi, M.; Shitani, T.; Vogel, T. Acoustic Emission Testing, Springer Berlin Heidelberg, 2008 http://www.springerlink.com/index/10.1007/978-3-540-69972-9 | Article

[13] Eitzen, D.G.; Wadley, N.G. Acoustic Emission : Establishing the Fundamentals, Journal of Research of the National Bureau of Standards, Volume 89 (1984) no. 1, pp. 75-100 | Article

[14] Fakhimi, A.; Carvalho, F.; Ishida, T.; Labuz, J.F. Simulation of failure around a circular opening using CWFS model, International Journal of Rock Mechanics and Mining Sciences, Volume 39 (2002), pp. 507-515 | Article

[15] Garboczi, E. J.; Day, A. R. An algorithm for computing the effective linear elastic properties of heterogeneous materials: Three-dimensional results for composites with equal phase poisson ratios, Journal of the Mechanics and Physics of Solids, Volume 43 (1995) no. 9, pp. 1349-1362 | Article | Zbl 0881.73094

[16] Godin, N.; Huguet, S.; Gaertner, R.; Salmon, L. Clustering of acoustic emission signals collected during tensile tests on unidirectional glass/polyester composite using supervised and unsupervised classifiers, NDT and E International, Volume 37 (2004) no. 4, pp. 253-264 | Article

[17] Hazzard, J F; Damjanac, Branko Further investigations of microseismicity in bonded particle models, 3rd International FLAC/DEM Symposium (2013), pp. 1-11 http://www.itascacg.com/documents/further-investigations-of-microseismicity-in-bonded-particle-models

[18] Houseknecht, Dw Use of cathodoluminescence petrography for understanding compaction, quartz cementation, and porosity in sandstones, Luminiscence Microscopy: Quantitative and Qualitative Aspects (1991), pp. 59-66 http://archives.datapages.com/data/sepm_sp/sc25/Use_of_Cathodoluminescence.pdf | Article

[19] Hazzard, J.F; Young, R.P Simulating acoustic emissions in bonded-particle models of rock, International Journal of Rock Mechanics and Mining Sciences, Volume 37 (2000) no. 5, pp. 867-872 http://linkinghub.elsevier.com/retrieve/pii/S1365160900000174 | Article

[20] Hazzard, James F.; Young, R. Paul Moment tensors and micromechanical models, Tectonophysics, Volume 356 (2002), pp. 181-197 | Article

[21] Hazzard, J. F.; Young, R. Paul Dynamic modelling of induced seismicity, International Journal of Rock Mechanics and Mining Sciences, Volume 41 (2004) no. 8, pp. 1365-1376 | Article

[22] Iturrioz, Ignacio; Birck, Gabriel; Riera, Jorge D. Numerical DEM simulation of the evolution of damage and AE preceding failure of structural components, Engineering Fracture Mechanics, Volume 210 (2019) no. 2018, pp. 247-256 | Article

[23] Itasca, CG PFC-particle flow code in 2 and 3 dimension, 2015

[24] Khazaei, Cyrus; Hazzard, Jim; Chalaturnyk, Rick Damage quantification of intact rocks using acoustic emission energies recorded during uniaxial compression test and discrete element modeling, Computers and Geotechnics, Volume 67 (2015) no. 2015, pp. 94-102 | Article

[25] Khazaei, Cyrus; Hazzard, Jim; Chalaturnyk, Rick A discrete element model to link the microseismic energies recorded in caprock to geomechanics, Acta Geotechnica, Volume 11 (2016) no. 6, pp. 1351-1367 | Article

[26] Labuz, J. F.; Biolzi, L. Experiments with rock: Remarks on strength and stability issues, International Journal of Rock Mechanics and Mining Sciences, Volume 44 (2007) no. 4, pp. 525-537 | Article

[27] Lockner, D. A.; Byerlee, J. D.; Kuksenko, V.; Ponomarev, A.; Sidorin, A. Chapter 1 Observations of Quasistatic Fault Growth from Acoustic Emissions, International Geophysics, Volume 51 (1992) no. C, pp. 3-31 | Article

[28] Labuz, Joseph F.; Cattaneo, Sara; Chen, Li Hsien Acoustic emission at failure in quasi-brittle materials, Construction and Building Materials, Volume 15 (2001) no. 5-6, pp. 225-233 | Article

[29] Li, Bing Qiuyi; Einstein, Herbert H. Comparison of Visual and Acoustic Emission Observations in a Four Point Bending Experiment on Barre Granite, Rock Mechanics and Rock Engineering, Volume 50 (2017) no. 9, pp. 2277-2296 | Article

[30] Lei, X.-L.; Kusunose, K.; Nishizawa, O; Cho, A; Satoh, T On the spatio-temporal distribution of acoustic emissions in two granitic rocks under triaxial compression: The role of pre-existing cracks, Geophysical Research Letters, Volume 27 (2000) no. 13, pp. 1997-2000

[31] Lisjak, A.; Liu, Q.; Zhao, Q.; Mahabadi, O. K.; Grasselli, G. Numerical simulation of acoustic emission in brittle rocks by two-dimensional finite-discrete element analysis, Geophysical Journal International, Volume 195 (2013) no. 1, pp. 423-443 | Article

[32] Lei, Xinglin; Masuda, Koji; Nishizawa, Osamu; Jouniaux, Laurence; Liu, Liqiang; Ma, Wentao; Satoh, Takashi; Kusunose, Kinichiro Detailed analysis of acoustic emission activity during catastrophic fracture of faults in rock, Journal of Structural Geology, Volume 26 (2004), pp. 247-258 | Article

[33] Lockner, D. A. The role of acoustic emission in the study of rock fracture, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, Volume 30 (1993) no. 7, pp. 883-899 http://www.sciencedirect.com/science/article/B6V4V-47YBB1M-NH/2/91dacc25df48866c4f74b196f54c03c9%5Cnhttp://linkinghub.elsevier.com/retrieve/pii/014890629390041B | Article

[34] Liu, H. Y.; Roquete, M.; Kou, S. Q.; Lindqvist, P. A. Characterization of rock heterogeneity and numerical verification, Engineering Geology, Volume 72 (2004) no. 1-2, pp. 89-119 | Article

[35] Labuz, J. F.; Shah, S. P.; Dowding, C. H. The fracture process zone in granite: evidence and effect, International Journal of Rock Mechanics and Mining Sciences and, Volume 24 (1987) no. 4, pp. 235-246 | Article

[36] Mahabadi, Ok; Grasselli, G.; Munjiza, A. Numerical modelling of a Brazilian Disc test using the combined finite-discrete element method, CANUS Rock Mechanics Sumposium (2009) http://www.geogroup.utoronto.ca/xe/geogroup/femdem_workshop/course_material/FEMDEM_Workshop-153_MAHABADI_numerical_modelling-triaxial_test.pdf

[37] Ma, Yifei; Huang, Haiying Tensile strength calibration in DEM modeling, American Rock Mechanics Association (2017)

[38] McLaskey, Gregory C.; Lockner, David A.; Kilgore, Brian D.; Beeler, Nicholas M. A robust calibration technique for acoustic emission systems based on momentum transfer from a ball drop, Bulletin of the Seismological Society of America, Volume 105 (2015) no. 1, pp. 257-271 | Article

[39] Meng, Qingbin; Zhang, Mingwei; Han, Lijun; Pu, Hai; Nie, Taoyi Effects of Acoustic Emission and Energy Evolution of Rock Specimens Under the Uniaxial Cyclic Loading and Unloading Compression, Rock Mechanics and Rock Engineering, Volume 49 (2016) no. 10, pp. 3873-3886 | Article

[40] Nitka, Michał; Tejchman, Jacek Mesoscopic Simulations of Concrete Fracture Based on X-ray CT Images of Interial Structure, 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures (2016) | Article

[41] Ostoja-Starzewski, M; Sheng, P Y; Jasiuk, I Influence of random geometry on effective properties and damage formation in composite materials, J. Eng. Mat. Tech., Volume 116 (1994) no. July 1994, pp. 384-391 | Article

[42] Potyondy, David O.; Cundall, P. A. A bonded-particle model for rock, International Journal of Rock Mechanics and Mining Sciences, Volume 41 (2004) no. 8, pp. 1329-1364 | Article

[43] Rodríguez, Patricia; Arab, Paola B.; Celestino, Tarcisio B. Characterization of rock cracking patterns in diametral compression tests by acoustic emission and petrographic analysis, International Journal of Rock Mechanics and Mining Sciences, Volume 83 (2016), pp. 73-85 | Article

[44] Rasband, WS ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA (2012), p. imagej.nih.gov/ij

[45] Rabczuk, T.; Eibl, J. Modelling dynamic failure of concrete with meshfree methods, International Journal of Impact Engineering, Volume 32 (2006) no. 11, pp. 1878-1897 | Article

[46] Rao, M V M S; Lakshmi, K J Prasanna Analysis of b -value and improved b -value of acoustic emissions accompanying rock fracture, Current Science, Volume 89 (2005) no. 9, pp. 1577-1582

[47] Sfantos, G. K.; Aliabadi, M. H. Multi-scale boundary element modelling of material degradation and fracture, Computer Methods in Applied Mechanics and Engineering, Volume 196 (2007) no. 7, pp. 1310-1329 | Article | Zbl 1173.74459

[48] Saksala, Timo Rate-Dependent Embedded Discontinuity Approach Incorporating Heterogeneity for Numerical Modeling of Rock Fracture, Rock Mechanics and Rock Engineering, Volume 48 (2015) no. 4, pp. 1605-1622 | Article

[49] Smilauer, Vaclav; Catalano, Emanuele; Chareyre, Bruno; Dorofeenko, Sergei; Duriez, Jerome; Dyck, Nolan; Elias, Jan; Er, Burak; Eulitz, Alexander; Gladky, Anton; Guo, Ning; Jakob, Christian; Kneib, Francois; Kozicki, Janek; Marzougui, Donia; Maurin, Raphael; Modenese, Chiara; Scholtes, Luc; Sibille, Luc; Stransky, Janek; Sweijen, Thomas; Thoeni, Klaus; Yuan, Chao Yade Documentation 2nd ed, Zenodo, 2015 | Article

[50] Scholz, C H The frequency-magnitude relation of microfrackturing in rock and its relation to earthquakes, Seismological Society of America, Volume 58 (1968) no. 1, pp. 399-415

[51] Scholtès, Luc; Donzé, Frédéric Victor A DEM model for soft and hard rocks: Role of grain interlocking on strength, Journal of the Mechanics and Physics of Solids, Volume 61 (2012), pp. 352-369 | Article

[52] Scholtès, Luc; Donzé, Frédéric-Victor Modelling progressive failure in fractured rock masses using a 3D discrete element method, International Journal of Rock Mechanics and Mining Sciences, Volume 52 (2012), pp. 18-30 http://linkinghub.elsevier.com/retrieve/pii/S1365160912000391 | Article

[53] Sondergeld, C H; Estey, L H Acoustic emission study of microfracturing during the cyclic loading of Westerly granite, Journal of Geophysical Research, Volume 86 (1981) no. B4, pp. 2915-2924 | Article

[54] Scholz, C. H.; Harris, R. A. “The Mechanics of Earthquakes and Faulting - Second Edition” by Christopher H. Scholz, Seismological Research Letters, Volume 74 (2003) no. 3, p. 333-333 http://srl.geoscienceworld.org/cgi/doi/10.1785/gssrl.74.3.333 | Article

[55] Shearer, P. Introduction to Seismology, Cambridge University Press, 2009

[56] Shah, K R; Labuz, J F Damage mechanism in stressed rock from acoustic emission, Journal of Geophysical Research, Volume 100 (1995), pp. 15527-15539

[57] Soma, Nobukazu; Niitsuma, Hiroaki; Baria, Roy Reflection technique in time-frequency domain using multicomponent acoustic emission signals and application to geothermal reservoirs, Geophysics, Volume 67 (2002) no. 3, pp. 928-938 | Article

[58] Tang, C.A; Kaiser, P.K Numerical Simulation of Cumulative Damage and Seismic Energy Release During Brittle Rock Failure—Part I: Fundamentals, International Journal of Rock Mechanics and Mining Sciences, Volume 35 (1998) no. 2, pp. 113-121 | Article

[59] Tan, Yuanqiang; Yang, Dongmin; Sheng, Yong Discrete element method (DEM) modeling of fracture and damage in the machining process of polycrystalline SiC, Journal of the European Ceramic Society, Volume 29 (2009) no. 6, pp. 1029-1037 | Article

[60] Wang, Xiao Liang; Li, Jia Chun Simulation of triaxial response of granular materials by modified DEM, Science China: Physics, Mechanics and Astronomy, Volume 57 (2014) no. 12, pp. 2297-2308 | Article

[61] Wang, S. Y.; Sloan, S. W.; Sheng, D. C.; Tang, C. A. Numerical analysis of the failure process around a circular opening in rock, Computers and Geotechnics, Volume 39 (2012) no. 2012, pp. 8-16 | Article

[62] Yang, Sheng Qi; Jing, Hong Wen; Wang, Shan Yong Experimental investigation on the strength, deformability, failure behavior and acoustic emission locations of red sandstone under triaxial compression, Rock Mechanics and Rock Engineering, Volume 45 (2012) no. 4, pp. 583-606 | Article

[63] Yang, T. H.; Tham, L. G.; Tang, C. A.; Liang, Z. Z.; Tsui, Y. Influence of heterogeneity of mechanical properties on hydraulic fracturing in permeable rocks, Rock Mechanics and Rock Engineering, Volume 37 (2004) no. 4, pp. 251-275 | Article

[64] Zietlow, W K; Labuz, J F Measurement of the Intrinsic Process Zone in rock using acoustic emission, Int. J. Rock Mech. Min. Sci., Volume 35 (1998) no. 3, pp. 291-299 | Article

[65] Zang, A; Wagner, F C; Stanchits, S; Dresen, G.; Andersen, R; Haidekker, M Source analysis of acoustic emission in Aue granite cores under symmetric and asymmetric loads, Geophysical Journal International, Volume 135 (1998), p. 1113

[66] Zhang, X.-P.; Zhang, Q; Wu, S Acoustic emission characteristics of the rock-like material containing a single flaw under different compressive loading rates, Computers and Geotechnics, Volume 83 (2017) no. 2017, pp. 83-97 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84994845448&doi=10.1016%2Fj.compgeo.2016.11.003&partnerID=40&md5=3b415e72c4e05cfa5d55390d6d218f3d | Article