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An Acoustic Emission Data-Driven Model to Simulate Rock Failure Process

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Abstract

Numerical simulation is a commonly used method for investigating rock failure. However, the numerical model is usually insufficient to predict real rock damage and failure because of rock microstructural heterogeneity. In fact, rock damage can be quantified using acoustic emission (AE) data. The aim of this study is to simulate and predict the failure of Brazilian and uniaxial compression specimens using AE data recorded during experiments. An AE data-driven model, in which cracks are assumed to be tensile in nature, is developed. AE data recorded from the test start up to a fraction of the peak stress (e.g., 20%, 40%, and 60%) are input into the data-driven model to predict the evolution of failure pattern beyond that stress level up to failure. First, we quantified stress-induced rock damage with AE data based on the tensile model. The results indicate that most of damage source radii are less than one millimeter, and the corresponding damage degree is close to one. Then, the inversed damage is input as the initial conditions for the numerical simulation to predict the future damage and failure of rock. With the increase of damage elements driven by AE data, the inversed damage zone develops from diffuse to localized, and the dominant factor for rock failure transits from microstructural heterogeneity into stress-induced rock damage. The damage and failure pattern of rock is well predicted when sufficient AE data are taken into account as known conditions.

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Abbreviations

C ap :

Akaike information criterion

n :

Total number of time data

σ21 , σ22 , l1 and l2 :

Variances and degrees of the auto-regression model

T mi :

Measured arrival time at the ith sensor

E i :

Internal energy

E d :

Dissipated energy

σ n :

Stress normal to the crack

E :

Young’s modulus of rock

γ :

Specific surface energy

L :

Length of the propagation path

V P :

P-wave velocity

\(\left\langle {R_{\text{P}} } \right\rangle\) :

Averaged value of radiation pattern coefficient

v(t):

Particle velocity waveform

t :

Time

u(t):

AE voltage waveform

D :

Damage variable

ui (i = x, y, and z):

Displacement in the i direction

F i :

Component of the net body force in the i direction

σ 1 :

Maximum principal stress

lg:

Base-10 logarithm symbol

k :

kth number of time data

E r :

Estimate of the error

T ci :

Calculated arrival time at the ith sensor

E a :

Surface energy

E k :

Kinetic energy

a :

Crack half-length

ν :

Poisson’s ratio of rock

K IC :

Mode I fracture toughness

ρ :

Rock density

R P :

Coefficient of the radiation pattern at each sensor

C v :

Correction term of the volumetric component

t d :

Source duration

M :

Moment tensor

S coef :

Sensitivity coefficient

E 0 :

Elastic moduli of undamaged material

G :

Shear modulus

f t0 :

Uniaxial tensile strength

σ 3 :

Minimum principal stress

References

  • Akaike H (1974) Markovian representation of stochastic processes and its application to the analysis of autoregressive moving average processes. Ann Inst Stat Math 26(1):363–387

    Article  Google Scholar 

  • Aker E, Kühn D, Vavryčuk V, Soldal M, Oye V (2014) Experimental investigation of acoustic emissions and their moment tensors in rock during failure. Int J Rock Mech Min Sci 70:286–295

    Article  Google Scholar 

  • Aki K, Richards PG (2002) Quantitative seismology, 2nd edn. University Science Books, New York

    Google Scholar 

  • Ashby MF, Sammis CG (1990) The damage mechanics of brittle solids in compression. Pure Appl Geophys 133(3):489–521

    Article  Google Scholar 

  • Cai M, Kaiser PK (2005) Assessment of excavation damaged zone using a micromechanics model. Tunn Undergr Space Technol 20(4):301–310

    Article  Google Scholar 

  • Cai M, Kaiser PK, Martin CD (1998) A tensile model for the interpretation of microseismic events near underground openings. Pure Appl Geophys 153(1):67–92

    Article  Google Scholar 

  • Cai M, Kaiser PK, Martin CD (2001) Quantification of rock mass damage in underground excavations from microseismic event monitoring. Int J Rock Mech Min Sci 38(8):1135–1145

    Article  Google Scholar 

  • Costin LS (1985) Damage mechanics in the post-failure regime. Mech Mater 4(2):149–160

    Article  Google Scholar 

  • Dai F, Wei MD, Xu NW, Ma Y, Yang DS (2015) Numerical assessment of the progressive rock fracture mechanism of cracked chevron notched Brazilian disc specimens. Rock Mech Rock Eng 48(2):463–479

    Article  Google Scholar 

  • Diederichs MS (2003) Manuel Rocha medal recipient rock fracture and collapse under low confinement conditions. Rock Mech Rock Eng 36(5):339–381

    Article  Google Scholar 

  • Dong LJ, Wesseloo J, Potvin Y, Li XB (2016) Discrimination of mine seismic events and blasts using the fisher classifier, naive bayesian classifier and logistic regression. Rock Mech Rock Eng 49(1):183–211

    Article  Google Scholar 

  • Falls SD, Young RP (1998) Acoustic emission and ultrasonic-velocity methods used to characterise the excavation disturbance associated with deep tunnels in hard rock. Tectonophysics 289(1):1–15

    Article  Google Scholar 

  • Gdoutos EE (2005) Fracture mechanics: an introduction. Springer, The Netherlands

    Google Scholar 

  • Girard L, Weiss J, Amitrano D (2012) Damage-Cluster distributions and size effect on strength in compressive failure. Phys Rev Lett 108(22):225502

    Article  Google Scholar 

  • Goodfellow SD, Young RP (2014) A laboratory acoustic emission experiment under in situ conditions. Geophys Res Lett 41(10):3422–3430

    Article  Google Scholar 

  • Hazzard JF, Young RP, Maxwell SC (2000) Micromechanical modeling of cracking and failure in brittle rocks. J Geophy Res Solid Earth 105(B7):16683–16697

    Article  Google Scholar 

  • He L, Ma G (2010) Development of 3D numerical manifold method. Int J Comput Methods 7(1):107–129

    Article  Google Scholar 

  • Heap MJ, Baud P, Meredith PG, Bell AF, Main IG (2009) Time-dependent brittle creep in Darley Dale sandstone. J Geophys Res Atmos 114(B07203):4288–4309

    Google Scholar 

  • Hoek E, Martin CD (2014) Fracture initiation and propagation in intact rock—a review. J Rock Mech Geotechn Eng 6(4):287–300

    Article  Google Scholar 

  • Ishida T, Labuz JF, Manthei G, Meredith PG, Nasseri MHB, Shin K, Yokoyama T, Zang A (2017) ISRM suggested method for laboratory acoustic emission monitoring. Rock Mech Rock Eng 50(3):665–674

    Article  Google Scholar 

  • Jia LC, Chen M, Zhang W, Xu T, Zhou Y, Hou B, Jin Y (2013) Experimental study and numerical modeling of brittle fracture of carbonate rock under uniaxial compression. Mech Res Commun 50(4):58–62

    Article  Google Scholar 

  • Jing LR (2003) A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. Int J Rock Mech Min Sci 40(3):283–353

    Article  Google Scholar 

  • Kachanov LM (1958) Time to failure under creep condition. Izvestia Akademii Nauk. SSSR, Tech Nauk 8:26–31

    Google Scholar 

  • Katsman R, Aharonov E, Scher H (2005) Numerical simulation of compaction bands in high-porosity sedimentary rock. Mech Mater 37(1):143–162

    Article  Google Scholar 

  • Krajcinovic D (1996) Damage mechanics. Elsevier, Amsterdam

    Google Scholar 

  • Kwiatek G, Goebel THW, Dresen G (2014) Seismic moment tensor and b value variations over successive seismic cycles in laboratory stick–slip experiments. Geophys Res Lett 41(16):5838–5846

    Article  Google Scholar 

  • Lan HX, Martin CD, Hu B (2010) Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading. J Geophys Res Atmos 115(B01202):1–14

    Google Scholar 

  • Lei QH, Latham JP, Xiang JS (2016) Implementation of an empirical joint constitutive model into finite-discrete element analysis of the geomechanical behaviour of fractured rocks. Rock Mech Rock Eng 49(12):4799–4816

    Article  Google Scholar 

  • Lemaitre J, Chaboche J-L (1994) Mechanics of solid materials. Cambridge University Press, Cambridge

    Google Scholar 

  • Li QY, Dong LJ, Li XB, Yin ZQ, Liu XL (2011) Effects of sonic speed on location accuracy of acoustic emission source in rocks. Trans Nonferr Metals Soc China 21(12):2719–2726

    Article  Google Scholar 

  • Liao ZY, Zhu JB, Tang CA (2019) Numerical investigation of rock tensile strength determined by direct tension, Brazilian and three-point bending tests. Int J Rock Mech Min Sci 115:21–32

    Article  Google Scholar 

  • Lisjak A, Grasselli G (2014) A review of discrete modeling techniques for fracturing processes in discontinuous rock masses. J Rock Mech Geotechn Eng 6(4):301–314

    Article  Google Scholar 

  • Lisjak A, Liu Q, Zhao Q, Mahabadi OK, Grasselli G (2013) Numerical simulation of acoustic emission in brittle rocks by two-dimensional finite-discrete element analysis. Geophys J Int 195(1):423–443

    Article  Google Scholar 

  • Liu JP, Li YH, Xu SD, Xu S, Jin CY (2015) Cracking mechanisms in granite rocks subjected to uniaxial compression by moment tensor analysis of acoustic emission. Theoret Appl Fract Mech 75(6):151–159

    Google Scholar 

  • Lockner DA (1993) The role of acoustic emission in the study of rock fracture. Int J Rock Mech Min Sci Geomech Abstr 30(7):883–899

    Article  Google Scholar 

  • Lockner DA, Walsh JB, Byerlee JD (1977) Changes in seismic velocity and attenuation during deformation of granite. J Geophys Res 82(33):5374–5378

    Article  Google Scholar 

  • Lockner DA, Byerlee JD, Kuksenko V, Ponomarev A, Sidorin A (1991) Quasi-static fault growth and shear fracture energy in granite. Nature 350(6313):39–42

    Article  Google Scholar 

  • Mahabadi OK, Randall NX, Zong Z, Grasselli G (2012) A novel approach for micro-scale characterization and modeling of geomaterials incorporating actual material heterogeneity. Geophys Res Lett 39(L01303):1–6

    Google Scholar 

  • Manouchehrian A, Cai M (2016) Influence of material heterogeneity on failure intensity in unstable rock failure. Comput Geotech 71(7):237–246

    Article  Google Scholar 

  • McCrory JP, Al-Jumaili SK, Crivelli D, Pearson MR, Eaton MJ, Featherston CA, Guagliano M, Holford KM, Pullin R (2015) Damage classification in carbon fibre composites using acoustic emission: a comparison of three techniques. Compos B Eng 68:424–430

    Article  Google Scholar 

  • McLaskey GC, Lockner DA (2016) Calibrated acoustic emission system records M−3.5 to M−8 events generated on a saw-cut granite sample. Rock Mech Rock Eng 49(11):4527–4536

    Article  Google Scholar 

  • McLaskey GC, Kilgore BD, Lockner DA, Beeler NM (2014) Laboratory generated M-6 earthquakes. Pure Appl Geophys 171(10):2601–2615

    Article  Google Scholar 

  • Nelder JA, Mead R (1965) A Simplex method for function minimization. Comput J 7(4):308–313

    Article  Google Scholar 

  • Pan PZ, Feng XT, Zhou H (2012) Development and applications of the elasto-plastic cellular automaton. Acta Mech Solida Sin 25(2):126–143

    Article  Google Scholar 

  • Pettitt S, Baker C, Young RP, Dahlström LO, Ramqvist G (2002) The assessment of damage around critical engineering structures using induced seismicity and ultrasonic techniques. Pure Appl Geophys 159(1):179–195

    Article  Google Scholar 

  • Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Article  Google Scholar 

  • Prugger AF, Gendzwill DJ (1988) Microearthquake location: a nonlinear approach that makes use of a Simplex stepping procedure. Bull Seismol Soc Am 78(2):799–815

    Google Scholar 

  • Sagar RV, Prasad BKR, Kumar SS (2012) An experimental study on cracking evolution in concrete and cement mortar by the b-value analysis of acoustic emission technique. Cem Concr Res 42(8):1094–1104

    Article  Google Scholar 

  • Sayers CM, Kachanov M (1995) Microcrack-induced elastic wave anisotropy of brittle rocks. J Geophys Res Solid Earth 100(B3):4149–4156

    Article  Google Scholar 

  • Scott TE, Ma Q, Roegiers JC (1993) Acoustic velocity changes during shear enhanced compaction of sandstone. Int J Rock Mech Min Sci Geomech Abstr 30(7):763–769

    Article  Google Scholar 

  • Shao JF, Rudnicki JW (2000) A microcrack-based continuous damage model for brittle geomaterials. Mech Mater 32(10):607–619

    Article  Google Scholar 

  • Shao JF, Chau KT, Feng XT (2006) Modeling of anisotropic damage and creep deformation in brittle rocks. Int J Rock Mech Min Sci 43(4):582–592

    Article  Google Scholar 

  • Tang CA (1997) Numerical simulation of progressive rock failure and associated seismicity. Int J Rock Mech Min Sci 34(2):249–261

    Article  Google Scholar 

  • Tang CA, Yang WT, Fu YF, Xu XH (1998) A new approach to numerical method of modelling geological processes and rock engineering problems: continuum to discontinuum and linearity to nonlinearity. Eng Geol 49(3):207–214

    Article  Google Scholar 

  • Wang P, Ren F, Miao S, Cai M, Yang T (2017) Evaluation of the anisotropy and directionality of a jointed rock mass under numerical direct shear tests. Eng Geol 225:29–41

    Article  Google Scholar 

  • Wang J, Elsworth D, Wu Y, Liu J, Zhu W, Liu Y (2018) The influence of fracturing fluids on fracturing processes: a comparison between water, oil and SC-CO2. Rock Mech Rock Eng 51(1):299–313

    Article  Google Scholar 

  • Wei MD, Dai F, Xu NW, Xu Y, Xia K (2015) Three-dimensional numerical evaluation of the progressive fracture mechanism of cracked chevron notched semi-circular bend rock specimens. Eng Fract Mech 134:286–303

    Article  Google Scholar 

  • Wei M-D, Dai F, Xu N-W, Liu J-F, Xu Y (2016) Experimental and numerical study on the cracked chevron notched semi-circular bend method for characterizing the mode I fracture toughness of rocks. Rock Mech Rock Eng 49(5):1595–1609

    Article  Google Scholar 

  • Wei M-D, Dai F, Xu N-W, Zhao T, Liu Y (2017) An experimental and theoretical assessment of semi-circular bend specimens with chevron and straight-through notches for mode I fracture toughness testing of rocks. Int J Rock Mech Min Sci 99:28–38

    Article  Google Scholar 

  • Wong T-f, Wong RHC, Chau KT, Tang CA (2006) Microcrack statistics, Weibull distribution and micromechanical modeling of compressive failure in rock. Mech Mater 38(7):664–681

    Article  Google Scholar 

  • Xie LX, Lu WB, Zhang QB, Jiang QH, Wang GH, Zhao J (2016) Damage evolution mechanisms of rock in deep tunnels induced by cut blasting. Tunn Undergr Space Technol 58:257–270

    Article  Google Scholar 

  • Xu S, Liu JP, Xu SD, Wei J, Huang WB, Dong LB (2012) Experimental studies on pillar failure characteristics based on acoustic emission location technique. Trans Nonferr Metals Soc China 22(11):2792–2798

    Article  Google Scholar 

  • Xu NW, Dai F, Liang ZZ, Zhou Z, Sha C, Tang CA (2014) The dynamic evaluation of rock slope stability considering the effects of microseismic damage. Rock Mech Rock Eng 47(2):621–642

    Article  Google Scholar 

  • Yamada T, Mori JJ, Ide S, Abercrombie RE, Kawakata H, Nakatani M, Iio Y, Ogasawara H (2007) Stress drops and radiated seismic energies of microearthquakes in a South African gold mine. J Geophys Res Solid Earth 112(B3):485–493

    Article  Google Scholar 

  • Yan CZ, Zheng H, Sun GH, Ge XR (2016) Combined finite-discrete element method for simulation of hydraulic fracturing. Rock Mech Rock Eng 49(4):1389–1410

    Article  Google Scholar 

  • Yang SQ, Jing HW, Wang SY (2012) Experimental investigation on the strength, deformability, failure behavior and acoustic emission locations of red sandstone under triaxial compression. Rock Mech Rock Eng 45(4):583–606

    Article  Google Scholar 

  • Yang SQ, Ni HM, Wen S (2014) Spatial acoustic emission evolution of red sandstone during multi-stage triaxial deformation. J Central South Univ 21(8):3316–3326

    Article  Google Scholar 

  • Yang YT, Tang XH, Zheng H, Liu QS, He L (2016) Three-dimensional fracture propagation with numerical manifold method. Eng Anal Bound Elem 72(11):65–77

    Article  Google Scholar 

  • Yoshimitsu N, Kawakata H, Takahashi N (2014) Magnitude -7 level earthquakes: a new lower limit of self-similarity in seismic scaling relationships. Geophys Res Lett 41(13):4495–4502

    Article  Google Scholar 

  • Young RP, Collins DS, Reyes-Montes JM, Baker C (2004) Quantification and interpretation of seismicity. Int J Rock Mech Min Sci 41(8):1317–1327

    Article  Google Scholar 

  • Yu Q, Yang S, Ranjith PG, Zhu W, Yang T (2016) Numerical modeling of jointed rock under compressive loading using X-ray computerized tomography. Rock Mech Rock Eng 49(3):877–891

    Article  Google Scholar 

  • Yue ZQ, Chen S, Tham LG (2003) Finite element modeling of geomaterials using digital image processing. Comput Geotech 30(5):375–397

    Article  Google Scholar 

  • Zang A, Wagner FC, Stanchits S, Janssen C, Dresen G (2000) Fracture process zone in granite. J Geophys Res Solid Earth 105(B10):23651–23661

    Article  Google Scholar 

  • Zhang R, Dai F, Gao MZ, Xu NW, Zhang CP (2015) Fractal analysis of acoustic emission during uniaxial and triaxial loading of rock. Int J Rock Mech Min Sci 79:241–249

    Article  Google Scholar 

  • Zhang F, Dontsov E, Mack M (2017) Fully coupled simulation of a hydraulic fracture interacting with natural fractures with a hybrid discrete-continuum method. Int J Numer Anal Meth Geomech 41(13):1430–1452

    Article  Google Scholar 

  • Zhao XD, Li YH, Yuan RF, Yang TH, Zhang JY, Liu JP (2007) Study on crack dynamic propagation process of rock samples based on acoustic emission location. Chin J Rock Mechan Eng 26(5):944–950

    Google Scholar 

  • Zhao GF, Russell AR, Zhao XB, Khalili N (2014) Strain rate dependency of uniaxial tensile strength in Gosford sandstone by the distinct lattice spring model with X-ray micro CT. Int J Solids Struct 51(7):1587–1600

    Article  Google Scholar 

  • Zhou ZL, Zhou J, Dong LJ, Cai X, Rui YC, Ke CT (2017) Experimental study on the location of an acoustic emission source considering refraction in different media. Sci Rep 7(1):7472

    Article  Google Scholar 

  • Zhou JR, Wei J, Yang T, Zhu W, Li L, Zhang P (2018) Damage analysis of rock mass coupling joints, water and microseismicity. Tunn Undergr Sp Technol 71:366–381

    Article  Google Scholar 

  • Zhu QZ, Shao JF (2015) A refined micromechanical damage–friction model with strength prediction for rock-like materials under compression. Int J Solids Struct 60–61:75–83

    Article  Google Scholar 

  • Zhu QZ, Shao JF (2017) Micromechanics of rock damage: advances in the quasi-brittle field. J Rock Mech Geotechn Eng 9(1):29–40

    Article  Google Scholar 

  • Zhu WC, Tang CA (2004) Micromechanical model for simulating the fracture process of rock. Rock Mech Rock Eng 37(1):25–56

    Article  Google Scholar 

  • Zhu JB, Zhou T, Liao ZY, Sun L, Li XB, Chen R (2018) Replication of internal defects and investigation of mechanical and fracture behaviour of rock using 3D printing and 3D numerical methods in combination with X-ray computerized tomography. Int J Rock Mech Min Sci 106:198–212

    Article  Google Scholar 

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Acknowledgements

We would like to thank three anonymous reviewers and the Editor for their helpful comments and suggestions that have greatly improved this paper. We also would like to thank Rufei Li, Feng Dai, and Long Zhao for their technical support and Leilei Niu, Penghai Zhang, and Feiyue Liu for their fruitful discussions. This work is funded by the National Key Research and Development Program of China (Grant no. 2016YFC0801607), National Science Foundation of China (Grant nos. 51525402, 51874069, and 51874069), Fundamental Research Funds for the Central Universities of China (Grant nos. N170108028 and N180115009), Korea Institute of Energy Technology Evaluation and Planning (KETEP) and Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (no. 20172510102340), and the Brain Korea 21 Plus Program (no. 21A20130012821). These supports are gratefully acknowledged.

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Authors and Affiliations

  1. Center of Rock Instability and Seismicity Research, School of Resources and Civil Engineering, Northeastern University, Shenyang, Liaoning, 110819, China

    Jiong Wei, Wancheng Zhu & Kai Guan

  2. Department of Energy Resources Engineering, Research Institute of Energy and Resources, Seoul National University, Seoul, 08826, Korea

    Jiong Wei & Jae-Joon Song

  3. Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing, 100084, China

    Jiong Wei

  4. State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resources and Hydropower, Sichuan University, Chengdu, Sichuan, 610065, China

    Jingren Zhou

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Wei, J., Zhu, W., Guan, K. et al. An Acoustic Emission Data-Driven Model to Simulate Rock Failure Process. Rock Mech Rock Eng 53, 1605–1621 (2020). https://doi.org/10.1007/s00603-019-01994-3

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