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

  • Jiong Wei
  • Wancheng ZhuEmail author
  • Kai Guan
  • Jingren Zhou
  • Jae-Joon Song
Original Paper
  • 226 Downloads

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.

Keywords

Rock damage Acoustic emission (AE) Source energy Crack radius Data-driven model Numerical simulation 

List of Symbols

Cap

Akaike information criterion

n

Total number of time data

σ12, σ22, l1 and l2

Variances and degrees of the auto-regression model

Tmi

Measured arrival time at the ith sensor

Ei

Internal energy

Ed

Dissipated energy

σn

Stress normal to the crack

E

Young’s modulus of rock

γ

Specific surface energy

L

Length of the propagation path

VP

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

Fi

Component of the net body force in the i direction

σ1

Maximum principal stress

lg

Base-10 logarithm symbol

k

kth number of time data

Er

Estimate of the error

Tci

Calculated arrival time at the ith sensor

Ea

Surface energy

Ek

Kinetic energy

a

Crack half-length

ν

Poisson’s ratio of rock

KIC

Mode I fracture toughness

ρ

Rock density

RP

Coefficient of the radiation pattern at each sensor

Cv

Correction term of the volumetric component

td

Source duration

M

Moment tensor

Scoef

Sensitivity coefficient

E0

Elastic moduli of undamaged material

G

Shear modulus

ft0

Uniaxial tensile strength

σ3

Minimum principal stress

Notes

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.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interests.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center of Rock Instability and Seismicity Research, School of Resources and Civil EngineeringNortheastern UniversityShenyangChina
  2. 2.Department of Energy Resources Engineering, Research Institute of Energy and ResourcesSeoul National UniversitySeoulKorea
  3. 3.Department of Engineering Mechanics and CNMMTsinghua UniversityBeijingChina
  4. 4.State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resources and HydropowerSichuan UniversityChengduChina

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