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


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.


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

List of Symbols


Akaike information criterion


Total number of time data

σ12, σ22, l1 and l2

Variances and degrees of the auto-regression model


Measured arrival time at the ith sensor


Internal energy


Dissipated energy


Stress normal to the crack


Young’s modulus of rock


Specific surface energy


Length of the propagation path


P-wave velocity

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

Averaged value of radiation pattern coefficient


Particle velocity waveform




AE voltage waveform


Damage variable

ui (i = x, y, and z)

Displacement in the i direction


Component of the net body force in the i direction


Maximum principal stress


Base-10 logarithm symbol


kth number of time data


Estimate of the error


Calculated arrival time at the ith sensor


Surface energy


Kinetic energy


Crack half-length


Poisson’s ratio of rock


Mode I fracture toughness


Rock density


Coefficient of the radiation pattern at each sensor


Correction term of the volumetric component


Source duration


Moment tensor


Sensitivity coefficient


Elastic moduli of undamaged material


Shear modulus


Uniaxial tensile strength


Minimum principal stress



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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