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An Acoustic Emission-Based Cluster Damage Model for Simulating Triaxial Compression Behaviors of Granite

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Abstract

The establishment of spatial correlation among scattering acoustic emission (AE) signals has great potential applied into a deep analysis of triaxial compression behaviors by the AE monitoring technology. Taking the randomly distributed AE signal could as the cube cluster by an introduction of covering strategy from the percolation theory, the quantitative evaluation of spatial correlation instead of spatial distribution is effectively made. It presents a cluster-based perspective to investigate the triaxial compression behaviors, especially including the dilatancy based on the volumetric strain correlated to the cube cluster evolution. Besides, considering a damage definition by the AE energy count, the cube cluster damage model is successfully established. Then, by implanting the cube cluster termed AE percolation cluster (APC) into the numerical software FLAC3D, the consistency between numerical and experimental results of four descriptors of strength, axial, hoop and volumetric strains excellently proves the reliability of the cluster damage model. In addition, the damaged cluster shows a potential application for quantitative analysis of the shear failure. Furthermore, a percolation analysis of the granite deformation under triaxial compression is made based on the cluster damage model. The effect of pressure-induced percolation transition (PIPT) is verified for the granite and the volume fraction shows a strong linear dependence on the covering length. Moreover, a series of discussion is made to analyze the influence of mechanical parameters on the sensibility of the cluster damage model. Finally, the influence of damage distribution of sub-clusters on the triaxial compression behaviors is quantitatively determined by the comparison between the linear and exponential distributions. The results verify the effectiveness and sensitivity of the cluster damage model in describing triaxial compression behaviors, which provides a new modeling method to extract more valuable information from the correlated AE signals.

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Abbreviations

AE:

Acoustic emission

APC:

AE percolation cluster

CVP:

Critical partial volume

DAC:

Damaged AE cluster

IP:

Inflection point

HP:

Highest point

AC:

All clusters

LC:

Largest cluster

MC:

Mohr–Coulomb

PIPT:

Pressure-induced percolation transition

SLC:

Single-link cluster

SCL:

Spatial correlation length

\( d \) :

Euclidean dimension

\( D \) :

Fractal dimension

\( D_{\text{AE}} \) :

AE energy count-based damage

\( N_{\text{E}} ,\;N_{{{\text{E}}i}} \) :

Average count and the \( i \)th

\( E,\;v \) :

Elastic modulus and Poisson’s ratio

\( c,\;\varphi \) :

Cohesion and internal friction angle

\( K,\;G \) :

Bulk modulus and shear modulus

\( V,\;V_{\text{m}} ,\;V_{\text{a}} \) :

Initial volume, matrix volume and damaged AP C volume

\( V^{\prime},\;V^{\prime}_{\text{m}} ,\;V^{\prime}_{\text{a}} \) :

Dilatant volume, matrix volume and damaged APC volume in dilatancy

\( l_{\text{min} } ,\;l_{\text{max} } \) :

Lower and upper limit of self-similar region

\( \varPhi_{\text{p}} ,\varPhi_{\text{r}} \) :

Volumetric fractions under peak or residual state

\( \varPhi_{0} ,\varPhi_{\text{c}} \) :

Initial and critical volumetric fraction

\( \sigma_{1} ,\;\sigma_{3} \) :

Axial stress and confining pressure

\( \sigma_{\text{m}} ,\;\Delta \sigma_{\text{m}} \) :

Average stress and its increment

\( \varepsilon_{\text{v}} ,\;\varepsilon_{\text{vc}} ,\;\Delta \varepsilon_{\text{v}} \) :

Volumetric strain, its critical value and increment

\( \gamma ,\gamma_{\text{c}} \) :

Connection probability and its critical value

\( s_{\text{L}} ,\;s_{i} \) :

LC size and \( i \)th clusters size

\( \varepsilon_{m1} ,\;\varepsilon_{m3} ,\;\varepsilon_{m\theta } \) :

Axial strain, hoop strain and volumetric strain

\( A,\;k \) :

Linear and exponential coefficients

\( B \) :

Compressibility

\( \delta ,\;\delta_{\text{max} } \) :

Covering length and its largest value

\( \sigma_{\text{m}} \) :

Strength

\( \varPhi \) :

Volumetric fraction

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Acknowledgements

This study was sponsored by the National Natural Science Foundation of China (Grant No. 51504257), the State Key Research Development Program of China (Grant No. 2016YFC0600704), the Fund of Yueqi Outstanding Scholars (Grant No. 2018B051616) and the Open Fund of the State Key Laboratory of Coal Mine Disaster Dynamics and Control (Grant No. 2011DA105287- FW201604).

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Authors and Affiliations

  1. School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing, 100083, China

    D. J. Xue, L. Gao, L. Lu & J. Zhou

  2. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400030, China

    D. J. Xue

  3. State Key Laboratory of Coal Resource and Safe Mining, China University of Mining and Technology, Beijing, 100083, China

    D. J. Xue & H. W. Zhou

  4. CNPC Key Laboratory of Oil and Gas Underground Storage Engineering, Langfang, 065007, China

    Z. D. Wu

  5. Architectural Engineering College, North China Institute of Science and Technology, Langfang, 065201, China

    H. Y. Yi

  6. State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu, 610065, China

    J. F. Liu

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  1. D. J. Xue
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Xue, D.J., Gao, L., Lu, L. et al. An Acoustic Emission-Based Cluster Damage Model for Simulating Triaxial Compression Behaviors of Granite. Rock Mech Rock Eng 53, 4201–4220 (2020). https://doi.org/10.1007/s00603-020-02169-1

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