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Modeling Damage Evolution in Heterogeneous Granite Using Digital Image-Based Grain-Based Model

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Abstract

A particle-based discrete element model combined with digital image processing to take into account the grain geometry and size distribution is used to investigate the mechanical and microcracking behavior of Beishan granite (BG), a typical crystalline rock potential for nuclear waste disposal in China. First, the procedure to construct a digital image-based grain-based model is introduced. The unsupervised K-means clustering algorithm is used to determine mineral boundaries, and four micro-parameters are assigned according to the Weibull distribution to reflect micro-heterogeneity of rock. Then, the model is calibrated to the macro-properties of BG obtained from laboratory tests, and consistency between model simulation and laboratory test results of both microcracking processes and failure modes is found. It is shown that intragrain cracks are initiated successively in quartz, feldspar, and mica; and their numbers in quartz and feldspar are much more than that in mica. Crack cluster, forking cracks and cataclastic microcracking are typical in quartz, while the “voids” is found in mica. Grain property heterogeneity has a significant impact on micro-cracking behavior and macro-properties of the model, with greater heterogeneity resulting in a lower uniaxial compression strength and elastic modulus, and a more scattered distribution of microcrack inclination. The modeling procedures presented here provide an effective method for investigating mechanical and damage behavior of granites, with specific consideration of heterogeneity involving the distribution of mineral grains and their mechanical properties.

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modified from Hudson and Harrison 1997)

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Abbreviations

f :

Gray value

k :

The number of clusters

E :

Young’s modulus

υ :

Poisson’s ratio

σ 1 :

Maximum principal stress

σ 3 :

Minimum principal stress

σ c :

Uniaxial compressive strength

m :

Heterogeneity index

R min :

Minimum radius

Rmax/Rmin :

Maximum-to-minimum radius ratio

kn/ks :

Normal-to-shear stiffness ratio

ρ :

Density of particle

\(E_{{\text{c}}}^{0}\) :

The characteristic modulus of particle

E c :

Modulus of particle

μ f :

Friction coefficient between particles of parallel bond

λ :

Radius multiplier of parallel bond

\(\overline{E}_{{\text{c}}}^{0}\) :

The characteristic modulus of parallel bond

\(\overline{E}_{{\text{c}}}\) :

Modulus of parallel bond

\(\overline{k}_{{\text{n}}}/\overline{k}_{{\text{s}}}\) :

Normal-to-shear stiffness ratio of parallel bond

\(\overline{\sigma }_{{\text{c}}}^{0}\) :

The characteristic tensile strength of parallel bond

\(\overline{\sigma }_{{\text{c}}}\) :

Tension strength of parallel bond

\(C_{{\text{c}}}^{0}\) :

The characteristic cohesion of parallel bond

\(\overline{C}\) :

Cohesion of parallel bond

\(\overline{\varphi }\) :

Friction angle of parallel bond

\(\overline{k}^{{\text{n}}}\) :

Normal stiffness of smooth-joint contact

\(\overline{k}^{{\text{s}}}\) :

Shear stiffness of smooth-joint contact

σ c :

Tensile strength of smooth-joint contact

C :

Cohesion of smooth-joint contact

φ :

Friction angle of smooth-joint contact

μ r :

Friction coefficient of smooth-joint contact

σ ci :

The stress for initiation of crack growth

σ cd :

The stress of unstable crack growth

σ f :

The peak stress

ε 1 :

Axial strain

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Acknowledgements

The authors are grateful to the National Natural Science Foundation of China for the financial support under Grant no. 41877265. Our deepest gratitude also goes to the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this paper substantially.

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Authors and Affiliations

  1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China

    Xunjian Hu

  2. University of Chinese Academy of Science, Beijing, China

    Xunjian Hu

  3. Faculty of Engineering, China University of Geosciences (Wuhan), Wuhan, 430074, China

    Ni Xie & PengCheng Li

  4. Geotechnical Research Institute, Hohai University, Nanjing, 210098, China

    Qizhi Zhu

  5. CNNC Key Laboratory on Geological Disposal for High-Level Radioactive Waste, Beijing Research Institute of Uranium Geology, Beijing, 100029, China

    Liang Chen

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Hu, X., Xie, N., Zhu, Q. et al. Modeling Damage Evolution in Heterogeneous Granite Using Digital Image-Based Grain-Based Model. Rock Mech Rock Eng 53, 4925–4945 (2020). https://doi.org/10.1007/s00603-020-02191-3

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