Modeling Damage Evolution in Heterogeneous Granite Using Digital Image-Based Grain-Based Model
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ORIGINAL PAPER
Modeling Damage Evolution in Heterogeneous Granite Using Digital Image‑Based Grain‑Based Model Xunjian Hu1,2 · Ni Xie3 · Qizhi Zhu4 · Liang Chen5 · PengCheng Li3 Received: 6 August 2019 / Accepted: 30 June 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
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 grainbased 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. Keywords Grain-based model · Damage · Heterogeneity · Digital image processing List of Symbols f Gray value k The number of clusters E Young’s modulus υ Poisson’s ratio σ1 Maximum principal stress σ3 Minimum principal stress * Ni Xie [email protected] 1
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China
2
University of Chinese Academy of Science, Beijing, China
3
Faculty of Engineering, China University of Geosciences (Wuhan), Wuhan 430074, China
4
Geotechnical Research Institute, Hohai University, Nanjing 210098, China
5
CNNC Key Laboratory on Geological Disposal for High‑Level Radioactive Waste, Beijing Research Institute of Uranium Geology, Beijing 100029, China
σc Uniaxial compressive strength m Heterogeneity index Rmin Minimum radius Rmax/Rmin Maximum-to-minimum radius ratio kn/ks Normal-to-shear stiffness ratio ρ Density of particle Ec0 The characteristic modulus of particle Ec Modulus of particle μf Friction coefficient between particles of parallel bond λ Radius multiplier o
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