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The Influence of Mechanical Heterogeneity of Grain Boundary on Mechanical and Microcracking Behavior of Granite Under Mode I Loading Using a Grain-Based Model

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Abstract

Granite is a heterogeneous material characterized by a significant population of mechanically distinct grain boundaries, which exert a substantial influence on crack propagation. An extended grain-based model was developed by integrating the geometric heterogeneity, represented by Voronoi tessellations, and the mechanical heterogeneity of grain boundary, as described by Weibull distribution. This study numerically investigates the influence of mechanical heterogeneity in grain boundary on the mechanical properties and microcracking behavior of semi-circular bend granite samples under mode I loading. The mechanical heterogeneity of grain boundary was assessed by independently varying the heterogeneity index, defined by the shape parameter m in the Weibull distribution. The findings indicate that the force–displacement curve and fracture toughness are primarily influenced by the parallel bond tensile strength and cohesion of grain boundary contacts. When the value of m in Weibull distribution is between 1.5 and 2, a compromise between failure patterns and diverse grain boundaries characterization can be reached. Considering the heterogeneous mechanical properties of grain boundary numerically is able to simulate the local stress concentration of the real rocks, thus accelerating the generation of microcracks and reflecting the brittleness of rock failure. Otherwise, the fracture toughness of the rock will may be overestimated. Generally speaking, models that consider grain boundary heterogeneity will produce larger fracture process zone and microscopically complex crack propagation patterns during loading, and these phenomena are more consistent with experimental observations than those models in which grain boundaries are homogeneous.

Highlights

  1. 1.

    The mechanical heterogeneity of grain boundary in granite is quantitatively characterized by the Weibull distribution;

  2. 2.

    The heterogeneous grain boundary could favor the local stress concentration, thus accelerating the generation of microcracks;

  3. 3.

    Considering both geometric heterogeneity of granite and mechanical heterogeneity of grain boundary result in the generation of larger fracture process zone and microscopically complex crack propagation patterns under mode I loading.

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Data Availability Statement

All data generated or analyzed during this work are included in this published paper and are available from the corresponding author on reasonable request.

Abbreviations

CCNBD:

Cracked chevron notched Brazilian disc

SCB:

Semi-circular bend

PFC:

Particle flow code

GB:

Grain boundary

IG:

Intra-grain

DEM:

Discrete element method

FDEM:

Finite discrete element method

BPM:

Bonded particle model

BBM:

Bonded block model

GBM:

Grain-based model

IGT, IGS:

Intra-grain tension and intra-grain shear

GBT, GBS:

Grain boundary tension and grain boundary shear

ROI:

Region of interest

AE:

Acoustic emission

JRC:

Joint roughness coefficient

Z 2 :

The root mean square of the first derivative of a profile

x i, z i :

The coordinates of the fracture surface profile

M :

The number of sampling points

d max :

The maximum deviation value

Qtz:

Quartz

Bi:

Biotite

Kfs:

K-feldspar

Pl:

Plagioclase

KIC :

Fracture toughness

ES :

Generalized stiffness

θ :

The orientation of microcrack

g s :

Surface gap

k n, k s :

Normal stiffness and shear stiffness

μ :

Friction coefficient

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

Parallel bond tensile strength

\(\overline{c}\) :

Parallel bond cohesion

\(\overline{\phi}\) :

Parallel bond friction angle

\(\overline{k}_{n}\), \(\overline{k}_{s}\) :

Parallel bond normal stiffness and shear stiffness

f :

The probability density function

F :

The cumulative distribution function

α :

The microparameter that follows Weibull distribution

α 0 :

The reference value of the microparameter

m :

Shape parameter of Weibull distribution

σ yy :

Vertical stress

N :

Number of microcracks

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (51778575). The authors would like to thank the anonymous reviewers and editors for their constructive suggestions which greatly improve the quality of this paper.

Funding

National Natural Science Foundation of China, 51778575, Xiaonan Gong

Author information

Authors and Affiliations

  1. Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, Hangzhou, 310058, China

    Xunjian Hu, Dong Liao, Haibo Hu, Senlin Xie & Xiaonan Gong

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

    Ni Xie

Authors
  1. Xunjian Hu
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  2. Dong Liao
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  3. Haibo Hu
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  4. Senlin Xie
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  5. Ni Xie
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  6. Xiaonan Gong
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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Correspondence to Dong Liao.

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Hu, X., Liao, D., Hu, H. et al. The Influence of Mechanical Heterogeneity of Grain Boundary on Mechanical and Microcracking Behavior of Granite Under Mode I Loading Using a Grain-Based Model. Rock Mech Rock Eng (2024). https://doi.org/10.1007/s00603-023-03752-y

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  • DOI: https://doi.org/10.1007/s00603-023-03752-y

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