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Simulation of Fracture Coalescence in Granite via the Combined Finite–Discrete Element Method

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Abstract

Fracture coalescence is a critical phenomenon for creating large, inter-connected fractures from smaller cracks, affecting fracture network flow and seismic energy release potential. In this paper, simulations are performed to model fracture coalescence processes in granite specimens with pre-existing flaws. These simulations utilize an in-house implementation of the combined finite–discrete element method (FDEM) known as the hybrid optimization software suite (HOSS). The pre-existing flaws within the specimens follow two geometric patterns: (1) a single-flaw oriented at different angles with respect to the loading direction, and (2) two flaws, where the primary flaw is oriented perpendicular to the loading direction and the secondary flaw is oriented at different angles. The simulations provide insight into the evolution of tensile and shear fracture behavior as a function of time. The single-flaw simulations accurately reproduce experimentally measured peak stresses as a function of flaw inclination angle. Both the single- and double-flaw simulations exhibit a linear increase in strength with increasing flaw angle while the double-flaw specimens are systematically weaker than the single-flaw specimens.

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Abbreviations

BD:

Brazilian disk

BEM:

Boundary element method

DEM:

Discrete element method

FDEM:

Finite–discrete element method

HOSS:

Hybrid optimization software suite

UCS:

Uniaxial compressive strength

C :

Damping matrix

M :

Lumped mass matrix

f :

Equivalent force vector

x :

Displacement vector

c :

Cohesion

D :

Damage

G I :

Mode I fracture energy

G II :

Mode II fracture energy

\(\alpha\) :

Angle of inclination

\({\delta ^{\text{e}}}\) :

Elastic threshold relative displacement

\(\delta _{{\text{n}}}^{{\text{e}}}\) :

Elastic threshold normal relative displacement

\(\delta _{{\text{t}}}^{{\text{e}}}\) :

Elastic threshold tangential relative displacement

\({\delta ^{\rm{max} }}\) :

Maximum relative displacement

\(\delta _{{\text{n}}}^{{\rm{max} }}\) :

Maximum normal relative displacement

\(\delta _{{\text{t}}}^{{\rm{max} }}\) :

Maximum tangential relative displacement

\({\mu _{\text{s}}}\) :

Coefficient of static friction

\({\sigma _{\text{n}}}\) :

Normal stress

\({\sigma _{\text{t}}}\) :

Tangential stress

\({\sigma ^{\rm{max} }}\) :

Maximum stress

\(\sigma _{{\text{n}}}^{{\rm{max} }}\) :

Maximum normal stress

\(\sigma _{{\text{t}}}^{{\rm{max} }}\) :

Maximum tangential stress

\({\phi _{\text{c}}}\) :

Internal angle of friction

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Acknowledgements

Support provided by the Department of Energy (DOE) Basic Energy Sciences program (DE-AC52-06NA25396). The authors would like to thank the LANL Institutional Computing program for their support in generating data used in this work.

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Authors and Affiliations

  1. Geophysics Group, Los Alamos National Laboratory, Los Alamos, NM, USA

    Bryan Euser, E. Rougier, Z. Lei & E. E. Knight

  2. Earth Systems Observations Group, Los Alamos National Laboratory, Los Alamos, NM, USA

    L. P. Frash & J. W. Carey

  3. Computational Earth Science Group, Los Alamos National Laboratory, Los Alamos, NM, USA

    H. Viswanathan

  4. Faculty of Civil Engineering, Architecture and Geodesy (FGAG), University of Split, Split, Croatia

    A. Munjiza

Authors
  1. Bryan Euser
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  2. E. Rougier
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  3. Z. Lei
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  4. E. E. Knight
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  5. L. P. Frash
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  6. J. W. Carey
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  7. H. Viswanathan
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  8. A. Munjiza
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Correspondence to Bryan Euser.

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Euser, B., Rougier, E., Lei, Z. et al. Simulation of Fracture Coalescence in Granite via the Combined Finite–Discrete Element Method. Rock Mech Rock Eng 52, 3213–3227 (2019). https://doi.org/10.1007/s00603-019-01773-0

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  • DOI: https://doi.org/10.1007/s00603-019-01773-0

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