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

  • Bryan EuserEmail author
  • E. Rougier
  • Z. Lei
  • E. E. Knight
  • L. P. Frash
  • J. W. Carey
  • H. Viswanathan
  • A. Munjiza
Original Paper


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.


Crack interaction Propagation FDEM Normal and tangential crack propagation 

List of Symbols



Brazilian disk


Boundary element method


Discrete element method


Finite–discrete element method


Hybrid optimization software suite


Uniaxial compressive strength



Damping matrix


Lumped mass matrix


Equivalent force vector


Displacement vector






Mode I fracture energy


Mode II fracture energy


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



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.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflicts of interest.


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Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2019

Authors and Affiliations

  1. 1.Geophysics GroupLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Earth Systems Observations GroupLos Alamos National LaboratoryLos AlamosUSA
  3. 3.Computational Earth Science GroupLos Alamos National LaboratoryLos AlamosUSA
  4. 4.Faculty of Civil Engineering, Architecture and Geodesy (FGAG)University of SplitSplitCroatia

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