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A Rigid Particle Model for Rock Fracture Following the Voronoi Tessellation of the Grain Structure: Formulation and Validation

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Abstract

It is known that rigid circular particle models proposed in the literature do not properly reproduce the rock friction angle and the rock tensile strength to compressive strength ratio. A 2D rigid particle model is here presented which tries to overcome these issues while keeping the simplicity and the reduced computational costs characteristic of circular particle models. A particle generation algorithm is adopted which generates polygonal shape particles based on the Laguerre–Voronoi diagrams of the circular particle gravity centres. Several parametric studies are presented to show the influence of the micromechanical properties on both the macroscopic elastic and strength properties. It is shown that a good agreement with the known rock direct tensile to indirect tensile test ratio requires the incorporation of bilinear softening contact laws under tension and shear. Finally, the proposed model is validated against known triaxial and Brazilian tests of a granite rock.

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Abbreviations

\(\bar{E}_{{}}\) :

Young’s modulus of the equivalent continuum material

\(\eta_{{}}\) :

Contact shear stiffness to contact normal stiffness ratio

\(\sigma_{{n{ \cdot }t}}\) :

Maximum contact tensile stress

\(\tau_{{}}\) :

Maximum contact cohesion stress

\(\mu_{\text{c}}\) :

Contact frictional term

\(G_{{{\text{f}}{ \cdot }{\text{n}}}}\) :

Contact tensile fracture energy

\(G_{{{\text{f}}{ \cdot }{\text{s}}}}\) :

Contact shear fracture energy

\(\bar{W}_{{}}\) :

Contact interface width given by the Voronoi cell edge length

\(E_{{}}\) :

Young’s modulus

\(\upsilon_{{}}\) :

Poisson’s coefficient

\(\sigma_{\text{c}}\) :

Uniaxial compressive strength

\(\sigma_{{{\text{t}}.{\text{dir}}}}\) :

Direct tensile strength

\(\sigma_{{{\text{t}}.{\text{ind}}}}\) :

Indirect tensile strength through Brazilian test

c :

Cohesion

φ :

Friction angle

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Acknowledgments

This work was developed within the research project PTDC/ECM/114492/2009 funded by the Portuguese Foundation of Science and Technology.

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Authors and Affiliations

  1. Concrete Dams Department, Laboratório Nacional de Engenharia Civil (LNEC), Av. do Brasil 101, 1700-066, Lisbon, Portugal

    N. Monteiro Azevedo, M. Candeias & F. Gouveia

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  1. N. Monteiro Azevedo
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  2. M. Candeias
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  3. F. Gouveia
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Correspondence to N. Monteiro Azevedo.

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Monteiro Azevedo, N., Candeias, M. & Gouveia, F. A Rigid Particle Model for Rock Fracture Following the Voronoi Tessellation of the Grain Structure: Formulation and Validation. Rock Mech Rock Eng 48, 535–557 (2015). https://doi.org/10.1007/s00603-014-0601-1

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