Skip to main content
SpringerLink
Log in

Voronoi-Based DEM Simulation Approach for Sandstone Considering Grain Structure and Pore Size

  • Original Paper
  • Published:
Rock Mechanics and Rock Engineering Aims and scope Submit manuscript

Abstract

This paper presents a new procedure to create numerical models considering grain shape and size as well as pore size in an explicit and stochastic equivalent manner. Four shape factors are introduced to reproduce shape and size of grains and pores. Thin sections are used to analyze grain shape and pore size of rock specimen. First, a particle-based numerical model is set up by best fitted clumps from a shape library according to thin sections. Finally, an equivalent Voronoi-based discrete element model is set up based on the superimposed particle model. Uniaxial compression and tensile tests are simulated for validation. Both tests indicate that grain boundaries and pores provide preferred paths of weakness for crack propagation, but they also reveal significant differences in terms of intra- and inter-granular fracturing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  • Bass JD (2013) Elasticity of minerals, glasses, and melts. In: Ahrens TJ (ed) Mineral physics & crystallography: a handbook of physical constants. American Geophysical Union, Washington, DC, pp 45–63

    Google Scholar 

  • Bolander JE, Sukumar N (2005) Irregular lattice model for quasistatic crack propagation. Phys Rev B 71(9):094106

    Article  Google Scholar 

  • Chao H, Jie B, Somnath G (2007) Micromechanical and macroscopic models of ductile fracture in particle reinforced metallic materials. Model Simul Mater Sci Eng 15(4):S377

    Article  Google Scholar 

  • Chen W, Konietzky H (2014) Simulation of heterogeneity, creep, damage and lifetime for loaded brittle rocks. Tectonophysics 633:164–175

    Article  Google Scholar 

  • Chen SG, Zhao J (1998) A study of UDEC modelling for blast wave propagation in jointed rock masses. Int J Rock Mech Min Sci 35(1):93–99

    Article  Google Scholar 

  • Chen W, Konietzky H, Abbas SM (2015) Numerical simulation of time-independent and -dependent fracturing in sandstone. Eng Geol 193:118–131

    Article  Google Scholar 

  • Christodoulou I, Tan PJ (2013) Crack initiation and fracture toughness of random Voronoi honeycombs. Eng Fract Mech 104:140–161

    Article  Google Scholar 

  • Correns CW (1969) Crystal physics. In: Introduction to mineralogy: crystallography and petrology, Springer, Berlin, pp 101–161. doi:10.1007/978-3-642-87134-4_3

  • Cox MR, Budhu M (2008) A practical approach to grain shape quantification. Eng Geol 96(1–2):1–16

    Article  Google Scholar 

  • Eberhardt E, Stimpson B, Stead D (1999) Effects of grain size on the initiation and propagation thresholds of stress-induced brittle fractures. Rock Mech Rock Eng 32(2):81–99

    Article  Google Scholar 

  • Fakhimi A, Alavi Gharahbagh E (2011) Discrete element analysis of the effect of pore size and pore distribution on the mechanical behavior of rock. Int J Rock Mech Min Sci 48(1):77–85

    Article  Google Scholar 

  • Fredrich JT, Evans B, Wong T-F (1990) Effect of grain size on brittle and semibrittle strength: implications for micromechanical modelling of failure in compression. J Geophys Res Solid Earth 95(B7):10907–10920

    Article  Google Scholar 

  • Groh U, Konietzky H, Walter K, Herbst M (2011) Damage simulation of brittle heterogeneous materials at the grain size level. Theor Appl Fract Mech 55(1):31–38

    Article  Google Scholar 

  • Itasca (2010) UDEC-manuals. Itasca Consulting Group Inc, Minneapolis

    Google Scholar 

  • ImageJ (https://imagej.nih.gov/ij/) Image processing and analysis in Java, an open source soft by USA National Institutes of Health

  • Kazerani T (2013) Effect of micromechanical parameters of microstructure on compressive and tensile failure process of rock. Int J Rock Mech Min Sci 64:44–55

    Google Scholar 

  • Lan H, Martin CD, Hu B (2010) Effect of heterogeneity of brittle rock on micromechanical extensile behavior during compression loading. J Geophys Res Solid Earth 115(B1):B01202

    Article  Google Scholar 

  • Lindqvist JE, Åkesson U, Malaga K (2007) Microstructure and functional properties of rock materials. Mater Charact 58(11–12):1183–1188

    Article  Google Scholar 

  • Liu HY, Roquete M, Kou SQ, Lindqvist PA (2004) Characterization of rock heterogeneity and numerical verification. Eng Geol 72(1–2):89–119

    Article  Google Scholar 

  • Moorthy S, Ghosh S (1998) A Voronoi cell finite element model for particle cracking in elastic–plastic composite materials. Comput Methods Appl Mech Eng 151(3–4):377–400

    Article  Google Scholar 

  • Olsson WA (1974) Grain size dependence of yield stress in marble. J Geophys Res 79(32):4859–4862

    Article  Google Scholar 

  • Palchik V (1999) Influence of porosity and elastic modulus on uniaxial compressive strength in soft brittle porous sandstones. Rock Mech Rock Eng 32(4):303–309

    Article  Google Scholar 

  • Paterson MS (1958) Experimental deformation and faulting in Wombeyan marble. Bull Geol Soc Am 69:465–476

    Article  Google Scholar 

  • Rice RW (1989) Relation of tensile strength-porosity effects in ceramics to porosity dependence of Young’s modulus and fracture energy, porosity character and grain size. Mater Sci Eng A 112:215–224

    Article  Google Scholar 

  • Tan X, Konietzky H, Frühwirt T, Dan D (2015) Brazilian tests on transversely isotropic rocks: laboratory testing and numerical simulations. Rock Mech Rock Eng 48(4):1341–1351

    Article  Google Scholar 

  • Tan X, Konietzky H, Chen W (2016) Numerical simulation of heterogeneous rock using discrete element model based on digital image processing. Rock Mech Rock Eng 49(12):4957–4964

    Article  Google Scholar 

  • Wadell H (1935) Volume, shape, and roundness of quartz particles. J Geol 43(3):250–280

    Article  Google Scholar 

  • Wong TF (1982) Micromechanics of faulting in Westerly granite. Int J Rock Mech Min Sci Geomech Abstr 19(2):49–64

    Article  Google Scholar 

  • Wong RHC, Chau KT, Wang P (1996) Microcracking and grain size effect in Yuen Long marbles. Int J Rock Mech Min Sci Geomech Abstr 33(5):479–485

    Article  Google Scholar 

  • Xiao F, Yin X (2016) Geometry models of porous media based on Voronoi tessellations and their porosity-permeability relations. Comput Math Appl 72(2):328–348. doi:10.1016/j.camwa.2015.09.009

    Article  Google Scholar 

  • Zorlu K, Gokceoglu C, Ocakoglu F, Nefeslioglu HA, Acikalin S (2008) Prediction of uniaxial compressive strength of sandstones using petrography-based models. Eng Geol 96(3–4):141–158

    Article  Google Scholar 

Download references

Acknowledgements

The first author would like to thank the Chinese Scholarship Council for its financial support provided for his Ph.D study at TU Bergakademie Freiberg, Germany. Special thanks to Mr. Jörn Wichert and Mr. Martin Herbst for technical supporting. And thanks to Mr. Tom Weichmann, Mrs. Beatrice Tauch, and Mr. Gerd Münzberger for help during lab testing.

Author information

Authors and Affiliations

  1. Geotechnical Institute, TU Bergakademie Freiberg, Freiberg, Germany

    Jun Li, Heinz Konietzky & Thomas Frühwirt

Authors
  1. Jun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heinz Konietzky
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas Frühwirt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Konietzky, H. & Frühwirt, T. Voronoi-Based DEM Simulation Approach for Sandstone Considering Grain Structure and Pore Size. Rock Mech Rock Eng 50, 2749–2761 (2017). https://doi.org/10.1007/s00603-017-1257-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00603-017-1257-4

Keywords

Search

Navigation