Paper contribution

Laboratory-Scale Assessment of 2D and 3D Bonded-Particle Models

Enes Zengin; Ömer Ündül; Özge Dinç Göğüş; Mehmet Mert Doğu

Proceedings
EUROCK 2026
Pages
983-988
Submitted
28 January 2026
Accepted
15 June 2026
Published
12 August 2026

Summary

Abstract

Discrete element simulations of intact rock typically use two-dimensional (2D) bonded-particle models (BPMs) rather than three-dimensional (3D) models due to their lower computational demands. However, the extent to which a calibrated 2D model can accurately reflect the three-dimensional behaviour seen in laboratory tests on brittle rock remains an ongoing area of research and discussion. In this study, a systematic laboratory-scale comparison is conducted between 2D and 3D BPMs for an intact, brittle Cebeciköy siltstone, a formation often encountered along tunnel alignments in Istanbul, Türkiye, and therefore of practical importance. Both model dimensions are independently calibrated in Particle Flow Code (PFC) using a parallel-bond contact model. The calibration targets encompass the mechanical parameters of the Cebeciköy siltstone, as well as the overall shape of the stress–strain response. The comparison between 2D and 3D models focuses on peak strength, stiffness, post-peak brittleness, fracture pattern evolution, and basic energy measures across various loading paths and strain rates. While both models can be calibrated to match the same reference data, their responses vary under different boundary conditions. Notably, differences are observed in strain localization, damage progression, and the impact of various parameters on strength. In some tests, the 2D model closely aligns with the 3D results within a narrow error margin; however, in others, it either underestimates or overestimates strength and brittleness, often in a non-conservative manner. These insights help establish practical criteria to determine when a calibrated 2D BPM of Cebeciköy siltstone can reliably approximate a 3D model, and when comprehensive 3D analysis is necessary for design purposes involving this or similar brittle rocks. These insights are particularly important for guiding subsequent discrete-element modelling and upscaling studies in more complex rock-mass settings, where intact-rock response provides the fundamental building block for jointed and heterogeneous models.

Contributors

Authors

  1. Enes Zengin Istanbul Technical University, Faculty of Mines, Department of Geological Engineering, Istanbul, Türkiye ORCID 0000-0002-5740-7763
  2. Ömer Ündül Istanbul Technical University, Faculty of Mines, Department of Geological Engineering, Istanbul, Türkiye
  3. Özge Dinç Göğüş Istanbul Technical University, Faculty of Mines, Department of Geological Engineering, Istanbul, Türkiye ORCID 0000-0003-3227-309X
  4. Mehmet Mert Doğu Istanbul Technical University, Faculty of Mines, Department of Geological Engineering, Istanbul, Türkiye ORCID 0009-0008-3802-8144

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References

  1. Cho, N., Martin, C. D., & Sego, D. C. (2007). A clumped particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 44(7), 997–1010. https://doi.org/10.1016/J.IJRMMS.2007.02.002
  2. Cundall, P. A. &Strack, O. D. L. (1979). A discrete numerical model for granular assemblies. Geotechnique, 1, 47–65.
  3. Jing, L. (2003). A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering. International Journal of Rock Mechanics and Mining Sciences, 40(3), 283–353. https://doi.org/10.1016/S1365-1609(03)00013-3
  4. Jing, L., & Hudson, J. A. (2002). Numerical methods in rock mechanics. International Journal of Rock Mechanics and Mining Sciences, 39(4), 409–427. https://doi.org/10.1016/S1365-1609(02)00065-5
  5. Kong, L., Shang, J., Ranjith, P. G., Li, B. Q., Song, Y., Cai, W., & Ling, F. (2024). Grain-based DEM modelling of mechanical and coupled hydro-mechanical behaviour of crystalline rocks. Engineering Geology, 339, 107649. https://doi.org/10.1016/j.enggeo.2024.107649
  6. Lisjak, A., &Grasselli, G. (2014). A review of discrete modeling techniques for fracturing processes in discontinuous rock masses. Journal of Rock Mechanics and Geotechnical Engineering, 6(4), 301–314. https://doi.org/10.1016/J.JRMGE.2013.12.007
  7. Potyondy, D. O. (2015). The bonded-particle model as a tool for rock mechanics research and application: current trends and future directions. Geosystem Engineering, 18(1), 1–28. https://doi.org/10.1080/12269328.2014.998346
  8. Potyondy, D. O., & Cundall, P. A. (2004). A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences, 41(8 SPEC.ISS.), 1329–1364. https://doi.org/10.1016/j.ijrmms.2004.09.011
  9. Qu, T., Feng, Y. T., Wang, M., & Jiang, S. (2020). Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation. Powder Technology, 366, 527–536. https://doi.org/10.1016/J.POWTEC.2020.02.077
  10. Ündül, Ö., Amann, F., Aysal, N., &Plötze, M. (2013). Micro-textural controlled variations of the geomechanical properties of andesites. In Rock Mechanics for Resources, Energy and Environment (pp. 357–361). CRC Press. https://doi.org/10.1201/b15683-60
  11. Ündül, Ö., & Zengin, E. (2025). The Influence of Strain Rate Variations on Bonded-Particle Models in PFC. Geotechnics, 4(5). https://doi.org/10.3390/geotechnics5040082
  12. Ündül, Ö., & Zengin, E. (2026). Bonded-particle modeling of sedimentary rocks: insights into model selection and mechanical response. Mediterranean Geoscience Reviews 2026 8:1, 8(1), 35–54. https://doi.org/10.1007/S42990-025-00214-1
  13. Vallejos, J. A., Salinas, J. M., Delonca, A., & Mas Ivars, D. (2017). Calibration and Verification of Two Bonded-Particle Models for Simulation of Intact Rock Behavior. International Journal of Geomechanics, 17(4), 06016030. https://doi.org/10.1061/(asce)gm.1943-5622.0000773
  14. Zengi̇n, E. (2022). Usability Assessment of Different Contact Models for Modelling the Failure Behaviour of Sedimentary Rocks Under Unconfined Stress Conditions. Yerbilimleri, 43(1), 61–75. https://doi.org/10.17824/YERBILIMLERI.1030332
  15. Zengin, E., & Erguler, Z. A. (2017). Comparison of Crack Initiation, Propagation and Coalescence Behavior of Concrete and Rock Materials. European Geosciences Union 2017, 19. https://meetingorganizer.copernicus.org/EGU2017/EGU2017-12090-2.pdf
  16. Zengin, E., &Erguler, Z. A. (2022). Experimental investigation of pore-fracture relationship on failure behaviour of porous rock materials. Bulletin of Engineering Geology and the Environment, 81(9), 351. https://doi.org/10.1007/s10064-022-02857-y