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Influence of pore structure on grain bulk modulus of underground rock masses under hydro-mechanical conditions
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  • Published: 01 March 2026

Influence of pore structure on grain bulk modulus of underground rock masses under hydro-mechanical conditions

  • Min-Jun Kim1,
  • Junhyung Choi1,
  • Eui-Seob Park1,
  • Byung-Gon Chae1,
  • Myungsun Kim1 &
  • …
  • Jong-Won Lee1 

Scientific Reports , Article number:  (2026) Cite this article

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We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Engineering
  • Solid Earth sciences

Abstract

We present an evaluation of the grain bulk modulus of rocks through experimental and theoretical methods. Unjacketed tests were performed on three rock types—Berea sandstone, Idaho sandstone, and Hwangdeung granite—to measure grain-scale compressibility. Theoretical estimates were obtained using mineral composition data and the Voigt–Reuss–Hill averaging method. To examine the role of pore structure, X-ray computed tomography (CT) was employed to visualize and quantify pore geometry, including isolated pores. Experimental results indicated material-dependent variation in grain bulk modulus not directly correlated with conventional mechanical properties. The theoretical values, as represented by the Hill average, were consistently higher than the experimental measurements, with overestimations of 7.2% for Berea sandstone, 37.3% for Idaho sandstone, and 31.7% for Hwangdeung granite. X-ray CT analysis confirmed that isolated pores contribute to additional volumetric deformation, which is unaccounted for in volume fraction-based models. A correlation between theoretical estimates and experimental values was derived to improve the applicability of the model. Conclusively, we present a systematic methodology for accurately evaluating grain bulk modulus by integrating experimental and theoretical approaches, offering foundational data and insight critical for geomechanical modeling in deep subsurface applications such as radioactive waste disposal or underground liquid hydrogen storage.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

References

  1. Blanco-Martín, L., Wolters, R., Rutqvist, J., Lux, K. H. & Birkholzer, J. T. Thermal–hydraulic–mechanical modeling of a large-scale heater test to investigate rock salt and crushed salt behavior under repository conditions for heat-generating nuclear waste. Comput. Geotech. 77, 120–133 (2016).

    Google Scholar 

  2. Yoon, S., Jeon, J. S., Kim, G. Y., Seong, J. H. & Baik, M. H. Specific heat capacity model for compacted bentonite buffer materials. Ann. Nucl. Ener. 125, 18–25 (2019).

    Google Scholar 

  3. Lee, J. W., Kim, J. S., Hong, C. H. & Oh, T. M. Permeability monitoring of underground concrete structures using elastic wave characteristics with modified Biot’s model. Sci. Rep. 14(1), 22110 (2024).

    Google Scholar 

  4. Selvadurai, A. P. S. & Suvorov, A. P. The influence of the pore shape on the bulk modulus and the biot coefficient of fluid-saturated porous rocks. Sci. Rep. 10(1), 18959 (2020).

    Google Scholar 

  5. Hart, D. J. & Wang, H. F. Variation of unjacketed pore compressibility using Gassmann’s equation and an overdetermined set of volumetric poroelastic measurements. Geophysics 75(1), N9–N18 (2010).

    Google Scholar 

  6. Wang, L., Rybacki, E., Bonnelye, A., Bohnhoff, M. & Dresen, G. Experimental investigation on static and dynamic bulk moduli of dry and fluid-saturated porous sandstones. Rock. Mech. Rock. Eng. 54 (1), 129–148 (2021).

    Google Scholar 

  7. Belmokhtar, M. et al. Poroelasticity of the Callovo–Oxfordian claystone. Rock Mech. Rock Eng 50, 871–889 (2017).

    Google Scholar 

  8. Selvadurai, A. P. S. On the poroelastic biot coefficient for a granitic rock. Geosciences 11(5), 219 (2021).

    Google Scholar 

  9. Qin, X., Han, D. H. & Zhao, L. Measurement of grain bulk modulus on sandstone samples from the Norwegian continental shelf. J. Geophys. Res. Solid Earth 127(9), e2022JB024550 (2022).

    Google Scholar 

  10. Hu, Q., Ewing, R. P. & Dultz, S. Low pore connectivity in natural rock. J. Contam. Hydrol. 133, 76–83 (2012).

    Google Scholar 

  11. Colombier, M. et al. The evolution of pore connectivity in volcanic rocks. Earth Planet. Sci. Lett. 462, 99–109 (2017).

    Google Scholar 

  12. Mikhaltsevitch, V., Lebedev, M., Chavez, R., Pervukhina, M. & Glubokovskikh, S. & do Amaral Vargas Jr, E. The dead volume effect on the elastic moduli measurements using the forced-oscillation method. Geophys. Prospect. 70 (3), 547–557 (2022).

    Google Scholar 

  13. Nwonodi, R. I., Dosunmu, A. & Okoro, E. E. An equation for the bulk modulus of composites derived from the effective medium theory. ASME Open Journal of Engineering 1, 011044 (2022).

    Google Scholar 

  14. Tarokh, A., Detournay, E. & Labuz, J. Direct measurement of the unjacketed pore modulus of porous solids. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 474(2219), 20180602 (2018).

    Google Scholar 

  15. Makhnenko, R. Y., Ge, C. & Labuz, J. F. AE from undrained and unjacketed tests on sandstone. In ARMA US Rock Mech/Geomech Symp (ARMA–2012). ARMA. (2012).

  16. Biot, M. A. Theory of propagation of elastic waves in a fluid-saturated porous solid. Ⅰ. Low-frequency range. J. Acoust. Soc. Am. 28(2), 168–178 (1956).

    Google Scholar 

  17. Biot, M. A. & Willis, D. G. The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24(4), 594–601 (1957).

    Google Scholar 

  18. Park, C. H., Kim, T., Park, E. S., Jung, Y. B. & Bang, E. S. Development and verification of ogsflac simulator for hydromechanical coupled analysis: Single-phase fluid flow analysis. Tunn. Undergr. Space 29(6), 468–479 (2019).

    Google Scholar 

  19. Yang, J. & Fall, M. A dual-porosity poroelastic model for simulation of gas flow in saturated claystone as a potential host rock for deep geological repositories. Tunn. Undergr. Space Technol. 115, 104049 (2021).

    Google Scholar 

  20. Yang, J., Fall, M. & Guo, G. A three-dimensional hydro-mechanical model for simulation of dilatancy-controlled gas flow in anisotropic claystone. Rock Mech. Rock Eng. 53, 4091–4116 (2020).

    Google Scholar 

  21. Lau, J. S. O. & Chandler, N. A. Innovative laboratory testing. Int. J. Rock Mech. Min. Sci. 41(8), 1427–1445 (2004).

    Google Scholar 

  22. Müller, T. M. & Sahay, P. N. Biot coefficient is distinct from effective pressure coefficient. Geophys 81(4), L27–L33 (2016).

    Google Scholar 

  23. Müller, T. M. & Sahay, P. N. Generalized poroelasticity framework for micro-inhomogeneous rocks. Geophys. Prospect. 64(4), 1122–1134 (2016).

    Google Scholar 

  24. Makhnenko, R. M. & Labuz, J. F. Unjacketed bulk compressibility of sandstone in laboratory experiments. In Poromech. Ⅴ: Proc. Fifth Biot Conf. Poromech. 481–488. (2013).

  25. Makhnenko, R. Y. & Labuz, J. F. Elastic and inelastic deformation of fluid-saturated rock. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 374(2078), 20150422 (2016).

    Google Scholar 

  26. Mavko, G., Mukerji, T. & Dvorkin, J. The rock physics handbook (Cambridge University Press, 2020).

    Google Scholar 

  27. Luo, Y. Isotropized Voigt-Reuss model for prediction of elastic properties of particulate composites. Mech. Adv. Mat. Struc. 29(25), 3934–3941 (2022).

    Google Scholar 

  28. Hill, R. The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. Sec A. 65 (5), 349 (1952).

    Google Scholar 

  29. ASTM D2938. Standard Test Method for Unconfined Compressive Strength of Intact Rock Core Specimens (ASTM International, 1986).

  30. Bieniawski, Z. T. & Bernede, M. J. Suggested methods for determining the uniaxial compressive strength and deformability of rock materials. Part 1. Suggested method for determining deformability of rock materials in uniaxial compression. Int. J. Rock Mech. Min. Sci. Geomech. Abst. 16(2), 138–140 (1979).

    Google Scholar 

  31. Franklin, J. A. Suggested methods for determining water content, porosity, density, absorption and related properties and swelling and slake-durability index properties: Part 1: Suggested methods for determining water content, porosity, density, absorption and related properties. Int. J. Rock Mech. Min. Sci. Geomech. Abst. 16(2), 143–151 (1979).

    Google Scholar 

  32. MTS. Circumferential Extensometer Strain Calculations (MTS Systems Corporation, 2000).

  33. Dudley, J. W. et al. ISRM suggested method for uniaxial-strain compressibility testing for reservoir geomechanics. Rock Mech. Rock Eng. 49, 4153–4178 (2016).

    Google Scholar 

  34. Kim, K. Y., Zhuang, L., Yang, H., Kim, H. & Min, K. B. Strength anisotropy of Berea sandstone: Results of X-ray computed tomography, compression tests, and discrete modeling. Rock Mech. Rock Eng. 49, 1201–1210 (2016).

    Google Scholar 

  35. Choens, I. I. et al. Impacts on mechanical strength of chemical reactions induced by hydrous supercritical CO2 in Boise sandstone. Int. J. Greenhou Gas Ctrl. 95, 102982 (2020).

  36. Park, J. W., Lee, Y. K., Park, C. & Kim, C. M. Crack initiation and propagation thresholds of Hwangdeung granite under elevated temperature. Geosci. J. 26(6), 715–729 (2022).

    Google Scholar 

  37. Zhou, X. et al. XRD-based quantitative analysis of clay minerals using reference intensity ratios, mineral intensity factors, Rietveld, and full pattern summation methods: A critical review. Solid Earth Sci. 3, 16–29 (2018).

    Google Scholar 

  38. Zimmerman, R. W. Compressibility of Sandstones (Elsevier, 1991).

  39. Dvorkin, J. & Nur, A. Elasticity of high-porosity sandstones: Theory for two North sea data sets. Geophys 61(5), 1363–1370 (1996).

    Google Scholar 

  40. Louis, L., Boyd, P., Hofmann, R. & Saxena, N. On the role and evolution of local grain size heterogeneity during confined compression of Boise sandstone as seen by X-ray micro-CT imaging. Rock Mech. Rock. Eng 1–22. (2024).

  41. Wang, Y. et al. Pore structure of the mixed sedimentary reservoir of Permian Fengcheng Formation in the Hashan area, Junggar Basin. Sci. Rep. 14(1), 20556 (2024).

    Google Scholar 

  42. Andrä, H. et al. Digital rock physics benchmarks—Part I: Imaging and segmentation. Computers & Geosciences 50, 25–32 (2013).

    Google Scholar 

  43. Koestel, J. et al. Estimating the permeability of naturally structured soil from percolation theory and pore space characteristics imaged by X-ray. Water Resour. Res. 54, 9255–9263 (2018).

    Google Scholar 

  44. Ruidong, L. I., Zhen-Yu, Y. I. N. & Shao-Heng, H. E. 3D reconstruction of arbitrary granular media utilizing vision foundation model. Appl. Soft Comput. 169, 112599 (2025).

    Google Scholar 

  45. Zheng, Z. et al. Coralscop: Segment any coral image on this planet. Proc. IEEE/CVF Conf. Comput. Vis. Pattern Recognit. 28170–28180. (2024) (2024).

  46. Li, R., Yin, Z. Y., He, S. & Sheil, B. Enhancement and assessment of large vision models for 3D particle reconstruction from X-ray tomography. Can. Geotech. J. 62, 1–28 (2025).

    Google Scholar 

  47. LI, R., Yin, Z. Y., He, S. & Wu, M. Novel particle reconstruction and tracking algorithms to reveal 3D micromechanical behaviors of coral sands. Can Geotech. Just-IN (2025).

  48. Dong, H. & Blunt, M. J. Pore-network extraction from micro-computerized-tomography images. Phys. Rev. E—Stat. Nonlin. Soft Matter Phys. 80(3), 036307. (2025) (2009).

  49. Gostick, J. et al. Putz, A. OpenPNM: a pore network modeling package. Comput. Sci. Eng. 18 (4), 60–74 (2016).

    Google Scholar 

  50. Shilko, E. V., Grigoriev, A. S., Korostelev, S. Y., Volobuev, A. S. & Andreev, K. Effect of geometrical features of pores on the mechanical properties and fracture of ceramic materials. Eng. Fract. Mech. 331, 111732 (2025).

    Google Scholar 

  51. Katre, S. & Nair, A. M. Modelling the effect of grain anisotropy on inter-granular porosity. J. Petrol. Explor. Prod. Technol. 12, 1–19 (2022).

    Google Scholar 

  52. Payton, R. L., Chiarella, D. & Kingdon, A. The influence of grain shape and size on the relationship between porosity and permeability in sandstone: A digital approach. Sci. Rep. 12(1), 7531 (2022).

    Google Scholar 

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Acknowledgements

This work was supported by Basic Research Project of the Korea Institute of Geoscience and Mineral Resources (KIGAM, GP2025-009) funded by the Ministry of Science, ICT and the Institute for Korea Spent Nuclear Fuel (iKSNF) and a Korea Foundation of Nuclear Safety (KOFONS) grant funded by the Korean government (Nuclear Safety and Security Commission, NSSC) (RS-2021-KN066110).

Funding

This work was supported by Basic Research Project of the Korea Institute of Geoscience and Mineral Resources (KIGAM, GP2025-009) funded by the Ministry of Science, ICT and the Institute for Korea Spent Nuclear Fuel (iKSNF) and a Korea Foundation of Nuclear Safety (KOFONS) grant funded by the Korean government (Nuclear Safety and Security Commission, NSSC) (RS-2021-KN066110).

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Authors and Affiliations

  1. Deep Geological Disposal & Energy Storage Research Center, Korea Institute of Geoscience and Mineral Resources (KIGAM), 124 Gwahang-no, Yuseong-gu, Daejeon, 34132, Korea

    Min-Jun Kim, Junhyung Choi, Eui-Seob Park, Byung-Gon Chae, Myungsun Kim & Jong-Won Lee

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  1. Min-Jun Kim
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  2. Junhyung Choi
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Contributions

Min-Jun Kim: Conceptualization; Methodology; Data curation; Writing–original draft; Writing–review&editing. Junhyung Choi: Conceptualization; Methodology; Validation. Eui-Seob Park: Supervision; Investigation. Byung-Gon Chae: Validation; Investigation. Myungsun Kim: Validation; Investigation. Jong-Won Lee: Writing–original draft; Writing–review&editing; Visualization; Validation.

Corresponding author

Correspondence to Jong-Won Lee.

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Kim, MJ., Choi, J., Park, ES. et al. Influence of pore structure on grain bulk modulus of underground rock masses under hydro-mechanical conditions. Sci Rep (2026). https://doi.org/10.1038/s41598-026-40373-1

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  • Received: 06 January 2026

  • Accepted: 12 February 2026

  • Published: 01 March 2026

  • DOI: https://doi.org/10.1038/s41598-026-40373-1

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Keywords

  • Pore structure
  • Grain bulk modulus
  • Unjacketed test
  • Volume fraction-based model
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