Abstract
The evolution of fracture–pore structures critically controls the mechanical stability and permeability of shale reservoirs. To clarify their coupled behavior during stress-induced failure, we investigate the multifractal evolution of fractures and pores in shale under uniaxial compression using digital rock reconstruction and discrete element modeling. The proposed fracture-damage framework reproduces fracture nucleation, propagation, and coalescence, and reveals a strong correspondence between energy conversion and damage development. Multifractal analyses show that pore heterogeneity primarily governs the fractal characteristics at the early loading stage, whereas fracture growth becomes increasingly dominant after peak stress; meanwhile, the multifractal parameters of fractures and pores evolve in broadly consistent trends. Together with the simulated porosity and permeability responses, these fractal descriptors capture the progressive reorganization of flow pathways during loading. Overall, this work provides a quantitative structure–property link between fracture activity, pore complexity, and transport evolution in shale, offering mechanistic insights for reservoir failure interpretation and stability evaluation.
Data availability
The datasets generated and analyzed during the current study are available from the corresponding author upon reasonable request.
References
Cai, Q. W. Three-dimensional fracture propagation model of rock strata fracturing and its application. China University of Mining and Technology. (in Chinese) (2024).
Zhao, Y. et al. Experimental study on microseismic, charge induction, self-potential, and acoustic emission during rock deformation and fracture. Chin. J. Rock Mech. Eng. 36(1), 107–123 (2017) ((in Chinese)).
Wu, J. et al. Challenges to sustainable large-scale shale gas development in China. Proc. Natl. Acad. Sci. USA 122(18), e2415192122 (2025).
Zhao, Y. et al. Study on the relation between damage and permeability of sandstone at depth under cyclic loading. Int. J. Coal Sci. Technol. 6(4), 479–492 (2019).
Zhao, Z. & Zhou, X. P. 3D digital analysis of cracking behaviors of rocks through 3D reconstruction model under triaxial compression. J. Eng. Mech. 146(8), 04020084 (2020).
Zhang, P. S. et al. Experimental study on permeability characteristics of red sandstone with different confining pressures and damage degrees. Chin. J. Rock Mech. Eng. 39(12), 2405–2415 (2020) ((in Chinese)).
Tang, M. et al. Stress‐dependent microcrack evolution and damage constitutive model of low permeability sandstone. Fatig. Fract. Eng. Mater. Struct. https://doi.org/10.1111/ffe.70112 (2025).
Yan, S., Han, L., Zhang, S., Zhao, W. & Meng, L. Evolution characteristics of pore–fractures and mechanical response of dehydrated lignite based on in situ computed tomography (CT) scanning. Fractal Fract. 9(4), 220 (2025).
Zhu, H. G. et al. CT identification of microcrack evolution in rock materials. Chin. J. Rock Mech. Eng. 30(6), 1230–1238 (2011) ((in Chinese)).
Zhao, Y. et al. Research and analysis of the impact of the pore structure on the mechanical properties and fracture mechanism of sandstone. Mater. Today Commun. 38, 107753 (2024).
Wu, J. et al. Discrete element modeling for investigating the mechanical behavior of porous granular sea ice specimens under uniaxial compression. Appl. Ocean Res. 162, 104710 (2025).
Xiao, N. et al. Study on the relationship between porosity and mechanical properties based on rock pore structure reconstruction model. Appl. Sci. 15(13), 7247 (2025).
Rotter, S., Dosta, M. & Düster, A. Discrete element simulation of the breakage behavior of porous granules utilizing bond models. Comput. Part. Mech. 11(1), 89–103 (2024).
Baud, P., Wong, T. & Zhu, W. Effects of porosity and crack density on the compressive strength of rocks. Int. J. Rock Mech. Min. Sci. 67, 202–211 (2014).
Lang, Y. X. et al. Reconstruction and parallel simulation of rock mesoscopic pore models based on CT experiments. Rock Soil Mech. 40(3), 1204–1212 (2019) ((in Chinese)).
Cheng, Z. L. et al. Study on microstructural characteristics of digital rock cores and their influence on rock mechanical properties. Chin. J. Rock Mech. Eng. 37(2), 449–460 (2018) ((in Chinese)).
Fu, Y., He, Y. & Li, C. Failure and acoustic emissions of coal–rock combinations with different dip angles in the Shaqu No. 1 Coal Mine. Adv. Civ. Eng. 2023(1), 9969802 (2023).
Zhang, Y. et al. Acoustic and thermal response characteristics and failure mode of gas-bearing coal–rock composite structure under loading. Infrared Phys. Technol. 142, 105517 (2024).
Klyuchkin, V. N. et al. Acoustic and electromagnetic emissions of rocks: Insight from laboratory tests at press and shear machines. Environ. Earth Sci. 81(3), 64 (2022).
Mingyang, S. et al. Evolution and correlation of acoustic emission and resistance parameters during coal fracture propagation. Nat. Resour. Res. 33(5), 2135–2154 (2024).
Yin, S. et al. Structural health monitoring of building rock based on stress drop and acoustic–electric energy release. Struct. Control Health Monit. 29(2), e2875 (2022).
Niu, Y., Liu, G. J., Hu, Y. J., Xu, K. & Wang, Y. W. Mechanical responses and temporal multifractal behaviors of rock–coal–rock composite body under uniaxial compression using an AE monitoring tool. Int. J. Geomech. 26(1), 04025302 (2026).
Liu, J. et al. Dynamic multifractal characteristics of acoustic emission from composite coal–rock samples with different strength rocks. Chaos Solitons Fractals 164, 112725 (2022).
Gu, Y. et al. Evolution of pore structure and fractal characteristics in transitional shale reservoirs: Case study of Shanxi Formation, Eastern Ordos Basin. Fractal Fract. 9(6), 335 (2025).
Li, J. et al. Study on meso-damage mechanism of shale reservoir rocks based on digital core models. Chin. J. Rock Mech. Eng. 41(6), 1103–1113 (2022) ((in Chinese)).
Liu, G., Fang, Z., Zhang, Z., Liu, H., Lv, R., Wang, X., & Barakos, G. Improved strategy for multifractal characterization of CO2 adsorption in micropores. EnergyFuels, 38(21), 20449–20461 (2024).
Gao, M., Yang, M., Lu, Y., He, P. & Zhu, H. Mechanical characterization of uniaxial compression associated with lamination angles in shale. Adv. Geo-Energy Res. https://doi.org/10.46690/ager.2024.07.07 (2024).
Feng, K. et al. Multifractal characterization of methane adsorption in coal pores. Langmuir https://doi.org/10.1021/acs.langmuir.5c01807 (2025).
Liu, G., Fang, Z., Zhang, Z., Liu, H., Lv, R., Wang, X., & Barakos, G. Improved strategy for multifractal characterization of CO2 adsorption in micropores. Energy Fuels, 38(21), 20449–20461 (2024).
Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I. & Shraiman, B. I. Fractal measures and their singularities: The characterization of strange sets. Phys. Rev. A. 33(2), 1141 (1986).
Xie, J. et al. Experimental study on triaxial fracture behavior and energy release law of deep coal under the effect of loading rates. J. Cent. South Univ. (Sci. Technol.) 52, 2713–2724 (2021).
Liu, X. H. et al. Study on energy release during coal–rock fragmentation process under impact loading. Chin. J. Rock Mech. Eng. 40(S2), 3201–3211 (2021) ((in Chinese)).
Gong, F. Q., Yan, J. Y. & Li, X. B. Criterion for rockburst tendency based on linear energy storage law and residual elastic energy index. Chin. J. Rock Mech. Eng. 37(9), 1993–2014 (2018) ((in Chinese).).
Kachanov, M. Effective elastic properties of cracked solids: Critical review of some basic concepts. Appl. Mech. Rev. 45(8), 304–335 (1992).
Yang, Y. J. et al. Study on rock damage characteristics based on triaxial compression acoustic emission tests. Chin. J. Rock Mech. Eng. 33(1), 98–104 (2014) ((in Chinese)).
Li, F. et al. Revisiting the normal stiffness–permeability relations for shale fractures under true triaxial stress. J. Rock Mech. Geotech. Eng. https://doi.org/10.1016/j.jrmge.2025.01.007 (2025).
Funding
This work was supported by the National Natural Science Foundation of China (Grant Nos. 42474156 and 42174143).
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Wang Ziqi: Conceptualization, Methodology, Writing—Original Draft Sun Jianmeng: Supervision, Funding acquisition, Resources Wen Haiou: Data curation, Formal analysis, Visualization Pan Weiliang: Writing—Review & Editing, Project administration Sun Xiaojun: Data curation, Formal analysis, Visualization All authors read and approved the final manuscript. Gao Honglin: Software, Validation, Investigation.
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Wang, Z., Sun, J., Wen, H. et al. Multifractal evolution of shale fracture and pore structures under uniaxial compression. Sci Rep (2026). https://doi.org/10.1038/s41598-026-43892-z
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DOI: https://doi.org/10.1038/s41598-026-43892-z
