Skip to main content

Advertisement

Log in

Fractal dimension and energy-damage evolution of deep-bedded sandstone under one-dimensional dynamic and static combined loading

  • Original Article
  • Published:
Geomechanics and Geophysics for Geo-Energy and Geo-Resources Aims and scope Submit manuscript

Abstract

A one-dimensional (1-D) SHPB was used to conduct dynamic tests on deep-bedded sandstone. The fractal dimension, energy evolution, and distribution curve of deep-bedded sandstone with diverse angles and impact pressures were obtained. In addition, the damage factors were defined and the damage evolution mechanism of deep-bedded sandstone was analyzed. The results show that (1) under low-impact pressure (0.05 MPa), the peak point elastic energy of deep-bedded sandstone occupies the main part of the total energy, while under high-impact pressure (0.4 MPa), the peak point dissipation energy occupies the main part of the total energy. (2) With increasing impact pressure, the energy accumulation rate of deep-bedded sandstone initially increases and subsequently becomes stable. The bedding effect is substantial under low pressure and disappears gradually under high pressure. (3) Under low-impact pressure (0.05 MPa), the damage factor evolution law of 0°, 30°, and 90° deep-bedded sandstone is stable at first and then increases rapidly. Under high-impact pressure (0.4 MPa), the damage factor of deep-bedded sandstone shows an apparent S-shaped curve.

Article highlights

  • The fractal dimension of deep-bedded sandstone under different angles and impact pressures was studied.

  • The energy-distribution characteristics of deep-bedded sandstone under different angles and impact pressures were studied.

  • The damage mechanism of deep-bedded sandstone under different angles and impact pressures was studied.

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

Access this article

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

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

Similar content being viewed by others

References

  • Cai X, Zhou Z, Du X (2020) Water-induced variations in dynamic behavior and failure characteristics of sandstone subjected to simulated geo-stress. Int J Rock Mech Min Sci 130

  • Clayton GC, Bond HE, Long LA, Meyer PI, Sugerman BEK, Montiel E, Sparks WB, Meakes MG, Chesneau O, De Marco O (2013) Evolution of the 1919 Ejecta of V605 Aquilae. Astrophys J 771(2)

  • Deng M, Zhang Z, Yu W, Xin J, Xu S (2022) Acoustic emission characteristics and damage law for prefabricated single‐crack sandstone under uniaxial compression. Struct Control Health Monit

  • Du W, Liu T, Xue F, Cai X, Chen Q, Zheng Y, Chen H (2020c) Fe3O4 mesocrystals with distinctive magnetothermal and nanoenzyme activity enabling self-reinforcing synergistic cancer therapy. ACS Appl Mater Interfaces 12(17):19285–19294

    Article  Google Scholar 

  • Du H-b, Dai F, Liu Y, Xu Y, Wei M-d (2020a) Dynamic response and failure mechanism of hydrostatically pressurized rocks subjected to high loading rate impacting. Soil Dyn Earthq Eng 129

  • Du H-b, Dai F, Xu Y, Yan Z, Wei M-d (2020b) Mechanical responses and failure mechanism of hydrostatically pressurized rocks under combined compression-shear impacting. Int J Mech Sci 165

  • Geng K, Chai J, Qin Y, Li X, Duan M, Liang D (2022) Exploring the brittleness and fractal characteristics of basalt fiber reinforced concrete under impact load based on the principle of energy dissipation. Mater Struct 55(2)

  • Gong F-Q, Si X-F, Li X-B, Wang S-Y (2019) Dynamic triaxial compression tests on sandstone at high strain rates and low confining pressures with split Hopkinson pressure bar. Int J Rock Mech Min Sci 113:211–219

    Article  Google Scholar 

  • Hokka M, Black J, Tkalich D, Fourmeau M, Kane A, Hoang NH, Li CC, Chen WW, Kuokkala VT (2016) Effects of strain rate and confining pressure on the compressive behavior of Kuru granite. Int J Impact Eng 91:183–193

    Article  Google Scholar 

  • Huang C, Wei S, Lei Z, Li C, Zhang L, Huang X, Xu S (2022) Experimental study of dynamic mechanical properties of water-saturated coal samples under three-dimensional coupled static–dynamic loadings. Processes 10(6)

  • Ke B, Zhang J, Deng H, Yang X (2020) Dynamic characteristics of sandstone under coupled static-dynamic loads after freeze-thaw cycles. Appl Sci 10(10)

  • Li Y, Huang R (2015) Relationship between joint roughness coefficient and fractal dimension of rock fracture surfaces. Int J Rock Mech Min Sci 75:15–22

    Article  Google Scholar 

  • Li X, Zhou T, Li D (2016) Dynamic strength and fracturing behavior of single-flawed prismatic marble specimens under impact loading with a Split–Hopkinson pressure bar. Rock Mech Rock Eng 50(1):29–44

    Article  Google Scholar 

  • Li X, Gong F, Tao M, Dong L, Du K, Ma C, Zhou Z, Yin T (2017a) Failure mechanism and coupled static-dynamic loading theory in deep hard rock mining: a review. J Rock Mech Geotech Eng 9(4):767–782

    Article  Google Scholar 

  • Li X, Tao M, Wu C, Du K, Wu Q (2017b) Spalling strength of rock under different static pre-confining pressures. Int J Impact Eng 99:69–74

    Article  Google Scholar 

  • Li D, Han Z, Sun X, Zhou T, Li X (2018) Dynamic mechanical properties and fracturing behavior of marble specimens containing single and double flaws in SHPB tests. Rock Mech Rock Eng 52(6):1623–1643

    Article  Google Scholar 

  • Li D, Han Z, Zhu Q, Zhang Y, Ranjith PG (2019) Stress wave propagation and dynamic behavior of red sandstone with single bonded planar joint at various angles. Int J Rock Mech Min Sci 117:162–170

    Article  Google Scholar 

  • Li D, Xiao P, Han Z, Zhu Q (2020a) Mechanical and failure properties of rocks with a cavity under coupled static and dynamic loads. Eng Fract Mech 225

  • Li Y, Zhai Y, Wang C, Meng F, Lu M (2020b) Mechanical properties of Beishan granite under complex dynamic loads after thermal treatment. Eng Geol 267

  • Tan L, Ren T, Yang X, He X (2018) A numerical simulation study on mechanical behaviour of coal with bedding planes under coupled static and dynamic load. Int J Min Sci Technol 28(5):791–797

    Article  Google Scholar 

  • Valente S, Capriulo C, He Q (2019) A compression-shear fracture growing on an arch-gravity dam. Theoret Appl Fract Mech 101:178–184

    Article  Google Scholar 

  • Wang P, Xu J, Fang X, Wang P (2017) Energy dissipation and damage evolution analyses for the dynamic compression failure process of red-sandstone after freeze-thaw cycles. Eng Geol 221:104–113

    Article  Google Scholar 

  • Wang W, Wang H, Li D, Li H, Liu Z (2018) Strength and failure characteristics of natural and water-saturated coal specimens under static and dynamic loads. Shock Vib 2018:1–15

    Google Scholar 

  • Wen T, Tang H, Ma J, Liu Y (2018) Energy analysis of the deformation and failure process of sandstone and damage constitutive model. KSCE J Civ Eng 23(2):513–524

    Article  Google Scholar 

  • Xiao P, Li D-Y, Zhao G-Y, Zhu Q-Q, Liu H-X, Zhang C-S (2020) Mechanical properties and failure behavior of rock with different flaw inclinations under coupled static and dynamic loads. J Central South Univ 27(10):2945–2958

    Article  Google Scholar 

  • Yan Z, Dai F, Liu Y, Du H (2020) Experimental investigations of the dynamic mechanical properties and fracturing behavior of cracked rocks under dynamic loading. Bull Eng Geol Env 79(10):5535–5552

    Article  Google Scholar 

  • Yan Z, Dai F, Zhu J, Xu Y (2021) Dynamic cracking behaviors and energy evolution of multi-flawed rocks under static pre-compression. Rock Mech Rock Eng 54(9):5117–5139

    Article  Google Scholar 

  • Zhang Y, Zhao G-F, Li Q (2020) Acoustic emission uncovers thermal damage evolution of rock. Int J Rock Mech Min Sci 132

  • Zhang J, Fan W, Niu W, Wang S (2022) Energy evolution characteristics of deep sandstone with different true triaxial stress paths. Geomech Geophys Geo-Energy Geo-Resour 8(2)

  • Zhou Z, Cai X, Li X, Cao W, Du X (2019) Dynamic response and energy evolution of sandstone under coupled static-dynamic compression: insights from experimental study into deep rock engineering applications. Rock Mech Rock Eng 53(3):1305–1331

    Article  Google Scholar 

Download references

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grant Nos. 52034009, 51974319) and the Yue Qi Distinguished Scholar Project (Grant No. 2020JCB01).

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [WF], [JZ], [XD], [YY] [WZ], [YZ] and [SW]. The first draft of the manuscript was written by [WF] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Junwen Zhang.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, W., Zhang, J., Dong, X. et al. Fractal dimension and energy-damage evolution of deep-bedded sandstone under one-dimensional dynamic and static combined loading. Geomech. Geophys. Geo-energ. Geo-resour. 8, 177 (2022). https://doi.org/10.1007/s40948-022-00487-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40948-022-00487-y

Keywords

Navigation