Skip to main content
SpringerLink
Log in

Lattice Boltzmann simulation and mesoscopic mechanism analysis of permeability in soil-rock mixtures

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

The subgrade constructed by soil–rock mixture (SRM) usually suffers from slope instability, subgrade collapse, and uneven settlement, which are closely related to the permeability of the SRM. In order to reveal the internal influence mechanism of the seepage characteristics of the SRM, the SRM models of dense structure (DS), medium-dense structure (MDS), and loose structure (LS) were generated based on the improved Monte Carlo method (IMCM) and the self-made MATLAB program, and the lattice Boltzmann method (LBM) was introduced to study the mesoscopic seepage characteristics of SRM under different influence factors. Finally, the internal mechanism of the influence of rock content rate (RCR) on the SRM permeability under different conditions was discussed in detail with a simplified model. The results show that the permeability of the SRM in DS, MDS, and LS cases tends to increase continuously with the increase of RCR when the loose-density degree (LD) and rock size (DR) are the same. The looser the structure of the SRM samples, the larger the permeability. When the RCR is lower than the threshold value, the larger the DR the slower the increase of the permeability; but when the RCR is higher than the threshold value, the larger the DR the significantly larger the increase of the permeability. In this study, the threshold value is determined to be about 35%. The RCR sensitivity index (S) shows an overall trend of increasing, then decreasing, and then slowly increasing with increasing RCR, in which large rocks and MDS have a facilitating effect on the sudden change of SRM permeability. When the soil/rock particle size is constant, the permeability of the simplified model tends to “decrease → increase → decrease” with the increase of RCR. This study provides an IMCM-LBM joint simulation method as a promising option to simulate realistic SRM particles permeability in geotechnical experiments.

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

Similar content being viewed by others

References

  1. Gao WW, Gao W, Hu RL, Xu PF, Xia JG (2018) Microtremor survey and stability analysis of a soil–rock mixture landslide: a case study in Baidian town, China. Landslides 15(10):1951–1961. https://doi.org/10.1007/s10346-018-1009-x

    Article  Google Scholar 

  2. Iqbal J, Thomasson JA, Jenkins J, Owens PR, Whisler FD (2005) Spatial variability analysis of soil physical properties of alluvial soils. Soil Sci Soc Am J 69(4):1338–1350. https://doi.org/10.2136/sssaj2004.0154

    Article  Google Scholar 

  3. Lin S, Zheng H, Zhang ZH, Li W (2022) Evaluation of permeability of soil and rock aggregate using meshless numerical manifold method. Comput Geotech 151:104953. https://doi.org/10.1016/j.compgeo.2022.104953

    Article  Google Scholar 

  4. Lee IW (2008) Wetting-induced collapse in fill materials for concrete slab track of high speed railway. J Korean Geotech Soc 24(4):79–88

    Google Scholar 

  5. Wang YY, Mao XS, Qian W, Dai ZY (2022) Study on the influence of seepage conditions with different rainfall intensities on the structural evolution of soil–rock mixture filler. Geofluids 2022:7694663. https://doi.org/10.1155/2022/7694663

    Article  Google Scholar 

  6. Zhou Z, Fu HL, Liu BT, Tan NH, Long WX (2006) Orthogonal tests on permeability of soil–rock-mixture. Chin J Geotech Eng 28(9):1134–1138

    Google Scholar 

  7. Pei YB, Li WP, Liu QQ, Wang QQ, Yan SS (2016) Research for the permeability of the earth-rock aggregate: a case study in the weathering zone on top Ordovician. Coal Eng 48(10):92–95

    Google Scholar 

  8. Wang Y, Li X, Zheng B, Li GF, Wu YF (2016) Experimental study on the non-Darcy flow characteristics of soil–rock mixture. Environ Earth Sci 75(9):1–18. https://doi.org/10.1007/s12665-015-5218-5

    Article  Google Scholar 

  9. Xu Y, Gao Q, Li X, Li JH, Jia YX (2009) In-situ experimental study of permeability of rock and soil aggregates. Rock Soil Mech 30(3):855–858. https://doi.org/10.16285/j.rsm.2009.03.025

    Article  Google Scholar 

  10. Xu WJ (2008) Study on meso-structural mechanics of soil–rock mixture and its slope stability. Doctor Thesis, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China. http://ir.iggcas.ac.cn/handle/132A11/11061

  11. Cao JS, Yang H, Zhao Y (2022) Experimental analysis of infiltration process and hydraulic properties in soil and rock profile in the Taihang mountains, North China. Water Supply 22(2):1691–1703. https://doi.org/10.2166/ws.2021.321

    Article  Google Scholar 

  12. Xu WJ, Wang YG (2010) Meso-structural permeability of S-RM based on numerical tests. Chin J Geotech Eng 32(4):542–550

    Google Scholar 

  13. Chen T, Yang YT, Zheng H, Wu ZJ (2019) Numerical determination of the effective permeability coefficient of soil–rock mixtures using the numerical manifold method. Int J Numer Anal Meth Geomech 43(1):381–414. https://doi.org/10.1002/nag.2868

    Article  Google Scholar 

  14. McNamara GR, Zanetti G (1988) Use of the Boltzmann equation to simulate lattice-gas automata. Phys Rev Lett 61(20):2332–2335. https://doi.org/10.1103/PhysRevLett.61.2332

    Article  Google Scholar 

  15. Nabovati A, Sousa ACM (2007) Fluid flow simulation in random porous media at pore level using the lattice Boltzmann method. In: Zhuang FG, Li JC (eds) New trends in fluid mechanics research. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75995-9_172

    Chapter  Google Scholar 

  16. Succi S (2001) Lattice Boltzmann equation for fluid dynamics and beyond. Clarendon Press, Oxford. https://doi.org/10.1063/1.1537916

    Book  Google Scholar 

  17. Eshghinejadfard A, Daróczy L, Janiga G, Thévenin D (2016) Calculation of the permeability in porous media using the lattice Boltzmann method. Int J Heat Fluid Flow 62:93–103. https://doi.org/10.1016/j.ijheatfluidflow.2016.05.010

    Article  Google Scholar 

  18. Cui X, Li J, Chan A, Chapman D (2012) A 2D DEM–LBM study on soil behaviour due to locally injected fluid. Particuology 10(2):242–252. https://doi.org/10.1016/j.partic.2011.10.002

    Article  Google Scholar 

  19. Jin L, Zeng YW, Cheng T, Li JJ (2022) Seepage characteristics of soil–rock mixture based on lattice Boltzmann method. Chin J Geotech Eng 44(4):669–677. https://doi.org/10.11779/CJGE202204009

    Article  Google Scholar 

  20. Bhatnagar PL, Gross EP, Krook M (1954) A model for collision processes in gases: I small amplitude processes in charged and neutral one-component systems. Phys Rev 94(3):511–525. https://doi.org/10.1103/PhysRev.94.511

    Article  Google Scholar 

  21. Qian YH, D’Humières D, Lallemand P (1992) Lattice BGK models for Navier–Stokes equation. Europhys Lett 17(6):479–484. https://doi.org/10.1209/0295-5075/17/6/001

    Article  Google Scholar 

  22. Feng YT, Han K, Owen DRJ (2007) Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: computational issues. Int J Numer Meth Eng 72(9):1111–1134. https://doi.org/10.1002/nme.2114

    Article  MathSciNet  Google Scholar 

  23. Liu YF, Jeng DS (2019) Pore scale study of the influence of particle geometry on soil permeability. Adv Water Resour 129:232–249. https://doi.org/10.1016/j.advwatres.2019.05.024

    Article  Google Scholar 

  24. Yin PJ, Song HH, Ma HR, Yang WC, He Z, Zhu XN (2022) The modification of the Kozeny–Carman equation through the lattice Boltzmann simulation and experimental verification. J Hydrol 609:127738. https://doi.org/10.1016/j.jhydrol.2022.127738

    Article  Google Scholar 

  25. You XH (2002) Stochastic structural model of soil rock mixture and its application. Chin J Rock Mech Eng 11:1748

    Google Scholar 

  26. Medley E (1994) The engineering characterization of melanges and similar block-in-matrix rocks (bimrocks). Doctor Thesis, University of California at Berkeley, San Francisco, America. https://www.researchgate.net/publication/35292215

  27. Abbireddy COR, Clayton CRI (2010) Varying initial void ratios for DEM simulations. Géotechnique 60(6):497–502. https://doi.org/10.1680/geot.2010.60.6.497

    Article  Google Scholar 

  28. Mao XS, Cai PC, Fu J, Dai ZY (2023) Study on internal erosion and structural evolution mechanism of soil–rock mixture. Nat Hazards. https://doi.org/10.1007/s11069-023-06086-8

    Article  Google Scholar 

  29. Zhang X, Zhao M, Wang K (2022) Understanding the influence of rock content on streaming potential phenomenon of soil-rock mixture: an experimental study. Sensors 22(2):585–585. https://doi.org/10.3390/s22020585

    Article  Google Scholar 

  30. Jin L, Zeng YW (2018) Refined simulation for macro-and meso-mechanical properties and failure mechanism of soil–rock mixture by 3D DEM. Chin J Rock Mech Eng 37(6):1540–1550. https://doi.org/10.13722/j.cnki.jrme.2017.1378

    Article  Google Scholar 

  31. Jin L, Cheng T, Zhang Y, Li JJ (2021) Three-dimensional lattice Boltzmann simulation of the permeability of soil–rock mixtures and comparison with other prediction models. Int J Numer Anal Meth Geomech 45(8):1067–1090. https://doi.org/10.1002/nag.3193

    Article  Google Scholar 

  32. Cai PC, Mao XS, Lou K, Yun ZH (2023) Lattice Boltzmann numerical study on mesoscopic seepage characteristics of soil–rock mixture considering size effect. Mathematics 11(8):1968. https://doi.org/10.3390/math11081968

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support provided by the National Natural Science Foundation of China (51878064), and the Key R & D and transformation plan of Qinghai Province (2021-SF-165).

Funding

National Natural Science Foundation of China,51878064,Xuesong Mao,Key R & D and transformation plan of Qinghai Province,2021-SF-165,Xuesong Mao

Author information

Authors and Affiliations

  1. College of Highway, Chang’an University, Xi’an, 710064, People’s Republic of China

    Pei-chen Cai, Xue-song Mao, Ze-yu Dai & Jing Fu

  2. Taiyuan Design Institute, China Railway Engineering Design Consulting Group Co., Ltd., Taiyuan, 030000, People’s Republic of China

    Ze-yu Dai

  3. China Merchants China Railway Holdings Co., Ltd., Nanning, 530201, People’s Republic of China

    Jing Fu

  4. Qinghai Traffic Investment Co., Ltd., Xining, 810000, People’s Republic of China

    Yi-ming Zhang & Xiao-qin Gong

Authors
  1. Pei-chen Cai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xue-song Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ze-yu Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jing Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yi-ming Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xiao-qin Gong
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

P-cC: analysis, resources, writing—original draft, writing—review and editing; X-sM: supervision, conventionalization, funding acquisition, writing—review and editing; Z-yD: writing—review and editing, data curation; JF: analysis, data curation; Y-mZ: analysis, funding acquisition; X-qG: analysis, funding acquisition.

Corresponding author

Correspondence to Xue-song Mao.

Ethics declarations

Conflict of interest

The authors declare that they have 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 (e.g. a society or other partner) 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

Cai, Pc., Mao, Xs., Dai, Zy. et al. Lattice Boltzmann simulation and mesoscopic mechanism analysis of permeability in soil-rock mixtures. Comp. Part. Mech. 11, 789–803 (2024). https://doi.org/10.1007/s40571-023-00653-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-023-00653-3

Keywords

Search

Navigation