Skip to main content
SpringerLink
Log in

The experiment and analysis of the repose angle and the stress arch-caused stress dip of the sandpile

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

The repose angle and characteristics of the vertical stress distribution beneath the sandpile can help to understand the physical and mechanical properties of the granular matter and guide the foundation design of the rock-soil deposits such as the rockfill dam and the storage structures of granular materials. Researches previously found that the stress dip phenomenon exists in piles constructed by the localized-source procedure, where the maximum vertical stress underneath the pile deviates from the center. The repose angle and the stress dip are affected by many internal and external factors and exhibit highly nonlinear and sensitive characteristics. However, the variation of the repose angle and the stress dip with influencing factors and the cause of the stress dip have not yet been fully explored. Based on the localized-source conical sandpile experiments and the discrete element method (DEM) simulation analysis, this paper studied the influences of the internal friction angle of granular matter and the construction history (the slowly raising funnel method SRFM and the fixed funnel method FFM) on the repose angle and the vertical stress dip beneath the pile; while the formation mechanism of the stress dip phenomenon was analyzed. The experimental results showed that the repose angle, physically different from the internal friction angle, has a relatively larger value and is positively related to the internal friction angle in the sandpile constructed by the FFM; the localized-source procedure and the internal friction angle are conducive to the formation of the macroscopic force chain arch structure in granular matter, which produces the arching effect and the stress shielding effect and leads to the stress dip beneath the pile; and the ratio of the stress dip RSD decreases with the increase of the local impact effect and the internal friction angle.

Graphic abstract

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

Similar content being viewed by others

References

  1. Gennes. P. G. D.: Granular matter: a tentative view. Rev. Mod. Phys. 71(2) (1999).

  2. Fang, Y., Li, B.: Multiscale problems and analysis of soil mechanics. Mech. Mater. 103, 55–67 (2016)

    Article  Google Scholar 

  3. Feng, D., Fang, Y.: Theoretical analysis and experimental research on multiscale mechanical properties of soil. Int. J. Geomech. 16(4), 04015094 (2016)

    Article  MathSciNet  Google Scholar 

  4. Kadanoff, L.P.: Built upon sand: theoretical ideas inspired by granular flows. Rev. Mod. Phys. 71(1), 435–444 (1999)

    Article  ADS  Google Scholar 

  5. Metcalf, J.R.: Angle of repose and internal friction. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 3(2), 155–161 (1966)

    Article  Google Scholar 

  6. Rackl, M., Grtsch, F.E., Willibald A. G.: Angle of repose revisited: when is a heap a cone? In: Powders and Grains —International Conference on Micromechanics on Granular Media (2017)

  7. Hamzah, M., Beakawi Al-Hashemi, O.S., Al-Amoudi, B.: A review on the angle of repose of granular materials. Powder Technol., 330, 397–417 (2018).

  8. Zhou, Z.Y., Zou, R.P., Pinson, D., Yu, A.B.: Angle of repose and stress distribution of sandpiles formed with ellipsoidal particles. Granular Matter 16(5), 695–709 (2014)

    Article  ADS  Google Scholar 

  9. Dai, B.B., Yang, J., Zhou, C.Y.: Micromechanical origin of angle of repose in granular materials. Granular Matter 19(2), 24 (2017)

    Article  Google Scholar 

  10. Shorts, D.C., Feitosa, K.: Experimental measurement of the angle of repose of a pile of soft frictionless grains. Granular Matter 20(1), 2 (2018)

    Article  Google Scholar 

  11. Liu, M., Dong, P., Zhong, R.: A rapid method for estimating the angle of repose and volume of grain piles using terrestrial laser scanning. Remote Sensing Lett. 11(7), 707–713 (2020)

    Article  ADS  Google Scholar 

  12. Mitchell, J.K., Soga, K.: Fundamentals of Soil Behavior (Vol. 3). New York (2005).

  13. K. Terzaghi.: Theoretical soil mechanics. USA (1943).

  14. George, H., Hentschel, E., Prabhat, K.J., Chandana, M., Itamar, P., Jacques, Z.: The sandpile revisited: computer assisted determination of constitutive relations and the breaking of scaling. Soft Matter 13, 5008–5020 (2017)

    Article  Google Scholar 

  15. Zhao, H., An, X., Dong, K., Yang, R., Xu, F., Fu, H., et al.: Macro-and microscopic analyses of piles formed by Platonic solids. Chem. Eng. Sci. 205, 391–400 (2019)

    Article  Google Scholar 

  16. Zhao, H., An, X., Gou, D., Zhao, B., Yang, R.: Attenuation of pressure dips underneath piles of spherocylinders. Soft Matter 14(21), 4404–4410 (2018)

    Article  ADS  Google Scholar 

  17. Wittmer, J.P., Claudin, P., Cates, M.E., Bouchaud, J.P.: An explanation for the central stress minimum in sand piles. Nature 382(6589), 336–338 (1996)

    Article  ADS  Google Scholar 

  18. Watson, A.: Searching for the sand-pile pressure dip. Science 273(5275), 579–580 (1996)

    Article  ADS  Google Scholar 

  19. Cates, M.E., Wittmer, J.P., Bouchaud, J.P., Claudin, P.: Jamming and static stress transmission in granular materials. Chaos Interdiscip. J. Nonlinear Sci. 9(3), 511–522 (1999)

    Article  Google Scholar 

  20. Liu, Y., Yeung, A.T., Ding, L., Yan, R.: Experimental study on the effect of particle shape on stress dip in granular piles. Powder Technol. 319, 415–425 (2017)

    Article  Google Scholar 

  21. Vanel, L., Howell, D., Clark, D., Behringer, R.P., Clément, E.: Memories in sand: experimental tests of construction history on stress distributions under sandpiles. Phys. Rev. E 60(5), R5040 (1999)

    Article  ADS  Google Scholar 

  22. Geng, J., Longhi, E., Behringer, R.P., Howell, D.W.: Memory in two-dimensional heap experiments. Phys. Rev. E 64, 060301 (2001)

    Article  ADS  Google Scholar 

  23. Altshuler, E., Ramos, O., Martínez, E., Batista-Leyva, A.J., Rivera, A., Bassler, K.E.: Sandpile formation by revolving rivers. Phys. Rev. Lett. 91(1), 014501 (2003)

    Article  ADS  Google Scholar 

  24. Krimer, D.O., Pfizner, M., Brauer, K., et al.: Granular elasticity: general considerations and stress dip in sand piles. Phys. Rev. E 74, 061310 (2006)

    Article  ADS  Google Scholar 

  25. Jiang, Y., Liu, M.: From elasticity to hypoplasticity: dynamics of granular solids. Phys. Rev. Lett. 99(10), 105501.1–10550.14 (2007)

    ADS  Google Scholar 

  26. Jiang, Y., Liu, M.: Granular solid hydrodynamics. Granular Matter 11(3), 139–156 (2009)

    Article  Google Scholar 

  27. Bouchaud, J.P., Cates, M.E., Claudin, P.: Stress distribution in granular media and nonlinear wave equation. J. Phys. I 5(6), 639–656 (1995)

    Google Scholar 

  28. Zheng, Q., Yu, A.: Why have continuum theories previously failed to describe sandpile formation? Phys. Rev. Lett. 113(6), 068001 (2014)

    Article  ADS  Google Scholar 

  29. Horabik, J., Parafiniuk, P., Molenda, M.: Discrete element modeling study of force distribution in a 3D pile of spherical particles. Powder Technol. 312, 194–203 (2017)

    Article  Google Scholar 

  30. Atman, A.P.F., Brunet, P., Geng, J., Reydellet, G., Clauidn, P., Behringer, R.P., Clément, E.: From the stress reponse function (back) to the sand pile “dip.” Eur. Phys. J. E. 17, 93–100 (2005)

    Article  Google Scholar 

  31. Peters, J.F., Muthuwamy, M., Wibowo, J., Tordesillas, A.: Characterization of force chains in granular material. Phys. Rev. E 72, 041307 (2005)

    Article  ADS  Google Scholar 

  32. Campbell, C.S.: A problem related to stability of force chains. Granular Matter 5, 129–134 (2003)

    Article  Google Scholar 

  33. Sanfratello, L., Fukushima, E., Behringer, R.P.: Using MR elastography to image the 3D force chain structure of a quasi-static granular assembly. Granular Matter 11, 1–6 (2009)

    Article  Google Scholar 

  34. Fu, L., Zhou, S., Guo, P., Wang, S., Luo, Z.: Induced force chain anisotropy of cohesionless granular materials during biaxial compression. Granular Matter 21, 52 (2019)

    Article  Google Scholar 

  35. Zuriguel, I., Mullin, T.: Effect of particle shape on stress dip under a sandpile. Phys. Rev. Lett. 98, 028001 (2007)

    Article  ADS  Google Scholar 

  36. Zuriguel, I., Mullin, T.: The role of particle shape on the stress distribution in a sandpile. Proc. R. Soc. A. 464, 99–116 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  37. Ostojic, S., Somfai, E., Nienhuis, B.: Scale invariance and universality of force networks in static granular matter. Nature 439, 828–830 (2006)

    Article  ADS  Google Scholar 

  38. Grima, A.P., Wypych, P.W.: Discrete element simulations of granular pile formation. Eng. Comput. 28(3), 314–339 (2011)

    Article  Google Scholar 

  39. Fang, Y., Guo, L., Hou, M.: Arching effect analysis of granular media based on force chain visualization. Powder Technol. 363, 621–628 (2020)

    Article  Google Scholar 

  40. Silbert, L.E., Grest, G.S., Landry, J.W.: Statistics of contact network in frictional and frictionless granular packings. Phys. Rev. E 66, 061303 (2002)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to acknowledge financial support from the State Key Lab of Subtropical Building Science, South China University of Technology (Grant No.2017 KB16), the National Key Scientific Instruments and Equipment Development Projects of China (Grant No.41827807), and the Open Research Fund of the State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant No. Z018019).

Author information

Authors and Affiliations

  1. School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, Guangdong, China

    Yingguang Fang, Xiaolong Li, Lingfeng Guo & Renguo Gu

  2. State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou, Guangdong, China

    Yingguang Fang & Renguo Gu

  3. China Railway Eryuan Engineering Group Co., LTD, Chengdu, Sichuan, China

    Weizhou Luo

Authors
  1. Yingguang Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaolong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lingfeng Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Renguo Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Weizhou Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lingfeng Guo.

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fang, Y., Li, X., Guo, L. et al. The experiment and analysis of the repose angle and the stress arch-caused stress dip of the sandpile. Granular Matter 24, 7 (2022). https://doi.org/10.1007/s10035-021-01171-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-021-01171-w

Keywords

Search

Navigation