Skip to main content
SpringerLink
Log in

A continuum model of drag and lift forces for inclined planes dragged through granular beds

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

Abstract

Both drag and lift forces impact an inclined plane when it is dragged through a granular bed. In this paper, the following results have been obtained: the drag and lift forces grow with the velocity of motion; when the immersion depth is constant, the inclination angle has no effect on drag force, however, the lift force increases linearly with this inclination angle. In order to describe this physical process macroscopically, a continuum wedge model based on the Coulomb model is established to predict drag and lift forces. Particularly, the dynamic friction angle in the assumed shear band is predicted as a function of both inclined angle and moving velocity.

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
Fig. 9

Similar content being viewed by others

References

  1. Goldsmith, J., Guo, H., Hunt, S.N., Tao, M., Koehler, S.: Drag on intruders in granular beds: A boundary layer approach. Physical Review E 88(3), 030201 (2013)

    Article  ADS  Google Scholar 

  2. Guo, H., Goldsmith, J., Delacruz, I., Tao, M., Luo, Y., Koehler, S.A.: Semi-infinite plates dragged through granular beds. Journal of Statistical Mechanics: Theory and Experiment 2012(07), P07013 (2012)

    Article  Google Scholar 

  3. Fang, Y.S., Chen, T.J., Wu, B.F.: Passive earth pressures with various wall movements. Journal of Geotechnical Engineering 120(8), 1307–1323 (1994)

    Article  Google Scholar 

  4. Percier, B., Manneville, S., McElwaine, J.N., Morris, S.W., Taberlet, N.: Lift and drag forces on an inclined plow moving over a granular surface. Physical Review E 84(5), 051302 (2011)

    Article  ADS  Google Scholar 

  5. Percier, B., Manneville, S., Taberlet, N.: Modeling a washboard road: From experimental measurements to linear stability analysis. Physical Review E 87(1), 012203 (2013)

    Article  ADS  Google Scholar 

  6. Taberlet, N., Morris, S.W., McElwaine, J.N.: Washboard road: the dynamics of granular ripples formed by rolling wheels. Physical review letters 99(6), 068003 (2007)

    Article  ADS  Google Scholar 

  7. Goldman, D.I., Umbanhowar, P.: Scaling and dynamics of sphere and disk impact into granular media. Physical Review E 77(2), 021308 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  8. Bitbol, A.F., Taberlet, N., Morris, S.W., McElwaine, J.N.: Scaling and dynamics of washboard roads. Physical Review E 79(6), 061308 (2009)

    Article  ADS  Google Scholar 

  9. Hewitt, I.J., Balmforth, N.J., McElwaine, J.N.: Granular and fluid washboards. Journal of Fluid Mechanics 692, 446–463 (2012)

    Article  ADS  Google Scholar 

  10. Mays, D.C., Faybishenko, B.A.: Washboards in unpaved highways as a complex dynamic system. Complexity 5(6), 51–60 (2000)

    Article  Google Scholar 

  11. Both, J.A., Hong, D.C., Kurtze, D.A.: Corrugation of roads. Physica A: Statistical Mechanics and its Applications 301(1), 545–559 (2001)

    Article  ADS  Google Scholar 

  12. Zhong, W.Z., He, K.J., Zhou, Z.Y., Xia, W., Li, Y.Y.: Calibration of the damping coefficient for the DEM simulation. Acta Physica Sinica 58(8), 5155–5161 (2009)

    Google Scholar 

  13. Jantzi, J., Olafsen, J.S.: Rotational statistics in granular flows of smooth cylindrical particles[J]. Granul. Matter 22(1), 1–7 (2020)

    Article  Google Scholar 

  14. Di-Ping, W., Xing-Xiang, L., Qin, Q., Ben, G., Yong, Z.:. Study on mechanical behavior of the transverse processing on a granular matter layer. Acta Physica Sinica 63(9), 098201 (2014)

    Google Scholar 

  15. Forterre, Y., Pouliquen, O.: Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  16. Maladen, R.D., Umbanhowar, P.B., Ding, Y., Masse, A., Goldman, D.I.: Granular lift forces predict vertical motion of a sand-swimming robot. In Robotics and Automation (ICRA), 2011 IEEE International Conference on (pp. 1398–1403). IEEE (2011, May).

  17. Trulsson, M., DeGiuli, E., Wyart, M.: Effect of friction on dense suspension flows of hard particles. Physical Review E 95(1), 012605 (2017)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

I would like to express my gratitude to all those who have helped me during the writing of the paper. Especially, I gratefully acknowledge the financial support of the National Natural Science Foundation of China.

Funding

This research was funded by National Natural Science Foundation of China, grant number 11702163; Shaanxi Province Key R&D Program, grant number 2020SF-430, 2019ZDLSF05-07, 2018ZDXM-SF-024, 2017ZDCXL-SF-03-01-01; Scientific Research Plan Projects of Shaanxi Education Department, grant number 19JK0174; and Research Foundation for Talented Scholars of Shaanxi University of Technology, grant number SLGQD2017-03.

Author information

Authors and Affiliations

  1. School of Civil Engineering and Architecture, Shaanxi University of Technology, Hanzhong, 723001, China

    Hong Guo, Jiangtao Fu, Rui Guo, Qian Xu & Hong Jiang

  2. China Electronic Research Institute of Engineering Investigations and Design, Xi’an, 710054, China

    Hong Guo & Nengyuan Chen

Authors
  1. Hong Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiangtao Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rui Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qian Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hong Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Nengyuan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

For research articles with several authors, a short paragraph specifying their individual contributions must be provided. The following statements should be used “conceptualization, Hong Guo; methodology, Hong Guo; software, Qian Xu, Hong Jiang; validation, Hong Guo; formal analysis, Rui Guo; resources, Nengyuan Chen; data curation, Qian Xu, Jiangtao Fu.; writing—original draft preparation, Hong Guo; writing—review and editing, Hong Guo, Rui Guo, Hong Jiang, Jiangtao Fu.”

Corresponding author

Correspondence to Hong Guo.

Ethics declarations

Conflict of interest

The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted

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

Guo, H., Fu, J., Guo, R. et al. A continuum model of drag and lift forces for inclined planes dragged through granular beds. Granular Matter 22, 62 (2020). https://doi.org/10.1007/s10035-020-01027-9

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-020-01027-9

Keywords

Search

Navigation