Advertisement

Granular Matter

, 20:75 | Cite as

Stability of granular tunnel

  • Elfi Yuliza
  • Nadya Amalia
  • Handika Dany Rahmayanti
  • Rahmawati Munir
  • Muhammad Miftahul Munir
  • Khairurrijal Khairurrijal
  • Mikrajuddin Abdullah
Original Paper
  • 118 Downloads

Abstract

We demonstrated that the stability of tunnels made of granular matter is strongly dependent on the grain size, tunnel diameter, and water content inside the granules. Larger tunnel radius, larger grain size, and too much water content tend to destabilize the tunnel. We also developed a model to describe such findings. We identified a phase diagram of stability which is significantly controlled by the granular bond order. For granular bond order of above unity, we always able to build a stable tunnel. For granular bond order of less than unity, we obtained a general expression for estimating the maximum thickness of the stable tunnel. The phenomena related to granular tunnel stability have occurred in human activities (such as a collapse of the sand hole made on the beach) as well as in living animals (such as burrows dug by crabs, antlions, mongoose, beetles, turtles, or some species of rats). To the best of our knowledge, this work is the first exploration regarding the stability of the granular tunnel.

Keywords

Granular tunnel Granular bond order Tunnel stability Phase diagram 

Notes

Compliance with ethical standards

Conflict of interest

This article is original. The corresponding author confirms that all of the other authors have read and approved the manuscript and no conflict of interest involved.

References

  1. 1.
    Møller, P.C.F., Bonn, D.: The shear modulus of wet granular matter. Europhys. Lett. 80, 1–5 (2007).  https://doi.org/10.1209/0295-5075/80/38002 CrossRefGoogle Scholar
  2. 2.
    Mason, T.G., Levine, A.J., Ertaş, D., Halsey, T.C.: Critical angle of wet sandpiles. Phys. Rev. E 60, 5044–5047 (1999)ADSCrossRefGoogle Scholar
  3. 3.
    Hornbaker, D.J., Albert, R., Albert, I., Barabási, A.-L., Schiffer, P.: What keeps sandcastles standing ? Nature 387, 765 (1997)ADSCrossRefGoogle Scholar
  4. 4.
    Schiffer, P.: A bridge to sandpile stability. Nat. Phys. 1, 21–22 (2005)CrossRefGoogle Scholar
  5. 5.
    Lefebvre, G., Jop, P.: Erosion dynamics of a wet granular medium. Phys. Rev. E 88, 1–9 (2013).  https://doi.org/10.1103/PhysRevE.88.032205 CrossRefGoogle Scholar
  6. 6.
    Pakpour, M., Habibi, M., Møller, P., Bonn, D.: How to construct the perfect sandcastle. Sci. Rep. 2, 2–4 (2012).  https://doi.org/10.1038/srep00549 CrossRefGoogle Scholar
  7. 7.
    Nowak, S., Samadani, A., Kudrolli, A.: Maximum angle of stability of a wet granular pile. Nat. Phys. 1, 50–52 (2005).  https://doi.org/10.1038/nphys106 CrossRefGoogle Scholar
  8. 8.
    Halsey, T.C., Levine, A.J.: How sandcastles fall. Phys. Rev. Lett. 80, 3141–3144 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    Scheel, M., Seemann, R., Brinkmann, M., Michiel, M.D.I., Sheppard, A., Breidenbach, B., Herminghaus, S.: Morphological clues to wet granular pile stability. Nat. Mater. 7, 189–193 (2008).  https://doi.org/10.1038/nmat2117 ADSCrossRefGoogle Scholar
  10. 10.
    Tatyana, K.: Crab digging a hole in the sand. https://www.youtube.com/watch?v=oUn8cmgFiOQ
  11. 11.
    Stellar, T.: Ghost crab digging a burrow at Braamspunt beach. https://www.youtube.com/watch?v=oUn8cmgFiOQ
  12. 12.
  13. 13.
  14. 14.
  15. 15.
    Dotinga, R., Reporter, H.: Digging holes in the sand beach can be deadly. https://abcnews.go.com/Health/Healthday/story?id=4507651&page=1
  16. 16.
    Morgenstein, M., Karimi, F.: Sand collapse kills 9 year-old girl at Oregon beach. https://edition.cnn.com/2014/08/31/us/oregon-beach-collapse/index.html,
  17. 17.
    Stow, N.: Dad dies after beach sand tunnel collapsed on him as he played with his kids. https://www.thesun.co.uk/news/5474400/lee-goggin-dead-sand-tunnel-beach-irving-texas-children/
  18. 18.
    Heggie, T.W.: Sand hazards on tourist beaches. Travel Med. Infect. Dis. 11, 123–125 (2013).  https://doi.org/10.1016/j.tmaid.2012.12.001 CrossRefGoogle Scholar
  19. 19.
    Maton, B.A., Haas, T.S., Maron, B.J.: Sudden death from collapsing sand holes. N. Engl. J. Med. 356, 2655–2656 (2007)CrossRefGoogle Scholar
  20. 20.
    Zarroug, A.E., Stavlo, P.L., Kays, G.A., Rodeberg, D.A., Moir, C.R.: Accidental burials in sand: a potentially fatal summertime hazard. Mayo Clin. Proc. 79, 774–776 (2004).  https://doi.org/10.4065/79.6.774 CrossRefGoogle Scholar
  21. 21.
    Castellanos, A.: The relationship between attractive interparticle forces and bulk behaviour in dry and uncharged fine powders. Adv. Phys. 54, 263–376 (2005)ADSCrossRefGoogle Scholar
  22. 22.
    Carstensen, J.T., Chan, P.C.: Relation between particle size and repose angles of powders. Powder Technol. 15, 129–131 (1976).  https://doi.org/10.1016/0032-5910(76)80037-X CrossRefGoogle Scholar
  23. 23.
    Mitarai, N., Nakanishi, H.: Granular flow: dry and wet. Eur. Phys. J. Spec. Top. 204, 5–17 (2012).  https://doi.org/10.1140/epjst/e2012-01548-8 CrossRefGoogle Scholar
  24. 24.
    Gladkyy, A., Schwarze, R.: Comparison of different capillary bridge models for application in the discrete element method. Granul. Matter 16, 911–920 (2014).  https://doi.org/10.1007/s10035-014-0527-z CrossRefGoogle Scholar
  25. 25.
    Denkov, N.D., Ivanov, I.B., Kralchevsky, P.A.: A possible mechanism of stabilization of emulsions by solid particles. J. Colloid Interface Sci. 150, 589–593 (1992)ADSCrossRefGoogle Scholar
  26. 26.
    Lian, G., Thornton, C., Adams, M.J.: A theoretical study of the liquid bridge forces between two rigid spherical bodies. J. Colloid Interface Sci. 161, 138–147 (1993)ADSCrossRefGoogle Scholar
  27. 27.
    Kudrolli, A.: Sticky sand. Nat. Mater. 7, 174–175 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    Lambe, T.W., Whitman, R.: V: Soil Mechanics. Wiley, New York (1969)Google Scholar
  29. 29.
    Fournier, Z., Geromichalos, D., Herminghaus, S., Kohonen, M.M., Mugele, F., Scheel, M., Schulz, M., Schulz, B., Schier, C., Seemann, R., Skudelny, A.: Mechanical properties of wet granular materials. J. Phys.: Condens. Matter 477, S477–S502 (2005).  https://doi.org/10.1088/0953-8984/17/9/013 CrossRefGoogle Scholar
  30. 30.
    Li, J., Cao, Y., Xia, C., Kou, B., Xiao, X., Fezzaa, K., Wang, Y.: Similarity of wet granular packing to gels. Nat. Commun. 5, 1–7 (2014).  https://doi.org/10.1038/ncomms6014 ADSCrossRefGoogle Scholar
  31. 31.
    Mikrajuddin, A., Shi, F.G., Chungpaiboonpatana, S., Okuyama, K., Davidson, C., Adams, J.M.: Onset of electrical conduction in isotropic conductive adhesives: a general theory. Mater. Sci. Semicond. Process. 2, 309–319 (2000)CrossRefGoogle Scholar
  32. 32.
    Mikrajuddin, Shi, F.G., Okuyama, K.: Electrical conduction in insulator particle—solid-state ionic and conducting particle-insulator matrix composites: a unified theory. J. Electrochem. Soc. 147, 3157–3165 (2000)CrossRefGoogle Scholar
  33. 33.
    Abdullah, M., Lenggoro, I.W., Okuyama, K., Shi, F.G.: In situ synthesis of polymer nanocomposite electrolytes emitting a high luminescence with a tunable wavelength. J. Phys. Chem. B 107, 1957–1961 (2003).  https://doi.org/10.1021/jp022223c CrossRefGoogle Scholar
  34. 34.
    Harthong, B., Jérier, J., Dorémus, P., Imbault, D., Donzé, F.: Modeling of high-density compaction of granular materials by the Discrete Element Method. Int. J. Solids Struct. 46, 3357–3364 (2009).  https://doi.org/10.1016/j.ijsolstr.2009.05.008 CrossRefzbMATHGoogle Scholar
  35. 35.
    Groger, T., Tuzun, U., Heyes, D.M.: Modelling and measuring of cohesion in wet granular materials. Powder Technol. 133, 203–215 (2003).  https://doi.org/10.1016/S0032-5910(03)00093-7 CrossRefGoogle Scholar
  36. 36.
    Weigert, T., Ripperger, S.: Calculation of the liquid bridge volume and bulk saturation from the half-filling angle. Part. Part. Syst. Charact. 16, 238–242 (1999)CrossRefGoogle Scholar
  37. 37.
    Willett, C.D., Adams, M.J., Johnson, S.A., Seville, J.P.K.: Capillary bridges between two spherical bodies. Langmuir 16, 9396–9405 (2000)CrossRefGoogle Scholar
  38. 38.
    Rabinovich, Y.I., Esayanur, M.S., Moudgil, B.M.: Capillary forces between two spheres with a fixed volume liquid bridge: theory and experiment. Langmuir 21, 10992–10997 (2005)CrossRefGoogle Scholar
  39. 39.
    Cox, S.J., McCarthy, C.: The shape of the tallest column. SIAM J. Math. Anal. 29, 547–554 (1998).  https://doi.org/10.1137/S0036141097314537 MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Elfi Yuliza
    • 1
  • Nadya Amalia
    • 1
  • Handika Dany Rahmayanti
    • 1
  • Rahmawati Munir
    • 1
  • Muhammad Miftahul Munir
    • 1
  • Khairurrijal Khairurrijal
    • 1
  • Mikrajuddin Abdullah
    • 1
  1. 1.Department of PhysicsBandung Institute of TechnologyBandungIndonesia

Personalised recommendations