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 AbdullahEmail author
Original Paper


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.


Granular tunnel Granular bond order Tunnel stability Phase diagram 


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.


  1. 1.
    Møller, P.C.F., Bonn, D.: The shear modulus of wet granular matter. Europhys. Lett. 80, 1–5 (2007). 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). CrossRefGoogle Scholar
  6. 6.
    Pakpour, M., Habibi, M., Møller, P., Bonn, D.: How to construct the perfect sandcastle. Sci. Rep. 2, 2–4 (2012). 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). 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). ADSCrossRefGoogle Scholar
  10. 10.
    Tatyana, K.: Crab digging a hole in the sand.
  11. 11.
    Stellar, T.: Ghost crab digging a burrow at Braamspunt beach.
  12. 12.
  13. 13.
  14. 14.
  15. 15.
    Dotinga, R., Reporter, H.: Digging holes in the sand beach can be deadly.
  16. 16.
    Morgenstein, M., Karimi, F.: Sand collapse kills 9 year-old girl at Oregon beach.,
  17. 17.
    Stow, N.: Dad dies after beach sand tunnel collapsed on him as he played with his kids.
  18. 18.
    Heggie, T.W.: Sand hazards on tourist beaches. Travel Med. Infect. Dis. 11, 123–125 (2013). 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). 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). CrossRefGoogle Scholar
  23. 23.
    Mitarai, N., Nakanishi, H.: Granular flow: dry and wet. Eur. Phys. J. Spec. Top. 204, 5–17 (2012). 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). 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). 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). 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). 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). 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). 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). 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
    Email author
  1. 1.Department of PhysicsBandung Institute of TechnologyBandungIndonesia

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