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Tensile stress relaxation in unsaturated granular materials


The mechanics of granular media at low liquid saturation levels remain poorly understood. Macroscopic mechanical properties are affected by microscale forces and processes, such as capillary forces, inter-particle friction, liquid flows, and particle movements. An improved understanding of these microscale mechanisms is important for a range of industrial applications and natural phenomena (e.g. landslides). This study focuses on the transient evolution of the tensile stress of unsaturated granular media under extension. Experimental results suggest that the stress state of the material evolves even after cessation of sample extension. Moreover, we observe that the packing density strongly affects the efficiency of different processes that result in tensile stress relaxation. By comparing the observed relaxation time scales with published data, we conclude that tensile stress relaxation is governed by particle rearrangement and fluid redistribution. An increased packing density inhibits particle rearrangement and only leaves fluid redistribution as the major process that governs tensile stress relaxation.

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  1. 1.

    Carr, J.F.: Tensile strength of granular materials. Nature 213(5081), 1158–1159 (1967)

  2. 2.

    Fisher, R.A.: On the capillary forces in an ideal soil; correction of formulae given by W. B. Haines. J. Agric. Sci. 16, 492–505 (1926)

  3. 3.

    François, D., Pineau, A., Zaoui, A.: Mechanical Behaviour of Materials. Springer, Berlin (2012)

  4. 4.

    German, R.M.: Coordination number changes during powder densification. Powder Technol. 253, 368–376 (2014)

  5. 5.

    Haines, W.B.: Studies in the physical properties of soils: II. A note on the cohesion developed by capillary forces in an ideal soil. J. Agric. Sci. 15, 529–535 (1925)

  6. 6.

    Hartley, R.R., Behringer, R.P.: Logarithmic rate dependence of force networks in sheared granular materials. Nature 421(6926), 928–931 (2003)

  7. 7.

    Herminghaus, S.: Dynamics of wet granular matter. Adv. Phys. 54(3), 221–261 (2005)

  8. 8.

    Hornbaker, D.J., Albert, R., Albert, I., Barabási, A.L., Schiffer, P.: What keeps sandcastles standing? Nature 387, 765 (1997)

  9. 9.

    Iveson, S.M., Litster, J.D., Hapgood, K., Ennis, B.J.: Nucleation, growth and breakage phenomena in agitated wet granulation processes: a review. Powder Technol. 117(12), 3–39 (2001)

  10. 10.

    Kim, T.H., Hwang, C.: Modeling of tensile strength on moist granular earth material at low water content. Eng. Geol. 69(34), 233–244 (2003)

  11. 11.

    Kohonen, M.M., Geromichalos, D., Scheel, M., Schier, C., Herminghaus, S.: On capillary bridges in wet granular materials. Phys. A Stat. Mech. Appl. 339(12), 7–15 (2004)

  12. 12.

    Kohonen, M.M., Maeda, N., Christenson, H.K.: Kinetics of capillary condensation in a nanoscale pore. Phys. Rev. Lett. 82, 4667–4670 (1999)

  13. 13.

    Kristensen, H., Holm, P., Schaefer, T.: Mechanical properties of moist agglomerates in relation to granulation mechanisms part II. Effects of particle size distribution. Powder Technol. 44(3), 239–247 (1985)

  14. 14.

    Labajos-Broncano, L., Antequera-Barroso, J., González-Martín, M., Bruque, J.: An experimental study about the imbibition of aqueous solutions of low concentration of a non-adsorbable surfactant in a hydrophilic porous medium. J. Colloid Interface Sci. 301(1), 323–328 (2006)

  15. 15.

    Lambert, P., Chau, A., Delchambre, A., Régnier, S.: Comparison between two capillary forces models. Langmuir 24(7), 3157–3163 (2008)

  16. 16.

    Lian, G., Seville, J.: The capillary bridge between two spheres: new closed-form equations in a two century old problem. Adv. Colloid Interface Sci. 227, 53–62 (2016)

  17. 17.

    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(1), 138–147 (1993)

  18. 18.

    Lu, N., Wu, B., Tan, C.: Tensile strength characteristics of unsaturated sands. J. Geotech. Geoenviron. Eng. 133(2), 144–154 (2007)

  19. 19.

    Mani, R., Kadau, D., Herrmann, H.: Liquid migration in sheared unsaturated granular media. Granul. Matter 15(4), 447–454 (2013)

  20. 20.

    Mani, R., Kadau, D., Or, D., Herrmann, H.J.: Fluid depletion in shear bands. Phys. Rev. Lett. 109, 248001 (2012)

  21. 21.

    Mani, R., Semprebon, C., Kadau, D., Herrmann, H.J., Brinkmann, M., Herminghaus, S.: Role of contact-angle hysteresis for fluid transport in wet granular matter. Phys. Rev. E 91, 042204 (2015)

  22. 22.

    Mitarai, N., Nori, F.: Wet granular materials. Adv. Phys. 55(1–2), 1–45 (2006)

  23. 23.

    Pierrat, P., Agrawal, D.K., Caram, H.S.: Effect of moisture on the yield locus of granular materials: theory of shift. Powder Technol. 99(3), 220–227 (1998)

  24. 24.

    Pierrat, P., Caram, H.S.: Tensile strength of wet granula materials. Powder Technol. 91(2), 83–93 (1997)

  25. 25.

    Rumpf, H.: Agglomeration, pp. 379–418. Interscience, New York (1962)

  26. 26.

    Scheel, M.: Experimental Investigations of the Mechanical Properties of Wet Granular Matter. Ph.D. thesis, Georg-August-Universität Göttingen (2009)

  27. 27.

    Scheel, M., Seemann, R., Brinkmann, M., Di Michiel, M., Sheppard, A., Breidenbach, B., Herminghaus, S.: Morphological clues to wet granular pile stability. Nat. Mater. 7(3), 189–193 (2008)

  28. 28.

    Scheel, M., Seemann, R., Brinkmann, M., Di Michiel, M., Sheppard, A., Herminghaus, S.: Liquid distribution and cohesion in wet granular assemblies beyond the capillary bridge regime. J. Phys. Condens. Matter 20(49), 494,236 (2008)

  29. 29.

    Schiffer, P.: A bridge to sandpile stability. Nat. Phys. 1, 21–22 (2005)

  30. 30.

    Schubert, H., Herrmann, W., Rumpf, H.: Deformation behaviour of agglomerates under tensile stress. Powder Technol. 11(2), 121–131 (1975)

  31. 31.

    Seemann, R., Mönch, W., Herminghaus, S.: Liquid flow in wetting layers on rough substrates. Europhys. Lett. 55, 698–704 (2001)

  32. 32.

    Takenaka, H., Kawashima, Y., Hishida, J.: The effects of interfacial physical properties on the cohesive forces of moist powder in air and in liquid. Chem. Pharm. Bull. 29(9), 2653–2660 (1981)

  33. 33.

    Turba, E., Rumpf, H.: Zugfestigkeit von preßlingen mit vorwiegender bindung durch van der waals-kräfte und ihre beeinflussung durch adsorptionsschichten. Chem. Ing. Tech. 36(3), 230–240 (1964)

  34. 34.

    Utter, B., Behringer, R.: Transients in sheared granular matter. Euro. Phys. J. E 14(4), 373–380 (2004)

  35. 35.

    Willett, C.D., Adams, M.J., Johnson, S.A., Seville, J.P.K.: Capillary bridges between two spherical bodies. Langmuir 16(24), 9396–9405 (2000)

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We acknowledge financial support from the European Research Council (ERC) Advanced Grant Nos. 319968 FlowCCS. The technical assistance of Daniel Breitenstein in constructing the experimental apparatus is greatly appreciated.

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Correspondence to Filippo Bianchi.

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Bianchi, F., Thielmann, M., Mani, R. et al. Tensile stress relaxation in unsaturated granular materials. Granular Matter 18, 75 (2016). https://doi.org/10.1007/s10035-016-0673-6

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  • Tensile stress
  • Capillary forces
  • Capillary bridges
  • Fluid redistribution
  • Grain rearrangement
  • Granular material