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An Approximate Stress Distribution in a Conical Heap of Jammed Dry Granular Material

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Abstract

This paper develops an approximate stress distribution in a conical heap of jammed dry granular material loaded by gravity. An Eulerian formulation of elastic-inelastic response is used to explain why the residual stresses in the heap can be approximated by the current state of stress in the material. The proposed normalized stress components are functions of the normalized radial and vertical coordinates and are parameterized by only the angle of repose. It is shown that the vertical stress distribution applied to the base of the heap compares well with experiments using a rain procedure for sand deposition.

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References

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

    Article  Google Scholar 

  2. Baker, J.L., Barker, T., Gray, J.: A two-dimensional depth-averaged \(\mu ({I})\)-rheology for dense granular avalanches. J. Fluid Mech. 787, 367–395 (2016)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  3. Didwania, A., Cantelaube, F., Goddard, J.: Static multiplicity of stress states in granular heaps. R. Soc. Lond. Proc., Ser. A, Math. Phys. Eng. Sci. 456(2003), 2569–2588 (2000)

    Article  ADS  Google Scholar 

  4. Drucker, D.C., Prager, W.: Soil mechanics and plastic analysis or limit design. Q. Appl. Math. 10(2), 157–165 (1952)

    Article  MathSciNet  Google Scholar 

  5. Goddard, J.D.: Dissipative materials as models of thixotropy and plasticity. J. Non-Newton. Fluid Mech. 14, 141–160 (1984)

    Article  CAS  Google Scholar 

  6. Goddard, J.D.: Continuum modeling of granular assemblies: quasi-static dilatancy and yield. Phys. Dry Granul. Media, 1–24 (1998)

  7. Goddard, J.D.: Parametric hypoplasticity as continuum model for granular media: from stokesium to Mohr-coulombium and beyond. Granul. Matter 12(2), 145–150 (2010)

    Article  CAS  Google Scholar 

  8. Hollenstein, M., Jabareen, M., Rubin, M.B.: Modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration. Comput. Mech. 52, 649–667 (2013)

    Article  MathSciNet  Google Scholar 

  9. Hollenstein, M., Jabareen, M., Rubin, M.B.: Erratum to: modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration. Comput. Mech. 55, 453 (2015)

    Article  MathSciNet  Google Scholar 

  10. Jaeger, H.M., Nagel, S.R.: Physics of the granular state. Science 255(5051), 1523–1531 (1992)

    Article  ADS  CAS  PubMed  Google Scholar 

  11. Jaeger, H.M., Nagel, S.R., Behringer, R.P.: Granular solids, liquids, and gases. Rev. Mod. Phys. 68(4), 1259 (1996)

    Article  ADS  Google Scholar 

  12. Jop, P., Forterre, Y., Pouliquen, O.: A constitutive law for dense granular flows. Nature 441(7094), 727–730 (2006)

    Article  ADS  CAS  PubMed  Google Scholar 

  13. Miura, K., Maeda, K., Toki, S.: Method of measurement for the angle of repose of sands. Soil Found. 37(2), 89–96 (1997)

    Article  Google Scholar 

  14. Nguyen, T.: Statically admissible stress fields in conical sand valleys and heaps: a validation of Haar–von Kármán hypothesis. Int. J. Geomech. 23(2), 04022286 (2023)

    Article  Google Scholar 

  15. Nguyen, T., Pipatpongsa, T., Kitaoka, T., Ohtsu, H.: Stress distribution in conical sand heaps at incipient failure under active and passive conditions. Int. J. Solids Struct. 168, 1–12 (2019)

    Article  CAS  Google Scholar 

  16. Peters, J., Muthuswamy, M., Wibowo, J., Tordesillas, A.: Characterization of force chains in granular material. Phys. Rev. E 72(4), 041307 (2005)

    Article  ADS  CAS  Google Scholar 

  17. Pipatpongsa, T., Siriteerakul, S.: Analytic solutions for stresses in conical sand heaps piled up with perfect memory. J. Appl. Mech. 13, 343–354 (2010)

    Google Scholar 

  18. Rubin, M.B.: Removal of unphysical arbitrariness in constitutive equations for elastically anisotropic nonlinear elastic–viscoplastic solids. Int. J. Eng. Sci. 53, 38–45 (2012)

    Article  MathSciNet  Google Scholar 

  19. Rubin, M.B.: Continuum Mechanics with Eulerian Formulations of Constitutive Equations. Springer, Berlin (2021)

    Book  Google Scholar 

  20. Rubin, M.B., Attia, A.V.: Calculation of hyperelastic response of finitely deformed elastic-viscoplastic materials. Int. J. Numer. Methods Eng. 39, 309–320 (1996)

    Article  Google Scholar 

  21. Rubin, M.B., Ciambella, J., Nadler, B.: A unified continuum constitutive model for granular. Submitted to J. Mech. Sci. (2024)

  22. Safadi, M., Rubin, M.: A new analysis of stresses in arteries based on an Eulerian formulation of growth in tissues. Int. J. Eng. Sci. 118, 40–55 (2017)

    Article  MathSciNet  Google Scholar 

  23. Sun, J., Sundaresan, S.: A constitutive model with microstructure evolution for flow of rate-independent granular materials. J. Fluid Mech. 682, 590–616 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  24. Trulsson, M.: Rheology and shear jamming of frictional ellipses. J. Fluid Mech. 849, 718–740 (2018)

    Article  ADS  MathSciNet  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  26. Zhou, Z., Zou, R., Pinson, D., Yu, A.: Angle of repose and stress distribution of sandpiles formed with ellipsoidal particles. Granul. Matter 16, 695–709 (2014)

    Article  ADS  Google Scholar 

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  1. Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    M. B. Rubin

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Rubin, M.B. An Approximate Stress Distribution in a Conical Heap of Jammed Dry Granular Material. J Elast (2024). https://doi.org/10.1007/s10659-024-10054-z

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