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The contact properties of naturally occurring geologic materials: contact law development

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Abstract

This effort develops contact laws and presents material-specific parameters for those laws for several granular geologic and two manufactured materials. The normal contact law includes a Hertzian elastic term and a linear delayed elastic (anelastic) term which accounts for hysteresis. The shear contact law contains terms for elastic and anelastic deformation and an additional nonlinear term for inelastic (permanent) deformation that acts above an experimentally determined threshold ratio of shear to normal force at the contact. The contact laws have been formulated for arbitrary, quasistatic loading paths and are shown to capture the behavior observed in grain-to-grain contact experiments under monotonic and cyclic loading. The findings are based on the results of previously published normal and shear contact experiments on four naturally occurring quartz sands, magnesite (limestone), crushed and ball-milled gneiss, ooids (precipitated calcium carbonate spheroids), glass beads and a synthetic (Delrin). A companion paper presents the implementation of these laws in a discrete element simulation of a standard geotechnical triaxial cell and validates the simulations with physical triaxial experiments.

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References

  1. Cole, D.M., Hopkins, M.A.: The contact properties of naturally occurring geologic materials: experimental observations. Granul. Matter 18, 62 (2016). doi:10.1007/s10035-016-0658-5

    Article  Google Scholar 

  2. Cole, D.M.: Laboratory observations of frictional sliding of individual contacts in geologic materials. Granul. Matter 17, 95–110 (2015). doi:10.1007/s10035-014-0526-0

    Article  Google Scholar 

  3. Cole, D.M., Hopkins, M.A.: Contact properties of naturally occurring grains: Experiments and discrete element modeling. In: Nakagawa, M., Luding, S. (eds.) Proceedings of the 6th International Conference on micromechanics of granular media, pp. 351–354. American Institute of Physics (2009)

  4. Yan, B., Regueiro, R.A., Sture, S.: Three dimensional discrete element modeling of granular materials and its coupling with finite element facets. Eng. Comput. 27(4), 519–550 (2010). doi:10.1108/02644401011044603

    Article  MATH  Google Scholar 

  5. Mindlin, R.D., Mason, P., Osmer, T.F., Deresiewicz, H.: Effects of an oscillating tangential force on the contact surfaces of elastic spheres. In: Proceedings of 1st U.S. National Congress of Applied Mechanics, pp. 203–208 (1951)

  6. Mindlin, R.D., Deresiewicz, H.: Elastic spheres in contact under varying oblique forces. ASME J. Appl. Mech. 20, 327–344 (1953)

    MathSciNet  MATH  Google Scholar 

  7. Deresiewicz, H.: Stress-strain relations for a simple model of a granular medium. J. Appl. Mech. 25, 402–406 (1958)

    MATH  Google Scholar 

  8. Johnson, K.L.: Contact Mechanics. Cambridge University Press, London (1985). 452p

    Book  MATH  Google Scholar 

  9. Johnson, K.L.: Surface interaction between elastically loaded bodies under tangential forces. Proc. R. Soc. Ser. A 230(1183), 531–548 (1955)

    Article  ADS  Google Scholar 

  10. Bureau, L., Caroli, C., Baumberger, T.: Elasticity and onset of frictional dissipation at a non-sliding multi-contact interface. Proc. R. Soc. Lond. A 459, 2787–2805 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Mindlin, R.D.: Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259–268 (1949)

    MathSciNet  MATH  Google Scholar 

  12. Spence, D.A.: The Hertz contact problem with finite friction. J. Elast. 5(3–4), 297–319 (1975)

    Article  MATH  Google Scholar 

  13. Greenwood, J.A., Johnson, K.L., Matsubara, E.: A surface roughness parameter in Hertz contact. Wear 100, 47–57 (1984)

    Article  Google Scholar 

  14. Liu, G., Wang, Q., Lin, C.: A survey of current models for simulating the contact between rough surfaces. Tribol. Trans. 42(3), 581–591 (1999)

    Article  Google Scholar 

  15. Batrouni, G.G., Hansen, A., Schmittbuhl, J.: Elastic response of rough surfaces in partial contact. Europhys. Lett. 60(5), 724–730 (2002)

    Article  ADS  Google Scholar 

  16. Cundall, P.A., Strack, O.D.L.: A discrete element model for granular assemblies. Geotechnique 29(1), 47–65 (1979)

  17. Chang, C.S., Sundaram, S.S., Misra, A.: Initial moduli of particulated mass with frictional contacts. Int. J. Numer. Anal. Methods Geomech. 13, 629–644 (1989)

  18. Chang, C.S., Misra, A., Sundaram, S.S.: Properties of granular packings under low amplitude cyclic loading. Soil Dyn. Earthq. Eng. 10(4), 201–211 (1991)

    Article  Google Scholar 

  19. Jiang, M., Leroueil, S., Zhu, H., Yu, H.-S., Konrad, J.-M.: Two-dimensional discrete element theory for rough particles. Int. J. Geomech. 9(1), 20–33 (2009)

    Article  Google Scholar 

  20. O’Sullivan, C., Cui, L.: Micromechanics of granular material response during load reversals: combined DEM and experimental study. Powder Technol. 193, 289–302 (2009)

    Article  Google Scholar 

  21. Cole, D.M., Peters, J.F.: Grain-scale mechanics of geologic materials and lunar simulants under normal loading. Granul. Matter 10, 171–185 (2008). doi:10.1007/s10035-007-0066-y

    Article  Google Scholar 

  22. Cole, D.M., Uthus, L., Hopkins, M.A., Knapp, B.R.: Normal and sliding contact experiments on gneiss. Granul. Matter 1434-5021 (Print) 1434-7636 (Online) (2010) doi:10.1007/s10035-010-0165-z

  23. Cole, D.M., Peters, J.F.: A physically based approach to granular media mechanics: grain-scale experiments, initial results and implications to numerical modeling. Granul. Matter 9(5), 309–321 (2007). doi:10.1007/s10035-007-0046-2

    Article  Google Scholar 

  24. Bhushan, B.: Contact mechanics of rough surfaces in tribology—multiple asperity contact. Tribol. Lett. 4, 1–35 (1998)

    Article  Google Scholar 

  25. Barber, J.R., Ciavarella, M.: Contact mechanics. Int. J. Solids Struct. 37, 29–43 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  26. Misra, A.: Modeling of rough contacts in geomaterials. In: Proceedings of 14th Engineering Mechanics Conference, ASCE, Austin, TX, 6p (2000)

  27. Persson, B.N.J.: Contact mechanics for randomly rough surfaces. Surf. Sci. Rep. 61, 201–227 (2006)

    Article  ADS  Google Scholar 

  28. Alshibli, K.A., Alsaleh, M.I.: Characterizing surface roughness and shape of sands using digital microscopy. ASCE J. Comput. Civ. Eng. 18, 36–45 (2004)

    Article  Google Scholar 

  29. Brendel, L., Dippel, S.: Lasting contacts in molecular dynamics simulations. In: Physics of Dry Granular Media, vol. 350 of NATO ASI Series, pp. 313–318 (1998)

  30. Alonso-Marroquin, F., Huang, P., Hanaor, D.A.H., Flores-Johnson, E.A., Proust, G., Gan, Y., Shen, L.: Static friction between rigid fractal surfaces. Phys. Rev. E 92, 032405-1–032405-12 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  31. Scaraggi, M., Persson, B.N.J.: General contact mechanics theory for randomly rough surfaces with application to rubber friction. J. Chem. Phys. 143, 224111 (2015)

    Article  ADS  Google Scholar 

  32. Luding, S.: Cohesive, frictional powders: contact models for tension. Granul. Matter 10, 235–246 (2008)

    Article  MATH  Google Scholar 

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Acknowledgements

This work was support by the Engineer Research and Development Center’s Military Engineering Basic Research Program. The authors are grateful to the following members of ERDC-CRREL’s Engineering Services Branch for their help in the development of the hardware and software used in the contact experiments: Douglas Punt, William Burch, Christopher Williams and John Gagnon.

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Authors and Affiliations

  1. ERDC-CRREL, 72 Lyme Rd., Hanover, NH, 03755, USA

    David M. Cole & Mark A. Hopkins

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  1. David M. Cole
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  2. Mark A. Hopkins
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Correspondence to David M. Cole.

Appendix

Appendix

Contact model parameter values.

Table 1 Parameter values for the normal and shear contact models for the four materials for which laboratory repeated load triaxial tests were conducted (file: Contact model parameter values used in 1st journal article plots)
Full size table
Table 2 Parameter values for the normal and shear contact models for materials that were not subjected to laboratory repeated load triaxial testing
Full size table

See Tables 1 and 2.

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Cole, D.M., Hopkins, M.A. The contact properties of naturally occurring geologic materials: contact law development. Granular Matter 19, 5 (2017). https://doi.org/10.1007/s10035-016-0683-4

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