Skip to main content
SpringerLink
Log in

Avalanches in anisotropic sheared granular media

  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

We study the influence of particle shape anisotropy on the occurrence of avalanches in sheared granular media. We use molecular dynamic simulations to calculate the relative movement of two tectonic plates. Our model considers irregular polygonal particles constituting the material within the shear zone. We find that the magnitude of the avalanches is approximately independent of particle shape and in good agreement with the Gutenberg–Richter law, but the aftershock sequences are strongly influenced by the particle anisotropy yielding variations on the exponent characterizing the empirical Omori’s law. Our findings enable one to identify the presence of anisotropic particles at the macro-mechanical level only by observing the avalanche sequences of real faults. In addition, we calculate the probability of occurrence of an avalanche for given values of stiffness or frictional strength and observe also a significant influence of the particle anisotropy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bolt B.A.: Earthquakes. W.H. Freeman, New York (2005)

    Google Scholar 

  2. Sykes L.R., Shaw B.E., Scholz C.H.: Rethinking earthquake prediction. Pure Appl. Geophys. 155, 207–232 (1999)

    Article  ADS  Google Scholar 

  3. Donzé F., Mora P., Magnier S.-A.: Numerical simulation of faults and shear zones. Geophys. J. Int. 116, 46–52 (1994)

    Article  ADS  Google Scholar 

  4. Mora P., Place D.: Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction. Pure Appl. Geophys. 159, 2413–2427 (2002)

    Article  ADS  Google Scholar 

  5. Ramos, O., Altshuler, E., Maløy, K.J.: Predicting power law distributed avalanches: implications for earthquake forecast. Private report (2007)

  6. Summers R., Byerlee J.D.: A note on the effect of fault gouge composition on the stability of frictional sliding. Int. J. Rock Mech. Min. Sci. 14, 155–160 (1977)

    Article  Google Scholar 

  7. Marone C.: Laboratory-derived friction laws and their application to seismic faulting. Ann. Rev. Earth Planet. Sci. 26, 643–696 (1998)

    Article  ADS  Google Scholar 

  8. Mair K., Frye K.M., Marone C.: Influence of grain characteristics on the friction of granular shear zones. J. Geophys. Res. 107, 2219 (2002)

    Article  ADS  Google Scholar 

  9. Mora P., Place D.: Simulation of the frictional stick-slip instability. Pageoph 143, 61 (1994)

    Article  Google Scholar 

  10. Tillemans H.J., Herrmann H.J.: Simulating deformations of granular solids under shear. Physica A 217, 261–288 (1995)

    Article  ADS  Google Scholar 

  11. Mora P., Place D.: The weakness of earthquake faults. Geophys. Res. Lett. 26, 123–126 (1999)

    Article  ADS  Google Scholar 

  12. Alonso-Marroquín F., Vardoulakis I., Herrmann H.J., Weatherley D., Mora P.: Effect of rolling on dissipation in fault gouges. Phys. Rev. E 74, 031306 (2006)

    Article  ADS  Google Scholar 

  13. Scholz C.H.: The Mechanics of Earthquakes and Faulting. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  14. Turcotte D.L., Schubert G.: Geodynamics. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  15. Abe S., Latham S., Mora P.: Dynamic rupture in a 3-d particle-based simulation of a rough planar fault. Pure Appl. Geophys. 163, 1881–1892 (2006)

    Article  ADS  Google Scholar 

  16. Wilson B., Dewers T., Reches Z., Brune J.: Particle size and energetics of gouge from earthquake rupture zone. Nature 434, 749–752 (2005)

    Article  ADS  Google Scholar 

  17. Mora P., Place D.: Numerical simulation of earthquake faults with gouge: toward a comprehensive explanation for the heat flow paradox. J. Geophys. Res. 103, 21067–21089 (1998)

    Article  ADS  Google Scholar 

  18. Peña, A.A., Lizcano, A., Alonso-Marroquín, F., Herrmann, H.J.: Biaxial test simulations using a packing of polygonal particles. Int. J. Numer. Anal. Meth. Geomech. (2007) (accepted)

  19. Peña A.A., García-Rojo R., Herrmann H.J.: Influence of particle shape on sheared dense granular media. Granul. Matter 9, 279–291 (2007)

    Article  Google Scholar 

  20. Kanamori H., Brodsky E.E.: The physics of earthquakes. Phys. Today 54, 34–40 (2001)

    Article  Google Scholar 

  21. Sethna J.P., Dahmen K.A., Myers C.R.: Crackling noise. Nature 410, 242–250 (2001)

    Article  ADS  Google Scholar 

  22. Gutenberg B., Richter C.F.: Seismicity of the Earth and Associated Phenomena. Princeton University Press, Princeton (1954)

    Google Scholar 

  23. Omori F.: On the aftershocks of earthquakes. J. Coll. Sci. Imper. Univ. Tokyo 7, 111 (1895)

    Google Scholar 

  24. Pöschel T., Schwager T.: Computational Granular Dynamics. Springer, Berlin (2005)

    Google Scholar 

  25. Chakrabarti K.B., Benguigui L.G.: Statistical Physics of Fracture and Breakdown in Disordered Systems. Clarendon, Oxford (1997)

    MATH  Google Scholar 

  26. Papoulis A.: Probability, Random Variables, and Stochastic Processes. McGraw-Hill, Boston (2002)

    Google Scholar 

  27. Peña A.A., Lind P.G., Herrmann H.J.: Modeling slow deformation of polygonal particles using DEM. Particuology 6, 506–514 (2008)

    Article  Google Scholar 

  28. Peña, A.A., Lind, P.G., McNamara, S., Herrmann, H.J.: Numerical improvement of the discrete element method applied to shear of granular media. Acta Mech. (2009) (in press)

  29. Nasuno S., Kudrolli A., Bank A., Gollub J.P.: Time-resolved studies of stick-slip friction in sheared granular layers. Phys. Rev. E 58, 2161–2171 (1998)

    Article  ADS  Google Scholar 

  30. Feder H.J.S., Feder J.: Self-organized criticality in a stick-slip process. Phys. Rev. Lett. 66, 2669–2672 (1991)

    Article  ADS  Google Scholar 

  31. Staron L., Radjai F.: Friction versus texture at the approach of a granular avalanche. Phys. Rev. E 72, 041308 (2005)

    Article  ADS  Google Scholar 

  32. Staron L., Vilotte J.P., Radjai F.: Preavalanche instabilities in a granular pile. Phys. Rev. Lett. 89, 204302 (2002)

    Article  ADS  Google Scholar 

  33. Radjai F., Jean M., Moreau J.J., Roux S.: Force distribution in dense two-dimensional granular systems. Phys. Rev. Lett. 77, 274 (1996)

    Article  ADS  Google Scholar 

  34. Radjai F., Wolf D.E., Jean M., Moreau J.J.: Bimodal character of stress transmission in granular packings. Phys. Rev. Lett. 80, 61–64 (1998)

    Article  ADS  Google Scholar 

  35. Majmudar T.S., Behringe R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature 435, 1079–1082 (2005)

    Article  ADS  Google Scholar 

  36. Staron, L., Radjai, F., Vilotte, J.P.: Granular micro-structure and avalanche precursors. J. Stat. Mech. P07014 (2006)

  37. Alonso-Marroquin, F., Peña, A.A., Herrmann, H.J., Mora, P.: Simulation of shear bands using polygonal particles. Discrete Element Methods (DEM) Conference, Brisbane, Australia, pp. 1–8 (2007)

Download references

Author information

Author notes

  1. Andrés A. Peña

    Present address: Bilfinger Berger GmbH, Structural Design, Geotechnics, 65189, Wiesbaden, Germany

  2. Sean McNamara

    Present address: Université Rennes 1, Institut de Physique de Rennes, UMR CNRS 6251, 35042, Rennes, France

  3. Pedro G. Lind

    Present address: CFTC, Complexo Interdisciplinar, University of Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisbon, Portugal

Authors and Affiliations

  1. Institute for Computational Physics, Universität Stuttgart, Pfaffenwaldring 27, 70569, Stuttgart, Germany

    Andrés A. Peña, Sean McNamara & Pedro G. Lind

  2. Departamento de Física, Universidade Federal do Ceará, Fortaleza, Ceará, 60451-970, Brazil

    Hans J. Herrmann

  3. Computational Physics, IfB, HIF E12, ETH Hönggerberg, 8093, Zürich, Switzerland

    Hans J. Herrmann

Authors
  1. Andrés A. Peña
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sean McNamara
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pedro G. Lind
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hans J. Herrmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pedro G. Lind.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peña, A.A., McNamara, S., Lind, P.G. et al. Avalanches in anisotropic sheared granular media. Granular Matter 11, 243–252 (2009). https://doi.org/10.1007/s10035-009-0136-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-009-0136-4

Keywords

Search

Navigation