Advertisement

Acta Geotechnica

, Volume 13, Issue 2, pp 317–328 | Cite as

On the stability of geotechnical systems and its fractal progressive loss

  • Gerd Gudehus
  • Asterios Touplikiotis
Research Paper

Abstract

Geotechnical systems, consisting of soil and embedded solid structures, are practically stable if inevitable actions cause at most harmless redistributions. This kind of robustness can often be achieved with limit state design, i.e. by assuming representative snapshots of worst cases. Changes in configuration and state due to changing boundary conditions can be better judged with quasi-static numerical simulations using validated constitutive relations. The ever-present fractality of the ground may be neglected as long as the system is stable, whereas it gets dominant during a progressive loss of stability with jerky critical phenomena which elude mathematical treatment until present. In this sense geotechnical systems can be or get sensitive, i.e. further actions can trigger detrimental chain reactions with seismogeneous collapse of the soil fabric, pore pressure increase up to liquefaction, erosion, cracking of ground and structural parts and/or tilting. The geotechnical risk can be better mitigated by taking into account chain reactions with wild randomness. It can be further reduced by monitoring the seismic emission in addition to mass flows, structural deformations and pore pressures. The paper is to clarify notions and concepts.

Keywords

Fractal Geotechnical system Limit state design Stability Sensitivity 

Notes

Acknowledgements

We owe Prof. W. Förster (Freiberg), Dr. M. Külzer (Stuttgart), Dr. A. Niemunis (Karlsruhe), Dr. K. Nübel (Stuttgart) and Prof. P. v. Wolffersdorff (Dresden) for valuable hints.

References

  1. 1.
    Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: an explanation of 1/f noise. Phys Rev Lett 59(4):381–384CrossRefGoogle Scholar
  2. 2.
    Binney JJ, Dowrick NJ, Fisher AJ, Newman MEJ (1992) The theory of critical phenomena—an introduction to the renormalization group. Oxford University Press, OxfordzbMATHGoogle Scholar
  3. 3.
    Boussinesq JV (1876) Essai théorique sur l’équilibre de l’elasticité des masses pulverulentes et sur la pousseé des terres sans cohésion. Mém Couronn 40(4)Google Scholar
  4. 4.
    Casagrande A (1936) Characteristics of cohesionless soils affecting the stability of slopes and earth fills. J Boston Soc Civ Eng 23:257–276Google Scholar
  5. 5.
    Darwin G (1883) On the horizontal thrust of a mass of sand. In: Proceedings of the Institution of Civil Engineers, London, vol LXXL, pp 350–378Google Scholar
  6. 6.
    Dhar D (2006) Theoretical studies of self-organized criticality. Phys A 369:29–70MathSciNetCrossRefGoogle Scholar
  7. 7.
    Griffith AA (1921) The phenomena of rupture and flow in solids. Phil Trans R Soc Lond A 221(582–593):163–198. doi: 10.1098/rsta.1921.0006 CrossRefGoogle Scholar
  8. 8.
    Gudehus G (2011a) Physical soil mechanics. Springer, BerlinCrossRefGoogle Scholar
  9. 9.
    Gudehus G (2011b) Windparks in the German Bight—a challenge for geotechnics. Geotechnik 1:3–10CrossRefGoogle Scholar
  10. 10.
    Gudehus G (2016) Mechanisms of partly flooded loose sand deposits. Acta Geotech 11:505–517CrossRefGoogle Scholar
  11. 11.
    Gudehus G, Touplikiotis A (2012) Clasmatic seismodynamics—oxymoron or pleonasm? Soil Dyn Earthq Eng 38:1–14CrossRefGoogle Scholar
  12. 12.
    Gudehus G, Touplikiotis A (2016) Wave propagation with energy diffusion in a fractal solid and its fractional image. Soil Dyn Earthq Eng 89:38–48CrossRefGoogle Scholar
  13. 13.
    Gudehus G, Jiang Y, Liu M (2011) Seismo- and thermodynamics of granular solids. Granul Matter 13(4):319–340CrossRefGoogle Scholar
  14. 14.
    Haimes YY (1998) Risk modeling, assessment and management. Wiley, New YorkzbMATHGoogle Scholar
  15. 15.
    Henke S, Grabe J (2008) Numerical investigation of soil plugging inside open-ended piles with respect to the installation method. Acta Geotech 3:2015–2223CrossRefGoogle Scholar
  16. 16.
    Hergarten S (2002) Self-organized criticality in earth systems. Springer, BerlinCrossRefGoogle Scholar
  17. 17.
    Hu W, Hicher P-Y (2016) Initiation mechanism and seismic precursor of fluidized landslide in loose soil. Nature (under preparation)Google Scholar
  18. 18.
    Jiang Y, Liu M (2009) Granular solid hydrodynamics. Granul Matter 11:139–145CrossRefzbMATHGoogle Scholar
  19. 19.
    Jiang Y, Liu M (2013) Proportional paths, Barodesy, and granular solid hydrodynamics. Granul Matter 15:237–249CrossRefGoogle Scholar
  20. 20.
    Külzer M (2015) State limits of peloids. Karlsruhe Institute of Technology, KarlsruheGoogle Scholar
  21. 21.
    Kulhawy FH, Phoon K-K (1996) Engineering judgment in the evolution from deterministic to reliability-based foundation design. In: Scheckelford CD et al (eds) Proceedings of uncertainty in the geologic environment—from theory to practice. ASCE, New YorkGoogle Scholar
  22. 22.
    Loukidis D, Salgado R (2012) Active pressure on gravity walls supporting purely frictional soils. Can Geotech J 49:78–97CrossRefGoogle Scholar
  23. 23.
    Mandelbrot B (1999) Multifractals and 1/f-noise—wild self-affinity in physics. Springer, New YorkzbMATHGoogle Scholar
  24. 24.
    Mortensen K (1983) Is limit state design a judgment killer? Danish Geotechnical Institute, Bulletin No. 35, CopenhagenGoogle Scholar
  25. 25.
    Nübel K (2002) Experimental and numerical investigation of shear localization in granular material. Veröff. Inst. Boden- u. Felsmech. Heft 159, Uni KarlsruheGoogle Scholar
  26. 26.
    Peck RB (1969) Advantages and limitations of the observational method in applied soil mechanics. Geotechnique 19(2):171–187CrossRefGoogle Scholar
  27. 27.
    Rankine WJM (1856) On the stability of loose earth. Philos Trans R Soc Lond 147(1):9–27Google Scholar
  28. 28.
    Robert R, Rosier C (2011) Long range predictability of atmospheric flows. Nonlinear Process Geophys 8:55–67CrossRefGoogle Scholar
  29. 29.
    Sato K-I (1999) Levy processes and infinitely divisible distributions. Cambridge University Press, CambridgezbMATHGoogle Scholar
  30. 30.
    Schofield A, Wroth P (1968) Critical state soil mechanics. Mc Graw Hill, LondonGoogle Scholar
  31. 31.
    Schwämmle A, Herrmann HJ (2003) Geomorphology, solitary wave behaviour of sand dunes. Nature 426(12):619–620CrossRefGoogle Scholar
  32. 32.
    Turcotte DL (2001) Self-organized criticality: does it have anything to do with criticality and is it useful? Nonlinear Process Geophys 8:193196CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institute of Soil and Rock MechanicsEmeritusKarlsruheGermany
  2. 2.KarlsruheGermany

Personalised recommendations