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Continuum Description of Natural Slopes in Slow Movement

  • Kolumban Hutter
Part of the International Centre for Mechanical Sciences book series (CISM, volume 337)

Abstract

A two-component mixture model is proposed that is capable of describing the slow motion of natural slopes which may creep (deform within their body) and slide along their basal surface under the effect of gravity. The field equations comprise the balance laws of mass and momentum and constitutive relations for the partial stresses of the fluid and the solid as well as the seepage force. The fluid is modelled as an incompressible perfect liquid and the soil as a viscous isotropic body in which the stress is rate dependent and may also depend on the porosity. The seepage force is described by Darcy’s law. Explicit constitutive formulas are prescribed. The kinematic and dynamic boundary conditions for the fixed basal surface and the movable free and phreatic surfaces are stated. All these equations comprise a well posed boundary value problem for the moving mass of soil that is saturated with water.

Keywords

Constitutive Relation Pore Water Pressure Slow Movement Soil Mechanics Shear Angle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Andersland, O. B., and Douglas, A. G. (1970). “Soil deformation rates and activiation energies.” Geotechnique, 20 (1), 1–16CrossRefGoogle Scholar
  2. Antoine, P., Biarez, J., Desvarreux, P., and Mougin, J.-P. (1971). “Les problèmes posés par la stabilité des pentes dans les régions montageneuses.” Géologie alpine, 47, 5–24Google Scholar
  3. Barden, L. (1965). “Consolidation of clay with non—linear viscosity.” Geotechnique, 15 (9), 345–362CrossRefGoogle Scholar
  4. Biarez, J., and Boucek, B. (1973). “Viscoplasticité de l’argile in situ et en laboratoire.” Proceedings, 8th Int. Conf. on Soil Mechanics and Foundation Engineering, Moscow, Vol. 1.1, 51–56.Google Scholar
  5. Blondeau, F., Morin, P., and Pouget, P. (1983). “Comportement d’un remblai construit jusqu’à la rupture sur un versant naturel, Site expérimental de Sallèdes.” Rapport de recherche Lpc, No. 126.Google Scholar
  6. Bjerrum, L., and Landva, A. (1966). “Direct simple-shear test on a Norwegian quick clay.” Geotechnique, 16 (1), 1–20CrossRefGoogle Scholar
  7. Bourdeau, P. L., Recordon, E., Vulliet, L., Pouget, P., Pilot, G, and Delmas, PH. (1988). “La stabilité des versants: Évolutions récentes du calcul.” Proceedings, 5th Int. Symposium on Landslides, Lausanne, Switzerland.Google Scholar
  8. Cacmak, A. S., Richards, R., and Cole, D. H. (1970). “Shift functions for hydrorheologically simple clays.” Proc., 5th Int. Congress on Rheology, Tokyo, Japan, 491–499.Google Scholar
  9. Calabresi, G. (1970). “Creep di argille indisturbate in prove di taglio di Lunga du-rate” (with English abstract). Estratto dalla rivista Italiana di Geotechnica, No. 1 (in Italian).Google Scholar
  10. Cartier, G., and Pouget, P. (1987). “Corrélation entre la pluviométrie et les déplacements de pentes instables.” Proceedings, 9th European Conference on Soil Mechanics and Foundation Engineering, DublinGoogle Scholar
  11. Chowdhury, R. N. (1978). “Slope analysis.” In Developments in geotechnical engineering, Vol. 22, Elsevier, Amsterdam, The Netherlands.Google Scholar
  12. Consiglio Nazionale Delle Richerche (1982). Progetto finalizzato “Convervazione del suolo.” Atti del convegno conclusivo, Roma, ItalyGoogle Scholar
  13. Christensen, R. W., and Wu, T. H. (1964). “Analysis of clay deformation as a rate process.” J. Soil Mech. Found. Div., Asce, 90 (SM6), 125–157.Google Scholar
  14. Courmeau, I. C. (1976). Visco-plasticity and plasticity in the finite element method. Thesis in the University of Wales, Swansea.Google Scholar
  15. Drucker, D. C., and Prager, W. (1952). “Soil mechanics and plastic analysis or limit design.” Q. J. Appl. Math., 10 (2), 157–165.MathSciNetMATHGoogle Scholar
  16. Duti (1983). Étude pluridisciplinaire du glissement du Day. Secteur des Gaudennes, secteur de Praz-Mattey. École polytechnique fédérale de Lausanne, Switzerland.Google Scholar
  17. Duti (1985). “Projet d’École Détection et Utilisation des Terrains Instables.” Rapport d’activité a fin 1983, Epfl, Lausanne, Switzerland.Google Scholar
  18. Dysli, M., and Recordon, E. (1981). “Fluage des formations argileuses alpines.” Proc., 10th Int. Conf. on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, Vol. 3, 395–400.Google Scholar
  19. Emery, J. J. (1978). “Simulation of slope creep.” Dev. in Geotech. Eng. Vol. 14A, Rock-slides and Avalanches, 1, B. Voight editor, Elsevier, Amsterdam.Google Scholar
  20. Engel, T. (1986). “Nouvelles méthodes de messure et d’analyse pour l’étude des mouvements du sol en terrains instables.” Thèse No. 601, Ècole polytechnique fédérale de Lausanne, Switzerland.Google Scholar
  21. Feda, J., Kamenov, B., and Klablena, P. (1973). “Investigation of creep and structure of clayed materials.” Proc., 8th Icsmfe, Moscow, Ussr, Vol. 1, 119–128.Google Scholar
  22. Fedder, D. (1972). “Zustandsgleichung eines Lehmes, ermittelt mit Hilfe einer neuentwickelten Versuchsapparatur.” Proc., 6th Int. Congress on Rheology, Lyon, France, 1372–1379.Google Scholar
  23. Fowler, A. C. (1981). “A theoretical treatment of the sliding of glaciers in the absence of cravitation.” Philosophical Transactions of the Royal Society of London, 298, 637–685.MathSciNetCrossRefMATHADSGoogle Scholar
  24. Garofalo, F. (1963). “An empirical relation defining the stress dependence of minimum creep rate in metals.” Trans., Metal Soc., Asme, 227, 351–355.Google Scholar
  25. Geuze, E. C. W. A., and Tan T. Jong-Kie (1950). “The shearing properties of soils.” Geotechnique, 2, 141–161.CrossRefGoogle Scholar
  26. Geuze, E. C. W. A. 1953 ). “Laboratory investigations, including compaction tests, Improvement of soil properties.” Proc., 3rd Int. Conf. on Soil Mechanics and Foundation Engineering, Zürich, Switzerland, Vol. 3, 119–122.Google Scholar
  27. Glasstone, S., Laidler, K. J., and Eyring, H. (1941). “The theory of rate processes.” McGraw Hill, New York, N. Y.Google Scholar
  28. Gudehus, G., Kolymbas, D., and Leinenkugel, H.-J. (1976). “Zeitverhalten von Böschungen und Einschnitten in weichem und steifem Ton.” Proc., 6th European Conf. on Soil Mechanics and Foundation Engineering, Wien, Austria, Vol. 1, 51–58.Google Scholar
  29. Haefeli, R. (1953). “Creep problems in soils, snow and ice.” Procedings, 3rd Int. Conf. on Soil Mechanics and Foundation Engineering, Zürich, Switzerland, Vol. 3, 238–251.Google Scholar
  30. Haefeli, R. (1965). “Creep and progressive failure in snow, soil, rock, and ice.” Proceedings, 6th Int. Conf. on Soil Mechanics and Foundation Engineering, Montreal, Canada, Vol. 3, 134–148.Google Scholar
  31. Hirst, J. T. (1968). “The influence of compositional factors on the stress-strain-time behavior of soils.” Thesis presented to the University of California at Berkely, Calif., in partial fulfillment of the requirements for a degree.Google Scholar
  32. Huder, J. (1976). “Creep in Bundner Schist”, Laurits Bjerrum Memorial Volume, Norwegian Geotechnical Institute, Oslo, Norway.Google Scholar
  33. Hutter, K. (1983). “Theoretical glaciology”. Terra Scientific Publishing Company, Tokyo, JapanGoogle Scholar
  34. Hutter, K., and Savage, S. B. (1988). “Avalanche dynamics: the motion of a finite mass of gravel down a mountain side.” Proceedings, 5th Int. Symposium on Landslides, Lausanne, Switzerland.Google Scholar
  35. Hutter, K., and Vulliet, L. (1985). “Gravity-driven slow creeping flow of a thermoviscous body at elevated temperatures.” J. Therm. Stresses, 8, 99–138.CrossRefGoogle Scholar
  36. Kavazanjian, E. (1978). “A generalized approach to the prediction of the stress-straintime behavior of soft clay.” Thesis presented to the University of California, at Berkeley, Calif., in partial fulfillment of the requirements for a degree.Google Scholar
  37. Kavazanjian, E., and Mitchell, J. K. (1984). “Time dependence of lateral earth pressure.” J. Geotech. Engrg., Asce, 110 (4), 530–533.CrossRefGoogle Scholar
  38. Kenney, T. C., and Lau, K. C. (1984). “Temporal changes of groundwater pressure in a natural slope of nonfissured clay.” Canadian Geotechnical Journal, 21, 138–146CrossRefGoogle Scholar
  39. Koerner, H. J. (1969). “Kinematische Betrachtung zum Rankineschen Spannungszustand in der geneigten, kriechenden Schicht.” Felsmechanik und Ingenieurgeologie, Suppl. Vol., 33–54.Google Scholar
  40. Komamura, F., and Huang, R. J. (1974). “New rheological model for soil behaviour.” J. Geotech. Engrg., Asce, 100 (GT7), 807–824.Google Scholar
  41. Krizek, R. J. (1970). “Constitutive behavior of clay soils.” Proc., 5th Int. Congress on Rheology, Tokyo, Japan, 469–489.Google Scholar
  42. Lambe, T. C., and Whiteman, R. V. (1969) “Soil Mechanics”, Wiley and Sons, N. Y.Google Scholar
  43. Lliboutry, L. A. (1975). “Loirs de glissement dun glacier sans cavitation”. Annales de géophysique, 31, 207–226.Google Scholar
  44. Lliboutry, L. A. (1979) “Local friction laws for glaciers: A critical review and new openings”. J. Glaciology, 23, 67–95.ADSGoogle Scholar
  45. Lms (1980) Glissement de Villarbeney. 2ème rapport intermédiaire, Lab. de Mec. des Sobs, Étude GX59, Août 1980, Epel, Lausanne.Google Scholar
  46. Meschyan, S. R. and Badalyan, R. G. (1976). “Regularity of creep of clays and deformation of slopes.” Proceedings 6th European Conference on Soil Mechanics and Foundation Engineering, Vienna, Austria, 1, 71–74.Google Scholar
  47. Mesri, G., et al. (1981). “Shear stress—strain—time behavior of clays.” Geotechnique, 31 (4), 537–552.CrossRefGoogle Scholar
  48. Mitchell, J. K. (1964). “Shearing resistance of soils as a rate process.” J. Soil Mech. and Found. Div., Asce, 90 (SM1), 29–61.Google Scholar
  49. Morin, P. (1979). “Etude du comportement avant rupture d’un remblai expérimental sur versant à Sallèdes.” Thésis ‘Ecole nationale des ponts et chausées, Paris, France.Google Scholar
  50. Muller, I. (1973). “Thermodynamik, Die Grundlagen der Materialtheorie.” Bertelsmann Universitätsverlag, Düsseldorf, West Germany.Google Scholar
  51. Muller,I. (1985) Thermodynamics, Pitman Advanced Publishing Program, Boston • London • Melbourne.Google Scholar
  52. Murayama, S. and Shibata, T., (1961). “Rheological characteristics of clays”. Proc. 5th Icsmfe, Paris.Google Scholar
  53. Murayama, S. (1983). “Formulation of stress-strain-time behaviour of soils under deviatoric stress condition.’ Soils Found., 23 (2), 43–57.MathSciNetCrossRefGoogle Scholar
  54. Murayama, S., Sekiguchi, H., and Ueda, T. (1974). “A study of the stress—strain-time behavior of saturated clays based on a theory of nonlinear viscoelasticity.’ Soils Found., 14 (2), 19–33.CrossRefGoogle Scholar
  55. Murayama, S., Shibata, T. (1961). “Rheological characteristics of clays.” Proc., 5th Int. Conf. on Soil Mechanics and Foundation Engineering, Paris, France.Google Scholar
  56. Nelson, J. D., and Thompson, E. G. (1974). “Creep failure of slopes in clay shale.” Extraordinary Symposium Soil Engineering and Engineering Geology, Idaho, Usa, 177–195Google Scholar
  57. Nelson, J. D., and Thompson, E. G. (1977). “A theory of creep failure in overconsolidated clay.” Journal of the Geotechnical Engineering Division, Asce, 103, 1281–1294.Google Scholar
  58. Noble, H. L. (1973). “Residual strength and landslides in clay and shale.” Journal of the Soil Mechanics and Foundations Division, Asce 99 (SM9), 705–719.Google Scholar
  59. Norton, F. H. (1929). “The creep of steel at high temperature.” McGraw Hill, New York, N. Y.Google Scholar
  60. Oka, F. (1981). “Prediction of time-dependent behavior of clay.” Proc. 10th Int. Conf. on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, 1, 215–218.Google Scholar
  61. Perzyna, P. (1966). “Fundamental problems in plasticity”. Adv. in Appl. Mech. 9, 243–377.CrossRefGoogle Scholar
  62. Pouget, P., and Cartier, G. (1988). “Étude du comportement d’un remblai construit sur un versant instable. Le remblai B de Sallèdes ( Puy de Dôme).” Rapport de recherche Lpc, No. 151.Google Scholar
  63. Pouget, P., Cartier, G. and Pilot, G. (1985). “Comportement d’un remblai constuit sur un sit instable.” Proceedings, 11th Int. Conference on Soil Mechanics and Foundation Engineering, San Francisco, 4, 2345–2348.Google Scholar
  64. Prandtl, L. (1928). “Ein Gedankenmodell zur kinematischen Theorie der festen Körper.” Ztschr. Angew. Math. u. Mech., 8, Heft 2, 85–105.Google Scholar
  65. Pusch, R., and Feltham, P. (1980). “A stochastic model of the creep of soils.” Geotechnique, 30 (4), 497–506.CrossRefGoogle Scholar
  66. Roscoe, K.H., and Burland, J.B., (1968). “On the generalized stress-strain behaviour of ”wet“ clay, in: Engineering Plasticity (ed J. Heyman and P.A. Leckie) Cambridge University Press, pp 535–609.Google Scholar
  67. Savage, S. B. and Hutter, K. (1989). “The motion of a finite mass of granular material down a rough incline.” Journal of Fluid Mechanics, 199, 177–215MathSciNetCrossRefMATHADSGoogle Scholar
  68. Singh, A., and Mitchell, J. K. (1968). “General stress-strain-time function for soils.” J. Soil Mech. Found. Div., Asce, 94 (SM1), 21–46.Google Scholar
  69. Skempton, A. W., (1964). “Long-term stability of clay slopes”, Geotechnique, 14 (2), 77–102.CrossRefGoogle Scholar
  70. Skempton, A. W., (1985). “Residual strength of clays in landslides, folded strata and the laboratory”, Geotechnique, 35 (1), 3–18.CrossRefGoogle Scholar
  71. Stroganov, A. S. (1961). “Visco-plastic flow of soils.” Proc., 5th Int. Conf. on Soil Mechanics and Foundation Engineering, Paris, France, 1, 721–726.Google Scholar
  72. Tan, TJ.—K. (1981). “Time dependent lateral pressures and Poisson’s ratio measurement.” Proc., 10th Int. Conf. on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, 1, 797–800.Google Scholar
  73. Tavenas, F., and Leroueil, S. (1981). “Creep and failure of slopes in clays.” Canadian Geotechnical Journal, 18, 106–120.CrossRefGoogle Scholar
  74. Ter-Martirosyan, Z. G. (1971). “Creep of an inclined bed under variable pore pressure.” Translated from Osnovaniya, Fundarnentry i Mekhanika Gruntov, No. 4, 8–10.Google Scholar
  75. Ter-Stephanian, G. (1963). “On the long-term stability of slopes.” Publ. No. 52, Norwegian Geotech. Inst., Oslo, Norway, 1–13.Google Scholar
  76. Ter-Stephanian, G. (1965). “In situ determination of the rheological characteristics of soils on slopes.” Proceedings, 6th Int. Conference on Soil Mechanics and Foundation Engineering, Montreal, 2, 575–577.Google Scholar
  77. Ter-Stephanian, G. (1973). “New rheological model of creep of a clay at shear.” Reported at the Symposium on the Theory of Landslide Processes, May, Dilijan.Google Scholar
  78. Ter-Stephanian, G. (1980). “Creep on natural slopes and cuttings. State-of-the-art Report.” Proceedings, Int. Symposium on Landslides, New Dehli, 2, 95–108.Google Scholar
  79. Terzaghi, C., (1931). “The static rigidity of plastic clays”. J. of Rheology 2 (3), 253–262.CrossRefADSGoogle Scholar
  80. Truesdell, C. (1977). “Rational continuum mechanics.” Vol. 1, Academic Press, New York, N. Y.MATHGoogle Scholar
  81. Truesdell, C. (1978). “Rational continuum mechanics.” Vol. 2, Academic Press, New York, N. Y.Google Scholar
  82. Trunk, F. J., Dent, J. D., and Lang, T. E. (1986). “ Computer modeling of large rock slides.” J. Geotechn. Engrg., Asce, 111 (3), 348–360.CrossRefGoogle Scholar
  83. Vulliet, L. (1986). “Modélisation des pentes naturelles en mouvement.” Thèse No. 635, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.Google Scholar
  84. Vulliet, L., and Hutter, K. (1988). “Continuum model for natural slopes under slow movement.” Géotechnique, 38, 199–217.CrossRefGoogle Scholar
  85. Vulliet, L., and Hutter, K. (1988). “A multi-layer, multi-sliding surface model for three-dimensional creeping slopes.” Proceedings, 5th Int. Symposium on Landslides, Lausanne, Switzerland.Google Scholar
  86. Vulliet, L., and Hutter, K. (1988). “Some constitutive laws for creeping soils and for rate-dependent sliding at interfaces.” Proceedings, 6th Int. Conference on Numerical Methods in Geomechanics, Innsbruck, Austria.Google Scholar
  87. Vulliet, L., and Hutter, K. (1988). “Set of constitutive models for soils under slow movement.” Journal of Geotechnical Engineering, Asce, 114 (9), 1022–1041.CrossRefGoogle Scholar
  88. Vulliet, L., and Hutter, K. (1988). “Viscous-type sliding laws for landslides.” Can. Geotech. J. 25, 467–477.CrossRefGoogle Scholar
  89. Vulliet, L., and Recordon, E. (1987). “The effect of groundwater seepage on the movement of natural slopes.” Proceedings, 9th European Conference on Soil Mechanics and Foundation Engineering, Dublin.Google Scholar
  90. Weertman, J. (1964). “The theory of glacier sliding”, J. Glaciology, 5, 287–303.ADSGoogle Scholar
  91. Weertman, J. (1979). “The unsolved general glacier sliding problem”, J. Glaciology, 23, 97–115.ADSGoogle Scholar
  92. Yen, B. C. (1969). “Stability of slopes undergoing creep deformation.” J. Soil Mech. Found. Div. Asce, 95 (SM4), 1075–1096.Google Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • Kolumban Hutter
    • 1
  1. 1.Institut für MechanikTechnische Hochschule DarmstadtDarmstadtGermany

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