The problem of limiting equilibrium of a slope in a state of plane strain is formulated in terms of the variational calculus. Formulated that way, the analysis is carried out without any a priori assumptions with respect to the shape of the slip surface, or the normal stress distribution along it. Thus, on the basis of only a formal definition of the concepts of limiting equilibrium, and factor of safety with respect to strength, it is proven that the minimal factor of safety must occur on slip surfaces with a special geometrical property. This geometrical property ensures that the resultant of the infinitesimal normal and frictional forces either pass through a common point or are parallel to a common direction. It is shown that as a result of this geometrical property the minimal factor of safety is independent of the normal stress distribution along the critical slip surface. In the homogeneous and isotropic case the analysis shows that the critical slip surface may be either a log-spiral or a straight line. In a layered profile the critical slip surface may consist of series of log-spirals that have a common pole or a series of straight lines. In some cases the boundary between layers may be part of the critical slip surface. All the results obtained are valid for a general non-homogeneous, non-isotropic soil with arbitrary distribution of pore water pressure and external loads.(a) /TRRL/

Media Info

  • Features: Figures; References;
  • Pagination: p. 395-411
  • Serial:
    • Volume: 28
    • Issue Number: 4
    • Publisher: Thomas Telford Limited
    • ISSN: 0016-8505

Subject/Index Terms

Filing Info

  • Accession Number: 00193939
  • Record Type: Publication
  • Source Agency: Transport Research Laboratory
  • Files: ITRD, TRIS
  • Created Date: Jun 13 1979 12:00AM