is based on the extension of four standard limit equilibrium methods to
three dimensions. The first is Bishop’s Simplified Method (Hungr, 1987,
Hungr et al., 1989). The present version includes modifications due to
Fredlund and Krahn (1977). This makes the method applicable to
non-rotational geometries, within limitations suggested in Hungr et al.
(1989). The second method is Janbu Simplified Method, extended into
three dimensions along the same lines.
also includes 3D extensions of the Spencer’s Method and the
Morgenstern-Price Method. These extensions have been derived using an
approach similar to that proposed by Lam and Fredlund (1993) and Hungr,
(1997), combined with an assumption that the resultant of the
interslice force on the lateral column surfaces is parallel with the
column base. The Morgenstern-Price method is implemented with only one
form of the interslice force function: the half-sine function.
result screen (2D)
the program is in its two-dimensional configuration, the solution
formulas revert mathematically to the standard forms of the well known
Bishop’s, Janbu, Spencer and Morgenstern-Price methods (e.g. Fredlund
and Krahn, 1977). Both the 2D and 3D forms use a common solver engine.
methods are highly accurate for problems which are symmetric with
respect to a vertical plane parallel with the direction of sliding.
Potential sources of error exist in some non-symmetric cases, as none
of the methods specifically satisfies the horizontal force equilibrium
and the moment equilibrium related to rotation around a vertical axis,
or a horizontal axis parallel with the direction of motion (cf. Hungr,
1997). A method of balancing lateral forces is implemented in
connection with the Bishop and Janbu algorithms, as described in Hungr
(1997). This provides results similar to those obtained by the rigid
wedge stability solutions (e.g. Hoek and Bray, 1977).
Fredlund, D.G. and Krahn, J., 1977. Comparison of
slope stability methods of analysis. Canadian Geotechnical Journal, 14:
E., and Bray, J., 1977. Rock slope engineering. The Institution of
Mining and Metallurgy, London, 250p.
O., 1987. An extension of Bishop’s Simplified Method of slope stability
analysis to three dimensions. Géotechnique, 37: 113-117.
O.,1994. A general limit equilibrium model for three-dimensional slope
stability analysis. Discussion of an article by L.Lam and D.G.
Fredlund. Canadian Geotechnical Journal, 31: 793-795.
O., 1997. Slope stability analysis. Keynote paper, Procs., 2nd.
Panamerican Symposium on Landslides, Rio de Janeiro, Int. Society for
Soil Mechanics and Geotechnical Engineering, 3: 123-136.
O., Salgado, F.M. and Byrne, P.M., 1989. Evaluation of a
three-dimensional method of slope stability analysis. Canadian
Geotechnical Journal 26: 679-686.
L. and Fredlund, D.G., 1993. A general limit equilibrium model for 3-D
slope stability analysis. Canadian Geotechnical Journal, 30: 905-919.