CLARA-W 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.
CLARA-W 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
Grid Search result screen (2D)
When 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
The 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: 429-439.
Hoek, E., and Bray, J., 1977.
Rock slope engineering. The Institution of Mining and
Metallurgy, London, 250p.
Hungr, O., 1987. An extension of
Bishop’s Simplified Method of slope stability analysis to three
dimensions. Géotechnique, 37: 113-117.
Hungr 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.
Hungr, 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.
Hungr, O., Salgado, F.M. and
Byrne, P.M., 1989. Evaluation of a three-dimensional method of
slope stability analysis. Canadian Geotechnical Journal 26:
Lam, L. and Fredlund, D.G., 1993.
A general limit equilibrium model for 3-D slope stability
analysis. Canadian Geotechnical Journal, 30: 905-919.