CLARA-W: Solution Algorithms

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 half-sine function.

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 engine.

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).

References

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: 679-686.

Lam, L. and Fredlund, D.G., 1993. A general limit equilibrium model for 3-D slope stability analysis. Canadian Geotechnical Journal, 30: 905-919.