A generalised framework is proposed in this paper incorporating almost all of the existing limit equilibrium methods of slices for slope stability analysis with general slip surfaces. The force and moment equilibrium equations are derived in terms of the factor of safety and the initially assumed normal stress distribution over the slip surface, multiplied by a modification function involving two auxiliary unknowns. These equations are then analytically solved to yield explicit expressions for the factor of safety. Various assumptions regarding the interslice forces can be transformed into a unified form of expression for the normal stress distribution along the slip surface. An iterative procedure is developed to expedite the convergence of the solution for the factor of safety. Experience to date indicates that the process generally converges within a few iterations. Computation schemes are suggested to avoid numerical difficulty, especially in computing the factor of safety associated with the rigorous Janbu method. The present framework can be readily implemented in a computer program, giving solutions of slope stability associated with a number of conventional methods of slices.

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The conventional methods of slices are commonly used for the analysis of slope stability. When anchor loads are involved, they are often treated as point loads, which may lead to abrupt changes in the normal stress distribution on the potential slip surface. As such abrupt changes are not reasonable and do not reflect reality in the field, an alternative approach based on the limit equilibrium principle is proposed for the evaluation of the stability of anchor-reinforced slopes. With this approach, the normal stress distribution over the slip surface before the application of the anchor (i.e., σ0) is computed by the conventional, rigorous methods of slices, and the normal stress on the slip surface purely induced by the anchor load (i.e., λpσp, where λp is the load factor) is taken as the analytical elastic stress distribution in an infinite wedge approximating the slope geometry, with the anchor load acting on the apex. Then the normal stress on the slip surface for the anchor-reinforced slope is assumed to be the linear combination of these two normal stresses involving two auxiliary unknowns, η1 and η2; that is, σ = η1σ0 + η2λpσp. Simultaneously solving the horizontal force, the vertical force, and the moment equilibrium equations for the sliding body leads to the explicit expression for the factor of safety (Fs)—or the load factor (λp), if the required factor of safety is prescribed. The reasonableness and advantages of the present method in comparison with the conventional procedures are demonstrated with two illustrative examples. The proposed procedure can be readily applied to designs of excavated slopes or remediation of landslides with steel anchors or prestressed cables, as well as with soil nails or geotextile reinforcements.Key words: slopes, factor of safety, anchors, limit equilibrium method.

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