Spatial Distribution of Safety Factors

Abstract

Classical limiting equilibrium analysis seeks the minimum factor of safety and its associated critical slip surface. This objective is mathematically convenient; however, it limits the analysis' practical usefulness. Introduced is a general framework for safety maps that allow for a physically meaningful extension of classical slope stability analysis. Safety maps are represented by a series of contour lines along which minimal safety factors are constant. Each contour line is determined using limit equilibrium analysis and thus represents a value of global safety factor. Since most problems of slope stability possess a flat minimum involving a large zone within which safety factors are practically the same, representation of the results as a safety map provides an instant diagnostic tool about the state of the stability of the slope. Such maps provide at a glance the spatial scope of remedial measures if such measures are required. That is, unlike the classical slope stability approach that identifies a single surface having the lowest factor of safety, the safety map displays zones within which safety factors may be smaller than an acceptable design value. The approach introduced results in a more meaningful application of limiting equilibrium concepts while preserving the simplicity and tangibility of limit equilibrium analysis. Culmann's method is used to demonstrate the principles and usefulness of the proposed approach because of its simplicity and ease of application. To further illustrate the practical implications of safety maps, a rather complex stability problem of a dam structure is analyzed. Spencer's method using generalized slip surfaces and an efficient search routine are used to yield the regions within the scope where the safety factors are below a certain value.