Spatial distribution of safety factors

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. Introduc ed is a general framework for safety maps that allow for a physically meani ngful extension of classical slope stability analysis. Safety maps are repr esented 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 o f:;lope stability possess a flat minimum involving a large zone within whic h safety factors are practically the same, representation of the results as a safety map provides an instant diagnostic tool about the state of the st ability of the slope. Such maps provide at a glance the spatial scope of re medial measures if such measures are required. That is, unlike the classica l slope stability approach that identifies a single surface having the lowe st factor of safety, the safety map displays zones within which safety fact ors 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 analys is. Culmann's method is used to demonstrate the principles and usefulness o f the proposed approach because of its simplicity and ease of application. Tea 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 ce rtain value.