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 use- fulness. 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 gen- eralized 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. INTRODUCTION Practical slope stability calculations are usually done in the framework of limiting equilibrium analysis. This framework defines a functional relation associating a numberF, called the safety factor, with a certain class Y(x) of admissible slip sur- faces. For the present purpose it is convenient to write this relationship in the general form F = F(Y(x)uData) (1) where F = safety factor associated with the slip surface Y(x); F( ) signifies a functional that relates slip surfaces to safety factors; and Data refers to all given information defining a particular problem. Slope stability procedures (e.g., Culmann 1866; Fellenius 1936; Bishop 1955; Morgenstern and Price 1965; Spencer 1967; Janbu 1973) differ from each other in the structure of F( ) and the class of potential slip surfaces Y(x) considered. However, all limiting equilibrium procedures define the safety factor of a given slope by the following minimization process: F = F (Data) = min{F(Y(x)uData)} = F(Y (x)uData) (2) min min min Y(x)