Slope Stability Evaluation Using Tangent Similarity Measure of Fuzzy Cube Sets

Abstract

Due to various geological problems and geological materials of slope, there is a kind of non-continuous and uncertain natural geological body. Because of the complexity of various external factors, the slope stability is not easy to be determined, which leads to the ambiguity of human's judgments between stability and instability. Therefore, it is crucial that a simple evaluation method for judging the slope stability with uncertain information is established in slope stability analysis. This study selects nine impact factors: the lithology type, the slope structure, the development degree of discontinuity, the relationship between inclination and slope of discontinuities, the slope height, the slope angle, the mean annual precipitation, the weathering degree of rock, and the degree of human action, which can be expressed as the fuzzy cubic information (the hybrid information of both a fuzzy value and an interval-valued fuzzy number). Then, a tangent similarity measure between fuzzy cube sets (FCSs) is developed for the slope stability evaluation, where the tangent similarity measure values between FCSs of the slope sample and FCSs of slope stability grades/patterns (stability, slight stability, slight instability, and instability) are used for the assessment of the slope stability in FCS environment. Lastly, eight slope samples are provided as the actual cases to show that the eight evaluation results of slope stability using the proposed similarity measure of FCSs are in accordance with the actual results of the eight actual cases, which indicate the effectiveness of the proposed method under FCS environment.