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Prediction of unconfined debris slide-flow travel distance using set theory Strimbu, Bogdan Mihai

Abstract

Mass movement risk assessments are usually separated into two components: movement initiation and the travel distance of the event. The initiation point is the point on the slope where the mass failed. This position is hard to determine and a common assumption is that it is the highest elevation of the scar. The travel distance is the distance from the initiation point to the point where all material is deposited. This study concentrates on particular forms of mass movements, namely unconfined debris flows and debris slides. The parameters that characterize mass movements change over time. Usually, measurements are performed after the event, resulting in the data being of questionable precision. The reliability of any mass movement travel investigation is dependent on the accuracy of the measured values. The results obtained are dependent on the precision of the original data, and can affect predictions made from the data in two ways: uncertainties in model lack-of fit (data suitability) and uncertainties in data meaning. This study builds a new debris slide-flow travel distance prediction model with a narrow confidence interval that can take into account the vagueness of the variables. Fuzzy set theory has been applied in order to overcome uncertainties related to the true value of the parameters. The study was performed using data from the Arrow Forest District, British Columbia, Canada. A total of 38 events were measured, classified as unconfined debris slide - flow, traveling through forested terrain, and used to build and test the debris slide - flow travel distance prediction model. The relationship between debris slide-flow length and other debris slide-flow attributes (i.e. geomorphology, geology, canopy closure and species) was established using regression analysis on crisp sets. A new attribute was introduced to capture the debris slide-flow path. The new path variable is based on the one-to-one relationship that exists between the binary and decimal numeration systems. The path variable uses uniform sections of the debris slide-flow, called reaches, which are larger than 25 m, except for first and last reach. Each reach can have a value 0 or 1 depending on the slope of the upstream reach. The first (uppermost) reach always has a value of 1. The values assigned to other reaches follows the rule that if the slope of the reach is less that the slope of the reach immediately above it, it is assigned value of 0; if the slope of the reach is greater than that of the upstream reach, it is assigned a value of 1. The event stops if the slope is less than 20° or it reach the stream. The analysis of the crisp data set revealed that the new path variable, slope, azimuth, height of the stand, canopy closure and horizontal and vertical curvature are the significant variables (at a significance level of a=0.05) affecting debris slideflow travel distance. The significant variables supplied by the regression analysis using crisp sets were fuzzified in order to introduce the vagueness of reality. The fuzzified variables were used in a fuzzy regression analysis, based on non-linear programming. The same variables used in the regression analysis of crisp sets were used in the fuzzy analysis. The confidence interval for debris slideflow travel distance prediction model using the fuzzy sets was smaller than 40% of the event travel distance. The models for the crisp and fuzzy sets show similar trends. Each model predicts the debris slide-flow travel distance with more than 80% precision. The final model used for the prediction combines both models, thereby minimising the confidence interval and the variable fuzziness. The equations derived from the models can be implemented in management software that uses digitized contour maps.

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