APPLICATION OF SETS THEORY TO THE MODELLING OF RUNOUT DISTANCES OF SLOPE FAILURES IN STEEP TERRAIN

The parameters that characterize slope failures change after the event. For example, the head scarp may be lengthened by post-event erosion. Consequently, there is uncertainty over the precision of data collected some time after an event. The precision of any model of run-out distance is dependent on the accuracy of the measured parameters. The goal of this study is to build a new model with a narrower confidence interval that takes into account the uncertainty of some of the variables.

As the true values of many of the parameters are uncertain, sets theory has been applied to a data set obtained in the Selkirk Mountains, British Columbia. Data were collected for unconfined, single-path landslides and debris flows. Regression analysis on crisp sets was used to establish the relationship between the failure length (from initiation point to deposit toe) and geomorphological elements, geology, canopy closure and tree species. A new variable was introduced to capture the landslide path. The significant variables supplied by the regression analysis were “fuzzified” in order to introduce the uncertainty associated with reality. The “fuzzified” variables were used in a fuzzy regression analysis, using the linear programming approach of Tanaka (1982). The analysis of crisp sets reveals that the new variables, namely path, slope, bearing, height of the stand, canopy closure and horizontal and vertical curvature, are significant (at a level of a=0.1). These variables were also used in the fuzzy analysis. The confidence interval for the predicted value of runout distance is narrower with the fuzzy approach than with the crisp data set for more than 80% of events, indicating a better predictive ability.

The resulting equations can be easily incorporated into any management software that uses contours. For the study area in question, the model predicts failure runout distance with more than 80% precision. The best model for the distance traveled by slope failures is one that combines the results of crisp and fuzzy sets.