An Inverse Analysis of Unobserved Trigger Factors of the Slope Failures Based on Structural Equation Modeling

This paper presents an inverse analysis of the unobserved trigger factors with respect to the slope failures based on the Structural Equation Modeling (SEM). The quantitative prediction models generally construct the relationship between the past slope failures and the causal factors (i.e. lithology, soil, slope, aspect, etc.), but does not deal with the trigger factors(i.e. rail fall, earthquake, etc.), due to the difficulties of pixel-by-pixel observation of the trigger factors itself. As a measure, in this study, an inverse analysis algorithm on the “trigger factors” is proposed, which consists of the following steps: Step1: The relationship between the slope failures (as the endogenous variables), the causal and trigger factors (as the exogenous variables) are delineated on the path diagram used in SEM. Step2: The regression weights in the path diagram are estimated in minimizing the errors between the observed and reemerged “variance-covariance matrix” by the model. Step3: As an inverse estimation, through the measurement equation in SEM between the causal and the trigger factors, a “Trigger Factor Influence map (TFI map)” is newly produced. As an application, the TFI maps are produced with respect to the “slope failures” and the “landslides,” respectively. Furthermore, as a final product, the difference of those TFI maps are delineated on a “Difference map (DIF map).” The DIF map and its interpretation are indeed useful not only for assessing the hazardous area affected by the trigger factors, but also as a “heuristic information” for locating places for setting the field measuring systems.