High dimensional model representation for reliability analyses of complex rock–soil slope stability

The high-dimensional model representation (HDMR) and its modifications, the fractional HDMR (FHDMR) and hybrid HDMR (HHDMR), are new tools for calculating reliability indexes in stability analyses when several variables with large uncertainties are used to describe rock and soil behaviours. Plain HDMR utilises an inverse reliability analysis for the study of unknown design parameters associated with target reliability index values. This approach uses implicit response functions, named limit state functions, according to the response surface method (RSM). In this study, both the FHDMR and HHDMR are applied to the reliability index calculation of safety factors related to the stability analyses of sliding failure mechanisms in complex formations. These two methods improve the computational efficiency of the RSM in reliability index calculations compared to the HDMR. A case study of Carpathian Flysch rock–soil slopes is presented, and the efficiency of the reliability index calculation is estimated by comparing results with ones from neural network application.