Probabilistic Slope Stability Analyses of the Sigsbee Escarpment
Authors: Nadim Farrokh , Krunic Dejan , Philippe Philippe 
Published: October 2008

Abstract
The development of the Mad Dog and Atlantis prospects included an integrated geohazard study which covered a variety of geological, geophysical and geotechnical subjects. Both prospect areas are located at the main geological feature in the area, the Sigsbee Escarpment. This paper describes the probabilistic slope stability evaluations performed for the Atlantis prospect in detail. The results obtained for the Mad Dog are also presented.
In a geohazards study of an offshore site, where the main hazard to the facilities is submarine slides, it is essential to establish a model of the slide frequency (i.e. the annual probability of failure) in order to perform a risk evaluation. The approach used for estimating the annual probability of slope failure is described in the paper.

Introduction
Evaluation of the stability of natural or man-made slopes has traditionally been based on a deterministic approach where the margin of safety is quantified by the safety factor. Many of the parameters that are used in a stability analysis, in particular the soil shear strength, are inherently uncertain. The geotechnical engineer tries to deal with the uncertainties by choosing reasonably conservative parameters for the deterministic stability evaluation. This approach, however, fails to address the problem of dealing with uncertainties properly. In order to address the uncertainties in the soil properties and slope stability calculation models quantitatively, probabilistic slope stability evaluation was performed in the Atlantis project. The probabilistic slope stability model for deep-seated failure built on a simplified 2-wedge model for slope stability and the firstorder reliability method, FORM (Ref. 1). An important byproduct of the FORM-analysis is the sensitivity factor for each uncertain variable. The sensitivity factors quantify the contribution of the individual random variables to the overall uncertainty affecting the margin of safety for the slope. An infinite slope model was used for evaluating the stability of shallow drapes of soft mud on steep slopes.

Model for deep-seated failure
Finite element analyses of the stability of typical deep-water slopes in the North Sea have shown that a two-wedge model of slope failure will be critical if a weak layer with relatively low undrained shear strength exists at the base of the slope (Ref. 2). Further investigations showed that a simple 2-wedge model consisting of sliding block and a collapsing block (Fig. 1) may be used to investigate the stability of slopes comprised of more-or-less horizontal soil layers, even if a distinct weak layer is not present. This simple model provides a clear insight into the main parameters controlling the slope stability and it can be easily adopted for reliability analysis using the firstand second-order reliability methods (FORM and SORM). Fig. 1: The 2-wedge failure mechanism(AVAILABLE IN FULL PAPER)
A closed-form solution for safety factor can be obtained by considering the equilibrium of the two wedges and assuming the same safety factor "F" on all slip planes: