Computation of Slopes Stability Over Large Areas of the Seafloor With Variable Topography
Authors: Liedtke E.A. , Wright S.G. 
Published: October 2008

Abstract
Slope stability must often be evaluated over relatively large expanses of the seafloor for design of pipelines and certain types of offshore structures having relatively large "footprints". Because of the large area of interest, the topography and, thus, the slope stability may vary significantly. In such cases it is appropriate to evaluate the stability (factor of safety) as a spatially varying quantity.
This paper addresses the stability of slopes over large areas and schemes for computing the factor of safety as a spatially varying quantity. Traditional methods used to compute stability of slopes on land do not work well for this purpose because often only a single value for the factor of safety is determined. In particular, the procedures that are typically used to seek the most critical sliding surfaces with the minimum factor of safety for slopes on land have to be altered in order to calculate the factor of safety as a spatial variable. For this paper several different search schemes were implemented to compute the factor of safety as a function of position along the slope. The search schemes are presented and results obtained from the implementation of the search schemes are evaluated for a deep water slope located in the Gulf of Mexico.

Introduction
Development of facilities offshore often requires that slope stability be evaluated over relatively large expanses of the seafloor. For example, pipelines may need to be routed over long stretches of the seafloor or offshore structures may utilize foundation schemes having relatively large footprints. The task of assessing slope stability over a large area is made more complicated by the inevitable variation in topography over the area of interest. In such instances it is appropriate to evaluate slope stability spatially and to compute factors of safety as a function of position along the seafloor.
The normal methods used for computing slope stability(factor of safety) are based on limit equilibrium procedures. All of these methods involve trial and error "searches" to locate the critical potential sliding surfaces. Methods for doing this are well-developed for land-based applications where a single critical shear surface and minimum factor of safety are sought. However, these methods do not work well for offshore applications where stability is to be evaluated spatially and the factor of safety is considered to vary with position along the slope. This paper addresses the issue of computing factors of safety for slopes where the factor of safety is a spatially varying quantity. In particular, several schemes are presented and evaluated for searching out critical potential sliding surfaces and corresponding minimum factors of safety.

Site Description
To illustrate the various computational schemes considered in this paper, computations were performed for an actual offshore slope profile. The profile was developed from bathymetric data for the Pigmy Basin area of the Gulf of Mexico. The bathymetric data are based on data originally compiled by NOAA1 and provided by Bryant et al.2.

Slope Profile.
The slope profile used was selected because it represents an area of relatively steep slopes and irregular bathymetry. The approximate latitude and longitude near the mid-point of the cross-section are 27°14'N and 91°26'W, respectively. The slope cross-section is shown in Fig. 1. The steepest portion of the slope is approximately 35 degrees. The profile spans a horizontal distance of approximately 4000 meters: Water depths for the slope range from 2240 to 1470 meters; the change in elevation is 770 meters.