# Regional slope stability and slope-failure mechanics from the two-dimensional state of stress in an infinite slope

## Abstract

Rapid estimates of regional submarine slope stability can be obtained using 1-D infinite-slope analysis or empirical 2-D analyses, such as the log-spiral or φ-circle methods. In these methods, slope stability is evaluated along a pre-defined slip surface because the principal stresses in the slope and the slip-plane directions they control are undefined. However, where these pre-defined slip surfaces are not a good approximation of the surface along which a slope failure actually occurs, the analyses cannot explain the physics and observed geometry of the failure. Here we present an alternative, 2-D analytical solution for the state of stress in an infinite slope that incorporates cohesion and constant pore pressure, and yields the principal stresses and possible slip-plane directions along which the slope can fail. As a result, the analysis provides a framework for understanding the general geometry and relative motion of mass movements not addressed by 1-D infinite-slope analysis or the empirical 2-D analyses. We use our 2-D infinite-slope analysis to show that if the compressive stresses in the lower part of a slope are great enough, slope failure will occur along a basal plane, which in turn will permit extensional deformation along a steeper, headwall plane farther upslope. We then discuss how such failure can be facilitated on slopes of low inclination by excess pore pressure. Based on this discussion, we suggest that if pore pressure becomes high enough, slope failure can be initiated at a lower pore pressure and along a lower-angle basal plane than predicted by 1-D infinite-slope analysis.