Stability Analyses and Charts for Undrained Slopes with Linearly Increasing Strength and an External Water Surface

Abstract

This paper will present stability analyses and charts to estimate the factor of safety (FS) for partially submerged undrained slopes with linearly increasing strength with depth and unlimited foundation depth. The problem has been tackled previously by ignoring the free standing water when the soil below and above the external water level, buoyant (γ′), and saturated unit weight (γsat), respectively, were assigned. This could then be combined with a simple unit weight averaging formula. In this paper, an analytical method that is based on optimization analyses will be proposed and charts will be presented that deliver an equivalent homogeneous unit weight as a function of slope angle (β), water depth (dw), and γsat. This equivalent unit weight (γequiv) will then be assigned to the entire slope and used in conjunction with the stability charts Hunter and Schuster proposed in 1968. The analyses will use an optimization approach that assumes circular failure mechanisms, which will be validated using finite-element (FE) strength reduction. In almost all cases, the charts that are presented in this paper led to a lower and more conservative FS than those obtained that used the simple weighted average approach. Some cases where the charts might lead to unconservative solutions when compared with FE solutions will be identified and discussed.