Three-Dimensional Stability Analyses of Soil-Nailed Slopes by Finite Element Method

Abstract

Modern computer capabilities enable complex slope stability problems to be analyzed using the finite element method (FEM), including three-dimensional slopes. This research presents the results of analyzing two-and three-dimensional, unreinforced and soil-nailed, reinforced slopes. Previously performed two-dimensional slopes were modeled as three-dimensional slopes in an effort to validate the modeling technique. The Shear Strength Reduction (SSR) Method was used throughout this study to determine the Factor of Safety (FOS). Both two-and three-dimensional FEM models compared well with conventional, two-dimensional Limit-Equilibrium (L-E) results. Overall, results show that the FEM is an extremely diverse and robust alternative to conventional, L-E slope stability analyses, especially when complex site geometries or conditions exist. When modeling two-dimensional, unreinforced soil slopes using FEM, the most efficient and accurate element type that provides an acceptable failure mechanism is the CPE4 (4-noded bilinear quadrilateral) element in conjunction with either the Mohr-Coulomb or Drucker-Prager soil failure yielding criteria. When modeling threedimensional, unreinforced soil slopes using FEM, the most efficient and accurate element type that provides an acceptable failure mechanism is the C3D8 (8-noded linear brick) element in conjunction with the Mohr-Coulomb soil failure yielding criteria. Although the Drucker-Prager soil yielding criteria assumptions seem to offer more potential for three-dimensional applications, this study found no significant benefit from its use. For unreinforced slopes, three-dimensional, unit-width FEM models provide identical results to FEM slope models with depth, when end conditions are not considered. For soil-nailed reinforced slopes, three-dimensional, unit-width FEM models yield FOS values marginally higher than two-dimensional FEM and L-E models for all slope angles. Unit-width FEM models provide designers with a valuable tool for performing parametric studies and preliminary design. Three-dimensional FEM models of soil-nailed reinforced slopes can be used to effectively determine the soil nail orientation that yields the highest FOS, also known as the optimum soil nail orientation. For slopes with a level backfill, the optimum soil nail orientation (in degrees measured downward from horizontal) can be first approximated using the equation 58º-0.6β, where β is the slope angle in degrees. Three-dimensional FEM models can also be used to effectively determine the most efficient soil nail length. For slope heights of about 10 meters, the most efficient soil nail length can be first approximated using a soil nail length to slope height ratio equal to 1.0. A maximum vertical soil nail spacing of 2.4 meters and 1.9 meters is recommended for soil-nailed slopes with slope angles less than or equal to 60° and greater than 60°, respectively. A maximum horizontal soil nail spacing less than 1.9 meters is recommended for soil-nailed slopes for all slope angles. When performing three-di...