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Comparison of 3D Finite Element Slope Stability With 3D Limit Equilibrium Analysis
Comparaison de la stabilité des éléments 3D pente finie avec l'analyse limite d'équilibre 3D
Lu H.H., Xu L.M., Fredlund M.D.
SoilVision Systems Ltd., Saskatoon, SK., Canada
Fredlund D.G.
Golder Associates Ltd., Saskatoon, SK., Canada
ABSTRACT: The two-dimensional (2D) limit equilibrium analysis is widely used in geotechnical engineering for slope stability
analysis. Three-dimensional (3D) slope stability analysis is rarely performed although all slope failures are 3D in reality. The 3D
shear strength reduction (SSR) technique using finite element method (FEM) analysis and 3D limit equilibrium method (LEM) based
on columns to predict a factor of safety for slopes have been in existence for decades. Recent software tools allow the improved
analysis of 3D slope stability through LEM and SSR techniques. The purpose of this paper is primarily to compare 3D FEM-SSR
analysis with 3D LEM analysis through the examination of benchmark slope stability analysis examples. The results indicate that
there is reasonable agreement between these two methods.
RÉSUMÉ : L'analyse d'équilibre limite en deux dimensions (2D) est la méthode d'analyse de stabilité des pentes la plus couramment
utilisée en géotechnique. L'analyse de stabilité des pentes en trois dimensions (3D) est rarement effectuée bien que tous les
glissements de terrain sont en réalité tridimensionnels. La technique de la réduction de résistance au cisaillement (SSR) en 3D
utilisant la méthode des éléments finis (FEM), ainsi que l'analyse d'équilibre limite (LEM) en 3D basée sur des colonnes pour prédire
un facteur de sûreté pour des pentes, existent depuis des décennies. Les codes de calcul récents permettent d'améliorer l'analyse de
stabilité des pentes en 3D à l'aide des techniques de LEM et de SSR.
Le but de cet article est principalement de comparer l'analyse de FEM-SSR en 3D avec l'analyse de LEM en 3D à travers des
exemples de référence d'analyse de stabilité. Les résultats indiquent qu'il y a un accord raisonnable entre ces deux méthodes.
KEYWORDS: 3D Slope Stability Analysis, Shear Strength Reduction, Limit Equilibrium Method, Finite Element Method.
1 INTRODUCTION
The 2D LEM is widely used in geotechnical engineering for
slope stability analysis. However all slope failures are 3D in
reality. The 2D approach is generally considered to be
conservative in that 3D influences of geometry are not
accounted for in a 2D analysis. Furthermore, the assumption
that 2D analyses lead to conservative factors of safety is correct
only when the critical pessimistic section of the 3D model is
selected for the 2D analyses. It is time consuming to ensure that
the 2D section model is the critical pessimistic 2D section for
some general slopes. The use of 3D slope stability analysis is
important to model real world problems, to make the designs
more economic, and to provide a guide for 2D designs. It is
useful, for example, to know exactly what percentage the 3D
FOS is higher than the 2D analysis. The most common methods
for 3D slope stability analysis are 3D LEM based on columns
and 3D SSR based on FEM analysis.
1.1
3D LEM slope stability analysis
3D LEM slope stability analysis is traditionally based on an
extension of 2D LEM analysis. Many researchers have done
work on 3D LEM analysis (Hovland 1977, Hungr, Zhang 1988,
Salgado and Byrne 1989, Lam and Fredlund 1993, Cheng, etc.
2005). The slicing method in 2D analyses has been extended
into 3D analysis with columns by various authors due to the
popularity of 2D LEM slicing methods. Some of the benefits of
the 2D slicing method include its ability to accommodate
complex geometries, variable soils, water pressure conditions
and different reinforcement systems, etc..
The majority of the 3D LEMs are based on the assumption
that the failure direction is pre-defined in order to derive the
FOS equations, i.e. the failure sliding direction is not part of the
slope stability analysis solution. Location of the critical failure
surface and its direction is a tough global optimization problem.
Jiang (1997), Yamagami and Jiang (1997) provided a
optimization-minimization procedure (OMP) for their Dynamic
Programming (DP) (Baker, 1980) and random number
generation technique to find the critical slip surface and
corresponding sliding direction. Cheng and Yip (2003) derived
3D asymmetric slope stability analysis equations based on
extensions of simplified Bishop, simplified Janbu and
Morgenstern-Price methods, and the direction of slide can be
determined from 3D force/moment equilibrium equations. Their
formulation is equivalent to Yamagami and Jiang's OMP.
SoilVision Systems Ltd. (SVS) has incorporated all the
popular 3D LEMs into its commercial 3D slope stability
analysis software - SVSLOPE 3D. Recently SVS has added a
new feature to search for the critical slip surface sliding
direction in 3D, which is similar to Jiang (1997)'s procedure.
This feature enables the modeling of 3D slopes by the LEM at
any angle and is applicable for municipal designs including
calculation of setback distrances as well as the stability of open
pits in the mining industry as well as other applications.
1.2
3D FEM-SSR slope stability analysis
The finite element method (FEM) has been extensively used to
analyze various geotechnical problems. To perform slope
stability analysis with the FEM, the SSR technique dictatates
that the soil shear-strength is gradually reduced until failure
conditions occur. The factor of safety (FOS) for a SSR analysis
is defined as the ratio of the shear strength of the soil to the
shear stress developed along the critical failure surface. This
relationship is presented in the following equations.
where and
∅
are the cohesion and angle of internal friction
for the Mohr-Coulomb shear strength parameters.
and are
factored shear strength parameters.
SRF
is called the strength
reduction factor. In order to reach to the state of limiting
