POISSON’S RATIO EFFECT OF SLOPE STABILITY CALCULATIONS

Murray Fredlund, Rob Thode

In the proceedings of: GeoQuébec 2015: 68th Canadian Geotechnical Conference & 7th Canadian Permafrost Conference

Session: Landslides and Slope Stability I / Mouvements de terrain et stabilité des pentes I

ABSTRACT: This paper presents the results of a study on the effect of varying Poisson™s ratios on limit equilibrium slope stability analyses performed using the dynamic programming search technique. An example model is completed to show the impact of Poisson™s ratio on the strain vectors, the critical slip surfaces and factor of safety. The results showed that decreasing Poisson™s ratio causes the location of the critical slip surface, selected by the dynamic programming method, to move deeper into the slope, leading to a higher factor of safety. The critical slip surface is selected based upon kinematic admissibility criteria. The results of the method were also shown to become numerically unstable as cohesion approaches zero if adjustments to the kinematic admissibility criteria are not made. Therefore, care needs to be taken when analyzing cohesionless soils with low values of Poisson™s ratio.

RÉSUMÉ: Cet article présente les résultats d™une étude sur les effets de la variation du coefficient de Poisson sur les analyses de stabilité de la pente d™équilibre limite, en utilisant la programmation dynamique. Un exemple de modèle est complété pour montrer les impacts du coefficient de Poisson sur les vecteurs de contrainte, les surfaces de glissement et le facteur de sécurité. Les résultats démontrent que la diminution du coefficient de Poisson cause l™emplacement d™une surface de glissement critique, sélectionnée par la méthode de programmation dynamique, pour progresser plus bas dans la pente, ce qui conduit à un facteur de sécurité plus élevé. La surface de glissement critique est choisie sur la base de critères d™admissibilité cinématiques. Les résultats de la méthode peuvent devenir instables numériquement, lorsque la cohésion tend vers zéro, si les ajustements du critère d™admissibilité cinématique ne sont pas faits. Par conséquent, une attention particulière doit être portée lors de l™analyse de sols non-cohésifs à faible coefficient de Poisson. 1 INTRODUCTION The results presented in this paper are intended to clarify the role of Poisson™s ratio when using the dynamic programming technique under certain modeling conditions. The influence of the Poisson™s ratio appears to be magnified under certain conditions as illustrated in Figure 1. This figure raised the following issues with regards to a slope stability analysis: The effect of the Poisson™s ratio appears to have an adversely large effect on the location of the critical slip surface. The effect of the Poisson™s ratio appears to have an adversely large effect on the calculated factor of safety (Fs). In the example problem used, the classic slope stability methods predict a factor of safety close to 1.0 and a critical slip surface near to the ground surface. However, this behavior is not observed in this figure when using a low Poisson™s ratio™s? The Poisson™s ratio effect was noted when undertaking a slope stability analysis on waste rock material. It is important to determine the reason for the variation of the computed factor of safety, Fs, because of its potential influence on the calculation of the Fs when dealing with cohesionless materials. There also appears to be a tendency in geotechnical engineering practice to ignore the cohesion component of the soil and analyze situations with cohesion set to zero. This study directly comments on the use of such practices. 2 ANALYSIS The use of the dynamic programming method can be viewed as comprising two separate processes, namely: A searching algorithm (i.e., the dynamic programming method) The algorithm calculating the factor of safety (i.e., the limit equilibrium analysis) Any critical review of the dynamic programming procedure should be studied by separating the algorithm into the two components and asking the following questions: Is the LOCATION of the critical slip surface reasonable and correct? Is the CALCULATION of the factor of safety for that location reasonable and correct? It must be noted that the definition of the factor of safety used for the dynamic programming method is the same as the definition used for classic limit equilibrium methods. It should also be noted that a finite element stress analysis is used as the basis for determining the shear stress and the normal stress on the slip surface.

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