Advances in Determining Δu and s_u for Limit Equilibrium Analyses

Abstract

It is well known that in undrained stability calculations, total stress and effective stress analyses do not give the same calculated factor of safety when FOS >1. This is due to the fact that shear strength is defined differently in these two approaches: In total stress analyses, the mobilised shear stress is compared to undrained shear strength, i.e. strength at failure. In undrained effective stress analyses, the shear strength is defined as corresponding to the mobilised effective stress state. This causes an overestimation of FOS in undrained φ′-c′ analyses. Modelling of excess pore pressure Δu has traditionally been source of most uncertainty in undrained effective stress analyses. Having the correct shear strength along the slip surface can be considered the most crucial detail in all stability analyses. It can be argued that in the context of Limit Equilibrium analyses where deformations are not considered, priority should be given to calculating the shear strength correctly, instead of attempting to obtain a “correct” mobilised Δu value. This paper gives a general introduction to the new HSU (Hybrid s _u ) method. For the purposes of LEM analyses, Δu is calculated so that the resulting Mohr-Coulomb shear strength corresponds to the assumed failure state. This approach solves the inherent overestimation of FOS in undrained φ′-c′ analyses. To predict the effective stress at failure, a constitutive effective stress soil model is employed. Also presented is a concept of deriving undrained shear strength s _u in LEM, based on an effective stress soil model. This makes it possible to conduct the LEM stability analysis in terms of total stresses, while deriving soil strength from effective strength parameters. The different approaches of calculating Δu and s _u with the HSU method are compared using a theoretical stability calculation example. The relative merits of the different approaches are discussed.