ABSTRACT

When the soil is plastic, its stress state must satisfy the yield function F = 0. Similar to Potts & Zdravkovic (2012), the partial factor of safety, γm, is included in the yield function, F, as an additional state parameter, in scalar form. Therefore:

( )eq m{ } { }k s 0= (7) The consistency condition requires that total

differential dF is also equal to 0. Applying the chain rule:

dF F F

k F s

s F

=

∂ ∂

⎧⎨⎩ ⎫⎬⎭ { } ∂⎨⎩

⎫⎬⎭ { }k +

∂ ∂

∂ ∂

σ

γ γ

+ ∂⎧

Δ Δ+ (8)

1 INTRODUCTION

Quantifying margins of safety in geotechnical problems is not naturally compatible with numerical analysis, but it is nonetheless required by the latest design codes such as Eurocode 7. The authors have developed a consistent approach for accounting for factors of safety in numerical analysis of saturated soils (Potts & Zdravković, 2012) and this paper presents its extension to unsaturated soil problems. It is recognised that changes to the software are needed at the level of the governing finite element equations and the constitutive model and both are shown below.