Evaluating Seismic Stability of Embankment Dams - Multiscale Geomechanics: From Soil to Engineering Projects - page 366

Beyond the critical state, the dilatancy is activated and controlled by the
following equation:

Ψ = 1.6 . ( ϕ pic - ϕ crit )

In the conditions of potential liquefaction, the relative density is sufficiently
small for the dilatancy angle Ψ to be between 0 and a few degrees.

10.6.5. Volumetricstrainlaw:liquefaction

Byrne's law is an incremental law that describes the volumetric strain or the
material contractancy under cyclic deviatoric loading. In undrained condition, the
total volume remains constant and, therefore, the material contractancy leads to an
isotropic unloading created by an increase in the pore pressure. The pore pressure
change du is given by [BYR 94]:

1

du = ⋅ ⋅ K Δε

vd

nK
K

1 +

w

with:

− du : pore pressure change;

− n : porosity;

− K : material bulk modulus;

− K w : water bulk modulus;
− Δε vd : volumetric strain increment.

Byrne's law is expressed as follows:

C ε
γ

⋅

2 vd

Δε vd ½ = 0.5. C 1. γ exp (- )

with:

− Δε vd ½ : volumetric strain increment created during a half-cycle of shear strain
amplitude γ;

− ε vd : sum of the increments due to the preceding cycles;
− C 1, C 2 : material constants.