Evaluating Seismic Stability of Embankment Dams - Multiscale Geomechanics: From Soil to Engineering Projects - page 363

10.6.3. Failurecriterion

The failure criterion corresponds to the Mohr-Coulomb criterion. The material
cohesion is equal to zero. The friction angles are determined from drained triaxial
tests, based on stress−strain curves through the following expression:

σ ' πφ

2

1
3

σ =

tan ( + )

4 2

with:

− ϕ , friction angle;

− σ' 1 , major effective stress;
− σ' 3 , minor effective stress.

Three friction angles control the behavior of cohesionless materials: the
characteristic angle φ CAR that corresponds to the change from contractive to dilative
behavior; the peak friction angle φ MAX that corresponds to the maximum strength;
and the critical friction angle φ C that corresponds to the residual strength and is,
therefore, extremely significant. In most cases, where liquefaction is analyzed, the
material density is low and the friction angle considered is the critical friction angle.
In the other cases, the peak friction angle is defined as a function of the initial e 0 and
critical e C void ratios, or as a function of the overconsolidation ratio p' c /p' o as
follows:

p A

C

t a n( ϕ ) tan( ) − ϕ = A .log = . −

MAX C 0 C

p ' C

0 C

i arez never stopped repeating that the critical state in soil mechanics is a unique
phenomenon. During liquefaction, discontinuities are created, corresponding either
to a thin water film at the base of an impervious layer or to shear strain localizations
and fissures in the neighboring material that disrupt the undrained condition. For this
reason, the relation between peak strength and the void ratio is measured from
undrained compression tests, whereas the ultimate strength S us at the end of the
earthquake, called the post-seismic or undrained residual strength, is measured from
extension tests following undrained cyclic loading. The ultimate strength S us is a
crucial parameter for the model because its value controls the post-seismic stability.
The model limits the pore pressure value in order to correctly simulate this ultimate
strength.