Soil Behavior: Dynamic Soil-Structure Interactions - Dynamic Behavior of Concrete and Seismic Engineering - page 159

foundations, the plastification is likely to take place at the angles of the base, owing
to the oscillation moment of the structure.
The extreme soil plastification case corresponds to mobilizing the ultimate
capability of the foundations. If loading is applied permanently, such a situation
would bring about failure through loss of the supporting capability of the
foundations. Because under seismic stress, the applied loading varies with time, this
temporary mobilizing of the strength capability does not lead to failure, but the
appearance of irreversible displacements. These are not necessarily harmful to the
good behavior of the structure. Their evaluation allows us to design foundations by
relying on performance criteria (performance - based design) rather than on a safety
criterion with regard to “failure” [PEC 00].
4.4.3. Modeling the non-linear soil-structure interaction
The most direct method for taking geometric or behavior non-linearities into
account is still the finite element method. Thanks to a behavior law adapted to the
materials and the soil-structure interface elements, this method is the most versatile.
However, we should not lose sight of the fact that implementing this method is quite
complex and requires modeling, digital analysis and soil and structural dynamics
competences. Furthermore, in spite of considerable computer advances, the
calculation times are still quite long. The result is that the method is best suited to
verifications, but not to pre-dimensioning, as this requires many varying studies.
To get round such difficulties, sub-structuration methods similar in spirit to the
methods developed for the study of linear phenomena have been developed recently.
We merely present the outlines that give birth to the dynamic macro-element
concept. For a more comprehensive presentation of the subject as well as an
exhaustive bibliographic study of those methods, see [CRE 01a], [CRE 01b] and
[CRE 02].
The general philosophy of the method involves defining two sub-structures: the
soil and the soil-foundation interface on the one hand, and the structure on the other.
The division is made at the level of the foundations. The soil-interface sub-structure
is conceptually sub-divided into the neighboring field and far field (Figure 4.16); the
exact boundary between both sub-fields is unknown, but it does not explicitly
intervene in the macro-element concept.
The far field corresponds to the region where the soil-structure interaction can be
neglected; the behavior in this area is governed by the propagation of seismic waves
and the energy dissipation there is mainly viscous radiative damping. Quite