Soil Behavior: Dynamic Soil-Structure Interactions - Dynamic Behavior of Concrete and Seismic Engineering - page 160

naturally, and by analogy with the impedance concept, the distant field is modeled
using a spring and a dashpot independent of the frequency for simplification.

The neighboring field represents the medium part interacting with the
foundations: all the behavior non-linearities (geometric, material) are concentrated
with their potential couplings. This element is formulated in terms of global
variables as the stress wrench acts on the foundations and its stiff body movements.

The whole displacement of the foundations equals the sum of an elastic
displacement u el , a plastic displacement u pl and a displacement linked to the uplift
u up .

tot el pl up

u u u u

[4.42]

Figure 4.16. Dynamic macro-element concept

The plastic displacement u pl is calculated on the basis of a conventional plastic
model defined by the data of a failure criterion, a loading surface and a flow rule for
strain hardening. The failure criterion is provided by the carrying capability of the
foundations [PEC 97]; the strain hardening law combines both isotropic and
kinematic strain hardenings and the flow rule is non-associated.

The displacement caused by the uplift is estimated from an uplift model for
foundations lying on elastic soil [CRE 98].

The macro-element thus constituted is placed in series with the one representing
the far field (Figure 4.16, on the left). Conceptually it can be represented by an
assembly of springs and “brush springs” that couple all the degrees of freedom of
the foundations.