Ground Motions and Structures - Earthquake Engineering for Structural Design - page 300

300 Earthquake Engineering for Structural Design

The forces acting on the foundation are different for static and dynamic loads. If the
static loads are constant in time, the dynamic ones vary with the time. The excessive
static loads may generate a general failure; the dynamic loads induce permanent
irreversible displacements. So, the limit seismic load can be defined as the one
producing excessive permanent displacements, which impede the proper functioning of
the structure (Pecker, 1996).
The seismic behavior of these kinds of foundations under both static and seismic
forces will be discussed in the following sections.

8.2.2 Spread Shallow Foundations

Spread shallow foundations are presented in Figure 8.4; they are used when the soil
conditions are adequate and the acting forces are not too strong. In seismic areas it is
recommended to inter-connect the footing elements, in order to restrain any relative
movement of the foundations.
There are two methods to evaluate the dynamic response of spread shallow
foundations:
Impedance method , which considers the opposition to the motion of the foundations
subjected to the dynamic forces acting on the structure. The structural impedance of the
foundation is the ratio between the force introduced by the structure and the resulting
velocity at the foundation level. This method is mainly used in the approach which
considers the interaction soil-foundations-structure, the inelastic deformation of soil
being ignored. This method is mainly based on the expansion of computers and
numerical analysis and it comes from the elastic half-space approach.
The main problem is the determination of the soil parameters: stiffness for different
displacement types. The displacements, which are considered for a single foundation,
are the vertical, the rocking and the horizontal (Carrubba et al, 2000):
(i) In case of vertical displacements, the foundation is constrained to settle
uniformly, by increasing the vertical load in the mass center of the basement
(Fig. 8.5a).
(ii) In case of rocking displacements, the applied system of forces being in the
mass center, the foundation is constrained to rotate, without uplifting, settling
or swaying (Fig. 8.5b).
(iii) In case of swaying displacements, the applied system of forces being in the
mass center, the foundation is constrained to translate, without rotating,
settling or uplifting (Fig. 8.5c).
For each displacement, the corresponding stiffness is determined. The method allows