Soil Behavior: Dynamic Soil-Structure Interactions - Dynamic Behavior of Concrete and Seismic Engineering - page 137

Figure 4.7. Definition of standard damping

The energy dissipated during a cycle then takes the form:

2
m

[4.9]

' W = ʌ G ȘȖ

The purpose of the equivalent linear visco-elastic models is to establish a
relationship of the form:

[4.10]

IJ G Ȗ

m m

where G * is a complex modulus that has to be chosen so as to involve the same
stiffness and energy dissipation properties as the real material. Several models have
been proposed for this purpose. Their characteristics are summarized in Table 4.3.

The first two models are due to Berleley's team [SEE 70]; the third was
developed by [DOR 90]. We note from Table 4.3 that the first model respects the
dissipated energy but overestimates stiffness; the second model respects stiffness but
underestimates dissipated energy. Only the third model satisfies both parameters.