Soil Behavior: Dynamic Soil-Structure Interactions - Dynamic Behavior of Concrete and Seismic Engineering - page 140

In the linear visco-elastic modeling described below, the properties of the
material (secant modulus, damping) are adjusted to a “medium” strain level to
approximately account for the non-linearity of the behavior.

The results developed above in the case of unidirectional stresses immediately
become generalized in the case of harmonic stress with all the limitations for the
experimental validity of such an extension that we have mentioned previously.

The behavior law is written in a form similar to a generalization of Hooke's law:

/ *

H = : V

[4.11]

~ ~ ~

* is formed thanks to the complex volume and shear moduli. The
previous behavior law leads to the same shaped solutions as the linear elastic law,
hence its unquestionable appeal.

where tensor ~

In the case of an isotropic material, the behavior is entirely described using two
moduli, G and B, and theoretically, using two damping ratios associated with the
shear and volume strains, as well as their dependence on the amplitude of the shear
strain. In practice, both critical damping ratios are chosen to be identical.

The variation of these characteristics with regard to strain takes the shape given
in Figure 4.8. It is the conventional form for the results of the tests:

G = G(Ȗ) , Ș = Ș(Ȗ)

[4.12]

As practice stands at the moment, measuring these values can only be performed
under laboratory conditions with intact samples. The trial best suited to the range of
strains required is the resonant column test.

Such models are extensively employed in common practice. When they are used
together with an iterative process allowing values of modulus G and the loss
coefficient K to be selected as those compatible with the average level of resultant
strain, they yield strain and acceleration values that compare favorably with those
obtained using more sophisticated models or observed during real earthquakes. Such
models have the virtue of simplicity: they only require measurement of three
parameters (one more than the elastic model): shear modulus, volume modulus and
loss coefficient. As the soil has a non-linear behavior, these parameters depend on
the state of stresses and strains (Figure 4.8). The main limitation of these models is
the fact that they are unable to give irreversible strain values: those calculated by the