Soil Behavior: Dynamic Soil-Structure Interactions - Dynamic Behavior of Concrete and Seismic Engineering - page 135

Figure 4.6. Linear visco-elastic model

As the visco-elastic models reveal hysteresis loops under harmonic stresses, it is
tempting to represent soil behavior using such models (Figure 4.6) for those stresses.
However, the linear visco-elastic model leads to an energy dissipation cycle
depending on the stress frequency, which contradicts the experimental observations
(section 4.1).

We must establish equivalence between the actual material and the model: the
equivalence is based on the equal dissipative qualities of both the material and the
model.

For one-dimensional stresses, the stress-strain relationship in the Kelvin-Voigt
model is written as follows:

IJ = G Ȗ + C Ȗ [4.3]

where G and C are the spring and dashpot constants, and J and J are respectively
the strain and strain rate.

Under harmonic stress:

iȦt

Ȗ = Ȗ e [4.4]

m

the previous relationship is written:

C Z

ª º

W = G 1 + i J = G

*

J [4.5]

« »

m m m

G

¬ ¼