c. Laboratory measurement of dynamic

hysteresis loop, and the strain level is taken as the

stress-strain properties. Low shear-strain amplitude, i.e.

single-amplitude (one-half the peak-to-peak amplitude or

-2

origin to peak value) cyclic strain for the condition during

less than 10 percent, shear modulus data may be

that cycle of the test. Note that the equations for modulus

obtained from laboratory tests and usually involve

and damping shown in figure 17-9 assume the soil

applying some type of high-frequency forced vibration to

behaves as an equivalent elastic viscous, dampened

a cylindrical sample of soil and measuring an appropriate

material, which is linear within the range of strain

response. Some types of tests allow the intensity level of

amplitude specified. This assumption is usually made in

the forced vibration to be varied, thus yielding moduli at

most soil dynamics analyses because of the low-

different shear strains.

vibration amplitudes involved. If the cyclic hysteresis

(1) High strain-level excitation, i.e. 0.01 to

loops are obtained from triaxial test specimens, the

1.0 percent, may be achieved by low-frequency, cyclic

resulting modulus will be the stress-strain modulus, E. If

loading triaxial compression tests on soil samples. The

the tests involve simple shear or torsion shear such that

modulus, damping, and strain level for a particular test

shear stresses and strains are measured, the resulting

are calculated directly from the sample response data.

modulus will be the shear modulus, G. In either case,

The usual assumption for calculating the modulus and

the same equations apply.

damping from forced cyclic loading tests on laboratory

(2) The shear modulus, G, can be

samples is that at any cyclic strain amplitude the soil

computed from the stress strain modulus and Poisson's

behaves as a linear elastic, viscous, damped material.

ratio as follows:

A typical set of results may take the form of a hysteresis

loop as shown in figure 17-9. Either shear or normal

G

=

E

(17-21)

stress cyclic excitation may be used. The shear modulus

2(1+)

is calculated from the slope of the peak-to-peak secant

line. The damping is computed from the area of the

U. S. Army Corps of Engineers

Figure 17-9. Idealized cyclic stress-strain loop for soil.

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