UFC 3-220-01N
15 AUGUST 2005
of both media and the incident angle are known. If a layer containing a lower modulus
overlies a layer with a higher modulus within the half-space, another surface wave,
known as a Love wave, will occur. This wave is a horizontally oriented S-wave whose
velocity is between the S-wave velocity of the layer and of the underlying medium.
The decay or attenuation of stress waves occurs for two reasons:
geometric or radiation damping, and material or hysteretic damping. An equation
including both types of damping is the following:
(12-18)
r1
C
exp [-α(r2 r1)]
A2 = A1
r2
where
A2 = desired amplitude at distance r2
A1 = known or measured amplitude at radial distance r1 from vibration source
C = constant, which describes geometrical damping
= 1 for body (P- or S-) waves
= 0.5 for surface or R-waves
α = coefficient of attenuation, which describes material damping
12-1.4.3
Isolation. The isolation of certain structures or zones from the effects of
vibration may sometimes be necessary. In some instances, isolation can be
accomplished by locating the site at a large distance from the vibration source. The
required distance, r2, is calculated from equation (12-18). In other situations, isolation
may be accomplished by wave barriers. The most effective barriers are open or void
zones like trenches or rows of cylindrical holes. Somewhat less effective barriers are
solid or fluid-filled trenches or holes. An effective barrier must be proportioned so that
its depth is at least two-thirds the wavelength of the incoming wave. The thickness of
the barrier in the direction of wave travel can be as thin as practical for construction
considerations. The length of the barrier perpendicular to the direction of wave travel
will depend upon the size of the zone to be isolated but should be no shorter than two
times the maximum plan dimension of the structure or one wavelength, whichever is
greater.
12-1.5
Evaluation of S-Wave Velocity in Soils. The key parameter in a
dynamic analysis of a soil-foundation system is the shear modulus, G. The shear
modulus can be determined in the laboratory or estimated by empirical equations. The
value of G can also be computed by the field-measured S-wave velocity and equation
(12-16).
12-1.5.1
Modulus at Low Strain Levels. The shear modulus and damping for
machine vibration problems correspond to low shear-strain amplitudes of the order of 1
to 3 x 10-4 percent. These properties may be determined from field measurements of
the seismic wave velocity through soil or from special cyclic laboratory tests.
12-14
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