UFC 3-220-01N
15 AUGUST 2005
transmitted. The characteristics that distinguish these three waves are velocity, wave
characteristics of these waves as they are generated by a circular footing undergoing
vertical vibration on the surface of an ideal half-space with u= 0.25. The distance from
the footing to each wave in figure 12-7 is drawn in proportion to the velocity of each
wave. The wave velocities can be computed from the following:
(12-17)
(12-15)
(12-16)
where
The P- and S-waves propagate radially outward from the source along
hemispherical wave fronts, while the R-wave propagates outward along a cylindrical
wave front. All waves encounter an increasingly larger volume of material as they travel
outward, thus decreasing in energy density with distance. This decrease in energy
density and its accompanying decrease in displacement amplitude are called
geometrical damping or radiation damping.
The particle motions are as follows: for the P- wave, a push-pull motion in
the radial direction; for the S-wave, a transverse motion normal to the radial direction;
and for the R-wave, a complex motion, that varies with depth and occurs in a vertical
plane containing a radius. At the surface, R-wave particle motion describes a
retrograde ellipse. The shaded zones along the wave fronts in figure 12-7 represent the
relative particle amplitude as a function of inclination from vertical.
12-1.4.2
Layered Media. In a layered medium, the energy transmitted by a body
wave splits into four waves at the interface between layers. Two waves are reflected
back into the first medium, and two waves are transmitted or refracted into the second
medium. The amplitudes and directions of all waves can be evaluated if the properties
12-13
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