UFC 3-220-01N
15 AUGUST 2005
12-1.3.5
Effect of Finite Thickness Of Elastic Layer. Deposits of real soils are
seldom homogeneous to significant depths; thus theoretical results based on the
response of a semi-infinite elastic media must be used with caution. When soil layers
are relatively thin, with respect to foundation dimensions, modifications to the theoretical
half-space analyses must be included.
Generally, the effect of a rigid layer underlying a single elastic layer of
thickness, H, is to reduce the effective damping for a foundation vibrating at the upper
surface of the elastic layer. This condition results from the reflection of wave energy
from the rigid base back to the foundation and to the elastic medium surrounding the
foundation. For vertical or torsional vibrations or a rigid circular foundation resting on
the surface of the elastic layer, it has been established that a very large amplitude of
resonant vibrations can occur if
In equation (12-13), Vs is the shear wave velocity in the elastic layer and fo
is the frequency of footing vibrations. When the conditions of equation (12-4) occur, the
natural frequency (equation (12-1)) becomes the important design criterion because at
that frequency excessive dynamic motion will occur. To restrict the dynamic oscillation
to slightly larger than the static displacement, the operating frequency should be
maintained at one half, or less, of the natural frequency (figure 12-2).
The relative thickness (expressed by H/ro) also exerts an important
influence on foundation response. If H/ro is greater than about 8, the foundation on the
elastic layer will have a dynamic response comparable to that for a foundation on the
elastic half-space. For H/ro < 8, geometrical damping is reduced, and the effective
spring constant is increase. The values of spring constant, k, in table 12-1 are taken as
reference values, and table 12-2 indicates the increase in spring constant associated
with a decrease in thickness of the elastic layer. Values of the increase in spring
constant for sliding and for rocking modes of vibration will tend to fall between those
given for vertical and torsion for comparable H/ro conditions.
12-8
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