STRUCTURAL MASS, DAMPING, AND RESTRAINT
53
équations similar to (2.74) and (2.75) for the calculation of (, for a pile in clayey
soil foundations.
DISC^
7/Àwk
w\\
(b) SOIL-D1SC MODEL
Figure 2.24 Dynamic model for disc-soil interactions.
(a) SOIL FOUNDATION
Consider now the measured effects soil behavior to the motion of a contacting
structure. Veletsos and Wei (1971) performed extensive laboratory experiments
on soils in contact with a dise of radius rg, 95 depicted in Figure 2.24a. In a
typical experiment, this dise was subjected to a harmonie frequency eu. first in
the direction of sliding, v, and then in pure rotation 0. Nataraja and Kirk (1977)
correlated these data for applications to gravity platform dynamics. For dise
sliding motion only, the respective constants for soil stiffnesss and damping are
Âq and ; and for rotational motion only, these respective constants are kg and
cg. These constants, shown in the dise model of Figure 2.24b, are as follows:
,
8G«
k\ = - ----2 — v
1 - O.O5euro^/^-^ 7*0 = Qi -
(2.76)
0.67 + 0.02u>ro^pJ r*
(2.77)
k* =
( 1 - 0.215u;ro Æ )
= a0 -
(2.78)
3(1 - v) \
y
/
“Psro
(2.79)
Here Gs, v, and p3 are the shear modulus, Poisson’s ratio, and mass density,
respectively, of the soil. The parameter eu (rad/sec) is the frequency of the dise.
The use of this dynamic soil model is illustrated in Example Problem 5.2.
The validity of employing équations (2.76)-(2.79) for full-scale design of gravity platforms still needs to be shown through full-scale testing. Efforts to employ
the generalizations of continuum mechanics to characterize the dynamic, mechanical properties of soil, including the formulation of constitutive équations
from carefully designed experiments, are discussed by Zienkiewicz et al. (1978,
Chapters 10-16) and Prévost et al.(1981).
53
équations similar to (2.74) and (2.75) for the calculation of (, for a pile in clayey
soil foundations.
DISC^
7/Àwk
w\\
(b) SOIL-D1SC MODEL
Figure 2.24 Dynamic model for disc-soil interactions.
(a) SOIL FOUNDATION
Consider now the measured effects soil behavior to the motion of a contacting
structure. Veletsos and Wei (1971) performed extensive laboratory experiments
on soils in contact with a dise of radius rg, 95 depicted in Figure 2.24a. In a
typical experiment, this dise was subjected to a harmonie frequency eu. first in
the direction of sliding, v, and then in pure rotation 0. Nataraja and Kirk (1977)
correlated these data for applications to gravity platform dynamics. For dise
sliding motion only, the respective constants for soil stiffnesss and damping are
Âq and ; and for rotational motion only, these respective constants are kg and
cg. These constants, shown in the dise model of Figure 2.24b, are as follows:
,
8G«
k\ = - ----2 — v
1 - O.O5euro^/^-^ 7*0 = Qi -
(2.76)
0.67 + 0.02u>ro^pJ r*
(2.77)
k* =
( 1 - 0.215u;ro Æ )
= a0 -
(2.78)
3(1 - v) \
y
/
“Psro
(2.79)
Here Gs, v, and p3 are the shear modulus, Poisson’s ratio, and mass density,
respectively, of the soil. The parameter eu (rad/sec) is the frequency of the dise.
The use of this dynamic soil model is illustrated in Example Problem 5.2.
The validity of employing équations (2.76)-(2.79) for full-scale design of gravity platforms still needs to be shown through full-scale testing. Efforts to employ
the generalizations of continuum mechanics to characterize the dynamic, mechanical properties of soil, including the formulation of constitutive équations
from carefully designed experiments, are discussed by Zienkiewicz et al. (1978,
Chapters 10-16) and Prévost et al.(1981).