TM 5-818-1 / AFM 88-3, Chap. 7
(3) For cohesive soils as clays and peat,
The shear strain amplitude, AΕ, may be computed from
the shear modulus is related to Su as follows:
the axial strain amplitude, Ε,and Poisson's ratio as
G = K2su
(17-25)
follows:
For clays, K2 ranges from 1500 to 3000. For peats, K2
AΕ = Ε(1 + )
(17-22)
ranges from 150 to 160 (limited data base).
For the special case of saturated soils, Poisson's ratio is
(4) In the laboratory, the shear modulus of
0.5, which leads to the following:
soil increases with time even when all other variables are
G = E/3
held constant. The rate of increase in the shear modulus
AΕ = 1.5Ε
is approximately linear as a function of the log of time
d. Correlations.
after an initial period of about 1000 minutes. The change
(1) Empirical correlations from many sets
in shear modulus, ∆G, divided by the shear modulus at
of data have provided several approximate methods for
1000 minutes, G1000, is called the normalized secondary
estimating the S-wave velocity and shear modulus for
increase. The normalized secondary increases range
soils corresponding to low-strain excitation. For many
from nearly zero percent per log cycle for coarse sands
undisturbed cohesive soils and sands:
to more than 20 percent per log for sensitive clays. For
2
G =1230(21973 - e) (OCR)" (o)0.5 (pounds 1 + per
good correlation between laboratory and field
square inch)
(17-23)
measurements of shear modulus, the age of the in situ
where
deposit must be considered, and a secondary time
e = void ratio
correction applies to the laboratory data.
η = empirical constant, which depends on
e. Damping in low strain levels.
Critical
the PI of cohesive soils (table 17-4). For sands, PI = 0
damping is defined as
and η = 0, so OCR term reduces to 1.0. For clays, the
cc = 2 √km
(17-26)
maximum value is η = 0.5 for PI > 100.
where k is the spring constant of vibrating mass and m
σ0 = 1/3 (σ1 + σ2 + σ3) = mean normal
represents mass undergoing vibration (W/g). Viscous
effective stress, pounds per square inch
damping of all soils at low strain-level excitation is
(2) For sands and gravels, calculate the
generally less than about 0.01 percent of critical damping
low-strain shear modulus as follows:
for most soils or:
G = 1000(K2)(σ0) (pounds per square foot) (17-24)
0.5
D = c/c, < 0.05
(17-27)
where
It is important to note that this equation refers only to
K2 =empirical constant (table 17-5)
material damping, and not to energy loss by radiation
=90 to 190 for dense sand, gravel, and cobbles
away from a vibrating foundation, which may also be
with little clay
conveniently expressed in terms of equivalent viscous
σ0 = mean normal effective stress as in equation
damping.
Radiation damping in machine vibration
problems is a function of the geometry of the problem
(17-23) (but in units of pounds per square foot)
rather than of the physical properties of the soil.
Table 17-4. Values of Constant r Used with Equation (17-23) to Estimate Cyclic Shear Modulus at Low Strains
Plasticity Index
K
0
0
20
0.18
40
0.30
60
0.41
80
0.48
>100
0.50
(Courtesy of 0. Hardin and P. Drnevich. "Shear
Modulus and Damping in Soils: Design Equations and
Curves," Journal., Soil Mechanics and Foundations
Division. Vol 98. No. SM7. 1972, pp 667-692. Reprinted
by permission of American Society of Civil Engineers,
New York.)
17-13
Previous Page
