frozen soil. In some cases a pumping action resulted,

Testing to date has not established definitive

wherein non-frozen soil and debris were ejected through

relationships with these variables but data indicating

the cracks in the frozen soil layer. There was mention, in

general trends are available.

(c) Measurements of velocity of the

a few oases, of sliding occurring along the interface of

the frozen and non-frozen layers.

dilatational wave have been made using seismic

(d) The design engineer should

methods. Table 4-6 lists velocities for a variety of frozen

visualize the possible effects of an earthquake on the

soils and rocks. If Poisson's ratio is known or assumed,

foundation, whether it may involve sliding of slabs of

Young's modulus may be calculated from such velocities

frozen soil in winter, sliding of saturated thawed soil over

as follows:

permafrost in summer, or other effect and should avoid

( 1 + ν ) ( 1 2ν ) ρ (Equation 7)

V 2

any situations or actions which may be hazardous or

E= c

1-ν

imprudent.

(3) Low stress, vibratory loads.

Vc =P-wave velocity

where:

(a) Design of foundations for radar

ν = Poisson's ratio

towers with rotating antennas and structures supporting

ρ = mass density

heavy machinery, turbines, generators, and the like,

must consider the response of the foundation and soil

mass to the vibration. Evaluation of natural foundation

frequency, displacements and settlement may be

(e) Figure 2-17 shows dynamic

required. The critical situation may be a condition of

moduli and Poisson's ratio determined by Kaplar for

which

can

produce

unacceptable

various frozen soils at various temperatures". It will be

displacements and settlements and/or interfere with the

noted that the stiffness decreases drastically as

operation of the facility. EM 1110-345-3102o gives a

temperature rises and approaches 32 F. The test

design procedure for predicting the resonant frequency

procedure used in this case did not allow measurement

and displacement under vibratory loads. Three modes of

of internal damping as a material property. No variation

motion are treated: vertical movement, rotation about a

of modulus and velocity with frequency or stress level

vertical axis, and rocking about a horizontal axis. The

was determined and test frequencies ranged from 830 to

equations are based on the elastic half-space concept.

4000 Hz. Stress levels were unknown but were low,

Damping is that involved in dissipation of energy with

such as to give a linear response.

distance; damping as a result of the viscous or internal

(f) The decrease in stiffness with

friction properties of the material is not accounted for.

rising temperature emphasizes the possibility that energy

However, as internal damping is small for many soils,

dissipation into the soil may raise the temperature

especially frozen soils, the procedure is adequate for

sufficiently to alter the foundation response or even its

most cases. A value for the shear modulus of the soil is

stability. A pile embedded in frozen soil and depending

required. Young's modulus and Poisson's ratio may also

for its bearing capacity on the adhesive strength between

be used. The elastic half-space method assumes that

the soil and pile may, under steady-state prolonged

the soil mass is more-or-less homogeneous and

vibration, dissipate energy into the soil sufficiently to

isotropic. If the soil mass radically departs from the

raise the temperature. The state-of-the-art does not

condition, as in the case of a strongly layered soil, a

currently allow calculation of energy dissipation into the

partially frozen condition or similar situation, special

soil and temperature rise at the soil/pile interface under a

design procedures must be employed. Computer codes

given dynamic load. However, the designer should

for calculation are available and two dimensional

consider the possibility.

computer codes are in the state-of-the-art. However, the

(g) Figures 4-56 through 4-60

required properties of the soils are not always directly

illustrate the effect of ice volume/soil volume ratio,

available from test. This is especially true of frozen soils.

degree of ice saturation, frequency and stress on the

Most material property inputs are based on one

modulus. Complete data including the complex Young's

dimensional plane strain tests. It is seldom possible to

and shear moduli, the corresponding velocity of wave

exactly reproduce in tests the complex stress and

propagation, Poisson's ratio, damping expressed as the

deformation states which govern actual behavior under

tangent of the lag angle between stress and strain, and

dynamic loads. Therefore, engineering judgment based

the attenuation coefficient have been reported by

on broad experience and knowledge must be employed

176

CRREL .

in choosing test procedures and in analyzing test results

to select suitable values for use in computer solutions.

(b) The response of frozen soils to

vibratory loads varies with the stress, strain, and

frequency imposed by the load, with exterior influences

such as temperature and confining pressure, and with

the soil characteristics such as void ratio, ice volume/soil

volume ratio, degree of ice saturation and soil type.