Permafrost, Phillips, Springman & Arenson (eds)
© 2003 Swets & Zeitlinger, Lisse, ISBN 90 5809 582 7
Physical properties of frozen soils measured using ultrasonic techniques
Y. Sheng, W. Peng & Z. Wen
State Key Laboratory of Frozen Soil Engineering, Cold and Arid Regions Environmental and Engineering
Research Institute, CAS, Lanzhou, China
M. Fukuda
Low Temperature Institute, Hokkaido University, Sapporo, Japan
ABSTRACT: The velocity of ultrasonic waves traveling in a media reflects the dynamic properties of that
media, which should depend on the physical properties. Taking advantage of the easy-operation and non-destructive
nature of the ultrasonic technology, it is possible to determine some physical properties of frozen soils indirectly
by using this technique, either in the laboratory or in the field. A series of experiments were carried out to obtain
dynamic properties of frozen soils and to establish relationships between ultrasonic velocities and unfrozen water
contents, as well as the strength of frozen soil. Experimental results have indicated that the strength of frozen soil
can be estimated as a function of a single factor by measuring the ultrasonic velocities. Additionally, ultrasonic
velocities can be used to predict the unfrozen water content of frozen soil for different temperatures.
velocities in frozen Tomakomai silt (in Hokkaido,
Japan), and proposed a linear relationship (Sheng &
Fukuda 1998, Sheng et al. 2000a). The propagating
features of ultrasonic waves in frozen soil reflect the
dynamic properties of frozen soils, and the dynamic
properties depend on the physical properties. Therefore,
the physical index of frozen soils should determine
their ultrasonic propagating characteristics. In other
words, measuring the ultrasonic velocities in frozen
soils may help us to understand the physical properties of frozen soils. Although we can not establish a
mechanistic model of the propagation of ultrasonic
waves in frozen soils (because frozen soil is a multiphase material, and each component depends on the
others during the mechanical vibration, which makes
the micro-vibration in frozen soil complicated), considering frozen soil as a macro-uniform material, it is
possible to get some empirical relationships between
ultrasonic velocities and macro-physical properties,
such as strength or unfrozen water content.
Using the empirical relationships, we can achieve
the measurement of physical properties of frozen soils
by ultrasonic technology. With this thought in mind,
this paper primarily studies the possibility of applying
ultrasonic technology to the measurement of physical
properties in frozen soils, by comparing ultrasonic
velocities with experimental results of mechanical
and physical tests.
1 INTRODUCTION
Sonic waves are generated by propagation of mechanical vibration in media. According to the vibrating
frequency, a sonic wave is divided into an infrasonic
wave (20 Hz), an audible wave (20 Hz⬃20 kHz) and
an ultrasonic wave (
20 kHz). As a non-destructive
technology, the ultrasonic wave has been widely used
in medical inspection, crack detection in metal, and so
on. Simply put, the mechanism of ultrasonic detection
is to distinguish the physical properties of the detected
material through analyzing the propagating features
of ultrasonic wave in the material. The higher the
frequency of the ultrasonic wave, the better the resolution of detection, because only more than 1/4 wavelength of a “spot” inspected can result in a distinct
response to the wave propagation. This is why the
ultrasonic wave (not the audible wave) is often chosen
as a detecting tool.
The selection of detection frequency is subject to the
properties of materials and the detection purpose.
Since the 1970’s, researchers have been trying to apply
ultrasonic technology to frozen soils. The studies were
mainly focused on the understanding of the propagating characteristics of ultrasonic wave in frozen soils.
The results indicated that the ultrasonic velocities
changed little with temperature in sand (Nakano et al.
1972, Nakano & Arnold 1973), but decreased with
increasing temperature in frozen silt (Inoue &
Kinoshita 1975, Fukuda 1989), and indicated that the
unfrozen water content might be an important factor
affecting the ultrasonic velocity in frozen soil (Fukuda
1989, Deschatres et al. 1988, Thimus et al. 1991).
Sheng et al. (2000a) have studied the relationship between unfrozen water content and ultrasonic
2 DIRECT DETERMINATION OF DYNAMIC
PARAMETERS OF FROZEN SOILS
Dynamic properties of frozen soils are important to
geophysical exploration, excavation by blasting, and
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of both longitudinal and shear waves decrease with
increasing temperature, and their Young’s modulus
and shear modulus also decreased with increasing
temperature. These results display the same trends as
the experimental results obtained from a uniaxial
strength test (He et al. 1993). The modulus obtained
from ultrasonic method is an order of magnitude
higher than the results from material test machine.
Considering the higher frequency and the lower strain
in the ultrasonic method, the higher modulus is understandable. It is not an easy job to determine Poisson’s
ratio with a common test machine. However, it is
relatively straightforward to obtain Poisson’s ratio
for frozen soils by using ultrasonic technology. Compared with normal elastic materials, Poisson’s ratio of
frozen soil is somewhat lower, and increases with
increasing temperature.
design involving vibrating machinery. Sonic propagation in frozen soils is determined by dynamic properties of frozen soils (Young’ modulus, shear modulus
and Poisson’s ratio). Elastic parameters should be
expressed as follow, as functions of ultrasonic velocities (Bourbie et al. 1987):
(
rVs2 3Vp2 4Vs2
E
Vp2
Vs2
)
(1)
G Vs2
m
Vp2 2Vs2
(
2 Vp2 Vs2
(2)
)
(3)
Here, E is Young’s modulus, Pa; G is shear modulus,
Pa, m is Poisson’s ratio; r is density, kg/m3. Vp refers
to longitudinal wave velocity, m/s; Vs refers to shear
wave velocity, m/s. Given the density of frozen soil,
we can calculate elastic constants from Equation (1)
by measuring the ultrasonic velocities of the frozen
soil. Figure 1 shows the changes of both longitudinal
and shear wave velocities with temperature in
Lanzhou Loess. The water content of the sample is
25%, and its dry density is 1.57 g/cm3. Calculated
Young’s modulus, shear modulus and Poisson’s ratio
are shown in Figures 2, 3. The ultrasonic velocities
3 UNIAXIAL COMPRESSIVE STRENGTH
AND ULTRASONIC VELOCITIES IN
FROZEN SOILS
Theoretically, the ultrasonic velocities should not
directly reflect the strength characteristics of frozen
soils. However, when a factor affecting the strength of
frozen soil changes, the ultrasonic velocity in frozen
soil also changes. If there is a good relationship
between the uniaxial strength and ultrasonic velocities, it should be possible to estimate the uniaxial
strength of frozen soils by the relationship through
measuring the ultrasonic velocities of frozen soils.
Inoue & Kinoshita (1975) conducted experiments on
ultrasonic velocity and strength for frozen silt and
sand with different water content at a constant temperature. Their results indicated that a linear relationship existed between uniaxial compressive strength
and shear velocity.
A series of tests of uniaxial strength are conducted
for different temperatures in frozen Lanzhou Loess.
The dry density of the samples is about 1.57 g/cm3, and
water content is about 25%. The results are plotted in
Velocity (m/s)
4000
Longitudinal wave
3000
2000
1000
0
Shear wave
-5
-10
Temperature (ºC)
-15
Figure 1. Relationship between ultrasonic velocities and
temperature in Lanzhou Loess.
25
0.40
Young's modulus
Poisson's ratio
Modulus (GPa)
20
15
10
Shear modulus
5
0
0
-5
-10
Temperature (ºC)
0.35
0.30
0.25
0.20
-15
0
-5
-10
Temperature (ºC)
Figure 3. Poisson’s ratio of Lanzhou Loess.
Figure 2. Young’s and shear modulus of Lanzhou Loess.
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-15
6
Strength (MPa)
Strength (MPa)
15
10
5
0
0
-5
-10
Temperature (ºC)
-15
4
3
-20
0
Figure 4. Uniaxial strength vs. temperature in Lanzhou
Loess.
20
30
Tire mixing fraction (%)
40
6
-5 ºC
Strength (MPa)
6
4
y = 8E-26x
2
7.263
2
R = 0.977
0
3000
10
Figure 6. Strength results of Tomakomai silt mixed with
tire powder.
8
Strength (MPa)
-5 ºC
5
3200
3400
3600
3800
Longitudinal velocity (m/s)
5
4
y = 0.002x - 2.0431
R2= 0.9378
4000
3
2500
Figure 5. Relationship between uniaxial compressive
strength and longitudinal wave velocities in Lanzhou Loess.
3000
3500
4000
Longitudinal velocity (m/s)
4500
Figure 7. Relationship between uniaxial compressive
strength and longitudinal wave velocities in Tomakomai silt.
Figure 4. Combining these test results with those presented in Figure 1, the uniaxial compressive strength
can be plotted against the longitudinal velocity on the
basis of temperature, as shown in Figure 5. It is found
that the strength of frozen soil can be expressed as a
power function of the longitudinal velocity when
changing temperature of frozen soil (longitudinal
velocity varies with temperature). The lower the temperature of frozen soil, the faster the ultrasonic longitudinal velocity, and the higher the strength of frozen
soil. This relationship between strength and wave
velocity in frozen soil makes it possible to estimate the
strength of frozen soil by ultrasonic measurement on
only one sample, after conducting a few strength tests
to calibrate the relationship.
Another experiment was carried out for Tomakomai
silt mixed with tire powder (from discarded rubber
tire) at different mixing fractions and the same temperature (5°C). An effort was made to reach about
95% saturation for all test samples. In this case,
the unique variable is tire powder fraction. Figure 6
shows the results of strength tests with tire mixing
fraction. Based on the tire powder fraction, the relation between strength and longitudinal velocity is
given in Figure 7. It is found that the compressive
strength of frozen Tomakomai silt has a linear relationship to longitudinal velocity as the mix with the
tire powder fraction (details of the experimental
results of frozen Tomakomai silt mixed with tire powder may be found in Sheng et al. 2000a, b).
4 UNFROZEN WATER CONTENT AND
ULTRASONIC VELOCITY
Unfrozen water content is one of the most important
factors affecting the physical and mechanical properties of frozen soils. Understanding the relationship
between unfrozen water content and ultrasonic velocities will make it possible to use ultrasonics to determine unfrozen water content (Fukuda 1989). Because
the change in unfrozen water content indicates a
change in ice content, which plays a cementing role
in frozen soils, the change of ice content must result in
the change in mechanical properties of frozen soils.
The authors have conducted ultrasonic experiments on
Tomakomai silt to study the effect of unfrozen water
content on the ultrasonic velocities (Sheng & Fukuda
1998, Sheng et al. 2000a). Their results showed a linear relationship between unfrozen water content and
both longitudinal and shear waves velocities.
Glass beads, with diameters ranging from 2.2 to
10 m, is selected to conduct these experiments. A
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may have an effect on the ultrasonic velocity and
physical properties. However, for a single influencing
factor, the existing relationships between ultrasonic
velocity and the physical and mechanical properties
make the estimation of uniaxial strength and unfrozen
water content possible.
Unfrozen water content (%)
50
y = 5E+07x-1.8001
R2= 0.9967
40
30
REFERENCES
20
2000
2500
Longitudinal velocity (m/s)
3000
Biot, M.A. 1956a. Theory of propagation of elastic waves in
a fluid saturated porous solid, I. Low frequency range.
Journal of Acoustic Society of America 28: 168–178.
Biot, M.A. 1956b. Theory of propagation of elastic waves
in a fluid saturated porous solid, I. High frequency
range. Journal of Acoustic Society of America 28:
179–191.
Bourbie, T., Coussy, O. & Zinszner, B. 1987. Acoustics of
porous media. Houston: Gulf Publishing Company.
49–95.
Deschatres, M.H., Cohon-Tènoudji, F., Aguirre-Puente, J. &
Khastou, B. 1988. Acoustic and unfrozen water content
determination. Proceedings of the 5th International
Conference on Permafrost, Trondheim: 324–328.
Fukuda, M. 1989. Measurement of Ultrasonic velocity of
frozen soil near 0°C. Low Temperature Science 50:
83–86.
He, P., Zhu, Y., Zhang, J., Shen, Z. & Yu, Q. 1993. Dynamic
elastic modulus and dynamic strength of saturated
frozen silt. Journal of Glaciology and Geocryology
15(1): 170–174.
Inoue, J. & Kinoshita, S. 1975. Compressive strength and
dynamic properties of frozen soils. Low Temperature
Science 33: 243–253.
Leclaire, P., Cohon-Tènoudji, F. & Aguirre-Puente, J. 1994.
Extension of Biot’s theory of wave propagation to
frozen porous media. Journal of Acoustic Society of
America 96(6): 3753–3768.
Nakano, Y. & Arnold, R. 1973. Acoustic properties of
frozen Ottawa sand. Water Resources Research 9(1):
178–184.
Nakano, Y., Martin, A.J. & Smith, M. 1972. Ultrasonic
velocities of the dilatational and shear waves in frozen
soils. Water Resources Research 8(4): 1024–1030.
Sheng, Y. & Fukuda, M. 1998. Characteristics of ultrasonic
velocities through frozen soil. Proceedings of the
1998 Conference on Japanese Society of Snow and
Ice, Shiozawa, Japan: 57.
Sheng, Y., Fukuda, M., Kim, H. & Imamura, T. 2000a.
Effect of unfrozen water content on the ultrasonic
velocities in Tire-mixed frozen soils. Chinese Journal
of Geotechnical Engineering 22(6): 716–719.
Sheng, Y., Fukuda, M. & Kim, H. 2000b. Strength behavior
of frozen silt mixed with tire powder. Journal of
Glaciology and Geocryology 22 (suppl.): 204–206.
Thimus, J., Aguirre-Puente, J. & Cohon-Tènoudji, F. 1991.
Determination of unfrozen water content of an overconsolidated clay down to 160°C by sonic
approaches-Comparison with classical method. Proceedings of the 6th International Symposium on
Ground Freezing: 83–88. Rotterdam: Balkema.
Figure 8. Relationship between unfrozen water content
and longitudial wave velocities in glass-bead.
power function is found between the unfrozen water
content and the longitudinal velocity, as shown in
Figure 8. The unfrozen water content of frozen soil
strongly affects the ultrasonic velocity. The higher the
unfrozen water content, the lower the ultrasonic velocity. The existing power function is different from the
linear function that was found for frozen Tomakomai
silt by Fukuda (1989) and Sheng & Fukuda (1998).
This may be a result of the difference in the nature
of the materials. The effect of unfrozen water content
on the ultrasonic velocity is a complex problem. It
involves the structure of frozen soil, the existing form
of unfrozen water, and the transforming process for the
mechanical wave within each phase in the frozen soil.
Leclaire et al. (1994) analysed the propagating mechanism of an ultrasonic wave in frozen soil using Biot’s
theory (Biot 1956a,b). This analysis supposed that
unfrozen water in frozen soil was inter-perfoliate. But
unfrozen water is generally in a state of separation for
most frozen soils, so that supposition is not satisfied by
many frozen soil structures. Empirically, the good correlation between unfrozen water content and ultrasonic
velocity suggests that there is a possibility to measure
unfrozen water content by ultrasonic techniques.
5 CONCLUSION
The propagation of ultrasonic waves in frozen soils
responds to the dynamic properties of the material.
Taking advantage of the simple, fast, non-destructive
nature of ultrasonic technology, the elastic parameters
can be measured directly. For a single change in factors
affecting the strength of frozen soil, the compressive
strength shows a good relationship to the ultrasonic
velocity. Unfrozen water content obviously affects the
ultrasonic velocity, and a good empirical relationship
exists between unfrozen water content and ultrasonic
velocity. Of course, many factors, such as ice content,
grain size, temperature, as well as structure of soil,
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