NBSIR 74-381

ELECTROMAGNETIC ATTENUATION PROPERTIES

OF CLAY AND GRAVEL SOILS

Doyle A. Ellerbruch

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

August 1974

NBSIR 74-381

ELECTROMAGNETIC ATTENUATION PROPERTIES

OF CLAY AND GRAVEL SOILS

Doyle A. Ellerbruch

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

August 1974

u s DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS Richard W Roberts Director
FOREWORD

In response to a request from the Air Force Weapons

Laboratory (AFWL) the National Bureau of Standards

undertook a project to investigate the microwave

penetrability of selected pavement materials. The

overall objective of the AFWL was to establish the

feasibility of using active microwave techniques to

differentiate layers in a pavement system and to

accurately measure the thickness of each layer for

a variety of soil types and moisture conditions.

Layer thickness measurements are needed to complement a field operational method currently being

developed by AFWL to nondestructively evaluate the

condition and load-carrying capacity of airfield

pavements

.

This initial effort consisted of investigating the

relationship between microwave penetrability in clay

and gravel soils as a function of moisture content

and microwave frequency.

ii
CONTENTS

Page

1. INTRODUCTION 1

2. THEORETICAL MODEL 2

3. PREPARATION OF SOIL SAMPLES 7

3.1 Gravel 7

3.2 Clay 10

4. EXPERIMENTAL RESULTS AND DISCUSSION 14

5. CONCLUSIONS 17

6. ACKNOWLEDGMENTS 19

7. REFERENCES 19

ILLUSTRATIONS

Figure Page

1. Plane waves normally incident on plane

dielectric boundary 4

2. Reflection coefficient relationship 6

3. Grain size distribution of gravel samples 8

4. Modified Proctor moisture and density curves

of gravel 9

5. Grain size distribution of clay samples 12

6. Modified Proctor moisture and density

curves of clay 13

7. Sample of measured data 15

TABLES

Table Page

I Properties of the Compacted Soils 11

II Skin Depths 16

iii
ABBREVIATIONS AND SYMBOLS

arjm bignax xevex witn respect:, uo x invv/ aeciDeis

m xncxaent execuiric intensity/ v/in

V

r

ivci icc ucci eiectj-ic inLensity/ v/ru

Average specific gravity of soil solids

cC Velocity of light in free space/ m/sec

e Natural logarithm base

Frequency/ Hz

L 1/ 2 for media 1 and 2 respectively

0 Sample depth/ m

t time / sec

.

fi Reflection coefficient of infinitely thick sample

P1 . in Kenecuion coerncient or rinite tnicKness sample

i m

Maximum reflection coefficient of finite thickness sample

ex 1 Attenuation constant/ nepers/m

Fnase constant/ raaians/m

Propagation constant

"Yd Dry density/ g/cm^

wet aensity/ g/ cm

0 oKin aeptn/ m

e . 1 Permittivity/ farad/m

1 Permittivity relative to free space/ farad/m

Permeability/ henry/m

0 conductivity/ mho/m

Angular velocity/ radians/sec

n Intrinsic impedance/ ohm

iv
The objective of this work was to establish the

feasibility of using active microwave techniques

to differentiate between the different subsurface

layers in a pavement system. The electromagnetic

attenuation properties of clay and gravel soils

were measured as a function of moisture content

and frequency. Measurements were done at frequencies in the 0.5 - 4.5 GHz range. Soil samples

were compounded in the laboratory at approximately

10, 50 and 90% saturation. Sample thickness was

in the range 2.5 - 20.3 cm. Each homogeneous sample was sealed in a polyethylene container to retain the total moisture and to maintain a constant

moisture content with depth.

KEY WORDS: Attenuation; clay; gravel; measurements;

microwave; skin depth.

1. INTRODUCTION

When using active microwave techniques to characterize

natural construction materials, three factors are of prime

importance: soil type, moisture content or saturation of the

soil, and frequency of the microwave signal. Demonstration of

the capability to distinguish between, and measure thickness

of various pavement layers first requires a demonstration of

the ability of microwave signals to penetrate a homogeneous

layer of pavement material.

This effort consisted of investigating the relationship

between soil penetrability as a function of soil type, moisture content, and microwave frequency. Measurements were

made on clay and gravel soils having saturation of approximately

10%, 50%, and 90%, and at microwave frequencies in the range

0.5 - 4.5 GHz. The skin depth was determined for all soil

type/frequency/saturation combinations.

All test samples were compounded in the laboratory. The

surface area of all samples was 1.22m x 1.22m. After preparation,

each sample was sealed in a polyethylene bag to retain total moisture content and to maintain a uniform moisture content within the

layer

.
2 . THEORETICAL MODEL

The following equations outline the properties of a

complex medium (see ref 1). In general, waves propagating

in a medium undergo attenuation and phase shift. The complex

propagation constants for plane waves is:

Y = Doa >F [i-J ^] (1)

and can be written as

Y = a (to) + j 3 (oj) (2)

Solving for a(a)) and 3(oo) gives

a (oo) =

6(w) =

-1 (3)

(4)

which for small losses ( — << 1) become.

we

a (w)

(w) ~ co-^y

e

(5)

(6)

The intrinsic impedance of a medium is given by

n =1

e(l-j-^)

-'we

(7)

-2-
The model used consisted of one layer of finite thickness of the material under test, sandwiched between air and

an aluminum sheet (fig. 1) . The medium is assumed to be isotropic and homogeneous with parallel plane boundaries. Electrical properties of the layer are described by permeability (y)

,

permittivity (e), and conductivity (a). The layer is assumed

7 non-magnetic (u = uo, where y o = 4 (10) H/m) . Additionally, e is assumed to be independent of frequency. Ray paths for electromagnetic energy are also assumed.

Due to the directivity of the ideal horns assumed in the

model, only reflected waves are received. In practice, considerable design placement and polarization strategy are required to reduce the direct coupling to an acceptable level.

The horns used were not ideal; however a single ray normal

incidence model was used.

The input reflection coefficient in medium 1 for a single

layer in a perfect conductor can be written as (see ref 1)

,

r. = 5

^

(8)

1 - lie

where Fi is the reflection coefficient of a semi-infinite medium

and is approximately given by

and Y2 by (2) , (3) and (4) . The magnitude of T will go

through successive maxima and minima as a function of frequency,

layer thickness, dielectric constant and loss. Minima (or

maxima) will occur approximately every 2tt radians. Thus, when

00 is varied, successive minima occur when

2 (A32) I2 = 27T -3-

(10)
r.=iL

medium

(/!,€,)

medium 2

sample (/ig^a^

transmit

horn

receive

horn

A A

measuring plane

aluminum sheet

Figure 1. Plane waves normally incident

on a plane dielectric boundary

-4-
from which

2Z2 (f2-f l)

(11)

where successive minima occur at frequencies fi and fa.

It has been shown (see ref 2) that an approximate

expression for the maxima of F . can be obtained when ^ in

cos 2 32^2 = 1. Equation (8) then becomes

r = ^ ^ ^

fl2^

m , ^ -2a2il2 ' 1 - i 1 e and solving for the attenuator factor, obtain

Ti - r m

1 - TiT^ m

(13)

Because £' > 1 the reflection Fi as given in (9) will always

2 be negative, thus the coefficient F as given in (12) is also

negative. Because |F^| >_ 1Fi|, logarithms of positive

numbers are involved.

Figure 2 shows how the reflection coefficients in this

model are related. |Fi| and |F. I are deduced from measurements.

|Fi| is determined by using frequencies fi and fa in (11). |Fj^^l

is determined by return loss measurement techniques (see ref 3)

.

The sample thickness is constant; thus the attenuation of the

sample can be determined from (13)

.

Skin depth is defined as the depth at which the wave

has been attenuated to 1/e of its original value. Thus,

skin depth, 6, can be determined from the relation

^26 - 1 . (14)

-5-

3. PREPARATION OF SOIL SAMPLES

3.1 Gravel

The gravel was blended by mixing coarse and fine concrete

aggregates in calculated proportions, so that the grain-size

distribution curve as shown in figure 3 was obtained. Soil

so prepared classifies as a poorly graded gravel (GP) in the

Unified Soil Classification system (see ref 4) . Compaction

characteristics were obtained by the modified Proctor method

and are given in figure 4. From figure 4, a moisture content

was selected for compacting soil in the test bed in order to

achieve a compacted degree of saturation of approximately 10%.

The actual degree of saturation of the test soil (based on

volume calculations) could not be accurately predicted until

the beds had been prepared.

Mixing of the dry gravel with the water was carried out in

a concrete mixer, and compaction of the bed was by means of a

gasoline-powered vibratory compactor, assisted by hand compaction. After compaction, the box and its compacted contents were

weighed by supporting it on a knife edge on one side and two

proving rings on the opposite side. Thus, with the wet density,

moisture content and grain average specific gravity known for

the soil in the box the void ratio, dry density and degree

of saturation could be calculated.

Two boxes of identical dimensions (1.22m x 1.22m x 20.3cm)

were built for making two beds of soil simultaneously. Slight

variation resulted in the density of the soil beds prepared.

The boxes were lined with polyethylene plastic sheets to prevent

loss of soil moisture.

The above techniques were employed in making the soil

beds at 10% degree of saturation. After measurements had

been made on them, the degree of saturation of the soil was

brought up to 50% by introducing water from the surface in

-7-

MOISTURE CONTENT. PERCENT

Figure 4. Modified Proctor moisture and density curves of gravel

-9-
an amount calculated from the dry density of the prepared

soil. The box was again weighed to provide data for accurate

determination of the new degree of saturation. Thus compacted

dry density of the soil stayed constant from one degree of saturation of the test specimen to another. The same technique was

also used to bring saturation to 90%, although the presence of

trapped air in the soil presented some difficulties in achieving

this high degree of saturation.

Data on the two soil beds at each of the three degrees of

saturations are given in table I . Target values for saturation

were 10%, 50%, and 90%. Table I gives the actual values obtained

for each sample.

3.2 Clay

Some difficulties were encountered in locating a soil

with a CL classification because of the large quantities required.

Finally, a soil was selected which was dried, crushed, and sieved,

retaining the minus number 50 sieve portion. The grain-size

distribution curve is shown in figure 5, which also gives its

Atterberg limits. It classifies as CL in the Unified Soil Classification System. Compaction characteristics are shown in figure 6.

Dry soil was mixed with an appropriate amount of water

in a soil mixer in batches of 110 kg. It was found that the best

way to mix soil and water was to add water as a fine mist while

the soil was being stirred. After placing the soil in the box,

it was compacted with a hand compactor to achieve the desired

density and, therefore, the required degree of saturation.

After measurements were taken of this soil bed, the soil was

remixed with additional water to bring it up to the moisture

content necessary to achieve 50% saturation. This time,

however, a gasoline-powered, rammer-type compaction machine

was used to attain the higher density. For the 90% saturation,

the soil bed with 50% saturation was percolated with water

-10-
M-l O -P O -HP

Q) as O U

U !3

Q) (0 Q W

0) 00 n CN ro 00 o

00 IT) cn o^ CN

00 iH 00 n 00

0) HH

0W

T3

(U 4JO

n)i-ou

o

cn0) •H

+J

<Da

o

u

>1'-

+J to >i-H g

W O Q C\

Q

3P

p

C

<D O

04 S U —

CN CN 00 00 o O o in CN CN

00 00 00 00 00 00 n in in

iH iH H rH H

O VO iH

CN 00 in o ^

CN CM

in CN

CN

Q) rH

EH

pq

CN

0

>

U

o

>1 u

-11-
o

o

o

o

o

o

o

E

E

UJ<

Q

<

C9

(00) iHa

E

r«to

>i

(0 H

O

M-l O

C

OH

-P

•H

J^ -Pw

•H

Q)N

-HW

•H

to

in

0)

5-1 P

•H

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o

CO o O OCVJ 1H9I3M Aa a3Nld lN30a3d

-12-

through four pliunbing fittings on the bottom of the box. This

process of increasing the saturation, was aimed at maintaining

a reasonable compaction of the soil, (that of the 50% saturated

sample) , and avoiding the need to compact a clay soil at 90%

saturation, took about four days to accomplish and worked satisfactorily. Data for the clay beds are shown in table I .

4. EXPERIMENTAL RESULTS AND DISCUSSION

Preliminary experiments showed that by sealing the sample

in polyethylene not only was the total moisture content retained,

but it was retained in a fairly uniform state. A measure of the

uniformity was obtained by comparing surface dielectric constant

data with the dielectric constant for the layer.

The surface area of all samples was 1.22m x 1.22m. The

thickness was intially 20.3 cm; however, that was reduced for

samples of higher moisture content in order to facilitate measurements under these conditions of higher microwave absorption.

A sample of the measured data obtained from these experiments

is shown in figure 7.

Skin depths derived from all measured data are tabulated in

table II, in which sample thicknesses, measured relative dielectric

constants, and relevant frequency ranges are also tabulated. The

ranges of skin depth includes all values obtained within the

corresponding tabulated bandwidth. Single values of relative

dielectric constant were obtained for all frequencies within the

bandwidth through (11)

.

A rigorous error analysis for the measurement system has not

been done. Sources of errors are discussed here in relation to

the effect produced in skin depth.

The measurements were made with a commercial microwave

network analyzer, which has an accuracy of ±0.5 dB. The uncertainty in measuring amplitude with this analyzer would therefore

produce the greatest skin depth uncertainty at lower frequencies

and saturation values because smaller values of attenuation are

involved.

-14-
ID oCM in

CO gp 'sson Ndni3d o

ro in

ro

O o

cJ

-15-
Table II. Skin Depths

Material Saturation

(percent)

Sample

Thickness

(cm)

Frequency

(GHz)

Relative

Dielectric

constant

Skin

Depth

(cm)

Clay 9.6 20.2 0.5 - 1.0 4.0 30 42

9.6 20.2 . 2.3 -- 2.6 5.1 13 19

9 . 6 10. 8 4.3 -- 4.5 4.8 7 15

39.3 -. 8.9 0.5 -- 1.0 9.2 10 20

39.3 8.9 2.3 -- 2.6 7.7 6 - 18

39.3 8.9 4.0 -- 4.5 7.5 6 9

82.8 2.5 0.6 -- 1.7 26.2 5 20

82.8 2.5 2.0 -- 3.0 22.1 3 6

82. 8 2.5 3.0 -- 4.5 20.8 1.5 - 3

Gravel 11.4 20.2 0.5 - 1.0 4.9 160 - 315

11.4 20.2 ' 2.2 - 2.5 4.9 60 - 80

11.4 20.2 4.0 - 4.5 4.6 17 - 30

48.9 20.2 0.5 - 1.0 11.2 30 - 200

48.9 12.1 2.2 - 2.5 13.3 15 - 35

48.9 7.6 4.0 - 4.5 14.7 4 8

85.9 20.2 ^ 0.5 - 1.0 15.2' 40 - 60

85.9 20.2 2.2 - 2.5 15.5 5 9

85.9 9.7 4.0 - 4.5

-16-
single ray theory was assumed in these measurements. The

sample was placed in the Fresnel diffraction zone of the antennas.

Departure from ray theory would increase the uncertainty in skin

depth, particularly for samples of lower moisture content. As the

moisture content increases, the dielectric constant increases, which

produces a focusing of the beam. The net effect is to produce a

physical configuration that improves the use of the ray theory

assumption. These errors can reasonably be as large as 1 to 2 dB.

Mismatch between antennas and the measuring system could

produce a systematic error. This error was minimized by

using low VSWR antennas.

An overall error of 1 dB corresponds to a fractional

uncertainty of 10% in the skin depth; and error of 2 dB

corresponds to a 50% fractional error.

The errors discussed here show that improvement in

measurement techniques and hardware could provide more accurate

measures of skin depth. In addition, more data of the type

provided in the report are required for baseline data purposes.

For example, samples having other moisture contents should be

prepared for evaluation. Measurements should be made in

in-situ situations to detect phenomena that may not be produced

in laboratory tests. Other materials, including concrete

and asphalt, should be studied to determine the feasibility of

using microwave techniques to evaluate surface layers.

5. CONCLUSIONS

The objective of this effort was to investigate relationships that exist between microwave penetration, soil type,

moisture content, and microwave frequency. Measurements

were made on samples of approximately 10%, 50%, and 90% saturation, at frequencies in the 0.5 - 4.5 GHz range.

-17-
Each sample was sealed in polyethylene. This retained

the total moisture in the sample and maintained a uniform

moisture distribution during the measurement process.

State-of-the-art microwave equipment can readily detect

signals of amplitude -80 dBm. Assuming a radiated power of

+10 dBm, a microwave system should penetrate a five-skindepth layer of material (remembering that in the field

applications of analyzing pavement systems, the signal would

travel through the material twice for a total propagation

length of ten skin depths)

.

Assuming total reflection at the subsurface interface,

as is the case with an aluminum baseplate, a 0.5 GHz microwave signal should penetrate a 150-cm layer of approximately

10% saturated clay, or a 25-cm layer of approximately 90%

saturated clay. A 4 . 5-GHz signal should penetrate a 35-cm

layer of approximately 10% saturated clay or a 1-cm layer

of approximately 90% saturated clay.

In general, gravel exhibited greater skin depths than

clay; thus thicker layers of gravel should be penetrated. A

0.5-GHz signal should penetrate 800 cm of approximately 10%

saturated gravel, or 120 cm of approximately 90% gravel.

Penetration depths given here should be realized in a

field application if the surface reflection can be removed,

or at least minimized during the measurement process. Possible

techniques for controlling the adverse effect of the surface

reflection include: providing an auxiliary circuit to cancel

the surface reflection, or making the measurement in the

time domain and eliminating the surface reflection with proper

gating circuitry.

Penetration depths given here are based on a total reflection at the lower boundary of medium 2. Total reflection was

accomplished in these experiments because aluminum was used

as the base material. In a pavement system consisting of a

layer of gravel over clay, the penetration capability of the

-18-
system would be reduced because total reflection at the gravelclay interface does not occur. A portion of the signal would

penetrate the clay. The degree of degradation is dependent

upon the moisture contents of both materials. A layer of 10%

saturated gravel over 10% saturated clay would reduce the penetration depth of the gravel to approximately three skin depths,

or 300 cm at 0.5 GHz. If the saturations are increased to 90%

for both, the penetration depth of the gravel is approximately

120 cm. These numerical values are based on the assumption

that surface reflection does not limit the measurement range

capability of the system.

6 . ACKNOWLEDGEMENTS

The author is indebted to Professors Hon-Yim Ko and

Edward Sampson, Jr. , Department of Civil and Environmental

Engineering, University of Colorado, for preparing the soil

samples

.

7 . REFERENCES

1. Stratton, J. A. , Electromagnetic Theory , McGraw-Hill,

New York (1941)

.

2. Lundien, J. R. , Determining Presence, Thickness, and

Electrical Properties of Stratified Media Using SweptFrequency Radar , Technical Report M-72-4, U.S. Army

Engineer Waterways Experiment Station, Vicksburg, Miss.,

(Nov. 1972) .

3. Beatty, Robert W. , Microwave Impedance Measurements and

Standards, NBS Monograph 82 (Aug. 12, 1965),

4. Lambe, T. W. , and R. V. Whitman, Soil Mechanics , John Wiley and Sons, Inc., New York (1969).

-19-
FORKii NBS'114A (1.71) U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. <jk>v't Acceaii^il BIBUOGRAPmC.DATA ^^^j^^ No.

^"f^^' 1 : i „, „ ,.,,,^1,1

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

ELECTROMAGNETIC ATTENUATION PROPERTIES

UF CliAx AND GRAVEL SOILS

5. Publication Date August 1974

7. AUTHOR(S)

Doyle A. Ellerbruch

9. PERFORMING ORGANIZATICW NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

U. Proiect/Task/Work Unit No. 2764374

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Department of the Air Force

Air Force Weapons Laboratory

Kirtland Air Force Base^ New Mexico

13. Type of Report & Period

Covered

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summaty of most significant information. If document includes a significant

bibliogr^hy or literature survey, mention it here.)

The objective of this work was to establish the

feasibility of using active microwave techniques

to differentiate between the different subsurface

layers in a pavement system. The electromagnetic

attenuation properties of clay and gravel soils

were measured as a function of moisture content

and frequency. Measurements were done at frequencies in the 0.5 ~ 4.5 GHz range. Soil samples

were compounded in the laboratory at approximately

10, 50 and, 90% saturation. Sample thickness was

in the range 2.5 - 20.3 cm. Each homogeneous sample was sealed in a polyethylene container to retain the total moisture and to maintain a constant

moisture content with depth.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Attenuation; clay; gravel; measurements; microwave; skin depth.

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