Measurement and Estimation of State Variables - Unsaturated Soil Mechanics in Engineering Practice - page 167

4.5.2.2 Gamma Ray Attenuation Methodology
In contrast to the neutron method, the gamma ray adsorp-
tion technique scans a thin layer of soil. Dual-probe gamma
devices have been quite commonly used for research stud-
ies in the soil laboratory. The water content of the soil is
determined from the difference between the total density
and the dry density attenuation values. The attenuation of
the gamma rays is related to mass and therefore it is neces-
sary to know the dry density of the soil in order to monitor
changes in water content.

time of an electronic pulse. The electrical pulse is in the
microwave (gigahertz) frequency range. The pulse is passed
along a waveguide consisting of two parallel rods that are
embedded in the soil. The pulse is reflected at the end of the
waveguide and its propagation velocity is measured. Theo-
retically, the propagation velocity is inversely proportional
to the square root of the dielectric constant of the material
in which the rods are embedded.
The parallel rods are commonly separated by 50mm and
vary in length from 100 to 500 mm. The rods can be made of
any metallic material. A sampling volume a few centimeters
in radius is formed around each of the metal rods. It is
preferable to place the rods in a horizontal manner when
attempting to measure the water content at a particular depth.
The volumetric water content versus dielectric constant
relationship is quite similar for many soils; however, it is not
unique for all soils and may require calibration for particular
soils (Hu et al., 2010). A widely used relationship between
the dielectric constant and volumetric water content, θ ,was
that published by Topp et al. (1980) and can be written as
follows:

4.5.3 Dielectric-Based Methods
The dielectric constant (or permittivity) of a material is
defined as the ratio of the amount of electrical energy stored
when a voltage is applied through a material in comparison
to the amount of electrical energy stored in a vacuum. A
dielectric material is a substance that is a poor conductor of
electricity but an efficient supporter of electrostatic fields.
The dielectric constant of water is approximately one
order of magnitude less than that of dry soil. Table 4.14
presents the dielectric constants for the components found
in soils. The contrast in dielectric constant among water,
air, and soil

0 . 00055 K 2 0 . 0000043 K 3

(4.32)

θ =− 0 . 053 + 0 . 029 K − +

forms the basis for the measurement of

volumetric water content in a soil.
The measurement of the dielectric constant for a soil
allows for a comparison between the value for a dry soil
and a wet soil. Consequently, the volumetric water content
of a soil can be determined. The technique is rapid and safe
to use and has increasingly been used for field measurements
of water content. Two methodologies have emerged which
make use of soil dielectric measurements for determining
the water content of a soil. The two methods are referred
to as (i) time-domain reflectrometry measurements and (ii)
frequency-domain measurements.

where:

K = dielectric constant for the soil-water system.

Equation 4.32 has been found to be applicable for many
soils. It is relatively independent of soil texture and gravel
content (Drungil et al., 1989). The dielectric constant can
also be written in terms of the volumetric water content:
√ K =

146 θ 2 76 . 7 θ 3

3 . 03 + 9 . 3 θ + − (4.33)

Various types of time-domain reflectometry sensors have
been developed that measure the dielectric properties of a
soil. Conventional time-domain reflectometry systems have
been manufactured by (i) Tektronix Inc. (TDR Cable Tester),
(ii) Campbell Scientific Inc. (TDR100), (iii) Dynanax Inc.
(Vadose TDR), (iv) Soil Moisture Corporation (Trase TDR),
and (v) Delta-T (Thetaprobe). The TRIME FM3 moisture
meter is manufactured in Germany and is classified as a
quasi-time-domain reflectometry system.
The conventional time-domain reflectometry devices have
a pulse generator that generates a square-wave pulse. The
pulse travels along the cable to the header connected to the
rods that are inserted into the soil. The pulse reaches the end
of the TDR rods and then returns. An oscilloscope electronic
system captures the pulse as shown in Fig. 4.90. The water
content of the soil influences the travel time of the pulse
along the rods surrounded by soil. It is the permittivity of
the soil that affects the travel time and the permittivity of
the soil is related to the volumetric water content of the soil.
Originally it was suggested that a single calibration curve
might exist for all soils. However, it is now suggested that

4.5.3.1 Time-Domain Reflectometry Methodology
The time-domain reflectometry (TDR) method determines
the dielectric constant of the soil by measuring the travel

Table 4.14 Typical Values for Dielectric Constants of
Soil Components

Dielectric Constant

Temperature, ◦ C Material (unitless)

Air 1.0

Water 88 0.0

Water 80.1 20.0

Water 55.3 100

Dry silica sand 2.2

Quartz 4.3

Soil 2.4-2.9