European Journal of Soil Science, September 1996, 47, 367-371

Influence of gravimetric water content and bulk density on the dielectric properties of soil

U.D. PERDOK, B. KROESBERGEN & M.A. HILHORST* Wageningen Agricultural University, Department of Soil Tillage, Diedenweg 20, 6703 G W Wageningen, The Netherlands, and *Institute of Agricultural and Environmental Engineering MAG-DLO, PO Box 43, 6700 AA Wageningen, The Netherlands

Summary

Moisture content and bulk density largely characterize physical and mechanical soil status and behaviour. A nondestructive determination of these soil properties is essential. Time domain reflectometry (TDR), although widely accepted for determination of volumetric water content, 8, has its limitations, and recently a frequency domain (FD) sensor has been developed and tested. An equation relating relative permittivity, E’, to gravimetric water content, w , and bulk density, p, was established for three soil types (sand, sandy loam and clay). If E’ and w are known, our model can be used to calculate bulk density and associated volumetric water content, 8, keeping in mind that 8 = pw. Utilization is found in long-term monitoring of moisture fluctuations or short-term detection of traffic-induced soil compaction.

Introduction strengths and weaknesses (Dirksen & Hilhorst, 1994; Hilhorst

Water status and bulk density

The gravimetric water content and bulk density of the soil determine how easily that soil can be worked and tilled. Gravimetric water content is hardly affected by variation in density caused by short-term loosening or compacting processes during tillage and traffic, as shown by Tijink (1988) and Lerink (1994) who studied the upper soil layers because that is where most mechanical stresses and deformations occur. The bulk density is much diminished by cultivation, of course, but after the soil has resettled it remains fairly stable during the growing season if the soil neither swells nor shrinks. So the main long-term interest is to follow changes in the volumetric water content from which to calculate the move- ment and use of water (Heimovaara et al., 1993). Volumetric water content, 8, can be determined from bulk density, p. and gravimetric water content, w, by the formula 8 = pw, assuming a specific gravity of 1 g cm-3 for water. Water- and air-filled porosity can be determined from p and w if the particle density of the soil is known.

Advanced sensor technology

Time domain reflectometry (TDR) is now widely accepted for measuring volumetric soil water content. Various workers have shown, however, that TDR has its own, specific set of

Received 31 May 1995; revised 6 February 1996 revised version accepted 23 May 1996 Correspondence: U.D. Perdok. E-mail: Udo.Perdok@Algemeen.GB. WAU.NL

& Dirksen, 1994). The calibration curve is not as unambiguous as the Topp curve suggests (Topp el al., 1980; Brisco et al., 1992; Rajkai & Ryden, 1992; Roth et al., 1992; Dirksen & Dasberg, 1993). It is for this reason that we evaluated the use of a new dielectric sensor working in the frequency domain (FD).

The FD sensor operates at a frequency of 20 MHz compared with 200 MHz for TDR. It is simple to operate. In one routine both relative permittivity and electric conductivity can be measured. Each sensor is equipped with a single and special integrated circuit, simplifying further data acquisition and handling (Hilhorst et al., 1993).

We explored and tested the capabilities of the technique to measure the relative permittivity, E’. The independent variables involved are gravimetric soil water content and bulk density. The aim was to obtain a consistent set of calibration curves of E’ as a function of w and p, and so we used samples of aggre- gated soil prepared in the laboratory to match the sensor’s dimensions and sphere of influence.

Materials and methods

Sensing technique

Hilhorst & Dirksen (1994) describe the main technical features of FD. The probe consists of three 2-mm diameter stainless steel rods, 60 mm long, spaced 10 mm apart. The measuring signal is received by a standard personal computer and analysed within a few seconds. The sensor measures the complex impedance of the soil using synchronous detection, a

0 1996 Blackwell Science Ltd. 367

368 U.D. Perdok et al.

Table 1 study

Composition of soils used in this Clay, < 2 pm Silt, 2-50 pm Sand, <50 pm Organic matter

Soil type I% 1% 1% 1%

Sand 4 8 88 4.3 Sandy loam 13 29 58 1.6 Clay 36 48 17 2.3

technique used by most impedance analysers for laboratory use. From the impedance the permittivity and electric conduct- ivity are derived by software.

The permittivity measured with the new FD sensor was compared with data found by TDR for the same sandy soil sample and with the well-known (Topp er al., 1980) cali- bration curve. The permittivity results where in close agree- ment with each other. The error was less than f 1.

Soil preparation

Three soil types, a sand, a sandy loam and a clay, with a wide range of texture were included in the test (Table 1). Each soil was dried sufficiently in advance in order to be easily crumbled and passed through a 6-mm sieve. After sieving, each soil was further dried or remoistened to give eight samples with water contents ranging from drier than wilting point to wetter than field capacity. The soil samples were allowed to equilibrate for several days and then packed in stainless steel cylinders, 9.93 cm in diameter and 12 cm tall and uniaxially compacted in two 5.7-cm-thick layers using a hydraulic press. From each compacted sample the height was measured. As a result of relaxation the height varied from 11.4 to 11.9 cm. For each water content, the soil was compacted to eight different bulk densities ranging approximately from 1 .O to 1.6 g (60-40% porosity). Because of the large ratio between the diameter and thickness of the compacted layers, the eight bulk densities were uniform for the three soil types. We could not prepare a very porous sample of dry sand because the soil collapsed. The clay soil when very wet formed clods, prevent- ing our preparing adequately homogeneous samples.

The dimensions of the samples and the sensor enabled us to measure the relative permittivity of each sample four times- twice from the top and twice from the bottom. There was usually little variation in the measurements from the four repli- cations, but the results from the more heterogeneous samples were more variable. Some of the compacted dry clay samples were too strong for us to install the sensor. When the tests were ended moisture content and bulk density were determined by weighing the samples before and after drying at 105°C.

Results Aggregate size

To assess possible problems caused by poor contact with the probes, a test run was done on two sizes of aggregates from the clay soil (0-5 and 5-10 mm). Fairly dry and wet soil

(16.5 and 26.0 weight % water) were compacted in 10 steps to bulk densities ranging from 1.01 to 1.48 g ~ m - ~ . No statistic- ally significant differences were found between the two classes of aggregate, and the results were almost identical to those of the other samples described in this paper. This suggests that a rod diameter of 2 mm does not interact with aggregates of 0-5 mm and 5-10 mm.

Sphere of influence

The effective volume sampled by the FD sensor was measured in the sandy loam so that an appropriate minimum size could be specified for the soil cylinder. The sensor was put in the middle of an oversized, free-standing and moderately com- pacted soil column. After each reading of E' a thin (1 mm) layer of soil, parallel to the rods, was cut away. This procedure was repeated until the E' value decreased. A decrease of 1% was accurately observed at a radius of less than 1.5 cm around the three rods that were 10 mm apart and 60 mm long. Thus, the probe's range of influence roughly extends to 7.5 cm x 5 cm x 3 cm, representing a volume of less than 100 cm3, excluding the sharp corners involved. This means that each cylindrical sample permitted four independent FD measurements.

The spatial weighting between the three conductors might not be uniform, and this could reduce the effective sampling volume (Knight, 1992). All results presented here were determined with the sensor described.

Moisture and density

The measured E' (0) values for the various samples are presented in Fig. 1. Only in the sand does this function roughly coincide in the wet range with the Topp curve. This shows that the volumetric water content largely determines the relative permittivity. The data for the sandy loam and clay (Fig. 1) are more scattered and lie above the Topp curve. They were obtained using the FD technique at 20 MHz, whereas the Topp relation is an empirical fit to data collected at approximately 200 MHz using TDR. The above observations for sandy loam and clay accord with previous studies (Campbell, 1990; Raythatha & Sen, 1986) in which there was an increase in relative permittivity for frequencies less than 100 MHz.

The model

To find a more appropriate mathematical description relative permittivity was plotted against gravimetric water content and

0 1996 Blackwell Science Ltd, European Journal of Soil Science, 47,367-371

Dielectric properties of soil 369

25 I 50

a

4 0 t

01 I

50 I I

l b

' O t 30 -

20 - 201/,/T0pp . :.*. ..***. . *. : ..*.' . .* .. . 10

01 I

50 I 1

C

30

20* * * ' ;. . . . . 10

0 ' I 0 5 10 15 20 25 30 35 40 45

Water content /% by volume

Fig. 1 Relative permittivity of (a) sand, (b) sandy loam, and (c) clay measured by the FD sensor, in relation to volumetric water content.

bulk density (Figs 2 and 3). Figure 2 suggests that for a given soil type and bulk density the relation between E' and w can be described by a power function:

€' = ua + ulwn2 (1)

in which a,, u1 and u2 are parameters with specific values for any one bulk density.

In Fig. 3 the relations between permittivity and bulk density appear linear for each moisture content, but their gradients

20 - 1.08

A 1.18

1 5 - A 1.23

0 1.30

- 1.37 10

5 -

30

25 -

-

20 -

15 -

10 -

5 -

1.04 /A+ 1.12

1.20

1.28

1.36

50 C

40 - o'oo 1.00

A 1.13

- A 1.20

0 1.27

- 1.34

0 1.41

30

20

1.48

l o t 01 I

0 5 10 15 20 25 30

Water content /% by volume

Fig. 2 Influence of water content on relative permittivity at different bulk densities ( p ) for (a) sand, (b) sandy loam and (c) clay; lines calculated from Equation (2).

increase with increasing w. Therefore it is possible to expand Equation (1) to:

( 2 ) E' = ua + u1wa2 + ( p - b)(u3 + u4w)

to describe the whole range of moisture contents and bulk densities. In this, b is a chosen bulk density, and u3 and u4 are two additional parameters. Regression lines were fitted for the different values of w to obtain the relevant values of a chosen bulk density b equal to 1.3 g cmP3 for the sand and sandy

0 1996 Blackwell Science Ltd, European Joumal of Soil Science, 47,361-311

370 U.D. Perdok et al.

*O

1 5 -

lo-

5

Table 2 Model parameters for three soils Coefficients of calibration formula

Z variance Soil type a0 a1 a2 a3 a4 b explained

Sand 2.82 0.0794 1.662 1.32 0.65 1.3 99.7 Sandy loam 4.89 0.0682 1.778 3.66 1.06 1.3 99.5 Clay 7.31 0.0371 1.971 11.89 1.56 I .2 99.0

% by weight - 0 2.9

1 6,O

A 0.0

A 12.0

0 14.0

17.7

0 20.8

- 23.7

25

W a

40

30

20

10

0

%by weight - 0

1 9 3

- a 1 2 ~ 6

A 1 6 0

0 1 9 0

- 2 2 2

Q 266

28 0 -

I

0 ' ' I 0.90 1.00 1.10 1.20 1.30 1.40 1.50

35 I I 3o 1% b y k i g h t b

O J J 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60

50 W C

loam and 1.2 g cmP3 for the clay. These E' values were then used to determine the coefficients ao, al and a2 of Equations (1) and (2) for the three soil types. The coefficients a3 and a4 of Equation (2) were then calculated. The results are given in Table 2 and shown by the sets of lines in Figs 2 and 3.

Discussion

Accuracy

The equations presented describe accurately the specific E ' ( w , ~ ) functions for all these soils and over the wide range of moisture contents and bulk densities (Table 2). However, the equations are least accurate for clay soil, especially for extreme moisture conditions outside the range between field capacity and wilting point. The differences between the coefficients a, to a4 for the various soil types show the importance of the soil texture.

Number of samples required for calibration

The minimum number of measurements required to be able to quantify the complete E'(w, p ) relation of a soil being tested is considered below. The function E'(w) can be established for one intermediate value p = b at increasing moisture steps, that is to say, for six to eight samples. The value b is best chosen to correspond to approximately a 25 volume % of air under conditions of field capacity. Next, two samples (one loose, one dense) are tested for two conditions: wet (near field capacity), and dry (near wilting point). Thus, a minimum of 10-12 key data are available to quantify the parameters fully.

Infiuence of density

In general, the dielectric properties of soil determined by FD or TDR are governed by the specific fractions of air, solid matter and water. Dirksen & Dasberg (1993), have described and quantified these relations for both techniques. For TDR, Whalley (1993), has presented the refractive index of bulk soil as a linear function of volumetric water content and an intercept that depends on bulk density and particle density.

Because FD operates at a relatively low frequency (20 MHz, in contrast to about 200 MHz for TDR) it yields a larger measured relative permittivity and depends differently on bulk density.

0 1996 Blackwell Science Ltd, European Journal of Soil Science, 47, 367-371

Dielectric properties of soil 37 1

Application

One of the independent variables, w or p, still has to be determined and substituted into the above model, whereas the other can be predicted very accurately. It is easy to determine w directly from disturbed soil. Precise values for the variables p and associated volumetric water content 0 can be found by measuring E’ and substituting w. This means that undisturbed cores of soil are not needed for determining p.

The model has other potential uses. Once the E ’ ( w , ~ ) equation has been established, the procedure can be used to calculate bulk density accurately in a field for detection of the immediate effects of traffic, for example. It should be noted that the moisture content, w, will remain unaltered for a short time before and after soil manipulation providing the weather is stable.

The probe can also be used to monitor soil water content if the bulk density stays constant throughout the test. If so, a single calibration at the beginning of the monitoring period will suffice.

Conclusions

The new frequency domain (FD) sensor can be used to measure the relative permittivity E’ of the soil matrix. In structureless and wet sandy soil, the data more or less coincide with the known Topp calibration curve ~’(8) in which 8 is a volume percentage. For other soils, for example, sandy soils under drier conditions and clayey, aggregated soils, E’ is governed not only by water content but also by bulk density. Expressing water content as % of weight w instead of % of volume 8, enabled a simple mathematical function E’(w, p ) to be determined.

A representative set of at least 10-12 prepared and measured soil samples is required for complete parameter- ization and calibration. The calibration curves eliminate the need for undisturbed soil core samples for determining bulk density and associated volumetric water content. Instead, easy measurements of output E’ and input w are sufficient.

References

Brisco, B., Pultz, T.J., Brown, R.J., Topp, G.C., Hares, M.A. & Zebchuk, W.D. 1992. Soil moisture measurement using portable

dielectric probes and time domain reflectometry. Water Resources Research, 28, 1339-1346.

Campbell, J.E. 1990. Dielectric properties and influence of conduct- ivity in soils at one to fifty megahertz. Soil Science Society of America Journal, 54,332-341.

Dirksen, C. & Dasberg, S. 1993. Improved calibration of time domain reflectometry soil water content measurements. Soil Science Society of America Journal, 57, 660-661.

Dirksen, C. & Hilhorst, M.A. 1994. Calibration of a new frequency domain sensor for soil water content and bulk electrical conduct- ivity. In: Proceedings of the Symposium on TDR in Environmental, Infrastructure and Mining Applications, pp. 143- 153. US Depart- ment of the Interior Special Publication SP 19-94, University of Evanston, Illinois.

Heimovaara, T.J., Freijer, J.I. & Bouten, W. 1993. The application of TDR in laboratory column experiments. Soil Technology, 6,

Hilhorst, M.A., Balendonck, J. & Kampers, F.W.H. 1993. A broad- bandwidth mixed analog/digital integrated circuit for the measure- ment of complex impedances. IEEE Journal of Solid-state Circuits,

Hilhorst, M.A. & Dirksen, C. 1994. Dielectric water content sensors: Time domain versus frequency domain. In: Proceedings of the Symposium on TDR in Environmental, Infrastructure and Mining Applications, pp.23-33. US Department of the Interior Special Publication SP 19-94. University of Evanston, Illinois.

Knight, J.H. 1992. The spatial sensitivity of time domain reflecto- meuy measurements to lateral variations in soil water content. Water Resources Research, 28, 2345-2352.

Lerink, P. 1994. Prediction of the Immediate Effects of Trafic on Field Soil Qualities. PhD thesis, Wageningen Agricultural University.

Rajkai, K. & Ryden, B.E. 1992. Measuring areal soil moisture distribution with the TDR method. Geoderma, 52,73-85.

Raythatha, R. & Sen, P.N. 1986. Dielectric properties of clay suspensions in MHz to GHz range. Journal of Colloid and Inteqace Science, 109, 301-309.

Roth, C.H., Malicki, M.A. & Plagge, R. 1992. Empirical evaluation of the relationship between soil dielectric constant and volumetric water content as the basis for calibrating soil moisture measure- ments by TDR. Journal of Soil Science, 43, 1-13.

Tijink, F.G.J. 1988. Load-bearing Processes in Agricultural Wheel- Soil Systems. PhD Thesis, Wageningen Agricultural University.

Topp, G.C., Davis, J.L. & Annan, A.P. 1980. Electromagnetic deter- mination of soil water content: Measurements in coaxial trans- mission lines. Water Resources Research, 16, 514-582.

Whalley, W.R. 1993. Considerations on the use of time-domain reflectometry (TDR) for measuring soil water content. Journal of Soil Science, 44, 1-9.

261 -212.

28,164-169.

0 1996 Blackwell Science Ltd, European Journal of Soil Science, 47, 367-371