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DIVISION S-1 - SOIL PHYSICS

Simultaneous Water Content, Air-Filled Porosity, and Bulk Density Measurements with Thermo-Time Domain Reflectometry

^a Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
^b Hebei Academy of Agricultural Sciences, 598 W. Heping Road, Shijiazhuang, Hebei 050051, PRC

* Corresponding author (rhorton{at}iastate.edu)

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

 
The partitioning of the soil volume between water, solids, and air strongly influences many soil processes. In this paper we demonstrate a new approach to nondestructively measure this partitioning. A thermo-time domain reflectometry (thermo-TDR) probe was inserted into sandy loam soil and used to apply thermal and electromagnetic pulses and to monitor the transport of these pulses through the soil. We used the resulting data to determine the soil water content, air-filled porosity, and volume fraction of solids, as well as degree of saturation and bulk density. When calibrated for this soil, the standard errors between thermo-TDR measurements and gravimetric measurements were 0.02, 0.07, and 0.05 m³ m^-3 for water content, volume fraction of solids, and air-filled porosity, respectively. The standard error for degree of saturation was 0.08 m³ m^-3, and for bulk density was 0.18 Mg m^-3. This technique has great potential for soil research and management, particularly if the accuracy of the bulk density measurement can be improved.

Abbreviations: , volume fraction of water in soil • C, soil volumetric heat capacity • K , soil dielectric constant • n_a, volume fraction of air in soil • S, soil degree of saturation • thermo-TDR, thermo-time domain reflectometry • v_s, volume fraction of solids in soil

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

 
PRODUCTION OF FOOD AND FIBER, storage and cycling of greenhouse gases, and movement and degradation of water-polluting chemicals are a few examples of important soil-based ecosystem processes. These processes are all strongly influenced by the basic partitioning of the soil volume between water, solids, and air. In addition, many construction and geotechnical engineering applications require measurements of this partitioning. In this paper, we present a new concept for measuring the partitioning of the soil volume between water, solids, and air, and for measuring the soil bulk density and degree of saturation. We also present data demonstrating the application of the technique.

Several radiation-based methods have been proposed for measuring the water and solid volume fractions of soil (, and v_s, respectively). Belcher et al. (1950) reported the use of neutron scattering to estimate soil moisture and gamma ray scattering to estimate soil density. Soane (1967) proposed a method to measure soil water content and density simultaneously based on the transmission of gamma rays from two sources with different photon energies. Radiation-based techniques, similar to those of Belcher et al., are commonly used in geotechnical engineering. However, the techniques raise some safety concerns, and certification is required for all users. Recently, attempts have been made to combine computer assisted tomography (CAT scan) technology with gamma ray and x-ray methods to determine the three-dimensional distribution of solids and water in laboratory soil cores (Phogat et al., 1991, Rogasik et al., 1999). Applications of these techniques are limited to laboratory settings and are further limited by lack of access to the equipment. The limitations of current techniques create a need for new techniques to measure the partitioning of the soil volume between water, solids, and air.

Our new technique for determining the , v_s, and the volume fraction of air in soil (n_a) follows from a unique combination of two widely accepted theories. The first theory is that the thermal properties of a system are related to the volume fractions of the individual components of the system. For example, the heat capacity of soil can be calculated by summing the heat capacities of the water, solids, and air present. Mathematically, this relationship is

[1]

where C is the soil volumetric heat capacity (J m^-3 K^-1); _w, _s, and _a are the densities of water, soil solids, and air (Mg m^-3); and c_w, c_s, and c_a are the specific heat capacities of water, soil solids, and air (J Mg^-1 K^-1) (de Vries, 1963). Notably, the density and specific heat capacity of air are very small relative to the other terms, so the third term in Eq. [1] is neglected. A second widely accepted theory is that the electrical properties of a system are influenced by the volume fractions of the individual components in the system. For example, soil dielectric constant (K) in the frequency range from 1 MHz to 1 GHz is strongly related to (Topp et al., 1980). For many soils, K can be reasonably estimated by Eq. [2] (Hook and Livingston, 1995).

[2]

where K_w and K_s are the dielectric constants of water and soil solids at the measurement temperature and frequency.

The unique aspect of our proposed technique lies in a simple combination of these two theories about the thermal and electrical properties of soil. First, we note that

[3]

Eq. [1], [2], and [3] form a set of three equations with five unknowns: K, C, , v_s, and n_a. Clearly, if K and C can be measured, then the system of equations can be solved to determine , v_s, and n_a. These and v_s values can also be used to determine the soil's degree of saturation, S.

[4]

Furthermore, using the fact that _b = v_ss, we can rearrange Eq. [1] to calculate _b using measured C and values.

[5]

Solving the system of Eq. [1]–[3] requires knowledge of four parameters: _wc_w, K_w, _sc_s, and K_s. These parameters can all be measured independently or estimated from values in the literature. Alternatively, a soil specific calibration can be used to estimate these parameters.

Ren et al. (1999) introduced a new device called a thermo-TDR probe that permits simultaneous measurement of K and C. Combining thermal and electrical property measurement capabilities in one probe was first attempted by Baker and Goodrich (1987) and later by Noborio et al. (1996) with limited success. The new thermo-TDR probe is the first device to accurately measure both K and C, thereby creating the first opportunity to utilize the approach described above.

	MATERIALS AND METHODS

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

 
We constructed a thermo-TDR probe following the design of Ren et al. (1999). The probe consists of three 4-cm long hollow stainless steel needles protruding from a 2-cm waterproof epoxy body. The needles are 1.3 mm in diameter and are spaced 6 mm apart in the same plane. The center needle houses a coil of resistance heater wire and the outer two needles contain chromel-constantan thermocouples. An external data logger controls the application of the heat pulse and records the resulting temperature data. The needles are also connected to a coaxial cable and serve as wave-guides for an electromagnetic pulse generated by an external metallic cable tester. The data logger controls the cable tester and stores the resulting waveforms. Further details of the probe design are presented in Ren et al. (1999).

We demonstrated the new method in a laboratory setting using Clarion sandy loam soil (fine-loamy, mixed, superactive, mesic Typic Hapludolls). Some physical properties of the soil are listed in Table 1. The soil was air-dried, ground, and sieved through a 2-mm screen. The soil was then moistened with water and carefully packed into 15 aluminum cylinders 7.6 cm in diameter and 7.6 cm long. Packing was performed by placing one-fourth of the moist soil into the cylinder, then packing the soil to an appropriate thickness by dropping a 1 kg lead weight onto the soil from a height of 5 cm. This process was repeated four times in an effort to create a uniform soil column built of four sections, each with the same bulk density. These packed columns ranged in v_s from 0.37 to 0.66, in from 0.12 to 0.40, and in n_a from 0.02 to 0.52 (Fig. 1) . The columns ranged in bulk density from 0.95 to 1.69 Mg m^-3. After packing, the columns were sealed and allowed to equilibrate in a constant temperature room at 20 °C for 2 wk prior to measurement.

View larger version (16K): [in this window] [in a new window]   Fig. 1. Thermo-time domain reflectometry (thermo-TDR) measured volume fractions of water (), solids (vs), and air (na) vs. gravimetrically measured volume fractions.

[6]

where L and L₀ are probe constants that may be calculated from TDR measurements in air and in water (Heimovaara, 1993). L is the electromagnetic average of the lengths of the three needles in the soil, and L₀ is some portion of the apparent length that must be attributed to travel time of the electromagnetic signal inside the body of the probe.

After the TDR waveform was collected, the heat pulse measurement was performed using a BK Precision direct current power supply model 1635 (Maxtec International Corp., Chicago, IL) and the 21X datalogger. Applying a voltage across the resistance heater wire in the middle needle of the probe for 15 s generated a heat pulse. Once generated, the heat pulse traveled radially through the soil, via conduction, away from the heater to the outer needles where the temperature change was measured by the thermocouples and recorded by the data logger. The temperature data were collected in 1-s intervals for 115 s after initiation of the heat pulse. Heating powers were selected to produce 1 °C temperature increase at the outer needles. Heating powers ranged from 34 to 61 W m^-1 depending on the thermal properties of the soil.

The analytical solution for temperature change as a function of time at a radial distance from the heat pulse source is given by

[7]

where t is time (s), t₀ is the duration of the heat pulse (s), r is the radial distance (m), is the soil thermal diffusivity (m² s^-1), q is the amount of heat applied (W m^-1), and -Ei(-x) is the exponential integral (de Vries, 1952, Bristow et al., 1994). Using the nonlinear regression algorithm of Welch et al. (1996) to fit this analytical solution to the temperature data collected from the probe yielded the thermal properties of the soil, including C, , and the thermal conductivity (W m^-1 K^-1). The spacing between the needles, r, was determined by calibrating the probes in agar-stabilized water (6 g agar L^-1), assuming the volumetric heat capacity of the agar-water solution is equal to the volumetric heat capacity of water (Campbell et al., 1991).

After the thermo-TDR measurements, the mass of water in each sample was determined by oven-drying the samples at 105 °C. Using the pycnometer method (Blake and Hartge, 1986), _s was measured and was found to be 2.58 Mg m^-3 (Table 1). Knowing the mass of water, the total mass and volume of the samples, and _s, we calculated , v_s, n_a, _b, and S gravimetrically.

We chose to estimate the parameters _wc_w, K_w, c_s, and K_s by creating a soil-specific calibration using our measured data. Thermo-TDR measurements of C and K calculated from Eq. [6] and [7] were compared with C and K modeled using Eq. [1] and [2] with gravimetrically measured values of and v_s. The parameters _wc_w, K_w, c_s, and K_s were estimated by minimizing the sum of squared errors between the measured and modeled C and K values. The calibrated value for _wc_w was 4.11 MJ m^-3 K^-1, which is 2% lower than the published value for pure water at 20 °C (4.17 MJ m^-3 K^-1; Weast, 1978). The calibrated value of K_w was 79.5, which is 1% lower than the published value for pure water at 20 °C (80.1; Weast, 1978). The calibrated value for c_s was 0.812 J g^-1 K^-1. Values for c_s reported in the literature range from 0.644 J g^-1 K^-1 (Johnston, 1937) to 1.092 J g^-1 K^-1 (Bristow et al., 1994). The calibrated value for K_s was 1.62, and values for K_s in the literature range from 1.30 to 3.84 (Hook and Livingston, 1995). All of the calibrated values of the parameters show excellent agreement with measured values from the literature.

	RESULTS AND DISCUSSION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

 
Our data show that the new thermo-TDR approach was effective for determining , v_s, n_a, _b, and S in this sandy loam soil. Figure 1 shows thermo-TDR measurements of , v_s, and n_a vs. the gravimetric measurements for the 15 soil samples. A linear regression on these combined data (, v_s, and n_a) yields an r² of 0.94, a slope of 0.976 (±0.04), and an intercept of 0.009 (±0.01). The standard errors between thermo-TDR measurements and gravimetric measurements of , v_s, and n_a are 0.02, 0.07, and 0.05 m³ m^-3, respectively. The fact that the n_a measurements have a lower standard error than the v_s measurements may seem surprising since v_s is required to calculate n_a, but this reduction in error follows logically from the theory of the method. In Eq. [1], note that underestimating and solving for v_s with C fixed should lead to overestimating v_s. Thus, when we put these and v_s values in Eq. [3], the errors tend to counteract, and thermo-TDR measured n_a is less sensitive than v_s to errors in determination.

Note that the differences between thermo-TDR and gravimetric measurements arise from three sources: (i) error in the thermo-TDR values, (ii) error in the gravimetric values, and (iii) spatial variation within the packed columns. Errors due to spatial variation in the packed columns may be significant because the thermo-TDR measurement volume is much smaller than the volume of the soil column. The first and third error sources are probably larger than the second error source.

The basic composition of any soil can be shown by a single point in three-dimensional space, the coordinates of which are given by the , n_a, and v_s. Figure 2 compares the three-phase composition of the 15 soil samples as determined gravimetrically with that determined using the new thermo-TDR technique. Qualitatively, this figure shows that the gravimetric measurements and thermo-TDR measurements occupy the same region in this three-dimensional space. Comparing thermo-TDR and gravimetric measurements in this three-dimensional space further demonstrates the effectiveness of the thermo-TDR technique.

View larger version (18K): [in this window] [in a new window]   Fig. 2. Three-dimensional comparison of thermo-time domain reflectometry (thermo-TDR) measured volume fractions of water (), solids (vs), and air (na), and gravimetrically measured volume fractions.

View larger version (13K): [in this window] [in a new window]   Fig. 3. Thermo-time domain reflectometry (thermo-TDR) measured degree of saturation (S) vs. gravimetrically measured S.

View larger version (13K): [in this window] [in a new window]   Fig. 4. Thermo-time domain reflectometry (thermo-TDR) measured bulk density (b) vs. gravimetrically measured b.

	CONCLUSION

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

 
The thermo-TDR technique, which combines thermal and electromagnetic signals, is a promising new method for measuring the , v_s, and n_a, as well as the degree of saturation and bulk density. The technique yielded good results in laboratory tests on a sandy loam soil. In contrast to currently available nondestructive methods, this new technique poses no radiation hazard. In addition, thermo-TDR measurements can be automated and take less than 3 min, so they should be useful for monitoring temporal changes in the partitioning of the soil volume between water, solids, and air. The measurements made possible by this technique may be valuable in improving our ability to study and manage soil-based biological, chemical, and physical ecosystem processes. These measurements may also prove useful in geotechnical engineering.

The positive results from this evaluation point to needs for further study. Particular needs include identifying the range of soil types on which the technique is accurate, investigating thermo-TDR probe performance in undisturbed soils, and evaluating the technique in a dynamic setting where the , v_s, and n_a change across time. In addition, future research should explore the applicability of this technique to porous materials other than soil.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

 
Journal Paper No. J-18890 of the Iowa Agriculture and Home Economics Exp. Stn., Ames, IA, Project No. 3287. Supported by the Hatch Act and the State of Iowa.

Received for publication January 31, 2001.

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