laboratory and field calibration of tdr probes for water content ...

OttawaGeo2007/OttawaGéo2007

LABORATORY AND FIELD CALIBRATION OF TDR PROBES FOR WATER CONTENT MEASUREMENT W.A. Take, D.N. Arnepalli, R.W.I. Brachman and R.K. Rowe GeoEngineering Centre at Queen’s-RMC – Queen’s University, Kingston, ON, Canada

ABSTRACT Laboratory and field calibration of Time Domain Reflectometry (TDR) probes for water content measurements are presented. Thirty-six probes were individually calibrated in the laboratory to assess the resulting accuracy of measurements of volumetric moisture content. These probes were then installed in the field, at which point their initial readings were taken and tube samplers were driven into the soil at the same elevation. A comparison of the volumetric moisture content inferred from the TDR measurements with those obtained from the oven-dried method are made using the general Topp’s equation. Finally, this paper quantifies the increase in precision which is possible using site-specific calibrations using the exact cable lengths, wiring, and soil type as found in the field. RÉSUMÉ Le calibrage de laboratoire et de champ des sondes de la réflectométrie de domaine de temps (TDR) pour des mesures de teneur en eau sont présentés. Trente-six sondes ont été individuellement calibrées dans le laboratoire pour évaluer l'exactitude résultante des mesures du contenu d'humidité volumétrique. Ces sondes ont été alors installées dans le domaine, lequel au point leurs lectures initiales ont été prises et des échantillonneurs de tube ont été conduits dans le sol à la même altitude. Une comparaison du contenu d'humidité volumétrique impliqué des mesures de TDR avec ceux obtenus à partir de la méthode séchée au four sont faites en utilisant l'équation du Topp général. En conclusion, cet article mesure l'augmentation de la précision qui est possible en utilisant des calibrages emplacement-spécifiques en utilisant les longueurs de câble, le câblage, et le type exacts de sol comme trouvé dans le domaine. 1

INTRODUCTION

Time Domain Reflectometry (TDR) is a commonly used technique to obtain laboratory and field measurements of volumetric moisture content in soils. In this technique, a pulse wave generator is used to send a short duration electromagnetic wave down a coaxial cable to a probe which typically consists of three stainless steel rods embedded into a soil. As the wave passes from the coaxial cable into the probe, a reflected wave is sent back to the source. Similarly, as the transmitted wave reaches the end of the probe, another reflection is returned to the source. Precise measurements of the time between these two reflected waves enable the velocity of the wave to be calculated as it travels the known length of the probe. This velocity is useful for the measurement of soil moisture as the velocity of an electromagnetic wave though a material is a direct function of its dielectric constant, Ka. In soils, the dielectric constants of interest are that of the pore water, the soil solids, and the pore air. Due to the high contrast in the dielectric constant between the pore water and the soil solids, the presence of moisture in soil will significantly alter the mixed, or “apparent” dielectric constant of a soil-water mixture. As a result, measurements of the apparent Ka of a soil have been shown to be highly successful in predicting the moisture content of a soil.

The most quoted calibration relationship between the volumetric moisture content of a soil θv and the apparent dielectric constant, Ka, is that of Topp et al. (1980):

θ v = −5.3 × 10−2 + 2.9 × 10−2 K a − 5.5 × 10−4 K a 2 + 4.3 × 10− 6 K a

3

[1]

It is important to note that this third-order polynomial relationship does not include any soil parameters. This is indicative of this equation being remarkably transferable to a wide range of different soils with a reasonable degree of accuracy. For example, Evett et al. (2005), found that for their soil the use of the “Topp equation” resulted in a maximum deviation from mass balance values of only 3 -3 0.042 m m . A simpler form of calibration equation which closely models the original “Topp equation” (and therefore has similar accuracy and universality) has subsequently been proposed in the literature (e.g. Ledieu et al. 1986 Topp and Reynolds, 1998) in the form of:

θ v = 0.115 K a − 0.176

[2]

In the field of geotechnical and geoenvironmental engineering, moisture contents are most often expressed

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Ka

ρw = 0.993 + 8.65w ρd

[3]

where, ρw is the density of water, and ρd is the dry density of the soil. Widespread use of the TDR principles to measure water content over the past twenty years has shown that a site specific calibration needs to be performed if higher accuracy is required than that provided by the standard Topp equation. In particular, site-specific empirical calibration is required for soils of high organic content (e.g. Herkelrath et al, 1991), soil texture (e.g. Ponizovsky et al, 1999), clays of high specific surface (e.g. Yu et al, 1999), or soils with either exceptionally high or low densities (e.g. Quinones et al., 2003). Indeed, research continues on the use of multi-phase mixing models (e.g. Roth et al., 1990; Evett et al., 2005) to predict these calibration constants theoretically from the properties of the soil and pore water. When site-specific calibration has been performed, it is generally reported that the root mean squared error (RMSE) associated with the TDR 3 -3 technique can be reduced to less than 0.01 m m (e.g. Evett et al. 2005). In this paper, a large sample of 36 TDR probes were individually calibrated in the laboratory to investigate the need for a site-specific calibration for the silty-sand soil of the Queen’s composite geosynthetic liner experimental site (Brachman et al., 2007). These probes were subsequently installed in the field, at which point their initial readings were taken and tube samplers were driven into the soil at the same elevation. A comparison of the volumetric moisture content inferred from the TDR measurements with those obtained from the oven-dried method are made using the general Topp’s equation.

2.2

Probe offset measurement

An initial water calibration exercise was performed to measure the specific probe offset associated with each of the 36 TDR probes individually as recommended by the manufacturer (Campbell Scientific, 2006). This procedure involves immersing each TDR probe in double distilled water of known temperature (i.e. a material of known dialectric constant, Ka), taking a reading, and then inferring the exact as-manufactured sensing length of the TDR probe. The measurement of this probe specific offset value effectively eliminates the error associated with inter-probe variability arising from the manufacturing process. 2.3

Characterisation of on-site soil

The Queen’s composite geosynthetic liner experimental field research project aims to use TDR measurements of soil moisture content to quantify the moisture changes which occur after construction in a composite landfill liner system (Brachman et al., 2007). Hundreds of soil samples were collected from the field site and were analyzed to quantify the geotechnical properties of this material. The specific gravity, Gs, from five replicate tests was found to be 2.69. The particle size distribution of the soil is given in Figure 1.This data indicates that the soil is a silty-sand with 40% passing the 0.075 mm sieve. These fines were found to be non-plastic. 100

80

Percent finer (%)

gravimetrically rather than on a volumetric basis. Mindful of this, Siddiqui et al. (2000) has successfully modified a calibration equation of the form of Equation 2 directly into gravimetric moisture content, w:

60 40

20 0

2

LABORATORY CALIBRATION OF TDR PROBES 1E-3

2.1

TDR System

0.01

0.1

1

10

Particle Size (mm)

The TDR equipment used in this experiment consisted of a Campbell Scientific CR1000 datalogger, TDR100 system, five SDMX50 50Ω coaxial multiplexers, and thirtysix CS635 TDR probes. These waveguide probes consist of three 3.18mm diameter, 150mm long rods which are inserted into the soil sample. The maximum suggested length of coaxial cable between the wave generator and the sensing probe is 35m. In this study, five different lengths of cable were used which were distributed over this range of possible values (12.2m, 19.2m, 25.3m, 30.8m, and 32.6m).

Figure 1. Gradational characteristics of the soil collected from field site and used for calibration of TDR probes 2.4

Sample preparation for laboratory calibration

The goal of any site-specific TDR calibration is to, as much as is possible, reproduce the soil conditions which will be present in the field installation including soil density. To this end, the compaction properties of the sandy silt were investigated by performing a series of Standard Proctor compaction tests (ASTM D 698). In order to obtain the soil for these compaction tests, bulk samples of site soil were retrieved from the field and were

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allowed to slowly air-dry before being mixed with a known mass of water in a rotary mixer. The resulting mixture was then stored in air tight polyethylene bags for 24 hours prior to compaction. The moist soil was then compacted in three layers into the cylindrical TDR calibration cell using a Standard Proctor hammer, as shown in Fig. 2.

15 cm

Top flange Tie rod 20 cm

PVC Cylinder

Details of the TDR calibration cell are presented in Fig. 3. The cell consists of a 20cm high section of nonconductive PVC pipe, compressed at the top and bottom by a top plate and base plate connected by four tie rods. This geometry ensures that, once installed, the entire TDR probe will be bounded by least 50mm of soil. This distance has been shown by Weitz et al. (1997) to eliminate boundary effects.

Base plate C/S View

15 cm

The relationship between dry-density, ρd, and gravimetric moisture content, w, for the site soil is presented in Fig. 4. These results indicate that the Standard-Proctor 3 maximum dry-density is 1.83 g/cm , the optimum moisture content is 11.4 %. At this maximum density, the corresponding degree of saturation, Sr, is 65%.

Plan View

Based on this calibration data the compaction effort was adjusted accordingly at each moisture content from the Standard Proctor effort (25 blows in three lifts) to reach a 3 target dry density of 1.6 g/cm . This dry density target corresponds to the mean density achieved during the construction of the field test site (Brachman et al., 2007)

Figure 3. TDR calibration cell 1.9

3

ρ d (g/cm )

Standard proctor hammer

Nut

1.8

1.7

Calibration cell 1.6

0

5

10

15

20

25

w (%) Figure 4. Standard Proctor compaction test results

2.5 Figure 2. Compaction of soil into TDR calibration cell

TDR installation and measurement

Once the soil was compacted, a single TDR probe was inserted into the compacted soil mass using the same method as would be used in the field: placement by hand as shown in Fig. 5. Care was taken to ensure proper contact between the probe rods with the surrounding soil mass during the insertion process, as air gaps have been reported to have a significant effect on the calibration relationship (e.g. Siddiqui et al, 2000). The surface of the soil with the installed TDR probe was then covered to prevent the loss of moisture due to evaporation, and the system left for approximately 15 minutes prior to the

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measurement of the mean and standard deviation of the apparent dielectric constant, Ka of the soil mass.

Performing a least-squares regression on this dataset 2 improves quality of the empirical curve fit (r =0.998; 3 -3 RMSE=0.004 m m ) and yields the following modified coefficients:

θv = −3.54 × 10−2 + 3.14 × 10−2 K a − 1.11× 10−3 K a 2 + 2.63 × 10− 5 K a Probe rods

3

Similarly, the quality of the universal calibration relationship of the form of Equation 2 can be improved ( 2 3 -3 r =0.995; RMSE=0.006 m m ) using a least squares regression on the site specific data:

θv = 0.117 K a − 0.169 PVC cylinder

Measurement of soil moisture content

Only a single TDR probe is calibrated in any one cylinder of compacted soil to eliminate the effect of potential macro voids arising from multiple probe insertions. Once the TDR probe was removed from the mould, the gravimetric moisture content, w, of the compacted soil mass was obtained using the oven dried method (ASTM D 2216) In order to quantify the moisture gradient across depth of compacted soil mass (i.e., along the full 150mm length of the TDR probe rods), nine samples at three different depths were collected. The dry density of the compacted soil mass was also obtained by calculated by measuring bulk density and gravimetric water content. Using the values of gravimetric water content and dry density, the volumetric water content of the soil can be calculated. The typical standard deviation of the volumetric moisture content obtained using the oven 3 -3 drying method was 0.003 m m . 2.7

[5]

Although the site-specific calibration of Eq. 4 has a slightly better fit with the calibration data than Eq. 5, the inherent danger in this polynomial form of calibration equation is shown in Figure 6. If a polynomial curve fit is extrapolated outside the range of data values used to 3 -3 obtain the empirical relationship (0.07 to 0.35 m m in this case), the prediction may be wildly in error.

Figure 5. Insertion of TDR probe into compacted soil 2.6

[4]

Results of laboratory calibration

The site-specific empirical TDR calibration relationship was first established for a sub-set of 5 TDR probes, one each of cable lengths 12.2m, 19.2m, 25.3m, 30.8m, and 32.6m to test for the influence of cable length at the outset of the study. The mean values of the measured apparent dielectric constant, Ka, and oven-based volumetric moisture content are presented in Figure 6 along with the universal equation of Topp et al. (1980). This data indicates that for the length of cable lengths investigated herein, there is not an influence of cable length on the calibration relationship. This data also indicates that for the range of moisture contents being 3 -3 investigated (0.07 to 0.35 m m ), the maximum deviation 3 -3 from the universal equation is 0.03 m m . Expressed as a coefficient of determination, the universal equation predicts the volumetric moisture content of the test site 2 3 -3 soil with a r = 0.980 and a RMSE of 0.013 m m .

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2.8

Laboratory validation of calibration relationship

In order to validate the quality of these calibration relationships, an additional 31 TDR probes (which were not used for soil calibration) were used to measure the apparent dielectric constant, Ka, of the 31 soil cylinders compacted at a wide range of moisture contents. Using the mean of the measured Ka values and the best sitespecific calibration (Equation 4), the volumetric water content of these samples was calculated and compared with those obtained by conventional oven dried method.. As shown in Figure 7, the site-specific calibration provides an excellent prediction of the moisture content of 2 3 -3 lab samples (r =0.995; RMSE = 0.007 m m ) within the range of volumetric moisture contents for which the sitespecific calibration was obtained.


Figure 8. Soil sampler and extruder

Figure 6. Results of laboratory calibration

(a) Excavation

60 cm

(b)

Additional excavation

TDR probe

30 cm

10 cm

Figure 9. a) initial sampling of volumetric moisture content and subsequent b) probe installation

Figure 7. Laboratory validation of TDR probes 3

Soil sample

IN-SITU VALIDATION OF TDR PROBES

To assess the influence of the increased soil heterogeneity inherent with field-scale monitoring, an additional validation exercise was performed as part of the field TDR probe installation process. Once the subgrade silty sand was brought to grade and compacted, roughly 30cm × 30cm × 60cm test pits were dug for TDR probe installation. Soil core samples were collected at the target installation depth of each TDR probe using an aluminium core sampler of 50 mm in diameter and 100 mm in length (Fig. 8). These samples were then subsequently used to establish the field volumetric moisture content. Once all of these soil samples had been collected (Fig. 9a), the soil face was further excavated (removing the shaded area of Fig. 9b) to provide an undisturbed excavated face of the pit for TDR installation. A picture of the as-installed TDR probes just prior to backfilling is included as Fig. 10.

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TDR Probes

Figure 10. TDR probes installed in a field test pit


After the final TDR probe was installed in each instrumentation pit, the pit was backfilled with the native excavated soil and compacted to its in-situ density using handheld compactor, taking care to avoid damaging the head of the TDR probe or the coaxial cables leading to the data acquisition system. Initial readings were then taken of the apparent dielectric constant of the soil with the TDR probes using the exact configuration (length of cable, multiplexer path, etc) of the field monitoring system. A comparison between the measured in-situ volumetric water content values of the soil core samples and that inferred from TDR measurements for 8 test pits is presented in Figure 11. This data confirms that the initial readings of the as-installed probes have a high 2 coefficient of determination (r = 0.985) and a root mean squared error similar to that of the laboratory validation 3 -3 exercise (0.006 m m ). This data confirms that the effect of soil heterogeneity at this specific field site is negligible.

Figure 11. Field validation of site-specific calibration 4

SUMMARY

Thirty-six TDR probes were individually calibrated in the laboratory to establish a site-specific calibration relationship for use with the Queen’s composite geosynthetic liner experimental field research project. In this case, the universal Topp equation yielded estimates 3 -3 of volumetric that were at most 0.03 m m in error from the measured value. The site-specific calibration 3 -3 relationship (valid between 0.07 – 0.35 m m ) was found to reduce the root mean squared error from 0.013 to 3 -3 0.006 m m . This calibration relationship was then validated in the lab and in the field during TDR probe installation. These validation exercises indicate that the calibration is independent of cable length for the lengths chosen in this study and insensitive to soil heterogeneity at the site.

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ACKNOWLEDGEMENTS This study was financially supported by the Natural Science and Engineering Research Council of Canada (NSERC), the Ontario Centres of Excellence, and Terrafix Geosynthetics Inc. The authors are grateful to their industrial partners, Solmax International, Terrafix Geosynthetics Inc, Ontario Ministry of Environment, Gartner Lee Ltd, AMEC Earth and Environmental, Golder Associates Ltd., and CTT Group. REFERENCES ASTM D 2216. 2005. Standard test method for laboratory determination of water (moisture) content of soil and rock by mass, Annual Book of ASTM Standards, 04.08, ASTM, West Conshohocken, PA, USA: 220224. ASTM D 422. 2005. Standard test method for particle size analysis of soils, Annual Book of ASTM Standards, 04.08, ASTM, West Conshohocken, PA, USA: 10-17. ASTM D 698. 2005. Standard test methods for laboratory compaction characteristics of soil using standard 3 3 effort (12400 ft-lbf/ft (600 kN-m/m )), Annual Book of ASTM Standards, 04.08, ASTM, West Conshohocken, PA, USA: 80-90. Brachman, R.W.I., Rowe, R.K., Take, W.A., Arnepalli, D.N., Chappel, M., Bostwick, L.E., and Beddoe, R. 2007. Queen’s composite geosynthetic liner th experimental site. 60 Canadian Geotechnical Conference, Ottawa, ON. Campbell Scientific, 2006. Instruction manual for TDR probes, Campbell Scientific Canada Corporation, Edmonton, Alberta, Canada. Evett, S.R., Tolk, J.A., and Howell,T.A. 2005. Time domain reflectometry laboratory calibration in travel time, bulk electrical conductivity, and effective frequency. Vadose Zone Journal 4:1020-1029. Herkelrath, W.N., Hamburg, S.P., and Murphy, F. 1991. Automatic, real-time monitoring of soil moisture in a remote field area with time domain reflectometry. Water Resources Research. 27(5): 857-864. Ledieu, J., De Ridder, P., De Clerck, P., and Dautrebande, S. 1986. A method of measuring soil moisture by time-domain reflectometry. Journal of Hydrology 88:319-328. Ponizovsky, A.A., Chudinova, S.M., and Pachepsky, Y.A. 1999. Performance of TDR calibration modes as affected by soil texture. Journal of Hydrology 218: 3543. Quinones, H., Ruelle, P., and Nemeth, I. 2003. Comparison of three calibration procedures for TDR soil moisture sensors. Irrigation and Drainage 52: 203-217. Roth, K., Schulin, R., Fluhler, H., and Attinger, W. 1990. Calibration of time domain reflectometry for water content measurement using a composite dielectric approach. Water Resources Research 26(10):22672273.


Siddiqui, S.I., Drnevich, V.P., and Deschamps, R.J. 2000. Time domain reflectometry development for use in Geotechnical Engineering, Geotechnical Testing Journal, 23(1):9–20. Topp, G.C. and Reynolds, W.D. 1998. Time domain reflectometry: a seminal technique for measuring mass and energy in soil Topp, G. C., Davis, J. L., and Annan, A. P. 1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines, Water Resources Research, 16(3): 574-582. Weitz, A.M., Grauel, W.T., Keller, M., and Veldkamp, E. 1997. Calibration of time domain reflectometery technique using undisturbed samples from humid tropical soils of volcanic origin. Water Resources Research. 33(6):1241-1249. Yu, C., Warrick, A.W., and Conklin, M.H. 1999. Derived functions of time domain reflectometry for soil moisture measurement. Water Resources Research 35(6):1789-1796.

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