PUBLICATIONS. Water Resources Research. Evaluation of measurement sensitivity and design improvement for time domain reflectometry penetrometers

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1 PUBLICATIONS Water Resources Research TECHNICAL REPORTS: METHODS Key Point: Measurement sensitivity of TDR penetrometers Correspondence to: T. L.-T. Zhan, Citation: Zhan, Tony L.-T., Q.-Y. Mu, Y.-M. Chen, and H. Ke (2015), Evaluation of measurement sensitivity and design improvement for time domain reflectometry penetrometers, Water Resour. Res., 51, , doi:. Received 29 AUG 2014 Accepted 27 MAR 2015 Accepted article online 1 APR 2015 Published online 26 APR 2015 Evaluation of measurement sensitivity and design improvement for time domain reflectometry penetrometers Tony Liang-tong Zhan 1, Qing-yi Mu 1, Yun-min Chen 1, and Han Ke 1 1 Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education, Department of Civil Engineering, Zhejiang University, Hangzhou, China Abstract The time domain reflectometry (TDR) penetrometer, which can measure both the apparent dielectric permittivity and the bulk electrical conductivity of soils, is an important tool for the site investigation of contaminated land. This paper presents a theoretical method for evaluating the measurement sensitivity and an improved design of the TDR penetrometer. The sensitivity evaluation method is based on a spatial weighting analysis of the electromagnetic field using a seepage analysis software. This method is used to quantify the measurement sensitivity for the three types of TDR penetrometers reported in literature as well as guide the design improvement of the TDR penetrometer. The improved design includes the use of semicircle-shaped conductors and the optimization of the conductor diameter. The measurement sensitivity to the targeted medium for the improved TDR penetrometer is evaluated to be greater than those of the three types of TDR penetrometers reported in literature. The performance of the improved TDR penetrometer was demonstrated by conducting an experimental calibration of the probe and penetration tests in a chamber containing a silty soil column. The experimental results demonstrate that the measurements from the improved TDR penetrometer are able to capture the variation in the water content profiles as well as the leachate contaminated soil. VC American Geophysical Union. All Rights Reserved. 1. Introduction The electrical properties of soil, such as the dielectric permittivity and electrical conductivity, are of significant interest in geotechnical and geoenvironmental engineering. These properties can be used to determine soil water content [Topp et al., 1980; Noborio, 2001; Lehmann et al. 2013] and soil dry density [ASTM D , 2005; Yu and Drnevich, 2004] as well as detect contaminated soil [Chen et al, 2010; Zhan et al, 2013]. Therefore, it would be significant to develop techniques that measure the distribution of the dielectric permittivity and the electrical conductivity along the depth in situ. Recently, scholars developed time domain reflectometry (TDR) penetrometers suitable for TDR measurements of soils at various depths [Redman and Deryck, 1994; Nissen et al., 1998; Young et al., 2000; Vaz and Hopmans, 2001; Persson and Wraith, 2002; Topp et al., 2003; Lin et al., 2006a; Kosugi et al., 2009; Miyamoto et al., 2012]. The general practice of using a TDR penetrometer was to place conductors around a nonconductor shaft. The current TDR penetrometers have been primarily constructed in three types: (a) two or three parallel copper wires are coiled around a nonconductor core, as indicated in Figure 1a [Vaz and Hopmans, 2001; Topp et al., 2003; Kosugi et al., 2009; Persson and Wraith, 2002]; (b) two straight grooves are produced on the nonconductor shaft surface in which stainless steel rods are embedded, as indicated in Figure 1b [Redman and Deryck, 1994; Miyamoto et al., 2012]; and (c) four straight strips are produced on the nonconductor shaft surface in which four similar copper strips are embedded, as indicated in Figure 1c [Young et al., 2000; Lin et al., 2006a]. Placing conductors around a nonconductor shaft allows the TDR penetrometer to sense the soil medium around the shaft at certain depths but decreases the sensitivity of the apparent dielectric permittivity and bulk electrical conductivity measurements [Lin et al., 2006a]. Therefore, minimizing the effect of materials inside the shaft and maximizing the influence zone in the surrounding medium are important to consider when designing the TDR penetrometer. Currently, most of the research focuses on the innovation of conductor styles [Vaz and Hopmans, 2001; Lin et al., 2006a; Miyamoto et al., 2012] or the disturbance caused by penetration [Rothe et al., 1997]. Insufficient attention was given to the measurement sensitivity of the TDR penetrometer. Young et al. [2000] proposed a TDR penetrometer and evaluated the energy distribution ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 2994

2 (a) Non-conductor Shaft Conductor wires (b) Non-conductor Shaft Conductor rods (c) Figure 1. Configuration of previous TDR penetrometers. Non-conductor Shaft Conductor plates around the conductors using an electromagnetic field simulation program. The optimal width and spacing of the conductor were determined to maximize the energy in the soil medium. Lin et al. [2006a, 2006b] developed a TDR penetrometer by placing multiplecopper strips around polyvinyl chloride (PVC) tubes and evaluated the measurement sensitivity through experiments. The results indicated that both the medium surrounding the TDR penetrometer and the material of the shaft contribute 50% to the measured apparent dielectric permittivity and bulk electrical conductivity. However, further study is necessary in this direction. The primary focus of the current study is as follows. Based on the definition of the spatial weighting function [Knight, 1992], an equation that represents the measurement sensitivity of the TDR penetrometer was first proposed. Then, the measurement sensitivity equation for three TDR penetrometers reported in literature was computed using a numerical method and verified using specially designed experiments. The measurement sensitivity of an improved TDR penetrometer configuration was analyzed using the verified numerical method, and the optimal conductor diameter was determined. After careful production and laboratory calibrations, the improved TDR penetrometer was applied in simulated penetration tests to evaluate its usefulness in determining water content profile and detecting leachate contaminated soil. 2. Analysis Theory for Measurement Sensitivity of TDR Penetrometer A TDR device generally consists of a pulse generator, a sampler, a coaxial cable, an oscilloscope, and an electrode that is normally at least partially in contact with the medium to be sensed. The TDR instrument sends a high frequency electromagnetic signal along an electrode. The signal is reflected at both the beginning and end of the electrode due to impedance mismatches. As shown in Figure 2, the travel time (Dt), source voltage (V s ) and long-term voltage (V f ) of the signal can be measured from the reflected waveform [Yu and Drnevich, 2004]. The apparent dielectric permittivity (e a ) and bulk electrical conductivity (r) of the testing medium are related to the travel time Dt and the ratio of V s and V f, respectively [Topp et al., 1980; Dalton et al., 1984]. In the computation equation of e a, c and L p are the velocity of light ( m/s) and the length of electrode in the testing medium, respectively. In the computation equation of r, C is a constant related to probe configuration, which can be obtained by calibration. Figure 2. Determination of apparent dielectric permittivity and bulk electrical conductivity from analysis of a typical TDR reflectometry waveform. Previous studies have indicated that the nonuniform spatial ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 2995

3 weighting in the plane transverse to the probe is inherent in the TDR measurement [Baker and Lascano, 1989; Knight, 1992; Rejiba et al., 2005, 2011]. Knight [1992] defined a spatial weighting factor (w(x,y)) at each point for the spatial sensitivity of TDR probes, which can be expressed in equation (1) as follows: wðx; yþ5ru 2 ðx; yþ= ru 2 eq ðx; yþdxdyþ (1) where U(x,y) is the electrical potential in the heterogeneous field; and U eq (x,y) is the electrical potential in the equalized homogeneous field. The physical interpretation of the weighting factor is the energy for a specific point in the heterogeneous medium field divided by the total energy for the equalized field of a homogeneous medium with the same boundary conditions. Nissen et al. [2003] and Ferre et al. [2003] concluded that the sensitivity of conventional three-rod and two-rod TDR probes to the lateral variation in the e a and r could be analyzed using this weighting factor. In equation (1), U(x,y) and U eq (x,y) could be computed using groundwater flow software [Ferre et al., 1998]. Therefore, in this study, the SEEP/W module in the Geostudio software package (CANADA, GEO-SLOPE) was used to compute the distribution of electrostatic potential surrounding the probe. The effective apparent dielectric permittivity is the spatially weighted sum of the apparent dielectric permittivity values over the domain, which can be expressed in equation (2) as follows: e a;eff 5 e a ðx; yþwðx; yþdxdy (2) where e a,eff is the effective apparent dielectric permittivity; and e a (x,y) and w(x,y) are the apparent dielectric permittivity and the weighting factor over the domain, respectively. The value of e a,eff measured using the penetrometer probe is a weighted average of the apparent dielectric permittivity of the surrounding soil (i.e., targeted medium) and the apparent dielectric permittivity of the nonconductor shaft. Therefore, by expanding the left side of equation (2), we can obtain: e a;eff 5e a;o w o ðx; yþdxdy1e a;t w t ðx; yþdxdy (3) where e a,o and e a,t are the apparent dielectric permittivity of the shaft and targeted medium, respectively; and w o (x,y) and w t (x,y) are the weighting factors that are distributed in the shaft zone and the targeted medium zone, respectively. The measurement sensitivity to a targeted medium of the TDR penetrometer may be defined as the parameter MST, as provided in equation (4). The physical interpretation of this parameter is the contribution level of the targeted medium to e a,eff. MST5 w t ðx; yþdxdy (4) Similarly, the parameter MSS is defined to represent the measurement sensitivity to the shaft material, which can be expressed in equation (5) as follows: MSS5 w o ðx; yþdxdy (5) Therefore, by substituting equation (4) and equation (5) into equation (3), we can determine the measurement sensitivity equation of the TDR penetrometer, which can be expressed in equation (6) as follows: e a;eff 5MST3e a;t 1MSS3e a;o (6) As indicated in equation (7), the weighting function has the property as follows: MST1MSS5 w t ðx; yþdxdy1 w o ðx; yþ dxdy51 (7) Based on the above analysis, a larger value of the MST parameter (correspondingly a smaller value of the MSS parameter) for the TDR penetrometer indicates a larger sensitivity to the targeted medium. The measurement accuracy would also be improved. Additionally, the measurement sensitivity equation (equation (6)) is the same as the homogenization model proposed by Birchak et al. [1974]. The dielectric material surrounding the TDR penetrometer probe has a parallel distribution with respect to the applied ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 2996

4 Figure 3. Cross sections of the TDR penetrometer used for numerical computation. electromagnetic field, and therefore the theoretical value of the parameter n in the homogenization model is n51 [Persson and Wraith, 2002]. 3. Numerical and Experimental Study of Measurement Sensitivity for TDR Penetrometer 3.1. Numerical Model for Analyzing Measurement Sensitivity of TDR Penetrometer The above analysis proposes the measurement sensitivity equation for a TDR penetrometer. In this section, numerical analyses were conducted to investigate the measurement sensitivity equations for three types of TDR penetrometers (i.e., Figures 3a, 3b, and 3c). Figures 3a and 3b configurations are similar to the probes reported by Young et al. [2000] and Lin et al. [2006], and C resembles the probe proposed by Redman and Deryck [1994] and Miyamoto et al. [2012]. Each of the TDR penetrometers consists of a 30 mm diameter nonconductor shaft and several conductors. The representative cross sections are summarized in Figure 3. Using the type-b TDR penetrometer as an example, the numerical model is presented in Figure 4. M1 and M2 represent the targeted medium and shaft material, respectively. S1, S2, S3, S4, and S5 represent the boundary conditions. According to the research of Ferre et al. [1998], S1 and S3 are set to a constant value for the hydraulic head (i.e., H5 21), which corresponds to a constant electric potential (U5 21). Similarly, S2 and S4 are set to a constant hydraulic head (i.e., H5 1). S5 is set as a zero flow boundary n 50). This boundary condition indicates that the energy flowing across the boundary S5 is negligible. This result is reasonable because a sufficiently large research area is chosen for analysis. Based on the model, U(x,y) and U eq (x,y) can be computed, and then w(x,y) can be determined using equation (1). Figure 4. Numerical model for computing the electrical potential field surrounding the TDR penetrometer. In the numerical analysis, the e a,o value is set to a constant value, and the e a,t value ranges from 10 to 80. The values are listed in Table 1. For each setting of e a,t and e a,o, the corresponding e a,eff value can be ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 2997

5 Table 1. Values of Apparent Dielectric Permittivity of Targeted Medium (e a,t ) and Apparent Dielectric Permittivity of Shaft Medium (e a,o ) Used in Numerical Computation Cases Apparent Dielectric Permittivity of Shaft Medium (e a,o ) Apparent Dielectric Permittivity of Targeted Medium (e a,t ) A a B a C a The A and B probes are used for verification experiments, and the e a,o are set to the measured values of nylon and Delrin VR. computed using equation (3). The measurement sensitivity equations can be determined through a linear regression between e a,t and e a,eff Experimental Settings for Determining Measurement Sensitivity of TDR Penetrometer In addition to the numerical analyses above, an experimental study was performed on two of the probes (i.e., types A and B) to determine the measurement sensitivity equations. The two types of TDR penetrometers were produced based on the description in the references, and their configurations are presented in Figures 5a and 5b. The length of the sensing waveguide is 20 cm. The shaft material for B and C is nylon (e a,o ) and Delrin (e a,o ), respectively. To determine the measurement sensitivity equation experimentally, a mixture of ethanol (e a is approximately 16) and deionized water (e a is approximately 80) is set as the targeted medium. The volume fraction of ethanol was varied from 0 to 1 at an interval of 0.2. After each of the mixture was prepared, the conventional three-rod TDR probe and TDR penetrometer were inserted in succession to measure the e a,t and e a,eff, respectively. Similarly, the measurement sensitivity equations can be determined through a linear regression of the experimental data Numerical and Experimental Results Figure 6 presents the results of the measurement sensitivity for the three types of TDR penetrometers determined using numerical and experimental investigations. The solid and hollow symbols are the experimental measurements and the computational values, respectively. Correspondingly, the continuous and dashed lines are the linear regression results of the experimental measurements and the computational values, respectively. The measurement sensitivity equations and the regression parameters are summarized in Table 2. Figure 5. Configurations of TDR penetrometer used for experiments. (a) Type A TDR penetrometer; (b) Type B TDR penetrometer; and (c) Improved design of TDR penetrometer. As indicated in Table 2, the linear regression is good for both the experimental measurements and the computational values, and all the regression coefficients (r 2 ) are 0.99 or above. The numerical results indicated that the measurement sensitivity to the targeted medium for the A, B, and C probes are , , and , respectively. The experimental results indicated that the measurement sensitivity to the targeted medium for the A ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 2998

6 Figure 6. Measurement sensitivity of the TDR penetrometers obtained from numerical and experimental study (ADP: Apparent dielectric permittivity). and B probes was and , respectively, which is slightly larger than the numerical results. This difference can be attributed to production errors in the TDR penetrometers. First, the size of the conductors is not completely consistent with the numerical model. Second, the fluid may seep into unavoidable tiny cracks between the conductors and the shaft and become another error source. Based on the above analysis, the measurement sensitivity of probe A is poor, and hence the measurement error may be great. The measurement sensitivity of probe B is close to that of probe C, and the targeted medium contributes approximately 50% to the e a,eff for both the probes. The result of the measurement sensitivity for probe B is consistent with the calibration results of Lin et al. [2006a]. 4. Improved Design of TDR Penetrometer The analysis results for probes A, B, and C indicate that the design of the TDR penetrometers significantly influences the measurement sensitivity. In this section, the design of the TDR penetrometer was improved to further enhance the measurement sensitivity with the aid of the above numerical method. Based on probes B and C in Figure 3, the authors improved the shape of the conductors and proposed a new design for the TDR penetrometer. The configuration of the improved TDR penetrometer is provided in Figure 5c. The probe consists of four semicircle-shaped conductors with a diameter of D and a nonconductor shaft with a diameter of 30 mm. Four arc-shaped grooves were cut out of the shaft with a thickness of D. The semicircle-shaped conductors were fit into the four grooves in the shaft and fastened with screws. This design of the TDR penetrometer not only increases the measurement sensitivity but also ensures a tight contact with the soil around the shaft. Numerical analyses were conducted to determine the optimum dimension of D. The variables considered included the diameter of the conductors (D54, 6, 8, 12, and 15 mm) and e a,o (5 and 10). The e a,t value is still set as 10, 20, 40, and 80. The computation results, i.e., the relationship of the measurement sensitivity to the value of D, are provided in Figure 7. As indicated in Figure 7, the coefficient of MST first increases and then decreases with an increasing value of D (i.e., solid square symbol). The peak value is and occurs at D58 mm. The coefficient of MSS follows an opposite trend (i.e., hollow square symbol). The minimum value is and also occurs at D58 mm. The results indicate that the measurement sensitivity reaches its maximum value in the case of Table 2. Measurement Sensitivity Equation (MSE) of TDR Penetrometers Cases MSE Fitted by Numerical Computation Results r 2 MSE Fitted by Experimental Results r 2 A e a,eff e a,t e a,eff e a,t B e a,eff e a,t e a,eff e a,t C e a,eff e a,t ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 2999

7 D58 mm. For the case of D58 mm, the MST and MSS coefficients are computed (i.e., the solid and hollow rhombuses) when the e a,o value changes from 5 to 10. The results indicate that the MST and MSS coefficients are consistent between the two cases. Therefore, the e a,o value has no influence on the measurement sensitivity of the TDR penetrometer. Based on the above optimization, an improved TDR penetrometer was fabricated. The Figure 7. Measurement sensitivity (MS) of the improved TDR penetrometer. cross section was similar to the configuration provided in Figure 5c. The diameter and length of the conductor were 8 and 200 mm, respectively. Stainless steel and high strength Poly Ether Ether Ketone (PEEK) were used for the conductor and shaft, respectively. 5. Calibration of Newly Designed TDR Penetrometer 5.1. Measurement of Apparent Dielectric Permittivity The newly designed TDR penetrometer was calibrated in Xiao-Shan silt soil [Jia et al., 2009]. The soil was first oven dried at 100 C and then passed through a 2 mm sieve. The prepared soil was evenly spread on a plastic liner and water was sprayed on the soil to slightly increase its water content. The spray-wetted soil was mixed thoroughly with a blender until the targeted water content was attained. The sample was stored in a closed plastic bag to allow redistribution and equilibration of the soil moisture. The targeted water content of the samples ranged from 0.05 to 0.35 m 3 /m 3 with an interval of 0.05 m 3 /m 3. All the calibration tests were conducted in a cylindrical plexiglass container that was 25 cm long and 15 cm in diameter. For TDR measurements, signal processing and acquisition were done with the TDR100 instrument manufactured by Campbell Scientific and its associated software PC-TDR. A 50 ohm coaxial cable was used to attach the electrode to the TDR100 instrument. The calculation of apparent dielectric permittivity and bulk electrical conductivity was explained in section 2 and Figure 2. The calibration tests included measuring both the e a,eff value using the improved TDR penetrometer and the e a,t value using the conventional three-rod probe. The calibration equations could also be determined through a linear regression. For the measurements made using the improved TDR penetrometer, the probe was first placed into the center of the plexiglass container, and the soil samples was added and compacted in the container to the prescribed dry density (1.45 g/cm 3 ). The compaction occurred in five layers, and each layer was 50 mm in thickness. For the measurements made using the conventional three-rod probe, the process of the sample preparation was similar to the measurements made using the TDR penetrometer. The only difference was that the three-rod probe was inserted into the sample after all the soil layers were compacted into the container. It is believed that the retroinsertion would not significantly change the soil density because the crosssection area of the three-rod probe is small. The calibration result is presented in Figure 8. As indicated in Figure 8, within the range of permittivity values considered in the calibration, there was a good linear relationship between the e a,t values measured using the conventional three-rod probe and the e a,eff values measured using the improved TDR penetrometer. The calibration results indicated that the measurement sensitivity to the targeted medium was , which is slightly larger than the numerically computed result (MST ). This difference may be attributed to the pore-water in the targeted medium that seeped into the tiny gap between the conductors and the shaft. Therefore, the calibration equation can provide a relationship to determine e a,t from the measurement of the TDR penetrometer (e a,eff ) as follows: e a;t 5ðe a;eff 215:0589Þ=0:5825 (8) ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 3000

8 Figure 8. Calibrated relationship between the effective apparent dielectric permittivity (ADP) and the apparent dielectric permittivity (ADP) of the targeted medium Measurement of Electrical Conductivity An accurate measurement of the electrical conductivity using the TDR relies on a detailed calibration of the instruments. Cable resistance and instrument error should be considered in the calibration [Persson and Wraith, 2002; Lin et al., 2006b, 2007]. In this study, the cable length used for the TDR penetrometer was relatively short (6 m), and all the measurements of electrical conductivity in this study were less than 250 ms/m. Hence, the cable resistance can be overlooked. Therefore, the traditional Giese-Tiemann method [Giese and Tiemann, 1975] was used to calibrate the TDR penetrometer to measure the bulk electrical conductivity of targeted medium (r t ). The salt solutions were prepared with a concentration between and mol/l and used as the testing medium. The electrical conductivity of the testing medium with a given concentration was measured using an electrical conductivity meter. The TDR penetrometer was inserted into the testing medium to measure the steady state reflection coefficients (i.e., the source voltage V s and the long term voltage V f ). The calibration result is provided in Figure 9. As presented in Figure 9, a good linear relationship was observed between the values of V s /V f measured using the TDR penetrometer and the r t values measured using the electrical conductivity meter. The regression coefficient (r 2 ) was nearly 1. Therefore, the calibration equation, as shown in equation (9), provides a relationship to determine the r t from the measurement of V s /V f using the TDR penetrometer as follows: r t 559:60273ðV s =V f Þ262:3498 (9) 6. Penetration Tests for the Improved TDR Penetrometer in a Chamber 6.1. Experimental Setup and Scheme Penetration tests were conducted by inserting the improved TDR penetrometer in a chamber containing a soil column. Figure 10 presents the experimental setup in the chamber. The chamber was 1 m in inner diameter, 1.5 m in depth, and constructed from plexiglass material. The chamber bottom was first lined with a gravel drainage layer (0.2 m in thickness) and a geotextile. Then, silty soil was filled and compacted in 13 layers to form a soil column with a depth of 1.3 m. The dry density for each compacted soil layer was controlled at 1.45g/cm 3. During the operation, three conventional three-rod TDR probes were installed at different depths of the soil column (i.e., 0.2, 0.7, and 1.1 m). A loading device was placed on top of the chamber to exert the penetration of the Figure 9. Calibration relationship for measuring the bulk electrical conductivity (EC). TDR penetrometer. A liquid ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 3001

9 Figure 10. Setup of the penetration tests in a soil column contained in a chamber. reservoir was connected to the chamber bottom to implement a rise/draw down of liquid in the soil column. After the chamber was assembled, the following test procedures were conducted. (1) The TDR penetrometer penetrated at point I (see Figure 10) to measure the apparent dielectric permittivity profile of the soil column, from which the initial water content profile (i.e., initial profile) could be determined based on the calibration result presented previously. Meanwhile, the three preinstalled TDR probes also obtained readings to measure the initial apparent dielectric permittivity at different depths of the soil column (i.e., 0.2, 0.7, and 1.1 m). The penetration hole at point I was lined with a PVC tube to prevent soil collapse and preferential flow. (2) The water reservoir was elevated to ensure the water level in the soil column rose to a depth of 1.1 m above the top surface of the gravel layer. When the water level was stable, the TDR penetrometer penetrated at point II to measure the water content profile corresponding to the partially submerging condition. Measurements taken using the three preinstalled TDR probes and treatment of the penetration were performed as above. These two steps, which are the same for all following procedures, will not be mentioned later. (3) The water reservoir was elevated to force the water level to rise to the top of the soil column. When the water level was stable, the TDR penetrometer penetrated at point III to measure the saturated or nearly saturated water content profile corresponding to the fully submerging condition as well as the bulk electrical conductivity profile of the soil column. (4) The water level in the soil column was then drawn down to the chamber bottom by drainage. When the drainage was complete, the reservoir containing a mixture of 20% leachate and 80% tap water (volume/volume) was elevated to allow the liquid level to rise gradually to the top of the soil column. When the liquid level was stable, the TDR penetrometer penetrated at point IV to measure the bulk electrical conductivity profile of the soil column. (5) The drawdown/ refilling procedure was repeated to replace the pore-liquid in the soil column with a mixture of 40% leachate and 60% tap water (volume/volume). For this step, the TDR penetrometer penetrated at point V to measure the bulk electrical conductivity profile of the soil column. It should be noted that the leachate was obtained from a landfill of municipal solid wastes in Hangzhou, and it had an electrical conductivity of approximately 2500 ms/m. Because of the high electrical conductivity for the leachate-based liquid, the apparent dielectric permittivity cannot be determined from the readings of the TDRs. After the first three penetration tests, it was found the shallow soil in the soil column was disturbed significantly as a result of the repeated penetration and pulling-out operation of the TDR penetrometer. In order to reduce the effect of the disturbance on the measurements, a new soil column was set up by following the same procedure to implement the last two penetration tests which determined the bulk electrical conductivity profiles of the leachate contaminated soil columns. Unfortunately, no three-rod TDR probe was ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 3002

10 installed in the new soil column. So the measurement of bulk electrical conductivity by the three-rod TDR probe was not done for the last two penetration tests. Alternatively, both the inflow and outflow leachate were collected just before each penetration test to measure their electrical conductivity. It is believed that the alternative measurements were able to give an indication for the bulk electrical conductivity of the leachate contaminated soil on the basis of Archie s law [Archie, 1942] and the calibration test on the same soil. The calibration test was performed by Figure 11. Measurements of water content profiles for different submerging conditions. using the conventional threerod TDR probe which was fixed in the middle of a plexiglass container. The calibration test was carried out on three soil samples with different void ratios (ranging from to 0.486). For each test, the soil sample was compacted to the required void ratio in the container, and then saturated with a salt solution with different values of electrical conductivity (ranging from 0 to 800 ms/m). The electrical conductivity of the solution (r solution ) was measured by an electrical conductivity meter. The bulk electrical conductivity of the soil (r soil ) was determined by using the three-rod TDR probe. Based on the calibrated relationship between r soil and r solution, the value of parameter m in Archie s equation could be determined through a linear regression. The average value of parameter m was The porosity (n50.461) in the soil column was considered homogenously and computed from the compaction dry density (1.45 g/cm 3 ). Therefore, the calibrated Archie s equation was determined as equation (10). r soil 50:461 1:4915 r solution (10) Thus, with the measurements of electrical conductivity for the inflow and outflow leachate (r solution ), the bulk electrical conductivity (r soil ) near the surface and bottom of the soil column was calculated Determination of Water Content Profiles Figure 11 presents the measurements of the water content profile in the soil column for the first three steps. The solid and hollow symbols are the measurements from the TDR penetrometer and the pre-installed conventional three-rod probes, respectively. For the measurements from the TDR penetrometer, the measured e a,eff value was first converted to the e a,t value using equation (8), and the volumetric water content was determined using the Topp equation [Topp et al., 1980]. For the measurements from the preinstalled conventional three-rod probes, the measured apparent dielectric permittivity was directly converted to the volumetric water content using the Topp equation [Topp et al., 1980]. The results measured using the preinstalled conventional three-rod probe were believed to be relatively reliable and provided a reference for the comparison with the profiles measured using the TDR penetrometer. As indicated in Figure 11, the water content profiles of the soil column measured using the TDR penetrometer were essentially consistent with the results measured using the pre-installed conventional three-rod probes. For the initial water content profile, the TDR penetrometer measurements were m 3 /m 3 greater than the measurements from the conventional three-rod probes for depths between 0 and 0.8 m, and the two measurements were identical below a depth of 0.8 m. This inconsistency, especially at shallow depths, is likely attributed to the penetration effect from the operation of the TDR penetrometer, as explained by Lin et al. [2006a]. The shallow soil was relatively loose and more susceptible to the penetration effect. When the water level in the soil column was raised to a depth of 1.1 m above the top surface of the ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 3003

11 Figure 12. Measurements of bulk electrical conductivity profiles for the soil column saturated by different concentrations of leachate. gravel layer, the water content profiles measured using the TDR penetrometer were also essentially consistent with the results measured using the preinstalled conventional three-rod probes. When the water level was raised to the top surface of the soil column, the soil column was saturated or nearly saturated. In this case, the measurements of water content from both the TDR penetrometer and the conventional three-rod probes were essentially maintained at a constant value with depth. Compared with the results from the conventional three-rod probes, the measurements of the water content profile measured using the TDR penetrometer were m 3 /m 3 greater. These greater measurements are likely attributed to a tiny gap existing between the steel conductors and the middle non-conductive shaft. The surrounding water may have tended to seep into the gap and resulted in a greater measurement of water content. The gap effect can be reduced by improving the production of the penetrometer. In addition, the possible nonlinearity in the calibration between dielectric permittivity of targeted medium and measured effective dielectric permittivity of TDR penetrometer could be another error source. As indicated in Figure 11, the water content profiles measured from the improved TDR penetrometer were able to detect the position of the water level Measurement of Bulk Electrical Conductivity for Leachate Contaminated Soil Figure 12 presents the profiles of the bulk electrical conductivity of soils (r soil ) measured by penetrating the TDR penetrometer into the soil column, which was contaminated by different concentrations of leachate (i.e., 0, 0.2, and 0.4 in terms of volume ratio between leachate and tap water). For the soil column saturated by tap water, the measurements of r soil by using the preinstalled three-rod probes are also plotted in Figure 12 (see the semi-hollow symbols besides the 0:1 (leachate: water) profile). For the other two cases (i.e., soil column saturated with the diluted leachate), the data points of r soil deduced from the measurements of electrical conductivity on the inflow and outflow leachate are plotted in Figure 12 (see hollow symbols besides the 0.2:0.8 (leachate: water) and 0.4:0.6 (leachate: water) profiles). As shown in Figure 12, for the soil column saturated by tap water, the r soil profile (0:1 (leachate: water)) determined by the TDR penetrometer are close to the data points measured by the preinstalled three-rod TDR probe. For the other two cases (i.e., soil column saturated with the diluted leachate), both the top and bottom points of the r soil profiles determined by the TDR penetrometer (0.2:0.8 (leachate: water) and 0.4:0.6 (leachate: water)) are close to the data points of r soil deduced from the measurements of electrical conductivity on the inflow and outflow leachate. A significant increase in the soil electrical conductivity was observed as the leachate volume fractions of the pore liquid increased from 0 to 0.2 and then 0.4. It was observed that the electrical conductivity indicated a decreasing trend with an increasing depth for the measured profile of tap water saturated soil column. This result occurred because the silty soil contained a certain salinity, and a part of that salinity was flushed from the bottom to the top when the soil column was saturated by water seeping upward. The experimental results provided in Figure 12 indicate that the TDR penetrometer is able to detect the leachate contamination in the soil. 7. Summary In this report, a theoretical method based on a spatial weighting analysis of the electromagnetic field was presented to evaluate the measurement sensitivity of a TDR penetrometer. The sensitivity evaluation ZHAN ET AL. MEASUREMENT SENSITIVITY OF TDR PENETROMETER 3004

12 method was verified by conducting a numerical and experimental study on the three types of TDR penetrometers reported in literature. Based on the sensitivity evaluation method, an improved design of the TDR penetrometer was proposed to enhance its measurement sensitivity. The performance of the improved TDR penetrometer was demonstrated by conducting an experimental calibration of the probe and penetration tests on a soil column. The following primary conclusions can be made: 1. The proposed method provides a useful approach for the sensitivity evaluation of a TDR penetrometer as well as its design improvement. Both theoretical and experimental studies demonstrated that the measurement sensitivity of a TDR penetrometer depends significantly on its cross section configuration and that it is not influenced by the apparent dielectric permittivity of the shaft material in the middle. 2. The improved design of the TDR penetrometer included the use of semicircle-shaped conductors and optimization of the conductor diameter. The measurement sensitivity for the improved TDR penetrometer with a shaft of 30 mm in diameter attained its maximum value when the diameter of the semicircleshaped conductors was equal to 8 mm. The measurement sensitivity to the targeted material for the newly designed TDR penetrometer was equal to , which was significantly greater than those of the three types of TDR penetrometers reported in literature (i.e., , , and for type A, B, and C, respectively). 3. The penetration tests in a chamber containing a silty soil column demonstrated that the measurements from the improved penetrometer were able to capture the variation in the water content profiles as well as the leachate concentration profiles of the pore fluids. Acknowledgments The data for this paper are available by contacting Tony Liang-tong Zhan ( zhanlt@zju.edu.cn). 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