Evaluation of TDR Penetrometer Performance

1 n n cable penetrometer cable

eff

material k R k R

a

a

[5-6]

where βpenetrometer is the calibration parameter for the measurement of electrical conductivity using the TDR penetrometer. The new calibration equations (Eq [5-4] and Eq [5-6] ) will be verified by experimental data.

5.3.3 Evaluation of TDR Penetrometer Performance TDR Waveforms and Measurement Sensitivity

Time domain reflectometry measurements were made by attaching the TDR probe to a

end. The multi-conductor penetrometer waveguides were submerged in a large tank (100cm*100cm*50cm) filled with tap water. Fig. 5-11 shows the TDR waveforms in water for waveguides with different numbers of conductors. Similarly, the waveforms in water for 2-conductor waveguides with different conductor width are shown in Fig. 5-12. The waveform of a coaxial probe is also shown in Fig. 5-11 and Fig. 5-12 for comparison. The length of the coaxial probe was 116 mm and the length of T2 was 146mm. All other probes were 200 mm. The TDR sends a step pulse down the cable and some of the wave energy is reflected from both the beginning and end of the probe as shown in Fig. 5-11 and Fig. 5-12.

The first positive reflection is due to the impedance change at the connector between the cable and the probe. The sudden drop of the waveform resulting from the negative reflection occurs when the pulse enters the probe section. The second positive reflection occurs at the end of the probe. From a practical perspective, the data shown in Fig. 5-11 and Fig. 5-12 suggest any of the 5 probe configurations can be used to identify reflection points. However, as the number of conductors and conductor width increases, the impedance of the probe decreases and the negative reflection at the beginning of the probe increases, causing the waveform to drop down to a lower level. Hence, the reflection points in probe T1 are clearest. This becomes more obvious especially when the dielectric constant of the surrounding medium decreases (e.g. soils with low water contents).

The travel time T of the penetrometer probe is about 70% of that of the coaxial probe with the same length. All penetrometer probes perform similarly in this aspect. The effective dielectric constants (Ka,eff) measured by the probes listed in Table 5-1 are all near 41, which is approximately equal to (Ka,water+Ka,probe)/2, in which Ka,water = 80 and Ka,probe ≈ 2. Ka,probe is the combination of dielectric constant of probe material, derlin® and air. Considering the theoretical value n=1.0, Eq. [5-3] can be simplified as

2

for all probe configurations. Regardless of the waveguide configuration, the material inside the probe weights the same as the material surrounding the probe in Ka measurements.

Unlike the traveltime measurement, the asymptotic value of the reflection coefficient ρ∞

depends on the impedance of the probe. As the number of conductors and conductor width increases, the impedance of the probe decreases and ρ∞ decreases. Therefore, the effective electrical conductivity (σeff) can not be determined unless the constant α in Eq. [5-5] is known for the multi-conductor probe with conductor arrangement identical to the TDR penetrometer but without the cone shaft. However, the relationship between the effective electrical conductivity and electrical conductivity of the surrounding medium can be revealed by comparing the ρ∞ value of the TDR penetrometer with that of the probe with the same conductor arrangement but without the cone shaft. The measurements in tap water showed that σeff = 0.5 σTap water and σprobe =0 (derlin® and air are nonconductive) for all probe types listed in Table 5-1. Considering the theoretical value n = 1.0, Eq. [5-5] can be simplified as

2

Regardless of the waveguide configuration, the material inside the probe also weights the same as the material surrounding the probe in σ measurements.

The material surrounding the TDR penetrometer contributes 50% to the effective dielectric constant and electrical conductivity. This percentage can not be increased by changing the conductor configuration. Placing multiple conductors around a non-conducting

sensitivity of dielectric and conductivity measurements. The measurement sensitivity is defined here as the derivative of the TDR response (i.e. the T or ρ∞) with respect to the dielectric constant or electrical conductivity of the material under test. The sensitivity of the TDR penetrometer is about 70% of the coaxial or conventional multi-conductor probes. This reduction in sensitivity is acceptable in practice.

1 1.5 2 2.5 3 3.5

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

V o lt a g e , r e la ti ve t o in p u t

Time (ns)

Coaxial T1 T2 T3

Fig. 5-11 The TDR waveforms of probes with different number of conductors.

1 1.5 2 2.5 3 3.5 0.2

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

V o lt a g e , r e la ti ve to i n p u t

Time (ns)

Coaxial T3 T4 T5

Fig. 5-12 The TDR waveforms of probes with different conductor spacing (width).

Weighting function for travel time and EC measurements

The radial sampling of TDR measurements using the TDR penetrometer may be investigated using electromagnetic field theory. Alternatively, an experimental approach was taken since the theoretical derivation is complicated and also needs to be verified experimentally. In order to investigate the radial sampling of the TDR penetrometer, the trial probes were submerged in water-filled PVC tubes of different diameters. Fig. 5-13 illustrates the cross section of the testing arrangement in the plane transverse to the probe. The material surrounding the TDR penetrometer is a composite medium with tap water located concentrically around the center rod and air outside the PVC pipe. The dielectric constant of the PVC material is close to that of air, so the inner diameter of the PVC tube can be considered as the boundary between tap water and air. Since the dielectric constants of water and air lie in the two opposite extremes (Ka,wate =80 and Ka,air = 1.0) the “spatial weighting function” for Ka

and σ may be defined experimentally as

%

where Ka,r and σ,r the effective dielectric constant and electrical conductivity measured in a water-filled PVC tube with inner diameter r, respectively, and Ka,eff is the effective dielectric constant measured in a large water-filled tank. Ka,eff is representative of the effective dielectric constant measured in a water-filled PVC tube with inner diameter r = ∞. It is applicable for electrical conductivity.

The Ka spatial weighting functions for different probe configurations are also shown in Fig.

5-13. The effective dielectric constant approaches an asymptotic value at a distance of 100 mm and greater. The majority of the electromagnetic response occurs within the first several centimeters in the radial direction. The four-conductor probe (T1) and three-conductor probe (T2) have similar spatial weighting functions; and the spatial weighting appears to be insensitive to the conductor width for the two-conductor configuration (see T3, T4, and T5).

In Ka measurements, the radial sampling of the four-conductor probe (T1) and three-conductor probe (T2) is more focused on the vicinity of the probe than that of the two-conductor probes (T3, T4, and T5).

Unlike dielectric permittivity, effective electrical conductivity is a directional and conductive parameter that depends on current flow paths and distribution of conductivity variation. Defining a unique radial sampling function for the electrical conductivity measurement is not possible. To compare the radial sampling of different probes, a spatial weighting function for electrical conductivity analogous to Eq. [5-9b] was experimentally

PVC tube was conductive with σ = 0.67 dS/m and the PVC material and air were considered non-conductive (σ = 0 dS/m). The σ spatial weighting functions for different probe configurations are shown in Fig. 5-14. In this case, the radial sampling is even more biased towards the probe for σ measurements than for Ka measurements. On the contrary to dielectric measurement, theσ radial sampling of the four-conductor probe (T1) and three-conductor probe (T2) is less focused on the vicinity of the probe than that of the two-conductor probes (T3, T4, and T5). Observations from Fig. 5-13 and Fig. 5-14 raise the concern for the penetration (disturbance) effect on Ka and σ measurements in soils. The soil displaced by the penetrometer may change the density of soil adjacent to the penetrometer, and hence the dielectric constant and electrical conductivity. The penetration effect appears to be a common problem to all electrical probes, and the degree of its influence should be quantified.

0 20 40 60 80 100

W e ight ing f unc ti on f o r di el ec tr ic c ons tant (% )

Diameter, r(mm)

Fig. 5-13 Spatial weighting function for dielectric constant Ka.

0 20 40 60 80 100

W ei ght ing f unc ti on fo r co n d u c ti vi ty ( % )

Diameter, r(mm)

Fig. 5-14 Spatial weighting function for electrical conductivity σ.

TDR penetromter Prototype

The spatial weighting functions of different probe types have different trends in dielectric constant and conductivity measurements, as shown in Fig. 5-13 and Fig. 5-14. There is a tradeoff between selecting an optimum probe design for dielectric measurements and that for conductivity measurements. A TDR dielectric penetrometer was actually fabricated using the design similar to probe T1. It was selected at the time when the major concern was to have TDR reflection that can be identified most easily for all cases (i.e. from dry to wet soils). Fig.

5-15 shows the design and a photo of the probe. The diameter of the prototype is the same as a standard CPT module (35 mm) and the sensing waveguide is 20 cm long. The probe consists of four arc-shape stainless steel plates and a Delrin^® shaft. The thickness of the stainless steel was maximized to increase the axial strength of the probe. The stainless steel plates were fit into four grooves in the Delrin^® shaft and fastened with screws. This probe was used to

perform simulated penetration tests in a calibration chamber.

Fig. 5-15 Prototype of the TDR penetrometer

Calibration of the Prototype

The TDR penetrometer shown in Fig. 5-15 differs slightly from probe T1 in that thick conductors are embedded in a dielectric shaft instead of thin conductors bonded to the surface of the dielectric shaft. Calibration tests need to be carried out before it can be used for measurements of dielectric constant and electrical conductivity. Several liquids of known dielectric constants and electrical conductivities were used for calibrating the probe using Eqs.

[5-4] and [5-6]. The materials used for calibrating dielectric measurements were air, butanol, ethanol, and water; while NaCl solutions of different concentrations were used for calibrating electrical conductivity measurements. According to Birchak et al. (1974), the theoretical value of n is 1.0 for the probe design. Assuming theoretical value n =1.0, the calibrated parameters a = 0.34 and b = 1.91 were obtained through linear regression. If n remained

Probe section =

unknown during calibration, the calibrated parameters are a = 0.35, b = 1.78, and optimal n = 0.96. Note that the a value is smaller than 0.5 (suggested by Eq. [5-7]), because the prototype used thick conductor plates fit into Delrin^® grooves rather than thin conductor plates stick on the surface of a dielectric shaft. Using the calibrated parameters, the apparent dielectric constants of the calibrating liquids are plotted against their known values in Fig. 5-16. Both calibrated results provide fairly good fit. The theoretical value n = 1.0 is verified, as can be inferred from Fig. 5-16. For simplicity, n =1.0, a=0.34, and b=1.91 are used. Similarly, the calibration constants for electrical conductivity were obtained as βpenetrometer =0.0362. The estimated electrical conductivities using the calibrated parameters are shown in Fig. 5-17 to fit the known values very well. These results prove the new calibration equations (Eqs. [5-4] and [5-6]) to be extremely accurate.

0 10 20 30 40 50 60 70 80

0 10 20 30 40 50 60 70 80

K_a from TDR penetrometer K a, true

n=1

n=optimum 1:1 line

Fig. 5-16 Ka calibration of TDR penetrometer with known values materials

0 0.01 0.02 0.03 0.04 0.05 0.06 0

0.01 0.02 0.03 0.04 0.05 0.06

σ from TDR penetrometer (S/m) σ, true (S/m)

Data point 1:1 line

Fig. 5-17 σ calibration of TDR penetrometer with known EC liquids

Spatial Weighting Function of the Prototype

To quantify the spatial weighting function of the prototype, the aforementioned radial sampling experiment was carried out on the prototype. The spatial weighting function of the prototype is also shown in Fig. 5-13 for Ka measurements and in Fig. 5-14 for σ measurements.

The Ka radial sampling characteristic of the prototype is similar to that of the trial probes T1 and T2. However, the σ radial sampling of the prototype is much less focused on the vicinity of the probe than that of all trial probes (T1-T5). This may be attributed to the fact that the prototype used thick conductor plates fit into grooves of a dielectric shaft rather than thin conductor plates attached to the surface of a dielectric shaft. This configuration alters the distribution of the electromagnetic response, further decreasing the measurement sensitivity but making the σ radial sampling less biased towards the probe.