Investigation of non-unique relationship between soil electrical conductivity and water content due to drying-wetting rate using TDR

Engineering Geology 252 (2019) 54–64

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Engineering Geology journal homepage: www.elsevier.com/locate/enggeo

Investigation of non-unique relationship between soil electrical conductivity and water content due to drying-wetting rate using TDR

T

⁎

Chih-Chung Chunga, , Chih-Ping Linb, Shi-Hui Yangb, Jhe-Yi Linb, Chun-Hung Linc a

Department of Civil Engineering, National Central University, 300 Zhongda, Rd., Zhongli Dist., Taoyuan 320, Taiwan Department of Civil Engineering, National Chiao Tung University, 1001 Ta-Hsueh, Rd., Hsinchu 300, Taiwan c Department of Marine Environment and Engineering, National Sun Yat-sen University, 70 Lienhai Rd., Kaohsiung 804, Taiwan b

A R T I C LE I N FO

A B S T R A C T

Keywords: Time domain reflectometry (TDR) Soil water content Electrical conductivity (EC) Hysteresis Drying-wetting rate

The characterization of the relationship between volumetric soil water content (θ) and bulk electrical conductivity (EC) (or electrical resistivity) is of high interest in fields of engineering, fundamental petrophysical, hydrological model parameterization, and quantitative hydrogeophysical interpretations. Based on the relationship, for instance, the broad-area image using electrical resistivity tomography (ERT) can be transformed into θ tomograms as initial/boundary conditions of the slope stability analysis. However, the relationship is affected by the hysteresis, leading the inconsistency in drying-wetting circles. Therefore, this study focused on the factor of soil drying-wetting rate using the proposed time domain reflectometry (TDR) method and related sensors for such characterization. A modified pressure plate apparatus enhanced by TDR was first employed with a relatively low rate in which EC and θ were measured simultaneously, without evident non-unique relationship. A TDR penetrometer was then designed for acquiring the temporal variations of θ and EC in the field. On the basis of certain assumptions, observations showed an apparent dependency of the slope of the θ–EC rating curve on rates, but no hysteresis pattern. Finally, a laboratory controlled fast wetting–drying cell was used to increase the response time, proving that both the hysteresis and slopes of the θ–EC rating curves were obviously affected by the soil drying-wetting rate, as a significant finding to the related topics.

1. Introduction Rain-induced shallow landslide is one of the important topics in the engineering geology area. The degree of soil saturation (S) is a key parameter in the stability of natural and engineered earthen slopes with unsaturated soil conditions (Fredlund et al., 1987; Lu and Godt, 2008; Bordoni et al., 2015; Cho, 2016, 2017; Jeong et al., 2017). Soil matric suction, which affects shear strength, also depends on the degree of soil saturation. Furthermore, soil hydraulic conductivity is drastically influenced by soil saturation and governs water infiltration in situations of rainfall-induced slope instability as well as flooding forecasting (Castillo et al., 2003; Brocca et al., 2009). For effectively performing real-time measurement of rainfall-induced slope stability and inundation forecasting, continuous observation of volumetric soil water content (θ) is a suitable method for determining soil saturation, provided that the soil dry density is predetermined at the situ. The automated techniques of soil water content measurement which use electrical instruments, such as capacitance probes, have been increasingly implemented since the 2000s (Smith and Mullins, 2000;

⁎

Evett et al., 2006; Brinkhoff et al., 2017) to achieve the aforementioned objectives. Comparing to traditional capacitance probes, time domain reflectometry (TDR) is also a technique based on electromagnetic (EM) wave, and it is more accurate because of containing a high range of ΕΜ wave measurement frequencies (500 MHz~1 GHz). Based upon this feature, TDR is relatively independent of the soil type (Topp et al., 1980; Ledieu et al., 1986; Dirksen and Dasberg, 1993). Although a new capacitance sensor uses up to 70 MHz (Decagon Devices, Inc., 2016) for such purpose, TDR, in addition, can simultaneously measure the bulk electrical conductivity (EC) of soil (Lin et al., 2007, 2008; Skierucha et al., 2012). If a special waveguide design is further used, such as a penetrometer, TDR can be employed to determine θ profiles at various depths more easily (Vaz et al., 2001; Lin et al., 2006a, 2006b). Compared to other TDR θ probe just placed at the soil surface (Acclima, 2018; Campbell Scientific, 2018), the θ profiling can support detailed information concerning initial or boundary values for numerical forecasts. Although TDR has attracted much attention, which has resulted in multipoint measuring using multiplexers for automated monitoring,

Corresponding author. E-mail addresses: [email protected] (C.-C. Chung), [email protected] (C.-P. Lin), [email protected] (C.-H. Lin).

https://doi.org/10.1016/j.enggeo.2019.02.025 Received 26 March 2018; Received in revised form 22 February 2019; Accepted 25 February 2019 Available online 26 February 2019 0013-7952/ © 2019 Elsevier B.V. All rights reserved.

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few localized points in the whole area of interest can be obtained. Interpolated spatial data, usually obtained using the Kriging method (Snepvangers et al., 2003), may not effectively represent the overall soil water content distribution in complex geological settings. To more accurately characterize the soil water content distribution in a large area, Zhou et al. (2001) and Brunet et al. (2010) have utilized electrical resistivity tomography (ERT) to image soil water content distribution in 2 or 3 dimensions on the basis of a predetermined relationship between θ and EC. Beff et al. (2013) further used TDR measurements to validate ERT-inverted θ values in a maize field. The soil water content images can be subsequently applied as more initial or boundary conditions in slope stability analysis. Meanwhile, induced polarization (IP) imaging, an extension of the ERT method in terms of complex conductivity, permits to gain much information about electrical conductive and capacitive properties of the subsurface for the understanding of landslide architecture, especially in clay-rich landslides (Orozco et al., 2018), indicating the importance of obtaining the relationship between θ and EC. In addition, Lesmes and Friedman (2005) claimed that the investigation of the relationship between θ (or hydraulic conductivity) and EC is of high interest in fundamental petrophysical field, as well as the hydrological model parameterization and quantitative hydrogeophysical interpretations in practice using an integrated exploration approach in which borehole and geophysical data sets are jointly interpreted. Owing to the importance of characterizing the rating curve between θ and EC for the aforementioned approach, the θ–EC relationship has been widely examined. It is usually classified into two types: one is the generalized Archie's form (Archie, 1942; Klein and Santamarina, 2003; Shan and Singh, 2005), which describes EC as a function of θ, and the other is the polynomial form (Lin et al., 2006b; Mojid et al., 2007), which includes the contributions of pore water EC and double-layer water EC. Both methods contain coefficients with values that mainly depend on soil types. The modified Archie's or polynomial forms of the rating curve were formulated after conducting experiments on limited samples in the laboratory; However, these modified forms might not completely represent field conditions. Nevertheless, the most prominent characteristic of the rating curves is the one-to-one transformation of EC from θ. Knight (1991) firstly found hysteresis behavior as the inconsistence between EC and θ in the wetting–drying cycles of sandstone. José et al. (2012) revealed that although the change in resistivity during a drying-wetting cycle did not exhibit any hysteresis in loess deposits by performing the resistivity probe in triaxial tests, a deviation from Archie's law was apparently observed at low degrees of saturation, which relates to the discontinuity of pore water within the clay fraction of the loess. Bai et al. (2013) found that EC decreases with the increase of the number of wetting–drying cycles in compacted lateritic soil. These previous findings indicated that the wetting–drying process does affect the EC–θ relationship, while the hysteresis or non-uniqueness in the EC–θ relationship due to the soil wetting – drying rate is purely qualitative and requires further examination. To meet the demand as shown previously, this study reveals the novelty of TDR, the related apparatus and waveguide at both laboratory and field scales. Then this study applied TDR to examine the EC–θ nonunique relationship with an extended focus on the effect of wettingdrying rate through laboratory and field tests. Subsequently, the first laboratory case using a modified pressure plate featuring continuous TDR measurements of EC and θ under relatively lowest wetting-drying rate was conducted, with a non-unique relationship also found. A new TDR penetrometer for long-duration EC–θ monitoring was developed for field observations with natural wetting-drying rates, while the effect of dynamic conditions in the field, such as temperature, soil salinity and evapotranspiration, are not completely considered as hypothesis. Observations revealed an apparent dependency of the slope of the field θ–EC rating curve on the soil wetting and drying rates, however, without any hysteresis pattern.

TDR Device Step Generator Coaxial Cable

Sampler

L

v

T0

v0

Waveguide

Oscilloscope

v

a t

t

Fig. 1. Typical TDR system and waveform of a TDR penetrometer showing travel time Δt determined using the dual-tangent-line method and a constant time offset (T0); EC can be estimated using the incident step (v0) and steadystate response (v∞).

Finally, a well-controlled laboratorial test with a modified compaction cell for attaining higher wetting and drying rates was performed. The laboratory results revealed obvious non-unique relationships, including the hysteresis pattern and slopes, between EC and θ. Among the results of the aforementioned tests, the study will conclude that the relationship between EC and θ is significantly affected by the soil wetting-drying rate in the discussion section, representing the second contribution to related topics. 2. Principles of θ and EC measurement by using TDR A typical TDR system, as depicted in Fig. 1, comprises a main TDR device and a transmission line system. The TDR device contains a step pulse generator, a digital sampler, and an optional oscilloscope. The transmission line system includes a leading coaxial cable and a sensing waveguide. The TDR technique involves transmitting an electromagnetic (EM) pulse through the coaxial cable connected to the sensing waveguide, then sampling the reflections due to a mismatch of characteristic impedance along the waveguide. A typical TDR reflected waveform is illustrated in Fig. 1. This waveform can be analyzed in the time domain to determine the apparent dielectric constant and EC of the tested material. The measurement principles are summarized as follows. A simplified analysis of the TDR waveform in the time domain for determining the apparent dielectric constant Ka was proposed by Topp et al. (1980). The apparent propagation velocity Va of the EM wave in a transmission line is related to the apparent dielectric constant Ka as.

Va =

c 2L = ∆t Ka

(1) 8

where c is the velocity of light (2.998 × 10 m/s), L is the length of the waveguide, and Δt is the round-trip EM wave travel time in the waveguide as shown in Fig. 1. To increase the precision of Ka measurement, the sensing waveguide length (L) and a constant time offset (T0) were calibrated using at least two materials with known dielectric properties (e.g. air and water), as proposed by Heimovaara (1993). The end reflection, defined as using either the single-tangent or dual-tangent method, was then used to determine the round-trip travel time Δt for computing Ka by using Eq. (1) as point a in Fig. 1. Although the dualtangent method is difficult to automate, it yields Ka with the highest effective frequency (i.e., a frequency at which Ka is equal to the frequency-dependent dielectric permittivity) and is less sensitive to EC and cable length (Chung and Lin, 2009). The measured Ka can be used to estimate θ using the existing rating curves (Topp et al., 1980; Lin et al., 55

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are illustrated in Fig. 2. The thermal meter is required to keep the temperature of the soil specimen constant. Because of the effect of air bubbles trapped in the ceramic porous plate, back pressure was applied to collect the residual bubbles in a gas collection tube. The amount of water movement between the water collection tube and the soil sample during the wetting–drying process depends on the change in the levels of both the water and gas collection tubes, as shown in Fig. 2. After 60 min for each suction pressure increase (or decrease), the previous and current values of the amount of water movement were recorded to confirm the balance of the soil water content. Pressure increases and decreases were stopped when the difference between the two records was smaller than 0.1 mL. For the drying processing, volumetric water content changed from 0.302 to 0.01 in 34 days, indicating the average drying rate equaled 3.58*10−4 (1/h), while the volumetric water content varied from 0.01 to 0.243 in 43 days during the wetting processing, indicating the average wetting rate equal to 2.26*10−4 (1/h) (see result details and discussions in next chapter). A Campbell Scientific TDR100 device with a SDMX50 multiplexer was used for both laboratory and field tests (Campbell Scientific, 2004). The number of data points acquired using the TDR100 device was 2048. The sampling window length for θ measurement was set to 5 m, which is equivalent to a sampling time interval of approximately 16 ps (estimated by 5 m*2/2048 points /2.998E8 m/s). The recording time for ΕC measurement was set long enough to accommodate > 10 multiple reflections within the waveguide and three multiple reflections in the lead cable according to the study of Lin et al. (2007). To examine the effect attributable to the soil wetting and drying rates, a relatively fast wetting–drying cell modified on the basis of the works of Cho and Santamarina (2001) was used to increase the response time. Actually, the modified cell test was carried out after the field test in the next section as the third case of the study because the expected apparent hysteresis pattern was not observed in the field test. To concisely compared the procedures of these two laboratory tests, the content of the modified cell test is revealed in this section, but the results is discussed after the field observation. A schematic diagram of the cell as the TDR coaxial mold is shown in Fig. 4. The size of the cell is also equal to the standard compaction mold. Cotton threads were mounted in each hole (diameter < 5 mm, and related positions are shown in Fig. 4(a)) to facilitate water absorption and drainage and to favor a homogeneous water distribution. The preparation of the silt sample was similar to that in the pressure plate test in the laboratory. Unlike the original pressure plate test, which had the lowest rate for the wetting–drying process, the modified tests were performed in two conditions, namely medium- and high-rate wetting–drying processes. Because of a lack of deionized water, tap water (EC is 430 μs/cm in average) was used in this test. For the high-rate test, the sample with the modified cell was completely submerged in the tap water for approximately 1 min, and retrieving the θ and EC measurements simultaneously by the TDR coaxial probe. This wetting process repeated until reaching maximum θ (38%), and the average wetting rate of the high-rate test was up to 0.432 (1/h). After the wetting process, the sample was naturally dried with 1-h constant time interval with TDR coaxial probe measurements, and the average drying rate of the highrate test was 0.0097 (1/h). The sample with medium-rate was submerged only 10 s in order to slow down the saturation process. The average wetting rate of the medium-rate test was up to 0.152 (1/h). Others procedures were the same with those of the aforementioned high-rate testing, and the average wetting rate of the medium-rate test was up to 0.0084 (1/h). Temperature of soil and water was kept constant in the laboratory.

2000). EC can be determined on the basis of the steady-state response of the step pulse. The EC-associated reflection coefficients ρ ∞ ′ can be derived from the TDR reflection coefficient by using the following equation, which compensates the TDR device system error (Lin et al., 2008):

′ =2 ρ∞

ρ∞ − ρ∞ , air ρ∞ , air + 1

+1 (2)

where the steady-state reflection coefficient ρ∞ of a measured material is defined as.

ρ∞ =

v∞ − v0 v0

(3)

in which v0 is the pulse step voltage and v∞ is the steady-state voltage, as shown in Fig. 1. ρ∞, air is the steady-state reflection coefficient of the open-circuit waveguide in air. According to the aforementioned equations, the EC of the measured material can be written as (Lin et al., 2007).

EC =

Kp ⎛ 1 − ρ′∞ ⎞ ⎡ ⎢ ⎜ ⎟ RS ⎝ 1 + ρ′∞ ⎠ ⎢ 1 − ⎢ ⎣

1 R cable RS

(

1 − ρ ′∞ 1 + ρ ′∞

)

⎤ ⎥ ⎥ ⎥ ⎦

(4)

where inner resistance RS is equal to TDR source impedance, which is 50 Ω typically equal to. The term of cable resistance Rcable can be rewritten as.

R cable =

RS

(

1 − ρ ′∞ , SC 1 + ρ ′∞ , SC

)

(5)

where ρ'∞, SC is obtained beforehand by using the steady-state reflection coefficient of the short-circuited waveguide. Finally, the geometric factor of the waveguide Kp in Eq. (4) can be determined using given EC materials through the least squares error method (Lin et al., 2007, 2008). 3. Material and methods 3.1. Laboratory test under different wetting–drying rate To experimentally investigate the wetting–drying rate effect that occurs between EC and water content, the pressure plate apparatus was modified using a TDR coaxial probe embedded for simultaneous EC and θ measurements with the lowest soil wetting–drying cycle as the first case of the study. The configuration of the novel TDR pressure plate apparatus is detailed in Fig. 2. The size of the test mold, as the outer conductor of the TDR coaxial probe, is equal to the standard compaction mold (the interior diameter of 6 in.). The diameter of the TDR inner conductor is set to 6 mm to reduce the penetration effect (Lin et al., 2006a). The first step in the wetting–drying test was to apply high back pressure (10–20 kPa) for at least 1 day to ensure that the porous ceramic plate was fully saturated. Second, a silt sample collected near the National Chiao Tung University (NCTU) campus was passed through a No. 4 standard sieve and then compacted in the TDR coaxial probe mold at a dry density of 15.5 kN/m3. The particle size distribution of the silt is shown in Fig. 3, which also illustrates the distribution of the NCTU red sand to be examined in the field test later. The parameters of the TDR coaxial probe mold for apparent dielectric constant Ka and EC measurements were calibrated as discussed previously. Third, the soil sample was saturated using back pressure (10 kPa) and deionized water without air bubbles. Finally, the suction pressure was incrementally increased for drying and decreased for wetting to control the soil water content of the sample. The steps were set almost to 1, 2, 10, 20, 30, and 40 N for both the increase and decrease procedures. The physical wetting and drying passages of the pressure plate apparatus

3.2. Development of modified TDR penetrometer for field tests To further investigate the relationship between θ and EC due to soil 56

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TDR

Gas flow Flushing Drying Wetting

Pressure transducer

TDR coaxial probe

Flush device

Ceramic porous plate

Water collection

Gas collection

Thermal meter

Pressure transducer

Fig. 2. Configuration of laboratory pressure plate apparatus with a TDR coaxial probe embedded for the tests with the lowest wetting and drying rates.

probe calibration and data reduction procedures of both θ and EC measurements for the new TDR penetrometer were conducted according to the study of Lin et al. (2006a, 2006b). The effective dielectric constant measurement of the TDR penetrometer includes the dielectric permittivity contributions from both surrounding soil and the insulator. The mixing rule of the effective dielectric constant Ka,bulk can be written as.

wetting and drying rates in the field, a new TDR penetrometer was developed. The TDR penetrometer proposed by Lin et al. (2006a, 2006b) was originally intended to be connected to a Dutch cone system to provide an almost continuous profile of soil water content and EC during a cone penetration test. To achieve long term monitoring in the field, the TDR penetrometer was modified into a complex TDR waveguide, with which several sensing sections could be connected in series at discrete depth intervals. A detailed schematic and a prototype are depicted in Fig. 5. A 29-cm-long insulated metallic plate (2.5 mm thickness) served as one of the two electrodes and was attached to the edge of the penetrometer's perimeter by creating a groove on the steel shaft so that the plate did not change the cross section of the penetration rod at any point, allowing it to penetrate smoothly into the soil. The other metallic electrode for the sensing waveguide was the penetrometer shaft (20 mm in diameter). A plastic plate (1.5 mm thickness) was placed underneath the metallic plate to avoid a short circuit between the two metallic electrodes. Both metallic electrodes were coated with polyvinyl chloride to reduce signal loss in high-EC conditions. The

(K a, eff )n = α (K a, soil )n + (1 − α )(K a, insulator )n

(6)

where Ka,soil and Ka,insulator are the dielectric permittivity of the soil and the penetrometer, respectively. n is a constant that represents the geometry of the medium with respect to the applied EM field, and α is a weighting factor of the surrounding soil. The n value ranges from −1 to 1, where n = 1 if the medium is modeled as capacitors in parallel, and where n = −1 if the medium is modeled as capacitors in series (Lin et al., 2006a). On the basis of at least three materials with a known dielectric constant Ka,insulator, n and α can be calibrated. The dielectric constant Ka, soil of the surrounding soil can then be estimated as.

Fig. 3. Soil particle size distributions of silt for laboratory experiments and NCTU red sand in field monitoring. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 57

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Fig. 4. (a) Schematic diagram and (b) photo of the modified compaction cell for medium- and high-rate wetting–drying tests.

Stanless

Forward thread

Reverse thread

Plastic

Forward thread

Stainless Plastic Stainless

Unit: mm

(a)

(b) Fig. 5. (a) Schematic diagram and (b) photo showing the modified TDR penetrometer.

K a, soil

(K a, eff )n − (1 − α ) ⎞1/ n ⎛ = ⎜⎛ ⎟ =⎜ α ⎜ ⎝ ⎠ ⎝

c Δt 2n 2L

( )

1/ n

− (1 − α ) ⎞ ⎟ α ⎟ ⎠

ECsoil = (7)

λ1/ m

=

⎡ 1 Kp ⎛ 1 − ρ′∞ ⎞ ⎢ ⎜ ⎟ RS ⎝ 1 + ρ′∞ ⎠ ⎢ 1 − ⎢ ⎣

λ1/ m

1 R cable RS

(

1 − ρ ′∞ 1 + ρ ′∞

)

⎤ ⎥ ⎥ ⎥ ⎦

(9)

1/m

can be treated as a new geometric The combination term of Kp/λ factor Kp’ of the TDR penetrometer, and this new geometric factor can be determined using several known EC materials by employing the least squares method.

where L is the original length of the waveguide. Round-trip EM wave travel time Δt was determined using the dual-tangent-line method as mentioned previously. The effective electrical conductivity ECeff measurements with the penetrometer can also be written as a function of soil electrical conductivity, ECsoil, and penetrometer electrical conductivity, ECinsulator, as.

(ECeff )m = λ (ECsoil )m + (1 − λ )(ECinsulator )m

ECeff

3.3. Long-term field monitoring A long-term field test was conducted at the NCTU campus to investigate the relationship between θ and EC. The configuration of the field test is illustrated in Fig. 6. The TDR penetrometer with three assembled sensing sections spaced at 1 m intervals was designed to penetrate 3 m deep into the ground, as shown in Fig. 6. However, during penetration up to the second sensing section (i.e., at 2 m deep) using the hydraulic jack of a drilling machine, the cone tip struck a cobble and the joint between the first and second sensing sections buckled. The cause was attributed to the concentration of stress attributable to the sudden cross-sectional change of the joint. This was noted for future improvements of waveguide construction and installation methods.

(8)

where m is a geometric factor representing the configuration of the two materials in the direction of the electrical field, and λ is a weighting factor of the surrounding soil. The m value ranges from −1 to 1, with m = 1 denoting that the two materials are in parallel, and with m = −1 denoting that the materials are in series in the direction of the electrical field (Lin et al., 2006b). According to Eq. (4) and assuming zero EC for the insulator, soil EC can be determined as. 58

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Fig. 7. Laboratory pressure plate results at the longest wetting–drying response time.

a testing material, which has a lower void ratio compared with silt. Furthermore, the sandstone was exposed to progressively higher levels of humidity and was soaked in a beaker of deionized water as the wetting process continued, and the sample had a lower θ because it was dried or placed in a dessicator with the dessicant calcium sulfate in the drying process. The wetting and drying rates of procedures may be faster than those of the pressure plate tests, but this = factor was not revealed in the results of Knight (1991). José et al. (2012) used the resistivity probe in the triaxial test with the loess deposits and did not observe hysteresis in resistivity – soil moisture. In addition, they showed that the influence of porosity changes on the resistivity – soil moisture curve may be neglected in this type of soil, but the wetting and drying rate was still not fully revealed as the critical concern.

Fig. 6. Configurations of the TDR penetrometer (for θ and EC measurements) and 3D ERT for the field test.

Although observation of the θ profile at depth was the initial goal, the monitoring results of the first sensing section of the TDR penetrometer at a 1-m depth provided valuable field information that can be utilized to study the θ–EC relationship at shallow depths. A three-dimensional (3D) ERT survey was also conducted in the long-term field test to derive a water content tomogram. The survey geometry of the 3D ERT was 11 m × 2 m, and the spacing between the electrodes was 1 m. The sensing depth was approximately 2.4 m with the dipole–dipole array configuration. Each 3D ERT survey was conducted after the completion of TDR sensing to avoid possible residual effects of the electric current on TDR measurements. By connecting the aforementioned TDR100 device and the multiplexer to an embedded system with an acquisition code developed for this study to collect data using an acquisition setting similar to that used in the laboratory experiments, TDR and ERT measurements could be automated in the field. The TDR and ERT data were collected with an intervals of 10 min during rainfall, 1 h for 1 day after rainfall, and 3 h of the drying process. Soil particle size distributions of the NCTU red sand in field are shown in Fig. 3 for comparison. Clearly, the particle size distribution of the soil is much uniform, meaning that the EC–θ relationship for these two types of soils might have different intrinsic properties as is discussed in Section 4.

4.2. Relationship between EC and θ in the field Before the discussion of the field testing results, the constant n, factor α, and the dielectric constants of the penetrometer were optimized using the least squares error method. n, α, and Ka,penetrometer were determined as 0.872, 0.209, and 3.492, respectively. The measured Ka values of four materials versus the true values (air, ethanol, butanol, and water) are shown in Fig. 8(a). The linear regression equation and R2 are also shown in Fig. 8(a). The results indicate that the TDR penetrometer can provide accurate dielectric measurements if the suggested calibration procedure is followed. Additionally, if the EC calibration procedure from Eq. (9) is followed, the system parameters can be estimated on the basis of several known EC water samples. The new Kp’ (equals Kp/λ1/m), Rcable, and ρ∞, air were determined as 4.85, 1.993 Ω, and 0.98, respectively, by using the TDR100 device. Fig. 8(b) shows the measured EC from the TDR penetrometer versus the true EC values. The linear regression equation and R2 are shown in Fig. 8(b). Similar to the dielectric measurements, EC measurements of the modified TDR penetrometer revealed its adequacy. Laboratory experiments validated using the modified TDR penetrometer for measuring θ and EC in the field. Field tests based on the modified TDR penetrometer and 3D ERT sensing survey were conducted at the NCTU campus. However, the joints of the TDR penetrometer failed because of stress during penetration, leaving only one TDR sensing segment at a 1-m depth functioning (the central sensing point was located at a depth of approximately 0.5 m, and the sensing range was 29 cm as shown in Fig. 5 (a)). TDR field monitoring data of θ and EC during a 3-month period are shown in Fig. 9. Daily rainfall data were collected from the observations

4. Results and discussion 4.1. Relationship between EC and θ in laboratory tests By following the previously outlined calibration procedures, the system parameters, namely the constant time offset (T0) and the probe length (L) of the coaxial waveguide, were calculated as 9.73 ns and 0.102 m, respectively. The system parameters for EC measurements were also calibrated using several given EC water sets, obtaining Kp of 3.995, Rcable of 1.081 Ω, and ρ∞, air of 0.957. Fig. 7 displays the data obtained in the pressure plate test in the laboratory. The highest θ in Fig. 7 represents the end of the wetting process, which is also the start of the drying process. The results indicate that the relationship between the θ and EC of silt was relatively unique without hysteresis, in contrast to the results of Knight (1991). This may be attributed to the fact that Knight (1991) used sandstone as 59

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Fig. 8. (a) Ka and (b) EC measured by the calibrated TDR penetrometer versus true values.

of the nearest weather station (Hsinchu). Some missing data in the time series plot were attributable to system maintenance and outlier picking. The collected data are plotted in terms of the relationship between θ and EC, as shown in Fig. 10. The measured θ ranged from 20% to 32%, and the related EC ranged from 25 μs/cm to 260 μs/cm, which larger than the value of the laboratorial plate test due to the EC of pore water and soil bounded water. A linear relationship between θ and EC was preliminarily observed on the basis of the overall data. The measurement sequences in the EC–θ plot were categorized as the wetting path (denoted by even numbers) and the drying path (denoted by odd numbers), as depicted in Fig. 11. The EC–θ relationship may be affected by the wetting and drying rates. The average wetting or drying rate of these measurement sequences was further analyzed and is shown in Fig. 12. Among the field data, different average wetting or drying rates can be classified into three zones, namely Zone 1, Zone 2, and Zone 3, in increasing order. The original results in Fig. 10 are reorganized in Fig. 13 according to their wetting and drying rates. Different zones of wetting and drying rates exhibit different slopes in the relationship between θ and EC, indicating that the relationship between θ and EC is a function of the wetting and drying rates. This observation reveals that using an appropriate slope of the relationship depending on the average wetting or drying rate is critical when converting ERT images to the water content tomogram at a particular moment. To investigate hysteresis in the field test, Events 1 to 3 were chosen

Fig. 10. Long-term relationship between EC and θ in situ.

from Fig. 9 on the basis of different wetting and drying rates. Event 1 had the lowest rate, whereas Event 2 had the highest rate. However, hysteresis between θ and EC in Fig. 14 was not clearly observed in field wetting–drying conditions compared to results of Knight (1991).

Fig. 9. Monitored time histories of EC and θ obtained using the TDR penetrometer. 60

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Depending on their wetting and drying rates, Events 1, 2, and 3 have slopes of the EC–θ relationship similar to those of Zones 1, 3, and 2, respectively as shown in Fig. 13. The slopes of Events 1 to 3 are negatively correlated with the average wetting and drying rates. In other words, the slope differences in the rating curves between θ and EC for the shallow depth (i.e., 1 m) might be affected by rainfall intensity and infiltration. Although some variables, such as EC of rainwater, ambient temperature, and evapotranspiration, are not considered as hypothesis in the field, this result highlights the need for on-site derivation of the relationship between θ and EC, which can be performed efficiently using the TDR penetrometer measurement. 4.3. Extended investigation of hysteresis between EC and θ Although no apparent hysteresis was observed during the pressure plate and field tests, the aforementioned slope differences in the field EC–θ relationship somehow reveal the influence of wetting and drying rates. Results of the test that featured increasing wetting and drying rates by the modified cell are shown in Fig. 15. The related EC ranged from 0 μs/cm to 200 μs/cm, which is twice as much as that of the laboratorial plate test due to the EC of pore water. The apparent hysteresis in the EC–θ relationship was observed during this test. The observed hysteresis is similar to that described in previous studies by Knight (1991). She reported that hysteresis described by EC (in terms of resistivity) measured during the wetting process is consistently higher than EC measured at the same θ during the drying process. Additionally, a considerable variation in the size of the hysteresis loop between the high- and medium-rate tests was observed in comparison with the results of the pressure plate and field tests, implying that the hysteresis in the EC–θ relationship would intensify as the rate of the wetting–drying process increases. Furthermore, in the test with a medium-rate wetting–drying process, the slope of the EC–θ relationship was steeper than that in the test with a fast wetting–drying process which is also revealed in the field test. This indicates that as the rate of wetting and drying decreases, the slope of the EC–θ relationship steepens and the degree of hysteresis decreases. In summary, the wetting and drying rates in both the pressure plate and the field tests are much lower than the rates in the modified cell test, and this slower process prevents the non-continuous distribution of soil pore water during the wetting–drying process, as revealed by Knight (1991), eliminating possible hysteresis in the EC–θ relationship. The discussions of previous sections and the comparison among the three tests in this study preliminarily verify that increases in the wetting and drying rates intensify hysteresis and reduce the slope of the EC–θ relationship.

Fig. 11. Wetting (denoted by even numbers) and drying (denoted by odd numbers) sequences for EC and θ in the field.

Fig. 12. Average wetting and drying rates of θ and EC derived from the events illustrated in Fig. 11.

4.4. Demonstration of θ mapping images from ERT 3D ERT was performed in the field to demonstrate the transformation to the soil water content variation over a broad area. Because the EC–θ relationship is affected by the wetting and drying rates, on-site calibration is necessary when transforming ERT data to a θ map. However, this study found the system constant offset between ERT EC and TDR EC in the field, and this error was corrected by shifting ERT EC values for θ mapping images. Fig. 16 shows the inverted 3D resistivity tomogram. For the slice cut in the x–z plane of the 3D resistivity image at the center of the y-axis, 2D water content mapping images were obtained based on the on-site calibration of the EC–θ relationship from TDR, as shown in Fig. 17. These results preliminarily reveal the potential and benefits of using onsite TDR and ERT monitoring for slope stability analysis and inundation evaluation. Fig. 13. Rating curves for θ and EC distinguished by zones that denote different wetting and drying rates according to Fig. 12.

5. Conclusion Several studies have revealed the importance of obtaining the 61

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Fig. 14. EC–θ relationship in a wetting–drying cycle for Events 1 to 3 as illustrated in Fig. 9.

Fig. 16. Inverted 3D resistivity tomogram from the field test.

hysteresis, which is defined as the inconsistent paths in the EC–θ relationship during wetting-drying cycles, as reported by Bai et al. (2013) and Knight (1991), respectively. To thoroughly examine the non-unique relationship between θ and EC due to wetting-drying rate as the main objective, this study attempted to use the Time Domain Reflectometry (TDR) method as the core technology and developed related apparatus and sensor in both laboratory and field scales to simultaneously measure these two indicators. The relevant TDR works are representing the novelty to the investigation of non-unique EC–θ relationship. Laboratory experiments were conducted first using the pressure plate apparatus enhanced by TDR to investigate the relationship between θ and EC with lower wetting-drying rate; However, none of nonunique relationship was observed. A modified TDR penetrometer was

Fig. 15. Laboratory EC–θ hysteresis results from the modified compaction cell under high- and medium-rate wetting–drying conditions.

relationship between soil bulk electrical conductivity (EC) and volumetric water content (θ) in engineering. For instance, broad-area tomography of electrical resistivity tomography (ERT) can be transformed into a soil θ map to support slope stability and inundation evaluations. However, caution must be taken in this EC–θ transformation because it is influenced not only by the variation of the slope but also the

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Fig. 17. Transformed 2D water content tomograms (according to the appropriate rating curves between θ and EC) from 3D ERT.

then proposed for θ and EC profiling in the field. Although the effect of dynamic conditions in the field, such as temperature, soil salinity and evapotranspiration, are not considered, the results of the field test indicated that the slope between θ and EC apparently depends on the average wetting or drying rate. The slope between θ and EC increases as the average wetting or drying rate decreases. Nevertheless, no hysteresis was observed in the test. To further examine the cause of the hysteresis in EC–θ relationship, a modified cell with higher wetting and drying rates was utilized. Results indicated that higher wetting and drying rates led to apparent hysteresis, enlarged the hysteresis loop, and decreased the slope of the rating curve between θ and EC. Hysteresis was not observed in the previous pressure plate and field tests because the slower wetting–drying process prevented nonuniform distribution of pore water inside the soil, which is similar to the studies of Knight (1991) and José et al. (2012). The non-unique relationship between EC–θ due to drying-wetting rate is consequently seen as the second contribution of this study. The relationship between EC and θ is affected by the drying-wetting rate even with the same base-material. Nevertheless, the evaluation of the other variables, such as soil type and void ratio are strongly suggested in the further study (laboratory scale first). Meanwhile, appropriate onsite θ–EC calibration supported by real-time TDR penetrometer monitoring is recommended for mapping water content images based on the ERT for broad-area investigations. This is considered as an efficient, accurate, and complete approach, and the joint-interpretation procedure is similar with the aforementioned concept by Lesmes and Friedman (2005). Of course, the insight of the non-unique EC–θ relationship due to other dynamic conditions in the field should be further investigated as well. The mechanism of the TDR penetrometer joint should be improved with more research so that water content can be monitored at multiple

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