Time Domain Reflectometry Waveforms Research Articles

Examination of the Dry Density Importances in TDR Use and of the ASTM D6780 Standard Based on a New Calibration Procedure

Abstract The use of time domain reflectometry (TDR) to monitor soil water content at either field or laboratory scales is highly common. Regarding the soil dry density, ρd, effect on the TDR application, three main approaches are found in the literature: (1) Ignore the density issue and use calibration to evaluate the water content regardless of the density. This approach is basic, yet common. (2) Include soil density in the calibration equation and use calibration for the water content as a function of both the TDR output and soil density. In this approach, the soil density should be provided from an independent source. (3) Determined ρd from the TDR waveform. In this case both water content and ρd are set from the TDR analysis. In cases where the ρd is not available, in order to use TDR for water content measurement, a decision has to be made whether to address the density issue although it requires resources, or to neglect it. This article reviews this issue and validates the density effect using an efficient TDR calibration methodology. A calibration scheme that controls ρd of the specimen has been developed and applied. The methodology creates continuous calibration curves over a range of volumetric water content from a single test specimen. Based on the results, it has been demonstrated that the soil density has a major effect on the TDR output and it cannot be ignored. In addition, this article presents a unique examination of ASTM D6780, Standard Test Methods for Water Content and Density of Soil In Situ by Time Domain Reflectometry (TDR). The ASTM dry density estimation was found to provide reliable results; however, the gravimetric water contents estimation gives unsatisfactory results, especially for low densities.

Evaluation of electrical resistivity of cement-based materials using time domain reflectometry

Time domain reflectometry (TDR) is a widely used electromagnetic wave–based technique for evaluating the volumetric water content of soils, although its use for moisture measurement in cement-based materials is limited. This paper presents a comprehensive analysis of the electrical properties of cement pastes and cement paste–slime mixtures using TDR. Both TDR and electrical resistivity probes are used to estimate the electrical resistivities of various cement-based materials over their curing period. The study reveals that these properties are significantly influenced by curing time, water–cement ratio, and water–solid ratio. The experimental results demonstrate a consistent increase in electrical resistivity with curing time, underscoring the significant role of hydration-induced water evaporation and microstructural changes. Furthermore, the interpretation of characteristic voltages on the TDR waveform significantly influences resistivity estimates. Thus, this study highlights the potential of TDR in accurately evaluating the electrical resistivity of cement-based materials.

Time Domain Reflectometry Waveform Interpretation With Convolutional Neural Networks

AbstractInterpreting time domain reflectometry (TDR) waveforms obtained in soils with non‐uniform water content is an open question. We design a new TDR waveform interpretation model based on convolutional neural networks (CNNs) that can reveal the spatial variations of soil relative permittivity and water content along a TDR sensor. The proposed model, namely TDR‐CNN, is constructed with three modules. First, the geometrical features of the TDR waveforms are extracted with a simplified version of VGG16 network. Second, the reflection positions in a TDR waveform are traced using a 1D version of the region proposal network. Finally, the soil relative permittivity values are estimated via a CNN regression network. The three modules are developed in Python using Google TensorFlow and Keras API, and then stacked together to formulate the TDR‐CNN architecture. Each module is trained separately, and data transfer among the modules can be facilitated automatically. TDR‐CNN is evaluated using simulated TDR waveforms with varying relative permittivity but under a relatively stable soil electrical conductivity, and the accuracy and stability of the TDR‐CNN are shown. TDR measurements from a water infiltration study provide an application for TDR‐CNN and a comparison between TDR‐CNN and an inverse model. The proposed TDR‐CNN model is simple to implement, and modules in TDR‐CNN can be updated or fine‐tuned individually with new data sets. In conclusion, TDR‐CNN presents a model architecture that can be used to interpret TDR waveforms obtained in soil with a heterogeneous water content distribution.

Feasibility of soil erosion measurement using time domain reflectometry

Scientific research and control technology of soil erosion both rely on accurate and efficient soil erosion measurements. Based on the principles of locating interfaces in layered media and measuring dielectric properties by time domain reflectometry (TDR), we developed TDR-based measurement of changes in the air–soil interface along the TDR probe for soil erosion measurement, and simultaneously measuring volumetric soil moisture content (θv). Part of a three-rod TDR probe was inserted in the soil and the rest exposed to air, so changes in the air–soil interface could be denoted by changes in the length of exposed probe (Lair). TDR waveforms were analyzed using a combination of tangent line method and second-order bounded mean oscillation methods to identify time points at positions of impedance discontinuity in electromagnetic propagation, then converting these data to Lair and θv by calibrated equations. According to the laboratory experiment using sandy loam and silt loam, Lair could be effectively measured within a wide soil moisture range by the calibrated equation and the thickness of the eroded soil layer could thus be determined. The RMSE of θv measurement ranged between 0.003 and 0.025 cm3 cm−3, which enabled the identification of the appropriate soil moisture range for measuring Lair, and achieve reliable simultaneous measurement of soil erosion and soil moisture content. The simulated rainfall experiment using sandy loam and silt loam and field scouring experiment conducted in loam also indicated that the proposed method could achieve high measurement accuracy in erosion environments, for which Lair with the RMSE from 1.8 to 2.1 mm and θv with the RMSE from 0.007 to 0.024 cm3 cm−3. The proposed method has various advantages, including versatility, minimal disturbance, easy automation of measurement at multiple positions, etc., could serve as a new technical option for soil erosion measurement, and extend the utilization of TDR.

Testing of a commercial vector network analyzer as low-cost TDR device to measure soil moisture and electrical conductivity

Time Domain Reflectometry (TDR) is a non-destructive technique to determine the soil apparent dielectric constant, εa, the volumetric water content, θ, and bulk electrical conductivity, σ. However, the high cost of TDR devices may limit its use. This study evaluates two different low-cost Vector Network Analyzers (VNA) commercially available (NanoVNA), with 1.5 (VNA1.5) and 3.0 (VNA3.0) GHz maximum operating frequency. NanoVNA can be used for measurements of Frequency Domain Reflectometry (FDR) or, after suitable post-processing, for θ and σ TDR measures. Although FDR and TDR are dual procedures, TDR is easier to interpret for soil experiments. The TDR waveforms and εa measured with NanoVNA connected to 10 and 20 cm length three-rod probes immersed in air, distilled water, and a soil column with different θ were compared to those measured using a TDR100 (Campbell Sci.) instrument. The capacity of VNAs to measure σ was evaluated by immersing a 10 cm length three-rod probe in different NaCl-water solutions. Measurements obtained with the VNA and TDR100 were compared in a field test using two-rod 22 cm length TDR probes inserted in soil plots with increasing water content. A robust fit was observed between TDR waveforms registered with the two VNAs and the TDR100. Although VNA3.0 doubles the frequency range of VNA1.5, both devices allowed for good estimates of εa (εaVNA1.5, 3.0 = 1.001 εaTDR100 – 0.2125; R2 = 0.999). These results indicate that the low-cost VNA devices can measure soil water content with similar accuracy and precision as the TDR100. A good agreement (σVNA1.5, 3.0 = 0.999 σCM + 0.0023; R2 = 0.999) was also observed between the σ measured using a conductivity meter (CM) and that estimated with the VNAs. Finally, a good correlation was also observed between θ measured in the field experiment with TDR100 and the VNA1.5 and VNA3.0 devices.

Estimation of bulk electrical conductivity in saline medium with contaminated lead solution through TDR coupled with machine learning

Time-domain reflectometry (TDR) has been used for the characterization of media; however, the results of TDR tests significantly differ according to the types of solutions. The objective of this study is to suggest a new relationship between TDR output values and bulk electrical conductivity based on a machine learning algorithm for enhancing the reliability of TDR measurement. Various salinities (0%, 1%, 2%, and 3%) and lead concentrations (0, 0.5, 1, 2, 5, and 10 mg/L) are applied along with silica sand, classified as SP in USCS, to create media. A laboratory test is performed to measure the TDR waveform at the bottom of the cylindrical cell, and a resistance probe is also installed to obtain the true bulk electrical conductivity in the cell. A deep neural network machine learning algorithm is applied to establish the relationship between the TDR output value and the bulk electrical conductivity at each frequency of 0.1, 0.12, 1, 10, and 100 kHz. The highly important variables are also defined through random forest. This study demonstrates that the TDR can be reliably converted into bulk electrical conductivity when two different solutions are mixed.

Research on the Method of Measuring Soil Water Content by Time Domain Reflectometry

Time domain reflectometry (TDR) can calculate the water content by testing the dielectric constant of the rock and soil medium, but the TDR measurement results under time domain conditions are susceptible to the influence of soil conductivity. This article introduces the basic theory of TDR measurement, then uses the transmission scattering matrix to describe the transmission equation, analyzes the dielectric constant in the frequency domain, simulates the TDR waveform with matlab based on the Debye model, and fits the simulated waveform to the measured waveform, and then according to the simulated waveform The matching degree proves the feasibility of calibrating the dielectric constant of the soil. Taking clay as the measurement object, finally fitting a simulation waveform with a higher degree of matching with the measurement waveform, which proves the feasibility of the method and has certain reference value for the study of the TDR method of measuring soil dielectric constant and water content.

Fault Location in 6.6kV Overhead Distribution System by Comparing TDR Waveforms Before and After Failure

The authors propose an effective method of fault location in overhead distribution system. In past studies, short pulse with high frequency injected into overhead distribution system can propagate through about 1km distance, but it has been a problem that pulse reflect at other than a fault point. In other words, it is necessary to find out a fault point from multiple reflected waves. In our proposed method, it is possible to extract a change of a fault point by comparing TDR (Time Domain Reflectometry) waveforms before and after failure. In this paper, we clarify theoretical concept and organize the algorithm of comparing TDR waveforms. Moreover we verify effectiveness of the proposed method by experiments in real-scale distribution system after confirming pulse transmission properties of section switch. The verification results show that the proposed method can locate a fault point (short-circuit fault or ground fault) with accuracy of tens of meters or less.

Laboratory Approach to Determine Roller Compacted Concrete Mixture Electrical Characteristics Using a New Time-Domain Reflectometry Interpretation Method

This work deals with using time-domain reflectometry (TDR) to measure the electrical properties of roller compacted concrete (RCC). It is well known that TDR provides a non-destructive method to measure the dielectric constant toward an estimation of moisture content for soil materials. However, few studies have used TDR to determine the moisture content in concrete because of the inability to obtain TDR traces after the concrete hardens. To obtain TDR traces, a transmission circuit is initiated where a wave signal moves through the medium and reflects back in accordance with transmission line theory. In the literature, the TDR waveform has been interpreted empirically to estimate the relative permittivity (or dielectric constant) and electrical conductivity in a given material relative to the determination of associated water content. However, empirical models tend to ignore certain aspects related to the electrical properties of a medium, which has made interpretation of TDR measurements prone to systematic errors. In this paper, a new approach of test configuration and TDR response interpretation has been developed. For the test setup, the approach uses disposable metal probes that can be embedded into the concrete at different depths to obtain the TDR traces. The approach also employs the transmission line equation to estimate the dielectric constant, electrical conductivity, and reflectivity of an instrumented RCC mixture. These properties will affect the understanding of the RCC pavement behavior, especially curling and warping behavior, placement density, and development of long-term distresses.

A piecewise analysis model for electrical conductivity calculation from time domain reflectometry waveforms

Electrical conductivity (EC) represents a material’s ability to conduct electric current. Soil EC has been used as a soil quality attribute related to soil pH, nutrient availability, crop suitability and soil microbial activity. Time domain reflectometry (TDR) estimates soil water content and EC based on the propagation/reflection and energy attenuation of voltage signals along a waveguide. To maximize the data use efficiency, waveform interpretations for simultaneous water content and EC determination are needed. A tangent line/bounded mean oscillation (TL-BMO) model is available to estimate soil water content from TDR waveforms, but an associated EC model is not yet available. The objectives of this study are (1) to introduce a piecewise analysis method for TDR waveform interpretation, and (2) to develop a model for EC computation along a TDR waveguide under homogeneous water content. The proposed model sequentially fits a TDR waveform for the coaxial cable, the connection, and the waveguide according to the transmission line equation. A TDR waveguide can be discretized into multiple successive pieces for the determination of EC variations along the waveguide. Simplifications of the fitting procedures via (1) existing models, e.g., TL-BMO and Topp et al. (1988) models, and (2) analysis of waveforms obtained from controlled conditions, e.g., in distilled water under room temperature (~20 °C) and air pressure (~101 kPa), are also applied. Accuracy and stability of the proposed model are tested via observed TDR waveforms obtained under uniform EC conditions but perturbated with a range of noise levels. EC values computed with only one discretized piece (i.e., no discretization along the waveguide) are consistent with the theoretical EC values, and the results are robust for all of the tested noise levels. As the number of discretized pieces and the noise levels increase, numerical oscillations in the results increase. The maximum relative errors are <20%, occurring when the mean power of noise is as large as the mean power of waveforms (0 dB noise). Flexibility of the proposed model is tested using waveforms simulated under spatially varying EC, and the EC variations along a TDR waveguide can be detected by the proposed model. In summary, the proposed model provides reliable EC estimations, and it can evaluate uniform or varying EC distributions along a TDR waveguide under uniform moisture conditions. This model can be imbedded into the TL-BMO model for integrated water content and EC determination for commonly measured (251-scanning point) TDR waveforms.

A TDR wireless device for volumetric water content sensing

Time Domain Reflectometry (TDR) is a widely used technique to estimate the soil volumetric water content (θ) and bulk electrical conductivity (σ). This paper presents TDR-WiFi, a wireless, portable and low cost interface to ease sensing of θ and σ by connecting TDR cable tester with a smartphone. TDR-WiFi consists of a microprocessor equipped with a WiFi microcontroller (M5Stack unit) and connected to the TDR device through an RS232-TTL adapter. The M5stack firmware is programmed in MicroPython language to act as a server between the user and the TDR device through a web page accessible from any smartphone web browser. TDR-WiFi is compatible with the Campbell TDR100 device and allows storing the TDR waveforms as well as estimating θ and σ. A complementary web page for subsequent analysis of the TDR waveforms was developed and is publicly available at http://swi.csic.es/tdrwifi/. The system was satisfactorily demonstrated in laboratory and tested in the field. The field trial allowed water content measurements in a steep road slope. TDR-WiFi demonstrated to be operative in the field and it can be satisfactorily used in difficult access areas.

Modeling and Monitoring of Wood Moisture Content Using Time-Domain Reflectometry

Time-domain reflectometry (TDR) can monitor the moisture content (MC) of water saturated logs stored in wet-decks where the MC exceeds the range that can be measured using traditional moisture meters (&gt;50%). For this application to become routine, it is required that TDR monitoring of wet-decks occurs after establishment, and tools are needed that automate data collection and analysis. We developed models that predict wood MC using three-rod epoxy encased TDR probes inserted into the transverse surface of bolts (prior wet-deck studies were installed on the tangential surface). Models were developed for southern pine, sweetgum, yellow poplar, hickory, red oak, and white oak using a Campbell Scientific TDR100. For each species, at least 37 bolts were soaked for a minimum of three months and then air dried with TDR waveforms, and MC was periodically recorded. Calibrations were developed between MC and the TDR signal using nonlinear mixed effects models. Fixed effects ranged from excellent (southern pine R2 = 0.93) to poor (red oak R2 = 0.36, hickory R2 = 0.38). Independent of wood species, random effects all had a R2 greater than 0.80, which indicates that TDR detects changes in MC at the individual sample level. Use of TDR combined with a datalogger was demonstrated in an operational wet-deck that monitored changes in MC over 12 months, and in a laboratory trial where bolts were exposed to successive wet-dry cycles over 400 days. Both applications demonstrated the utility of TDR to monitor changes in wood MC in high MC environments where periodic measurement is not feasible due to operational safety concerns. Because a saturated TDR reading indicates a saturated MC, and because of the relatively accurate random effects found here, developing individual species models is not necessary for monitoring purposes. Therefore, application of TDR monitoring can be broadly applied for wet-decks, regardless of the species stored.

Applying time domain reflectometry to quantification of slope deformation by shear failure in a landslide

This study employed time domain reflectometry (TDR) to monitor the deformation of grouted coaxial cables in a landslide over an extended period. Laboratory experiments were performed to quantify the magnitude of the deformation by shear failure to simulate types of cable deformation in the field when two localized shear types had been detected using TDR. The study applied two qualification methods to measure the magnitude of the laboratory shear deformation. The integration method of the TDR reflection coefficients demonstrated a stronger significant positive correlation with the shear displacement than did the linear regression method of reflection coefficients in relation to the deformation magnitude of the cables. The integration method indicated increases of localized shear displacements from 15 to 47 mm over time at 10.33- and 13.36-m depths in the landslide. The average maximum magnitude of the cable deformation by shearing was 47 mm corresponding to a 210-mρ reflection coefficient when the cable ruptured in the case study. Overall, the location and magnitude of shear deformation in the landslide can be determined using changes in the TDR waveforms and calculations of the integration method of reflection coefficients.

Using Time Domain Reflectometry to Determine Depth of Fouling and Fouling Type in Railway Track Substructure

Abstract This study documents the development of a procedure for the identification of the depth and type of ballast fouling using the time domain reflectometry (TDR) technique. Ballast fouling leads to a reduction in the bearing capacity of the railway substructure, a decrease in the drainage capacity, and an increase in track deformation. As a consequence of these detrimental effects, rail tracks lose load capacity, ride comfort deteriorates, and trains may ultimately derail. The determination of type and extent of ballast fouling may be used to assess the expected life of rail track and to plan maintenance operations. TDR waveforms of variably fouled ballast and subballast layers were evaluated in the lab to yield relative dielectric permittivity and electrical conductivity and to thus characterize the effect of ballast gradation, mineralogy, and water content on electromagnetic response. Strong relationships between depth of fouling, volumetric water content, and relative dielectric permittivity were developed. These results were then expanded to the interpretation of ground penetrating radar (GPR) inspection and to quantify the level of fouling in larger-scale maintenance operations. The proposed technique can be complementary to GPR as it reduces the uncertainty in determining the depth and type of fouling when using GPR alone.

Laboratory based continuous bedload monitoring in a model retention basin: Application of time domain reflectometry

AbstractIn this study, we applied time domain reflectometry (TDR) to determine the deposition height and porosity of sediment at a fine spatiotemporal resolution, and developed a continuous bedload monitoring method that can be applied to pools in steep mountain rivers. The TDR monitoring system consisted of sensor probes, a cable tester, multiplexers and coaxial cables. When the embedded probes penetrated both water and sediment, the boundaries of the sediment and water were consistent with the transition points in the observed waveforms of each TDR measurement. A semi‐automatic analysis of the recorded TDR waveforms, which did not require calibration or parameter fitting, was conducted to establish continuous monitoring. In addition, a flume experiment was performed to test the monitoring system in a model retention basin connected to a flume, with sand of uniform grain size (1.4 mm diameter) supplied for 30 min. The sediment volume in the container representing the model basin was monitored using a load cell underlying the container and eight sensor probes, with a length of almost 0.27 m. The sediment thickness determined by the TDR indicated a gradual deposition, and was consistent with manual measurements. Despite a marginal overestimation of 13% for a sand feed of 30 kg, the sediment volume in the model retention basin and the bedload transport rate were successfully estimated. A combination of our monitoring system and other indirect methods, such as geophones, can potentially serve as useful tools for better understanding bedload transport processes in steep mountain streams. Copyright © 2018 John Wiley &amp; Sons, Ltd.

Comparison of performance of inclinometer casing and TDR technique

TDR (Time Domain Reflectometry) and GPR (Ground Penetrating Radar) are two of the electromagnetic methods in applied geophysics, which using them for various applications are developing. The Time Domain Reflectometry is a remote sensing method that has been used for years to determine the nature of the materials and spatial location. The use of TDR system has led to innovative applications of it and comparing it with previous measuring techniques, since it has developed. In this study, not only a summary of the basics of TDR application for monitoring of ground deformation is offered, but also a comparison of this technology with other measurement techniques (inclinometer casing) is provided. Actually, this paper presents a case study in which the opportunity arose to compare these two technologies in detecting subsurface deformation in slopes. A TDR system includes a radar wave receiver & generator, a transmission line and a waveguide. The generated electro-magnetic pulse moves toward the waveguide within the conductor cable and enters the test environment. For this study, slopes overlooking the Darian dam bottom outlet, power house and spillway were instrumented with RG59/U coaxial cables for TDR monitoring and slope inclinometer. Coaxial cables - as a TDR sensor - and inclinometer casings were installed in a same bore hole where coaxial cable was attached to the inclinometer casing. Shear and tensile deformations of the cable, which is caused by ground movements, significantly impacts on cable reflection coefficient. In Darian dam boreholes, the cable points subject to the shear and stretch were correlated with deformation points of the inclinometer casings in incremental displacement graphs. This study shows that TDR technique is more sensitive than inclinometer casing for small movement in the slide planes. Because manual processing of TDR data is hard and need experienced personnel, the authors have designed an algorithm to compare the shape of the new TDR waveforms with the base reading waveform in order to monitor the subsurface deformations.

Interpreting TDR Signal Propagation through Soils with Distinct Layers of Nonaqueous‐Phase Liquid and Water Content

Core Ideas The TDR response in the presence of NAPL transport was investigated in a homogeneous soil. The experimental framework was designed to simulate sharp NAPL fronts that moved in the soil. The TDR waveforms were analyzed to deduce the influence of NAPLs on TDR signal propagation. A general procedure to determine the location of an NAPL‐contaminated front was developed. Several studies have demonstrated that time‐domain reflectometry (TDR) has an enormous potential to detect and monitor nonaqueous‐phase liquids (NAPLs) in uniformly contaminated soils with reference to different‐textured soils and under different saturation conditions. Few attempts have been proposed to describe NAPL distribution by using TDR when a contaminated front propagates through a soil. In this study, the TDR response in the presence of NAPL‐contaminant transport processes was investigated in a homogeneous soil under confined conditions with a series of laboratory‐controlled tests. The laboratory procedure involved measurements of dielectric permittivity (εb) and electrical conductivity (ECb) and the acquisition of the reflected TDR waveforms. The experimental framework was designed to simulate sharp NAPL fronts that moved in the soil columns and generated zones of contrasting permittivity. During the experiments, different initial conditions were assumed, as well as different degrees of contamination, by varying the volumetric water (θw) and NAPL (θNAPL) contents. The acquired TDR waveforms were systematically analyzed to deduce the influence of NAPLs on TDR signal propagation. A general procedure to determine the location of an NAPL‐contaminated front within a soil column was developed. Equipment calibration, measurement accuracy, and error sources were investigated in relation to the experimental procedure setup and the column preparation conditions. The results show that there may be some difficulties when interpreting TDR signals to locate the NAPL front for two main reasons: first, the expected additional reflection at the interface is not always distinguishable; second, there may be problems even locating both the first peak and the reflection point at the end of the TDR probe, especially when the signal shifts from a low to a high impedance layer. The suggested methodology provides a tool to overcome such intrinsic difficulties in NAPL front detection during the propagation of the contaminant.

A New Approach to Estimating the Path Loss in Underground Wireless Sensor Networks

Unlike terrestrial Wireless Sensor Networks (WSNs), communication between buried nodes in WUSNs happens through the ground. Due to the complexity of soil, accurate estimation of the underground signal attenuation is challenging. Existing path loss models mainly rely on semi-empirical and empirical mixing models for calculating the dielectric properties of the soil. In this paper, two existing models for estimating the path loss in soil (i.e., the CRIM-Fresnel and Modified-Friis models) are compared with measurements obtained at three locations. In addition, an improved method is proposed for estimating the path loss based on a new approach for calculating the dielectric properties of soil from Time Domain Reflectometry (TDR) measurements. The proposed approach calculates the complex permittivity values from TDR waveform based on a new modified method and subsequently use them as inputs into the Modified-Friis model. The results from the field trials were compared with the proposed method and the existing models. The results of this comparison showed that the proposed estimation technique provides a better estimation of Radio Frequency (RF) attenuation than the existing models. It also eliminates the need to take samples back to the laboratory by providing in situ calculation of attenuation based on TDR.

A Comparison of Second‐Order Derivative Based Models for Time Domain Reflectometry Waveform Analysis

Core Ideas Two methods, AWIGF and second‐order BMO, were evaluated on long‐ and short‐probe TDR waveforms. A corner‐preserving filter was designed to improve the performance of AWIGF. With the new filter, AWIGF performance was consistent with second‐order BMO analysis. Adaptive waveform interpretation with Gaussian filtering (AWIGF) and second‐order bounded mean oscillation Z2(u,t,r) are time domain reflectometry (TDR) analysis models. The AWIGF was originally designed for relatively long‐probe (&gt;150 mm) TDR waveforms, while Z2(u,t,r) was originally designed for relatively short‐probe (&lt;50 mm) TDR waveforms. The performances of AWIGF and Z2(u,t,r) on both long and short TDR probes have not been evaluated. The main objective of this study was to evaluate theoretically and experimentally the AWIGF and Z2(u,t,r) performances on long and short TDR probes. The evaluations are performed via mathematical analysis, and measurements of long probe and short probe waveforms in CaCl2 solutions with various electrical conductivities (EC), adding Gaussian noise, and testing the stability of Z2(u,t,r) and AWIGF. A corner‐preserving filter (CPF) is proposed to improve the stability of AWIGF on short‐probe TDR waveforms. The CPF preserves the second order derivatives of the waveforms, and emphasizes the reflection positions (t2) compared to the original Gaussian filter. Both theoretical and experimental tests illustrate the consistency of Z2(u,t,r) and AWIGF. The standard deviations of relative permittivity (εr) are &lt;5% for all noise levels. In conclusion, Z2(u,t,r) and AWIGF can provide stable analysis for long and short probe TDR waveforms. The AWIGF with CPF is capable of stably analyzing challenging short probe TDR waveforms. The original AWIGF exhibits the lowest standard deviation of εr at a given EC, whereas AWIGF with CPF filter exhibits the lowest bias of εr across solutions varying in EC.

Estimating Nonaqueous‐Phase Liquid Content in Variably Saturated Soils Using Time Domain Reflectometry

Core Ideas A TDR waveform interpretation method for NAPL content in soils was developed. Correlations between the dielectric response and the NAPL content were determined. The α dielectric mixing model for predicting NAPL presence in soils was expanded. This methodology can be used to obtain predictions of volumetric NAPL content. In recent years, several studies have been conducted in the detection and observation of nonaqueous‐phase liquids (NAPLs) in contaminated soils. Successful remediation of an NAPL‐contaminated site requires appropriate characterization of both the plume extent and the soil volumetric NAPL content (θNAPL). Noninvasive geophysical techniques, such as time domain reflectometry (TDR), may be used to discriminate between θNAPL and soil volumetric water content (θw). Accordingly, the main aim of this work was to develop a TDR waveform interpretation method based on soil dielectric permittivity measurement and observation of the change in the reflected TDR signal amplitude at relatively long times from the waveform source. We demonstrated that the asymptotic value of the reflection signal coefficient can be univocally related with θNAPL in an unsaturated soil. In the procedure adopted, a new formulation of a dielectric mixing model was also derived, introducing a fourth phase that takes the NAPL presence into account. Multiple samples of sandy, silt loam, and loamy soils, at predetermined different θw and θNAPL, were tested, each test consisting in emitting a TDR signal to the soil sample and receiving and analyzing the reflected electromagnetic wave. An empirical dielectric mixing model was calibrated and implemented to estimate the θNAPL. Equipment calibration, measurement accuracy, and error sources, related both to the experimental procedure setup and to the sample preparation conditions, are discussed. The results show that the suggested methodology can be used to obtain predictions of volumetric NAPL content (θNAPL) with acceptable accuracy (R2 = 0.95).