Spatial Time Domain Reflectometry Research Articles

Quantification of spatial heterogeneity and its influence on particle migration

Suffusion experiments were utilised to quantify the evolving degree of heterogeneity in gap-graded soils. Upward flow was imposed on test specimens comprising a mixture layer with varying finer fraction contents overlaid by a coarse layer. A coaxial permeameter cell enabled the local permeability to be obtained using spatial time domain reflectometry. Three methods (coefficient of variation, Dykstra-Parsons coefficient, and Lorenz coefficient) were employed to quantify heterogeneity based on spatial variability in local permeability. For the two-layered specimen in this study, all three methods demonstrated that suffusion had a homogenising effect with particle migration from the mixture layer to the coarse layer. Detailed insights were obtained from a multi-layered approach, where the Dykstra-Parsons coefficient was found to be more sensitive to spatial variations, while the Lorenz coefficient was less dependent on the amount of data. The key observation was that an increase in heterogeneity led to a reduction in particle migration. This is an important finding as prior studies focused on homogeneous specimens, while this study demonstrates that small amounts of heterogeneity can significantly impact particle migration characteristics. This reinforces the need to quantify the evolving degree of heterogeneity.

Dynamic effects in soil water retention curves: an experimental exploration by full-scale soil column tests using spatial time-domain reflectometry and tensiometers

Dynamic effects in soil water retention curves: an experimental exploration by full-scale soil column tests using spatial time-domain reflectometry and tensiometers

Spatial and Temporal Evolution of Particle Migration in Gap-Graded Granular Soils: Insights from Experimental Observations

This study presents physical observations and insights into particle migration characteristics throughout the suffusion process. Using a purpose-built coaxial permeameter cell, suffusion experiments were conducted on idealized internally unstable gap-graded granular soils at varying fines content and hydraulic loading conditions. The specimens were prepared with a mixture layer comprising finer and coarser fractions underlying a coarse layer composed of the coarser fraction alone. This enabled the finer fraction within the mixture layer to migrate through the coarse layer with upward seepage flow. The local porosity profile along the specimen was determined using spatial time-domain reflectometry and an inversion algorithm, which enabled the development of a novel field map of the difference in porosity from the initial condition. This field map provided a visual guide of the spatial and temporal variation in porosity and enabled particle migration internally within the specimen to be quantitatively characterized from onset to progression to washout. The limiting onset condition identified from the field map was shown to be comparable to that obtained using conventional approaches, thereby providing strong validation for the application of porosity-based field maps. As suffusion progressed, the height of infiltrating finer particles into the coarse layer increased linearly with time, while the overall rate of particle migration from the mixture layer to the coarse layer evolved in a non-linear manner with the rate of migration increasing as the specimen reached a complete mixture condition, where the finer fraction infiltrated the entire coarse layer. The attainment of a complete mixture condition was dependent on the fabric of the gap-graded soil. Specimens with an underfilled fabric showed a gradual migration process, while specimens with a transitionally underfilled fabric resulted in minimal particle migration followed by a very rapid formation of the complete mixture.

Accurate Detection and Localization of Water Pipe Leaks through Model-Based TDR Inversion

The problem of water scarcity affects many areas of the world due to water mismanagement and overconsumption and, more recently, to climate change. Monitoring the integrity of distribution systems is, therefore, increasingly important to avoid the waste of clean water. This paper presents a new signal processing technique for enhancing the performance of the methodology of leak detection in water distribution pipes based on time domain reflectometry (TDR). The new technique is based on a particular kind of TDR inversion (spatial TDR) based on a "gray-box" lumped parameter model of the system. The model does not include, e.g., radiative phenomena, non-TEM (transverse electromagnetic) modes etc. but is capable of reproducing accurately the complicated reflectograms obtained by a TDR leak detection system assuming a proper profile of capacitance per unit length along the sensing element. Even more importantly, the model is identified using only the reflectograms taken by the system with very little prior information about the system components. The developed technique is able to estimate with good accuracy, from reflectograms with unclear or ambiguous interpretation, the position and the extension of a region where water is located. The measurement is obtained without prior electromagnetic characterization of the TDR system components and without the need of modeling or quantifying a number of electromagnetic effects typical of on-site measurements.

Investigating scale effects in soil water retention curve via spatial time domain reflectometry

The soil water retention curve (SWRC) is usually measured by the axis translation technique (ATT), assuming a specimen thickness of a few centimetres. Usually, this assumption is unquestionable to ensure the representative elementary volume (REV). However, such an assumption cannot always be conserved with coarser soil regarding the local heterogeneities generated by larger pore sizes. In addition, the authentic SWRC is supposed to be the soil moisture profile above the phreatic surface. Those issues, therefore, raise concerns about the scale effects in SWRC. With an aim to investigate them, this work compared the primary drainage SWRCs of coarse, medium and fine sand measured by the standard hanging column and full-scale soil column (150 cm). The soil moisture profile at the final drainage stage was detected using the spatial time domain reflectometry (spatial TDR) technique with a presentation of sensor calibrations and validations. The observations showed discrepancies between SWRCs given by two methods in terms of air entry value (AEV) and slope of SWRC but agreements on residual moisture content. Moreover, such differences could be alleviated with the soil becoming finer and better graded. Finally, the physical reasons are discussed, referring to local heterogeneity and pressure gradient changes on the top boundary. In conclusion, the full-scale soil column test can be utilised to avoid scale effects, despite demanding high costs and massive labour efforts. Also, a shorter soil column incorporating point-wise suction and moisture sensors in prior studies could be an alternative solution.

The Technical Challenges for Applying Unsaturated Soil Sensors to Conduct Laboratory-Scale Seepage Experiments.

Although many unsaturated soil experiments have successfully delivered positive outcomes, most studies just concisely illustrated sensor techniques, because their main objectives focused on bridging research gaps. Inexperienced research fellows might rarely follow up those techniques, so they could encounter very trivial and skill-demanding difficulties, undermining the quality of experimental outcomes. With a motivation to avoid those, this work introduces technical challenges in applying three sensor techniques: high precision tensiometer, spatial time-domain reflectometry (spatial TDR) and digital bench scales, which were utilized to measure three fundamental variables: soil suction, moisture content and accumulative outflow. The technical challenges are comprehensively elaborated from five aspects: the functional mechanism, assembling/manufacturing approaches, installation procedure, simultaneous data-logging configurations and post data/signal processing. The conclusions drawn in this work provide sufficient technical details of three sensors in terms of the aforementioned five aspects. This work aims to facilitate any new research fellows who carry out laboratory-scale soil column tests using the three sensors mentioned above. It is also expected that this work will salvage any experimenters having troubleshooting issues with those sensors and help researchers bypass those issues to focus more on their primary research interests.

Improving the Brillouin frequency shift measurement resolution in the Brillouin optical time domain reflectometry (BOTDR) fiber sensor by artificial neural network (ANN)

We propose to use an artificial neural network (ANN) model to improve the Brillouin frequency shift (BFS) resolution of the sub-meter spatial resolution differential cross-spectrum Brillouin optical time domain reflectometry (DCS-BOTDR) fiber sensor. ANN technique was chosen due its nonlinear mapping characteristic that makes it suitable to effectively extract the BFS distribution along the fiber optic. Importantly, the ANN model offers more flexibility in estimating the BFS because one does not need to set the initial parameters like the conventional polynomial function based on Lorentzian curve fitting (LCF) model. In our ANN model, we used the BFS distribution data measured by the pulse duration TL = 14 ns at 56,000 times averaging as the ground truth in the training phase, because they provided the highest BFS resolution compared to that of obtained by other pulse duration cases, as reported previously. After training the data, we tested them with the BFS distribution results for TL = 2, 4 and 60 ns cases, which they showed poor BFS resolution when processed by the conventional model. For TL = 2 and 4 ns cases, the deployment of ANN has significantly improved the BFS resolution at least two times higher than that by the conventional polynomial fitting. Surprisingly, for TL = 60 ns case, despite the reduced number of averaging from 56,000 to 7000 times (i.e., eight times faster measurement), the BFS resolution has improved about seven times from 21.13 MHz to 2.88 MHz. This indicates the significant contribution of the ANN model in reducing the measurement time in the DCS-BOTDR

Computation of local permeability in gap-graded granular soils

This paper proposes semi-analytical methods to obtain the local permeability for granular soils based on indirect measurements of the local porosity profile in a large coaxial cell permeameter using spatial time-domain reflectometry. The porosity profile is used to obtain the local permeability using the modified Kozeny–Carman and Katz–Thompson equations, which incorporated an effective particle diameter that accounted for particle migration within the permeameter. The profiles of the local permeability obtained from the proposed methods are compared with experimentally obtained permeability distributions using pressure measurements and flow rate. The permeabilities obtained with the proposed methods are comparable with the experimentally obtained permeabilities and are within one order of magnitude deviation, which is an acceptable range for practical applications.

Physical observations of the transient evolution of the porosity distribution during internal erosion using spatial time domain reflectometry

A purpose-built permeameter was used to explore the transient evolution of porosity during the mixing process in filtration experiments. The experiments considered upward seepage flow and explored the influence of base and filter particle sizes, along with different hydraulic conditions. The permeameter acted as a coaxial transmission line enabling electromagnetic measurements based on spatial time domain reflectometry, from which the porosity profile was obtained using an inversion technique. Quantitative characteristics of the onset and progression of the mixing process were extracted from a porosity field map. The limiting onset condition was influenced by geometric and hydraulic factors, with the critical flow rate exhibiting a strong dependence on the base particle size, while the critical hydraulic gradient exhibited a stronger dependence on filter particle size. The progression of the mixing process was characterised by both the transport of base particles into the filter layer, as well as the settlement of the filter particles into the base layer due to the reduction of the effective stress at the base–filter interface leading to partial bearing failure. The rate of development of the mixture zone was strongly dependent on the hydraulic loading condition and the base particle size, but the final height of the sample after complete mixing was independent of the hydraulic loading path.

Application of Spatial Time Domain Reflectometry for Investigating Moisture Content Dynamics in Unsaturated Loamy Sand for Gravitational Drainage

The strength of unsaturated soil is defined by the soil water retention behavior and soil suction acting inside the soil matrix. In order to obtain the suction and moisture profile in the vadose zone, specific measuring techniques are needed. Time domain reflectometry (TDR) conventionally measures moisture at individual points only. Therefore, spatial time domain reflectometry (spatial TDR) was developed for characterizing the moisture content profile along the unsaturated soil strata. This paper introduces an experimental set-up used for measuring dynamic moisture profiles with high spatial and temporal resolution. The moisture measurement method is based on inverse modeling the telegraph equation with a capacitance model of soil/sensor environment using an optimization technique. With the addition of point-wise soil suction measurement using tensiometers, the soil water retention curve (SWRC) can be derived in the transient flow condition instead of the static or steady-state condition usually applied for conventional testing methodologies. The experiment was successfully set up and conducted with thorough validations to demonstrate the functionalities in terms of detecting dynamic moisture profiles, dynamic soil suction, and outflow seepage flux under transient flow condition. Furthermore, some TDR measurements are presented with a discussion referring to the inverse analysis of TDR traces for extracting the dielectric properties of soil. The detected static SWRC is finally compared to the static SWRC measured by the conventional method. The preliminary outcomes underpin the success of applying the spatial TDR technique and also demonstrate several advantages of this platform for investigating the unsaturated soil seepage issue under transient flow conditions.

Determination of the Porosity Distribution during an Erosion Test Using a Coaxial Line Cell.

The detection of porosity changes within a soil matrix caused by internal erosion is beneficial for a better understanding of the mechanisms that induce and maintain the erosion process. In this paper, an electromagnetic approach using Spatial Time Domain Reflectometry (STDR) and a transmission line model is proposed for this purpose. An original experimental setup consisting of a coaxial cell which acts as an electromagnetic waveguide was developed. It is connected to a transmitter/receiver device both measuring the transmitted and corresponding reflected electromagnetic pulses at the cell entrance. A gradient optimization method based on a computational model for simulating the wave propagation in a transmission line is applied in order to reconstruct the spatial distribution of the soil dielectric permittivity along the cell based on the measured signals and an inversion algorithm. The spatial distribution of the soil porosity is deduced from the dielectric permittivity profile by physically based mixing rules. Experiments were carried out with glass bead mixtures of known dielectric permittivity profiles and subsequently known spatial porosity distributions to validate and to optimize both, the proposed computational model and the inversion algorithm. Erosion experiments were carried out and porosity profiles determined with satisfying spatial resolution were obtained. The RMSE between measured and physically determined porosities varied among less than 3% to 6%. The measurement rate is sufficient to be able to capture the transient process of erosion in the experiments presented here.

Application of spatial time domain reflectometry measurements in heterogeneous, rocky substrates

Measurement of soil moisture across depths using sensors is currently limited to point measurements or remote sensing technologies. Point measurements have limitations on spatial resolution, while the latter, although covering large areas may not represent real-time hydrologic processes, especially near the surface. The objective of the study was to determine the efficacy of elongated soil moisture probes—spatial time domain reflectometry (STDR)—and to describe transient soil moisture dynamics of unconsolidated mine waste rock materials. The probes were calibrated under controlled conditions in the glasshouse. Transient soil moisture content was measured using the gravimetric method and STDR. Volumetric soil moisture content derived from weighing was compared with values generated from a numerical model simulating the drying process. A calibration function was generated and applied to STDR field data sets. The use of elongated probes effectively assists in the real-time determination of the spatial distribution of soil moisture. It also allows hydrologic processes to be uncovered in the unsaturated zone, especially for water balance calculations that are commonly based on point measurements. The elongated soil moisture probes can potentially describe transient substrate processes and delineate heterogeneity in terms of the pore size distribution in a seasonally wet but otherwise arid environment.

Quantifying spatiotemporal dynamics of root-zone soil water in a mixed forest on subtropical coastal sand dune using surface ERT and spatial TDR

Summary We jointly used surface electrical resistivity tomography (surface ERT) and spatial time domain reflectometry (spatial TDR) to quantify spatial patterns and seasonal dynamics of root-zone soil water under three contrasting vegetation covers in a sand dune forest of subtropical coastal Australia. We wanted to obtain a better understanding of the applicability of both techniques in these environments as well as investigate vegetation–soil water interactions. Soil temperature and topographic changes were taken into account in soil resistivity interpretation. The results demonstrated the capability of both surface ERT and spatial TDR to spatially monitor root-zone soil water dynamics, with root mean square error (RMSE) 3 cm −3 and absolute deviation 3 cm −3 between gravimetrically derived water content and those derived by the two geophysical techniques. Soil water was depleted to low levels during the dry season but quickly replenished with onset of the wet season. Soil water content profiles revealed obvious differences in water dynamics of the dune sands under different vegetation covers, with highest infiltration and deep drainage under the grassland compared with tree cover. The spatial variation in soil water content due to rainfall interception by trees, root water uptake and preferential infiltration associated with stemflow could be detected by the joint use of surface ERT and spatial TDR. We conclude that surface ERT can be an effective method for quantifying two-dimensional root-zone soil water dynamics and understanding the hydrological processes in these sand dune environments, if complemented by the one-dimensional high-resolution soil water measurements from spatial TDR.

Determination of Porosity Distributions of Water Saturated Granular Media Using Spatial Time Domain Reflectometry (Spatial TDR)

Abstract A sensor has been developed for the investigation of erosion processes in cylindrical specimens that permits the determination of porosity distributions using spatial time domain reflectometry (spatial TDR). Spherical glass beads saturated with water were used as a model material. The porosity was varied by mixing different size glass beads, and a physical mixing rule was optimized to determine a temperature dependent calibration function between dielectric permittivity and porosity. Homogeneous specimens were used to calibrate the sensor. An inversion algorithm was used for the analysis of the TDR signals. Both the sensor and the procedure were tested using specimens of glass beads comprised of layers with different porosities. The comparison between the measured and predefined porosity distributions shows satisfactory agreement.

Potentials and constraints of different types of soil moisture observations for flood simulations in headwater catchments

Flood generation in mountainous headwater catchments is governed by rainfall intensities, by the spatial distribution of rainfall and by the state of the catchment prior to the rainfall, e.g. by the spatial pattern of the soil moisture, groundwater conditions and possibly snow. The work presented here explores the limits and potentials of measuring soil moisture with different methods and in different scales and their potential use for flood simulation. These measurements were obtained in 2007 and 2008 within a comprehensive multi-scale experiment in the Weisseritz headwater catchment in the Ore-Mountains, Germany. The following technologies have been applied jointly thermogravimetric method, frequency domain reflectometry (FDR) sensors, spatial time domain reflectometry (STDR) cluster, ground-penetrating radar (GPR), airborne polarimetric synthetic aperture radar (polarimetric SAR) and advanced synthetic aperture radar (ASAR) based on the satellite Envisat. We present exemplary soil measurement results, with spatial scales ranging from point scale, via hillslope and field scale, to the catchment scale. Only the spatial TDR cluster was able to record continuous data. The other methods are limited to the date of over-flights (airplane and satellite) or measurement campaigns on the ground. For possible use in flood simulation, the observation of soil moisture at multiple scales has to be combined with suitable hydrological modelling, using the hydrological model WaSiM-ETH. Therefore, several simulation experiments have been conducted in order to test both the usability of the recorded soil moisture data and the suitability of a distributed hydrological model to make use of this information. The measurement results show that airborne-based and satellite-based systems in particular provide information on the near-surface spatial distribution. However, there are still a variety of limitations, such as the need for parallel ground measurements (Envisat ASAR), uncertainties in polarimetric decomposition techniques (polarimetric SAR), very limited information from remote sensing methods about vegetated surfaces and the non-availability of continuous measurements. The model experiments showed the importance of soil moisture as an initial condition for physically based flood modelling. However, the observed moisture data reflect the surface or near-surface soil moisture only. Hence, only saturated overland flow might be related to these data. Other flood generation processes influenced by catchment wetness in the subsurface such as subsurface storm flow or quick groundwater drainage cannot be assessed by these data. One has to acknowledge that, in spite of innovative measuring techniques on all spatial scales, soil moisture data for entire vegetated catchments are still today not operationally available. Therefore, observations of soil moisture should primarily be used to improve the quality of continuous, distributed hydrological catchment models that simulate the spatial distribution of moisture internally. Thus, when and where soil moisture data are available, they should be compared with their simulated equivalents in order to improve the parameter estimates and possibly the structure of the hydrological model.

Coupled hydrogeophysical parameter estimation using a sequential Bayesian approach

Abstract. Coupled hydrogeophysical methods infer hydrological and petrophysical parameters directly from geophysical measurements. Widespread methods do not explicitly recognize uncertainty in parameter estimates. Therefore, we apply a sequential Bayesian framework that provides updates of state, parameters and their uncertainty whenever measurements become available. We have coupled a hydrological and an electrical resistivity tomography (ERT) forward code in a particle filtering framework. First, we analyze a synthetic data set of lysimeter infiltration monitored with ERT. In a second step, we apply the approach to field data measured during an infiltration event on a full-scale dike model. For the synthetic data, the water content distribution and the hydraulic conductivity are accurately estimated after a few time steps. For the field data, hydraulic parameters are successfully estimated from water content measurements made with spatial time domain reflectometry and ERT, and the development of their posterior distributions is shown.

Comparison of invasive and non-invasive electromagnetic methods in soil water content estimation of a dike model

Water infiltration through a dike model under controlled flooding and drainage conditions was investigated using the gravimetric soil water sampling technique and electromagnetic techniques, in particular ground penetrating radar (GPR) applied in different forms, time domain reflectometry with intelligent microelements (TRIME-TDR) and spatial-time domain reflectometry (S-TDR). The experiments were conducted on the model in two phases. In the first phase, the model was flooded with varying water levels between 0 and 1.25 m above the waterproof base of the model. In the second phase, the characteristics of the temporal water content changes were investigated over a period of 65 days as the flood water drained off from the 1.25 m level. The dike model was constructed with soil of the texture class loamy sand. The aim of the experiment was to investigate whether GPR-based invasive and non-invasive methods were able to quantitatively observe and correctly monitor temporal changes in the volumetric water content (VWC) within embankment dams. The VWC values from the various techniques corresponded very well, especially with low VWC values. A comparison with the VWC of gravimetric soil water sampling showed a satisfactory reproducibility. Characteristic discrepancies were recorded with higher values of the VWC. Under saturated conditions only the invasive methods were able to produce reasonable values of the VWC. After the release of the highest flood level, the drainage phase could be characterized by two invasive methods based on the TDR and GPR techniques.

Spatial time domain reflectometry and its application for the measurement of water content distributions along flat ribbon cables in a full‐scale levee model

Spatial time domain reflectometry (spatial TDR) is a new measurement method for determining water content profiles along elongated probes (transmission lines). The method is based on the inverse modeling of TDR reflectograms using an optimization algorithm. By means of using flat ribbon cables it is possible to take two independent TDR measurements from both ends of the probe, which are used to improve the spatial information content of the optimization results and to consider effects caused by electrical conductivity. The method has been used for monitoring water content distributions on a full‐scale levee model made of well‐graded clean sand. Flood simulation tests, irrigation tests, and long‐term observations were carried out on the model. The results show that spatial TDR is able to determine water content distributions with an accuracy of the spatial resolution of about ±3 cm compared to pore pressure measurements and an average deviation of ±2 vol % compared to measurements made using another independent TDR measurement system.

Soil water content monitoring on a dike model using electrical resistivity tomography

ABSTRACTWe explore the viability of electrical resistivity tomography (ERT) to quantify soil water content in a full‐scale dike model. While ERT is an established method to detect changes in soil water content, the retrieval of two‐dimensional water content distributions from surface‐based surveys is a much more challenging application. We conducted a series of experiments on a full‐scale dike model comprising rainfall and flooding events. The dike was surveyed with an ERT line down the land‐side slope and monitored with permanently installed spatial time‐domain reflectometry (TDR) cables for comparison. Water content changes were calculated by applying Archie’s equation and agreed well with comparison measurements from spatial TDR measurements. The saturation exponent in Archie’s equation was estimated by combining spatial TDR and ERT measurements and agreed well with literature data of comparable sands. The choice of the inversion type, e.g., time‐lapse inversion or least‐squares versus robust constraint, as well as the influence of inversion parameters, such as regularization and the choice of convergence criterion, is discussed in the context of an apparent inversion artefact for the rainfall experiment, using forward modelling of synthetic data sets. The results indicate that ERT may be a feasible method to quantify water content changes under certain conditions, provided an initial water content estimate is available.