TY - JOUR
AU - Wilhelm,, Helmut
AB - Abstract Guided wave sounding (GWS), an invasive application of ground-penetrating radar (GPR), and time domain reflectometry with intelligible micro elements (TRIME-TDR®) were used to investigate the distribution of volumetric water content (VWC) in a dike model under controlled conditions in order to detect possible dike damage. The dike model, which was constructed with soil of the texture class loamy sand, was flooded at different levels of water between 0.3 and 1.25 m high from a waterproof baseline. The two techniques were applied to retrieve VWC information from the same location at the crest of the dike model. Both techniques assessed reflection data from the lower end of a metal probe lowered through a common access borehole and successfully detected a water content inhomogeneity in the model at a depth of about 0.6 m from the crest. Comparison of the colocated VWC measurements from the two techniques showed almost identical trends with a root mean square deviation of 0.018 m3 m-3. GWS, however, showed a much higher depth resolution than TRIME-TDR®. Accompanying analytical and numerical modelling show that GWS sounding should be applicable to water content exploration in existing, 10–20 m deep boreholes. guided wave, dike, soil water, reflection, electromagnetic sounding Nomenclature Nomenclature Abbreviations CRIM complex refractive index model ERT electrical resistivity tomography GPR ground-penetrating radar GWS guided wave sounding GSSI Geophysical Survey Systems, Inc. IMKO Intelligent Micro-module Koehler GmbH MATLAB© The MathWorks, Inc. Software Reflexw Sandmeier Scientific Software SIR subsurface interface radar RMSD root mean square deviation TDR time domain reflectometry TRIME-TDR© time domain reflectometry with intelligible micro elements (IMKO GmbH TDR technology) USDA US Department of Agriculture VWC volumetric water content Latin symbols A arbitrary constant, introduced in equations (29)–(31) a radius of inner part of cylindrical model (m) ab selected reflection picks used in figures 6 and 7 C arbitrary constant, introduced in equations (26)–(28) c 3×108 m s-1 free space velocity of electromagnetic waves cd selected reflection picks used in figures 6 and 7 d depth interval (m), defined in equation (36) df, i depth of layer number f, i, respectively E Eρ, Eφ, Ez cylindrical electric field components (Vm-1) e* 2.92×10-2-1.10×10-3 εr + 1.29× 10-5 εr2, differentiated equation (3) F Farad (A s V-1) f linear frequency (s-1) H Henry (V s A-1) H Hρ, Hφ, Hz cylindrical magnetic field components (A m-1) h complex wave number (m-1), introduced in equation (15) Hz (Hz = s-1) frequency unit J J0, 1(x) Bessel function, first kind, order 0,1 k complex wave number (m-1), k2 defined in equation (13) ka, i complex wave number (m-1) for outer (a) and inner (i) part of cylindrical model kx real wave number for wave propagation in the x-direction (m-1) R reflection coefficient S Siemens (S = AV-1) t travel time interval (s), defined in equation (36) v phase velocity of electromagnetic wave (m s-1) va ω/kx phase velocity of wave propagating in the x-direction (m s-1), equation (40) vif estimated interval velocity (m s-1) used in equation (36) vph phase velocity of guided electromagnetic wave (m s-1) x independent variable in equation (16) Y Y0, 1(x) Bessel function, second kind, order 0,1 y dependent variable in equation (16) Z dielectric impedance (S-1) z z-coordinate of cylindrical coordinate system (m) Greek symbols α Re(h) (m-1) real part of h, defined in equation (17) β Im(h) (m-1) imaginary part of h, defined in equation (17) ε dielectric permittivity (F m-1) ε0 1/(μ0c2) = 8.854 × 10-12 F m-1 free space dielectric permittivity εa, i dielectric permittivity for outer (a) and inner (i) part of cylindrical model εr ε/ε0 relative dielectric permittivity Δεr estimated error in relative dielectric permittivity Δθ estimated error in volumetric water content (m3 m-3) Δt estimated error of travel time difference (s) Δv estimated error of phase velocity (m s-1) φ φ-coordinate of cylindrical coordinate system (rad) ϕ porosity (m3 m-3) γ x = γρ scale factor γ (m-1), γ2 introduced in equation (15) γa, i scale factor (m-1) for outer (a) and inner (i) part of cylindrical model ι index of MATLAB Bessel functions besselj and bessely λ wavelength (m) μ magnetic permeability (H m-1) μ0 4π × 10-7 H m-1 μr μ/μ0 relative magnetic permeability θC corrected value of θT (m3 m-3), defined in equation (37) θv volumetric water content (m3 m-3), defined in equation (3) θT volumetric water content (m3 m-3), measured by TRIME-TDR© ρ ρ-coordinate of cylindrical coordinate system (m) ρb dry bulk density (kg m-3) ρs solid particle density (kg m-3) σ electrical conductivity (S m-1) σa, i electrical conductivity for outer (a) and inner (i) part of cylindrical model index of Bessel function solution of equation (16) ω 2πf circular frequency (rad s-1) 1. Introduction Recent flood events in many parts of the world have put many question marks over the safety of river and sea dikes. This stresses the need to investigate flood-prone zones in order to come up with safe and comprehensive inundation assessment strategies to mitigate the astronomical cost of life and property, and the risk of environmental damage that are usually a consequence of dike failures. Concerning river dikes, geophysical methods are primarily used for the investigation of structural composition. In this connection, electrical resistivity tomography (ERT) is frequently applied, but also ground-penetrating radar (GPR) comes into the picture when the question of homogeneity arises (Barner et al2001). The guided wave sounding (GWS) survey is an invasive application of the GPR technique in a mode similar to that of the conventional time domain reflectometry (TDR). This GWS method records the volumetric water content (VWC) by making use of two-way reflection time data from the lower end of a metal rod which is lowered into the soil by constant increments through a vertical access tube (Igel et al2001, Schmalholz et al2004, Preko and Wilhelm 2006, Preko and Rings 2007). The waveguide principle has over the past few decades been employed by a number of authors, including Topp et al (1980, 1982), Ledieu et al (1986), Roth et al (1990), Scheuermann et al (2001), Becker et al (2002), Becker and Schlaeger (2005), Wraith et al (2005), Königer et al (2005), Schlaeger et al (2005) amongst many others, to investigate soil water content. Time domain reflectometry (TDR) has most often been used for this purpose due to its reliability and handling speed. The principle of time domain reflectometry with intelligent micro-elements (TRIME-TDR®) is similar to that of the conventional analogue TDR system. However, unlike the latter, which records the entire voltage trace and from this determines the two-way travel time of the reflected pulse, the former uses an algorithm which records the arrival times of specific voltage levels. TRIME-TDR® is a patented trademark of the company IMKO, Germany. This technique has been used by a number of investigators (Stacheder et al1994, 1997, Debruyckere et al1996, Beldring et al1999, Laurent et al2001, 2005, Evett et al2002) to measure soil water content. Evett et al (2002) and also Laurent et al (2005) have reported root mean square deviations (RMSD) of 0.01–0.07 m3 m-3 with TRIME-TDR® as compared with VWC values from gravimetric soil water sampling. Besides metal waveguides whose application in soil water content determination has been discussed, natural waveguides also occur in a number of cases. A low-velocity medium sandwiched between two media of relatively higher velocity is one example. This might occur where a wet soil is underlain by a dry sediment (e.g. Arcone et al2003), where there is permafrost at depth beneath unfrozen or wetter sediments (e.g. Arcone et al1998) or in the case where a soil layer is underlain by a low-porosity bedrock (e.g. Arcone et al2003, van der Kruk et al2006, Strobbia and Cassiani 2007). A guided wave transmission may also occur when a high-velocity medium is sandwiched between media of relatively low velocity, especially in cases where the lower medium is a strong reflector, e.g., that of a dry soil lying on top of wet clay or ice on top of water (e.g. Arcone et al2003). Sommerfeld (1899) investigated the guided wave propagation along an infinitely long cylindrical conductor of finite conductivity enclosed by an infinite homogeneous dielectric. Although Sommerfeld's guided wave, a non-radiating mode, has restricted practical application in modern times, it has provided possible solutions to Maxwell's equations and had an attenuation which was considered far lower than guided waves in coaxial cables (e.g. Goubau 1950). Guided electromagnetic waves are usually forced by conductors and/or dielectrics to transport energy in a particular direction, mainly perpendicular to the transverse plane. Guided wave sounding has a number of applications. For example, deep-seated hydrocarbon accumulations have been successfully detected through guided wave sounding from active electromagnetic sources (e.g. Johansen et al2005, Navarkhele et al2006). Other applications of guided waves include the detection of fractures and defects (Olsson et al1992, Yeh and Zoughi 1994, Sato and Miwa 2000, Hayashi 2005), location of underground tunnels (e.g. Deryck 1978, Olhoeft 1993) and interpretation of geologic features (e.g. Nickel et al1983, Dubois 1995). In order to assess the state condition inside embankment dams with respect to moisture distribution and leakages, temperature measurements are frequently used (Dornstädter 1997, Aufleger et al2005). In combination with other methods, this technique comes into use for the assessment of erosion processes inside embankments (Johansson 2007). So far there are only a few techniques used for the quantitative determination of water content inside embankments and dikes (Scheuermann et al2008, Rings et al2008). However, information about the hydraulic situation inside the construction is indispensable for a monitoring and forecast system. Generally, observation wells or pore pressure gauges are used to receive point-wise information about the hydraulic situation. However, more sophisticated methods are still being developed. This paper discusses the determination of soil water content in a dike model under controlled conditions using the application of electromagnetic guided waves with GWS and TRIME-TDR® techniques. The waveguide used here comprises a metal conductor embedded in a dielectric which is principally a wet soil. The aim of the experiment is to investigate whether GPR- and TDR-based invasive methods are able to quantitatively observe and correctly monitor spatial and temporal changes of water content in a dike structure in order to protect it. 2. Background to electromagnetic methods The velocity v(ω) of an electromagnetic wave in a host medium depends on its angular frequency ω, the speed of light in vacuum c, the relative dielectric permittivity εr, the relative magnetic permeability µr, and the electrical conductivity σ of the host medium. Mathematically, v(ω) is given by the expression 1 where c = 3 × 108 m s-1, εr is the ratio of the permittivity ε of the host medium to the permittivity of free space ε0 = 8.854 × 10-12 F m-1, μr is the magnetic permeability of the host medium µ relative to that of free space μ0 = 4π × 10-7 H m-1, is the material loss tangent, ω = 2πf and f is the linear frequency. In a low-loss medium (σ < 0.1 S m-1) and over a frequency range of 0.01–1 GHz, which is typical for GPR, the influence of σ is negligibly small with (Davis and Annan 1989). For non-magnetic materials at radar frequencies, μr = 1 applies (Daniels et al 1988). Under these conditions, the velocity v (ω) is practically independent of ω and equation (1) simplifies (e.g. Huisman et al2003) to 2 Thus, the velocity of electromagnetic waves in a low-loss medium is mainly controlled by the relative dielectric permittivity. The relative dielectric permittivity of water (in the MHz–GHz frequency range) is about 80 and that of air is 1 while that of most common geological materials lies in the range of 3–10 (e.g. Davis and Annan 1989, Daniels 1996). The relative permittivity of the soil is strongly controlled by the presence of water and the GPR signal is very sensitive to changes in the sediment/air/freshwater ratio (Baker 1991). The large permittivity contrasts within this frequency range permit the application of electromagnetic methods in the determination of the VWC. Petrophysical relationships, either developed for specific soils in the laboratory or with appropriate mixing rules (such as CRIM (Birchak et al1974, Shen et al1985), Hanai–Bruggeman–Sen (Hanai 1961, Shen et al1981) or Maxwell Garnett (Sihvola and Alanen 1991) formulas or empirical relationships (Topp et al1980)) can then be used to relate the permittivity to the soil water content. In the present study, the third-degree polynomial equation (equation (3)) by Topp et al (1980) was used to retrieve the volumetric soil water content θv from the relative dielectric permittivity εr: 3 Thus, θv was determined from the GPR technique from soil dielectric permittivity measurements in two main steps. The relative dielectric permittivity εr of the soil is determined from the propagation velocity v of the GPR signal (equation (2)). The VWC is then determined from a suitable calibration equation, and this paper uses that given in equation (3). Soil water content plays a dominant role in the propagation of electromagnetic waves. When a propagating electromagnetic wave incident normally in a medium encounters discontinuities in εr, μr and σ, part of the incident energy is reflected. The reflection strength depends on the magnitude of change in the electrical and magnetic properties. If we assume that there is a low-loss non-magnetic medium, the reflection coefficient R is expressed as (Brewster and Annan 1994) 4 where Z1, Z2, εr1, εr2 and v1, v2 are respectively the impedances, the relative dielectric permittivities and the velocities of soil layers 1 and 2 immediately above and below the discontinuity ⁠. R determines how sharp a boundary reflection might be. A sudden change in εr with depth gives a sharp reflection signal, whereas pulse widening results from a gradual change in εr (van Dam et al2002). equation (4) shows that the phase of the electromagnetic wave at a boundary remains unaltered when v2 > v1. There is, however, a phase shift of 180° when v2 < v1. In all cases, R has values between +1 and -1. Modelling exercises estimating R for a number of geological materials reveal that the GPR is sensitive to changes in the sediment/air/freshwater ratio (Neal 2004). A number of authors (van Overmeeren 1994, Endres et al2000, Doolittle et al2000, Preko et al2009) have successfully used GPR to detect the boundary layer between the vadose zone and the saturated zone. 2.1. Modal analysis of GPR guided wave propagation along a metal rod The electrical properties that control the propagation of the GPR signal through the soil are the electric conductivity σ, the dielectric permittivity ε = ε0εr and the magnetic permeability µ = µ0µr where εr is the relative dielectric permittivity and µr the relative magnetic permeability. In TDR and GPR applications, it is generally assumed that the guided waves propagate with the phase velocity of the free electromagnetic wave in the medium surrounding the wave guide. In order to explore the validity of this assumption, the propagation velocity is analysed using a cylindrical soil model with a metal rod of radius a in its centre (figure 1). Figure 1. Open in new tabDownload slide Cylindrical soil model with a metal rod of radius a at the centre surrounded by a thin air pocket. Figure 1. Open in new tabDownload slide Cylindrical soil model with a metal rod of radius a at the centre surrounded by a thin air pocket. Writing Maxwell's equations for the main transverse magnetic (TM) mode in the cylindrical coordinates ρ, φ, z with ∂/∂φ = 0 gives 5 6 7 Equations (5)–(7) are three equations in the three variables Eρ, Ez and Hφ: 8 9 Subtraction of equation (9) from equation (8) yields 10 11 12 and using (7), 13 This identity leads to the equation for Hφ, 14 Assuming Hφ ∼ eihz, 15 Substituting γ2 = k2 - h2 results in a Bessel differential equation in the form 16 with the solutions J1(x) and Y1(x) where x = γρ and ⁠. Writing 17 yields 18 with the guided wave phase velocity vph = ω/α and β > 0, assuming a damped wave, valid for both regions (Sommerfeld 1964). Then, disregarding a constant factor, 19 From (5), 20 Thus, 21 From (6), 22 with 23 Equation (22) reads 24 Thus, with (13), 25 For the two regions of interest, i.e. the inner region (0 < ρ < a) and the outer region (a < ρ < ∞) of the model, we obtain the solutions by using J0(γρ) and J1(γρ) for ρ < a with γ2i = ki2 - h2, where k2i = i ωμ0(σi - i ωεiε0) and Y0(γρ) and Y1(γρ) for ρ > a with γ2a = ka2 - h2, where k2a = i ωμ0(σa - i ωεaε0), respectively. Here and are the phase velocities of the free waves in the inner and outer regions. The complete set of solutions for ρ < a is 26 27 28 with and an arbitrary constant C. Similarly, for ρ > a the set of solutions is 29 30 31 with and an arbitrary constant A. For ρ = a, the tangential components Ez and Hφ must be continuous. Thus, 32 33 Dividing (32) by (33) gives 34 i.e. 35 Equation (35) must be solved for h. The solution is obtained with MATLAB software using Bessel function representations besselj(ι, x) and bessely(ι, x), with ι = 0, 1 and searching for the minimum of its absolute value with fminsearch. A corresponding equation for the propagation conditions of the TM guided surface wave along a cylindrical conductor embedded in a homogeneous lossless dielectric was published by Sommerfeld (1899), Harms (1907) and Goubau (1950), using approximative expressions for the Bessel functions in the solution of equation (35). Here, these considerations are expanded to the case of a dissipative, electrically conducting host medium. Realizing that ω/α is the phase velocity of the guided wave, is the phase velocity of the free wave in the outer region and is the velocity used in TDR applications, the expressions and define the relative phase velocity difference respectively between the guided and the free wave and between the guided wave and the wave velocity used in TDR applications. The expression 1/β defines the propagation width of the guided wave, i.e. the distance after which the amplitude has decreased to 1/e. Table 1 shows the values of Re(ka)/α - 1, and 1/β for different conductivities of the embedding dielectric σa with the assumption that σi = 107 S m-1 for the iron cylindrical conductor, a = 0.02 m for the radius of the conductor, f = 5 × 108 Hz for the radar frequency, εi = 1 F m-1, εa = 9 F m-1, k2i = εiω2/c2 + i ωμ0σi and k2a = εaω2/c2 + i ωμ0σa. The results show that the considered phase velocities remain practically identical for σa <1 S m-1, whereas the propagation width soon becomes very small for increasing σa. It is therefore permitted to determine the dielectric permittivity of the host medium as done with a TDR tool. There is, however, a strong dependence of the propagation width 1/β on the conductivity of the embedding medium. In the guided wave modelling example described in section 2.2, the conductivities are σi = 9 S m-1 and σa = 10-3 S m-1, while the other parameters remain unchanged. Then, as well as ⁠, yielding a larger reduction of the phase velocity of the guided wave than in the more realistic case of the preceding example for the same σa, and a smaller propagation width 1/β = 3.79 m. In this case, the TDR velocity is equal to the velocity of the free wave, whereas the guided wave velocity is significantly different from the free wave velocity than in the case considered in table 1. Table 1. Attenuation effects of the electromagnetic wave propagation for different conductivities of the embedding dielectric. σa(S m-1) . . . (m) . 1 × 10-3 -1.91 × 10-5 -2.61 × 10-5 15.9 3 × 10-2 -1.99 × 10-5 -2.11 × 10-3  0.531 5 × 10-2 -2.04 × 10-5 -4.93 × 10-3  0.320 0.1 -2.16 × 10-5 -1.87 × 10-2  0.162 0.5 -2.43 × 10-5 -2.14 × 10-1  0.0405 1 -2.98 × 10-5 -3.75 × 10-1  0.0255 σa(S m-1) . . . (m) . 1 × 10-3 -1.91 × 10-5 -2.61 × 10-5 15.9 3 × 10-2 -1.99 × 10-5 -2.11 × 10-3  0.531 5 × 10-2 -2.04 × 10-5 -4.93 × 10-3  0.320 0.1 -2.16 × 10-5 -1.87 × 10-2  0.162 0.5 -2.43 × 10-5 -2.14 × 10-1  0.0405 1 -2.98 × 10-5 -3.75 × 10-1  0.0255 Open in new tab Table 1. Attenuation effects of the electromagnetic wave propagation for different conductivities of the embedding dielectric. σa(S m-1) . . . (m) . 1 × 10-3 -1.91 × 10-5 -2.61 × 10-5 15.9 3 × 10-2 -1.99 × 10-5 -2.11 × 10-3  0.531 5 × 10-2 -2.04 × 10-5 -4.93 × 10-3  0.320 0.1 -2.16 × 10-5 -1.87 × 10-2  0.162 0.5 -2.43 × 10-5 -2.14 × 10-1  0.0405 1 -2.98 × 10-5 -3.75 × 10-1  0.0255 σa(S m-1) . . . (m) . 1 × 10-3 -1.91 × 10-5 -2.61 × 10-5 15.9 3 × 10-2 -1.99 × 10-5 -2.11 × 10-3  0.531 5 × 10-2 -2.04 × 10-5 -4.93 × 10-3  0.320 0.1 -2.16 × 10-5 -1.87 × 10-2  0.162 0.5 -2.43 × 10-5 -2.14 × 10-1  0.0405 1 -2.98 × 10-5 -3.75 × 10-1  0.0255 Open in new tab 2.2. Guided wave modelling Modelling and analysis of guided wave propagation through the soil was done with the help of the finite difference time domain (FDTD) modelling tool of Reflexw. A simplified model with an air layer above the soil surface with soil of constant relative dielectric permittivity εr was considered. The source was placed 0.02 m below the surface and about 0.08 m away from the metal rod. For the soil, the parameters chosen are µr = 1, σ = 10-3 S m-1 and εr = 9 which correspond to a signal propagation velocity ⁠. For the metal rod, µr = 1, σ = 9 S m-1 and εr = 1 were considered (figure 2). The selected conductivity value σ = 9 S m-1 for the metal was the highest conductivity possible with the software package Reflexw. The source Tx transmits an electromagnetic wave of central frequency 500 MHz which is polarized in the x-direction. Results of the modelling are shown in figure 3. Figure 3 displays 24 slides representing snapshots of the spherical waves from the emitter, their reflection at the lower end of the metal rod as well as their eventual travel to the receiver. The time arrangement of the snapshots as shown in figure 3 begins from the top and the order is from the left- to the right-hand side. Figure 2. Open in new tabDownload slide Conceptual model of the metal rod in soil used for GWS guided wave modelling. Figure 2. Open in new tabDownload slide Conceptual model of the metal rod in soil used for GWS guided wave modelling. Figure 3. Open in new tabDownload slide Snapshots in time intervals of 1.23 ns from FDTD modelling. Figure 3. Open in new tabDownload slide Snapshots in time intervals of 1.23 ns from FDTD modelling. Transmitted free spherical waves from the source get coupled to the metal rod and travel along it. Spherical guided waves reach the lower end of the metal rod after a time of 14.73 ns and the reflected waves are recorded after 29.46 ns (figure 3). By knowing the depth to the lower end of the metal rod and the corresponding reflection times recorded by the receiver, the average velocities of the guided wave for various depths of the metal rod can be estimated. From these, interval velocities for each 0.025 m change in depth can be deduced. From these, the corresponding interval relative permittivities εr and finally the interval VWCs are determined. The ≈1 mm thick plastic sheathing and the corresponding thin air column between the metal rod and the soil were not overseen in the modelling. The sheathing is very thin vis-à-vis the much larger wavelengths (100 mm < λ < 300 mm) of the GPR signals employed, and thus has insignificant influence on the reflections from the metal rod. The inclusion of the air column on the other hand would have made the modelling more complicated, making the snapshots hardly recognizable. We excluded this for the sake of clarity. 3. Materials and methods 3.1. Site description The experiments were performed on a large-scale dike model (figure 4) built in the Theodor Rehbock Laboratory at the Institute for Water and River Basin Management, Karlsruhe Institute of Technology, Germany. The height of the model was 1.4 m and both the upstream and downstream sides of the model were inclined at 1:2.5. With a crest width of 1 m, the total width of the dike was 8 m and the length was approximately 2.3 m. To avoid the water bypassing along the boundary of the model, the external wall was inclined at a low angle of 2°. On the upstream side of the dike, there was a basin with an adjustable water level. Further information about the construction of the model and its instrumentation can be found in Wörsching et al (2006). Figure 4. Open in new tabDownload slide Cross-section of the dike model showing common sampling point G for GWS and TRIME-TDR® measurements, and apparent wetting front from flooding. Figure 4. Open in new tabDownload slide Cross-section of the dike model showing common sampling point G for GWS and TRIME-TDR® measurements, and apparent wetting front from flooding. The model was constructed with soil of the texture class loamy sand (USDA 1975) in a series of phases, in which a total of 13 soil layers of the same material but of varying thicknesses were used. These layers were compacted individually using standard devices with the aim of acquiring a density, which is comparable to densities prevailing in real dikes. Table 2 shows the soil layers with the used thicknesses, porosities, the achieved dry densities and their depth from the dike crest. The porosity ϕ was calculated from the dry bulk density ρb and the normal solid particle density ρs (= 2.65 g cm-3) by ϕ = 1 - ρb/ρs. Table 2. Construction of the dike model with loamy soil layers of varying thickness and density. Soil layer . Soil layer thickness (m) . Depth from crest (m) . Dry density (g cm-3) . Porosity (%) . 1 (first layer in the crest) 0.115 0.115 1.61 ± 0.05 39.25 ± 0.98 2 0.110 0.225 1.61 ± 0.05 39.25 ± 0.98 3 0.105 0.330 1.67 ± 0.06 36.98 ± 0.98 4 0.110 0.440 1.68 ± 0.04 36.60 ± 0.98 5 0.110 0.550 1.66 ± 0.06 37.36 ± 0.98 6 0.120 0.670 1.69 ± 0.02 36.23 ± 0.99 7 0.115 0.785 1.72 ± 0.02 35.09 ± 0.99 8 0.110 0.895 1.68 ± 0.03 36.60 ± 0.99 9 0.100 0.995 1.74 ± 0.12 34.34 ± 0.95 10 0.085 1.080 1.73 ± 0.03 34.71 ± 0.99 11 0.120 1.200 1.73 ± 0.08 34.71 ± 0.97 12 0.085 1.285 1.69 ± 0.09 36.23 ± 0.97 13 (last layer on the basis) 0.115 1.400 1.64 ± 0.05 38.11 ± 0.98 Soil layer . Soil layer thickness (m) . Depth from crest (m) . Dry density (g cm-3) . Porosity (%) . 1 (first layer in the crest) 0.115 0.115 1.61 ± 0.05 39.25 ± 0.98 2 0.110 0.225 1.61 ± 0.05 39.25 ± 0.98 3 0.105 0.330 1.67 ± 0.06 36.98 ± 0.98 4 0.110 0.440 1.68 ± 0.04 36.60 ± 0.98 5 0.110 0.550 1.66 ± 0.06 37.36 ± 0.98 6 0.120 0.670 1.69 ± 0.02 36.23 ± 0.99 7 0.115 0.785 1.72 ± 0.02 35.09 ± 0.99 8 0.110 0.895 1.68 ± 0.03 36.60 ± 0.99 9 0.100 0.995 1.74 ± 0.12 34.34 ± 0.95 10 0.085 1.080 1.73 ± 0.03 34.71 ± 0.99 11 0.120 1.200 1.73 ± 0.08 34.71 ± 0.97 12 0.085 1.285 1.69 ± 0.09 36.23 ± 0.97 13 (last layer on the basis) 0.115 1.400 1.64 ± 0.05 38.11 ± 0.98 Open in new tab Table 2. Construction of the dike model with loamy soil layers of varying thickness and density. Soil layer . Soil layer thickness (m) . Depth from crest (m) . Dry density (g cm-3) . Porosity (%) . 1 (first layer in the crest) 0.115 0.115 1.61 ± 0.05 39.25 ± 0.98 2 0.110 0.225 1.61 ± 0.05 39.25 ± 0.98 3 0.105 0.330 1.67 ± 0.06 36.98 ± 0.98 4 0.110 0.440 1.68 ± 0.04 36.60 ± 0.98 5 0.110 0.550 1.66 ± 0.06 37.36 ± 0.98 6 0.120 0.670 1.69 ± 0.02 36.23 ± 0.99 7 0.115 0.785 1.72 ± 0.02 35.09 ± 0.99 8 0.110 0.895 1.68 ± 0.03 36.60 ± 0.99 9 0.100 0.995 1.74 ± 0.12 34.34 ± 0.95 10 0.085 1.080 1.73 ± 0.03 34.71 ± 0.99 11 0.120 1.200 1.73 ± 0.08 34.71 ± 0.97 12 0.085 1.285 1.69 ± 0.09 36.23 ± 0.97 13 (last layer on the basis) 0.115 1.400 1.64 ± 0.05 38.11 ± 0.98 Soil layer . Soil layer thickness (m) . Depth from crest (m) . Dry density (g cm-3) . Porosity (%) . 1 (first layer in the crest) 0.115 0.115 1.61 ± 0.05 39.25 ± 0.98 2 0.110 0.225 1.61 ± 0.05 39.25 ± 0.98 3 0.105 0.330 1.67 ± 0.06 36.98 ± 0.98 4 0.110 0.440 1.68 ± 0.04 36.60 ± 0.98 5 0.110 0.550 1.66 ± 0.06 37.36 ± 0.98 6 0.120 0.670 1.69 ± 0.02 36.23 ± 0.99 7 0.115 0.785 1.72 ± 0.02 35.09 ± 0.99 8 0.110 0.895 1.68 ± 0.03 36.60 ± 0.99 9 0.100 0.995 1.74 ± 0.12 34.34 ± 0.95 10 0.085 1.080 1.73 ± 0.03 34.71 ± 0.99 11 0.120 1.200 1.73 ± 0.08 34.71 ± 0.97 12 0.085 1.285 1.69 ± 0.09 36.23 ± 0.97 13 (last layer on the basis) 0.115 1.400 1.64 ± 0.05 38.11 ± 0.98 Open in new tab 3.2. Flooding experiments Flooding experiments were conducted on the crest of the dike. From its adjustable basin, the dike was flooded to six different flood levels of 0.30, 0.60, 0.80, 1.00, 1.20 and 1.25 m as measured from its baseline as reference. After each flooding phase, the dike was rested for 72 h, after which time, according to short-term measurements by Wörsching et al (2006) using TDR probes distributed in the dike, we expected it to have approximately attained hydrostatic equilibrium. Data were then taken with the GWS technique using the 500 MHz antenna. Colocated measurements were taken using the TRIME-TDR® technique. All observations were made from the crest of the model at the point G (figure 4). 3.2.1. GWS measurements The SIR-20 GPR equipment manufactured by Geophysical Survey Systems, Inc. (GSSI) was used for the GWS measurements. These measurements were taken with the help of a vertical access tube pre-installed on the dike model. This served as a passage for a metal rod of about 1.4 m in length and with an external diameter of 38 mm graduated at 2.5 cm intervals. The lower end of this rod served as a reflector for the transmitted GPR signal. The 500 MHz monostatic antenna was then positioned close (≈1 cm) to the access tube with the metal rod midway between the receiver and transmitter. This position was maintained throughout the experiment. The metal rod was then lowered into the access tube at intervals of 2.5 cm. Guided waves travelling along the rod were reflected from the lower end of the rod to the receiving antenna by reason of the impedance contrast between this end and the medium below it. When the rod was lowered down from the depth di to the depth df, the interval velocity vi, f was calculated from the difference between the guided wave travel times ti and tf, respectively, taking 36 Interval velocities calculated with equation (36) were very sensitive to the position and times of the reflection picks. In order to reduce processing errors in vi, f (resulting from the small distance of 2.5 cm considered), running harmonic mean values of three interval velocities were calculated. For example, a harmonic mean velocity v (10, 15) calculated over depths between 10 and 15 cm was assigned to a depth of 12.5 cm. The harmonic mean velocity was then related to the permittivity of the soil with equation (2) and subsequently the VWC was determined with equation (3). 3.2.2. TRIME-TDR® measurements with TRIME T3 probe TRIME-TDR® measurements were carried out with the TRIME-T3 tube access probe, which is a hand-held battery-operated commercial TDR device made by IMKO. It comprises a probe about 18 cm in length fitted with a high-frequency cable about 2.5 m long. The probe was lowered down the pre-installed access tube at intervals of 10 cm. The device produced a high-frequency pulse (up to 1 GHz), which generated an electromagnetic guided wave along the probe. It then determined the velocity of the propagating guided wave from the transit time of the reflected wave. The VWC could easily be read on the display panel. The TRIME-T3 access tube probe uses a standard calibration to determine the VWC. Hence, the probe had to be calibrated to the specific material properties of the dike model. This was done against VWC values from gravimetric soil water sampling by using the dry bulk densities of the soil samples. Subsequently, the measured TRIME-T3 water content data θT (m3 m-3) were corrected with the third-order polynomial equation (Preko et al2009) 37 where θC is the corrected value. The use of this calibration function eliminated the need to apply equation (3). 4. Data processing 4.1. Processing of GWS data GPR data were processed with the software Reflexw (Sandmeier 2011). Each observation from the end of the metal rod at a given depth comprised a minimum of 120 traces. A complete survey from the crest to the base of the dike for a flood level comprised 53 observation points. Traces from each observation point were first stacked into a single trace and stored as a file. Subsequently, all 53 files were merged into a single radargram. We corrected for static errors and performed a background removal and f–k filtering (Yilmaz 1987) to remove steeply dipping diffraction hyperbolae tails (Lunt et al2005) arising from the 2.5 cm-interval graduation holes bored in the metal rod. Zero-crossing distance–time picks from the radargram (figures 6 and 7) were loaded in an ASCII-format, and interval velocities (over every 0.025 m) and subsequently harmonic velocities (of every 3 interval velocities) were calculated. Equation (2) was used to calculate the corresponding relative dielectric permittivities and the Topp et al (1980) calibration equation was eventually used to determine the VWC. 4.1.1. Processing of GWS data with the f–k filter Reflections from the equipment components and the surroundings as well as diffractions from the graduation holes interfered with reflections from the lower end of the metal rod reducing signal quality and introducing errors in the arrival times of the reflections. These spurious reflections and diffractions had to be removed to improve the signal-to-noise ratio. The signal acquired by the GPR in the x-direction is a two-dimensional (2D) signal in time t and space x which can be represented as f(t, x). In the time-space domain, it is relatively difficult to separate true reflections (from the lower end of the metal rod) from noise. Data were hence filtered from noise with the help of the Reflexw tool f–k filter. The f–k filter performs a 2D Fourier transformation of f(t, x) from the t–x (time–space) domain into the f–k (frequency–wavenumber) domain. A 2D Fourier transformation and inverse transformation of the raw data in the t–x domain f (t, x) are defined by 38 39 If va is the phase velocity of the wave travelling in the x-direction, then the wave number kx and angular frequency ω are related by 40 A line of constant phase velocity in the t–x domain transforms to a line of constant slope in the f–k domain. A dipping line in the t–x domain transforms into a line through the origin in the f–k domain, the orientation of the latter being perpendicular to the former. Horizontal lines in the t–x domain will correspondingly map to vertical lines in the f–k domain and dipping features that overlap in the t–x domain can be identified by their dips in the f–k domain and thus separated. The f–k filter is hence effective in separating linear coherent noise from the GPR signal. An apparent velocity filter range of 0.05–0.15 m ns-1, which is a reasonable propagation velocity range for an electromagnetic wave in a geological structure, was chosen to filter out spurious signals from the f–k spectrum. On the f–k spectrum, this velocity range defines a fan (figure 5). Figure 5. Open in new tabDownload slide Diagram of an f–k spectrum F(f, kx). Va1 ( = 0.15 m ns-1) and Va2 ( = 0.05 m ns-1) define the range of the apparent velocity filter. Signals outside this fan are suppressed, while signals with velocities between 0.15 and 0.05 m ns-1 will be retained. Figure 5. Open in new tabDownload slide Diagram of an f–k spectrum F(f, kx). Va1 ( = 0.15 m ns-1) and Va2 ( = 0.05 m ns-1) define the range of the apparent velocity filter. Signals outside this fan are suppressed, while signals with velocities between 0.15 and 0.05 m ns-1 will be retained. After this operation, the data were transformed back to the t–x domain (equation (39)). Through this process, spurious signals were suppressed from the original data and reflections from the lower part of the metal rod were thus enhanced (figure 7). Figures 6 and 7 show the difference in data quality between data processed without and with an f–k filter. Without the application of the f–k filter, reflections from the lower end of the metal rod were of poor quality and contained spurious reflections from other sources, which resulted in spikes in the interval velocities with resultant errors in the calculated interval VWC. For example, in figure 6 the interval velocity between picks a and b resulted in a negative value, while that between picks c and d resulted in a value far greater than the velocity of electromagnetic waves in air, i.e. > 0.3 m ns-1. Figure 6. Open in new tabDownload slide Data processed without f–k filter; ab and cd are pairs of arbitrary selected zero-crossing distance–time reflection picks depicting stark irregularities in the calculated interval velocities. Figure 6. Open in new tabDownload slide Data processed without f–k filter; ab and cd are pairs of arbitrary selected zero-crossing distance–time reflection picks depicting stark irregularities in the calculated interval velocities. Figure 7. Open in new tabDownload slide Data processed with f–k filter. Stark irregularities in the calculated interval velocities from picks ab and cd are suppressed. Figure 7. Open in new tabDownload slide Data processed with f–k filter. Stark irregularities in the calculated interval velocities from picks ab and cd are suppressed. However, with the application of the f–k filter, the zero-crossing picks indicated by a hatched line in figure 7 were much improved and stark irregularities in the interval velocities caused by spurious reflections were relatively suppressed. This time interval velocity between picks a and b was found to be positive and that between c and d fell reasonably well within the propagation velocities of electromagnetic waves in porous media. 4.2. Discussion of errors For the GWS data, several exercises for selecting the travel times of the reflected phase from the radargram revealed a maximum deviation of about 5%. From equation (36), we obtain 41 and 42 which with equation (3) finally leads to 43 where εr is 6.25, |Δt/t| is 5% and e* is 2.92 × 10-2-1.10 × 10-3 εr + 1.29 × 10-5 εr2 ≈ 0.0228. A dry soil with εr = 2.5 and a highly moist soil with εr = 25 would thus yield estimated errors of 0.007 and 0.023 m3 m-3, respectively, in the measured VWC. A comparison with TRIME-TDR® measurements on a natural-scale dike model built of sand has shown VWC differences of about ±0.02 m3 m-3 (cf Scheuermann et al2009). The accuracy of the TRIME T3 Tube Access Probe used in the measurements depends on its contact with the soil. For example, at the assumed water content of 0.15 m3 m-3, an air gap of 1 mm around the probe length could result in an error of about 0.01–0.02 m3 m-3. An error of 0.05 m3 m-3 is possible at a water content value of 0.25 m3 m-3 (IMKO GmbH 2001). The accuracy is improved through good capacitive coupling between the sensor and the access tube. In order to reduce the error of the TRIME-TDR® measurements in the presented study, multiple measurements were conducted and a mean value was calculated. 5. Results Figures 8(a)–(g) show GWS- and TRIME-TDR®-derived soil water content profiles with depth in the dike model. The 13 soil layers used for the construction of the model are indicated by vertical hatched lines and marked from 1 to 13. TRIME-TDR® and GWS show almost identical trends; however, GWS shows a much higher depth resolution due to the relatively shorter depths at which the latter retrieved VWC information. The GWS method calculated the interval soil water content over an average distance range of 2.5 cm, while the TRIME-TDR® determined the soil water content over an average distance corresponding to the length of its sensor (i.e. 18 cm). This gives GWS a much higher depth resolution than TRIME-TDR®. Figure 8. Open in new tabDownload slide (a)–(g) VWC distribution in the dike model (a) before flooding and at (b) 0.3, (c) 0.6, (d) 0.8, (e) 1.0, (f) 1.2 and (g) 1.25 m flood level. The horizontal lines mark soil layers 1–13. Figure 8. Open in new tabDownload slide (a)–(g) VWC distribution in the dike model (a) before flooding and at (b) 0.3, (c) 0.6, (d) 0.8, (e) 1.0, (f) 1.2 and (g) 1.25 m flood level. The horizontal lines mark soil layers 1–13. In addition, GWS is seen to show a more sporadic VWC distribution as compared to TRIME. This is because the interval VWC was determined from the average interval velocity over a relatively small distance of 2.5 cm, a distance which corresponds to a displacement of the lower end of the metal rod. Over such a small displacement, any error in picking the travel time created peaks in the interval VWC. The use of the running harmonic mean velocities (calculated from three interval velocities) helped to smooth the GWS-derived VWC data and remove these peaks. This process was not required for TRIME-TDR®. Comparison of GWS with TRIME-TDR® shows a RMSD of 0.018 m3 m-3. The depths for the different flood levels 0, 30, 60, 80, 100, 120 and 125 cm from the crest of the dike were 1.4, 1.1, 0.8, 0.6, 0.4, 0.2 and 0.15 m, respectively. The water table at which the measurements were conducted is shaded in figures 8(b)–(g). In figures 8(a)–(c), there is hardly any remarkable change in the soil water content profile for flood levels 0 and 0.60 m besides a marginal change in the VWC distribution in figure 8(c). Apart from a minimum change in the soil water content in the 12th soil layer, the distribution trend between flood levels 0 and 60 cm hardly changes. This is due to the fact that the point of observation was located approximately at the midpoint of the crest. From this observation point, the loci of the rising wetting front changed slowly with depth (figure 4). The wetting front moved gradually upwards with flooding. At lower flood levels of 30 and 60 cm, this mobile front had only reached the 12th and 13th soil layers as seen from the centre line of the crest. It was observed that as the level of flooding increased, the dike had ample time to store water, its pores became more filled from previous flooding and with the wetting front gradually rising to the upper soil layers (figures 8(d)–(g)), the flood waters easily infiltrated the opposite plane. The different soil layers display variation in their water storage capacities. Three main zones can be identified in figures 8(a)–(g). These are distinguished as follows. An apparently unsaturated zone by a continuous increase in VWC with depth: this is indicated by the soil layers 1–6 (figures 8(a)–(c)). The soil water content rises at higher flood levels reaching a maximum at depths between 0.6 and 0.7 m in the sixth and seventh soil layers. An apparently saturated zone: this is indicated by the soil between the 8th and 12th soil layers where the VWC value reaches an approximately constant value of about 0.22 m3 m-3 between depths of 0.8 and 1.4 m (figures 8(d)–(g)). A zone of sharp decrease in VWC with depth: this is indicated by the soil layer 7 (figures 8(f) and (g)). As the wetting front rises gradually with increasing flooding, the hydraulic conductivity rises accordingly with the VWC registering a maximum value of 0.32 m3 m-3. The porosities of the soil layers are a little above 34% indicating partial saturation. The zone of apparent saturation has an average soil layer porosity of 35% against a virtually constant VWC value of 0.22 m3 m-3. This situation is likely triggered by a lateral flow scenario depicted in the soil layers 6 and 7 in figures 8(f) and (g). The almost complete saturation in layers 6 and 7 obviously impedes an increase of saturation in the layers below. The last zone of interest is the VWC distribution anomaly occurring at the border zone between the sixth and seventh soil layers (figures 8(f) and (g)) which exhibits a sharp decrease in VWC with depth. The dike was constructed with homogeneous loamy sand with minor differences in the soil layer densities as a result of compaction. The transition zone between soil layers 6 and 7 is seen to record the highest soil water content compared to the layers below it. This region is highlighted in figure 8(g). As the wetting front approaches from the side (see figure 4), local fronts may build up and propagate e.g. causing some kind of interflow phenomena on the higher density layer 7 which may be initiated as soon as the flood level in the reservoir rises above this layer boundary. Such an occurrence takes place especially when a fine-grained material with greater porosity overlies a coarse-grained material in an unsaturated condition. For such a case, more water is drawn from the coarse-grained material into the fine-grained material through the effect of capillarity. However, close examination of the VWC distribution reveals a sharp increase followed by an abrupt decrease. This anomaly occurs at the boundary between layers 6 and 7. This is likely due to the break in cohesion between the soil particles of the two adjacent soil layers giving way to lateral water flow along the boundary. This occurrence might have resulted from local grain rearrangement from the hydraulic load due to the flooding. The flood water accumulates along this infiltration path and easily reaches the other plain. It is not observed for flood levels below 1.2 m till the rising wetting front (figure 4) reaches the soil layers 6 and 7. Such dike breaches occur in dikes of granular soils, in particular, soils without cohesion (Mohamed et al2002, Zhu 2006). A breach of this nature weakens the dike model and when not earlier detected and checked leads to its eventual collapse. The breaching of dikes and other levee structures are often accompanied by huge loss of life as well as property. A solution to a breach of this kind might be to construct the dike from more cohesive material, e.g. clay. However, such a construction would limit the application of GPR and TRIME-TDR® due to the high wave attenuation of these electromagnetic techniques in clay. 6. Summary and conclusions We have shown that GWS and TRIME-TDR® can be credibly used to measure water infiltration and material inhomogeneities through dike bodies by measurements based on dielectric permittivity under simulated flooding events. The two electromagnetic techniques used in this paper were able to detect a loose contact in the soil layers used to construct the dike model at a depth of about 0.6 m. Thus, these techniques could be effectively applied to detect material inhomogeneities in a levee structure and may help prevent its potential collapse and possible disaster. The dike model was carefully constructed with soil layers which were compacted together using standard devices to acquire appropriate densities prevalent in real dikes. Compared with most commonly used monitoring techniques for embankment dams and other water-retaining levee structures, the ability of GWS and TRIME-TDR® to map out material inhomogeneities and consequent internal state of the dike means that these methods can be reliably used to map out material inhomogeneities in real dikes. Both GWS and TRIME-TDR® methods showed comparable trends in the VWC distribution with a RMSD of 0.018 m3 m-3. In the dry range, VWCs measured with the TRIME-TDR® sensor are systematically ∼0.02 m3 m-3 lower than the GWS estimates. This observation is likely due to the effect of the air column between the soil and the metal rod. The systematic difference registered by the two methods is perhaps less pronounced in the wet than the dry range. The advantage of TRIME-TDR® is that it is faster to use than GWS as the VWC value was readily read from the display panel of its measuring equipment. However, the latter has a much higher depth resolution. Hence, the chance of detecting small-scale features in soil water content mapping with GWS is higher than with TRIME-TDR® due to its higher sampling density. The analysis of GWS guided waves along the metal cylinder presents formulae for the calculation of the attenuation constants (table 1) and thus gives the investigator the possibility to assess the extent of attenuation and damping of the electromagnetic wave in soil. Unlike the GWS, the TRIME-TDR® had to be first calibrated to match the specific material properties of the dike model. Another advantage of GWS is its potential use in existing boreholes of appropriate diameter within the 10–20 m depth range. TRIME-TDR needs the installation of a special tube with a specified diameter. For both methods, the contact between the access tube and the soil must be very good in order to avoid measuring too small VWC values. In estimating the interval velocities, the f–k filter was needed to suppress noise and enhance the signal quality of GWS data due to the small depth interval of 2.5 cm over which these velocities were calculated. A modelling exercise with the finite-difference time domain helped to explain the GWS application. GWS has the following limitations. The modelling software Reflexw limits the conductivity of the metal cylinder to 9 S m-1. Metal conductors, in reality, have much higher conductivities. This puts the brakes on the modelled propagation width (1/β) of the guided wave signal. As a GPR-based technique, its application becomes limited in highly conductive soils, e.g. wet clays. GWS can be applied to real dikes of larger dimensions than the model. In such a case, however, pre-installed access tubes from the crest down to the base of the structure disturb the homogeneity of the medium. Besides, the model assumption of a constant dielectric permittivity εr might be too restrictive for real dikes. Future water infiltration measurements on the dike model should include the use of standard TDR probes, temperature measurements, matrix potentials or water level measurements from a piezometer or resistivity measurements This would help substantiate any anomalous observation indicated by GWS and TRIME-TDR®. Acknowledgments We are very grateful to K-J Sandmeier and Volker Mayer (Sandmeier Scientific Software, Karlsruhe, Germany) for providing us with additional tools for processing field data. We acknowledge the invaluable assistance given to us by Boris Lehrmann and Werner Helm (Department of Water Resources Management and Rural Engineering, Karlsruhe Institute of Technology, Germany), and the permission to carry out our lengthy experiments on their dike models. Finally, we thank our anonymous referees for the painstaking review of the manuscript and for the many useful suggestions. 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TI - Detection of water content inhomogeneities in a dike model using invasive GPR guided wave sounding and TRIME-TDR® technique
JF - Journal of Geophysics and Engineering
DO - 10.1088/1742-2132/9/3/312
DA - 2012-06-01
UR - https://www.deepdyve.com/lp/oxford-university-press/detection-of-water-content-inhomogeneities-in-a-dike-model-using-j1SGWYmMdB
SP - 312
VL - 9
IS - 3
DP - DeepDyve
ER -