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Water content evaluation in unsaturated soil using GPR signal analysis in the frequency domain
Journal of Applied Geophysics 71 (2010) 26–35
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Journal of Applied Geophysics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j a p p g e o
Water content evaluation in unsaturated soil using GPR signal analysis in the frequency domain Andrea Benedetto Department of Sciences, Civil Engineering, University Roma Tre, Rome, Italy
a r t i c l e
i n f o
Article history: Received 10 March 2009 Accepted 4 March 2010 Keywords: Ground penetrating radar Moisture content Frequency analysis Rayleigh scattering Road pavement Clay Polarization
a b s t r a c t The evaluation of the water content of unsaturated soil is important for many applications, such as environmental engineering, agriculture and soil science. This study is applied to pavement engineering, but the proposed approach can be utilized in other applications as well. There are various techniques currently available which measure the soil moisture content and some of these techniques are non-intrusive. Herein, a new methodology is proposed that avoids several disadvantages of existing techniques. In this study, ground-coupled Ground Penetrating Radar (GPR) techniques are used to non-destructively monitor the volumetric water content. The signal is processed in the frequency domain; this method is based on Rayleigh scattering according to the Fresnel theory. The scattering produces a non-linear frequency modulation of the electromagnetic signal, where the modulation is a function of the water content. To test the proposed method, five different types of soil were wetted in laboratory under controlled conditions and the samples were analyzed using GPR. The GPR data were processed in the frequency domain, demonstrating a correlation between the shift of the frequency spectrum of the radar signal and the moisture content. The techniques also demonstrate the potential for detecting clay content in soils. This frequency domain approach gives an innovative method that can be applied for an accurate and non-invasive estimation of the water content of soils – particularly, in sub-asphalt aggregate layers – and assessing the bearing capacity and efficacy of the pavement drainage layers. The main benefit of this method is that no preventive calibration is needed. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Measuring the water content of soils is important for applications such as flood defense, agriculture, determining the geomorphologic stability of slopes, construction, and finding the bearing capacity of structural foundations. Moreover, the variation of the water content in space cannot be neglected for most of these applications. In fact, it has been demonstrated that different spatial distributions of the moisture content produce different effects. Some examples include run-off generation for basins with spatially varying saturation zones (Weihermüller et al., 2007), foundations of structures with variable moisture content (Diefenderfer et al., 2005) and non-homogeneous moisture distributions in the soil beneath road pavement (Benedetto et al., 2004; Grote et al., 2002, 2003; Maser, 1996; Saarenketo and Scullion, 2000). It is well known that the conditions of the pavement influence the safety of driving (Tighe et al., 2000). A significant percentage of accidents are caused by surface deformations, cracks and potholes that induce an unexpected acceleration on a vehicle and reduce the effective friction between the tires and the pavement. Such road
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damage is often caused by a decrease in the bearing capacity of the sub-asphalt soils (Diefenderfer et al., 2005; Grote et al., 2005). The bearing capacity is defined as the ability to carry a defined number of repetitions of a set of loads. The bearing capacity of the sub-asphalt soil is greatly affected by the soil's water content and soil suction, and it can be measured indirectly using a falling weight deflectometer. It has been widely demonstrated that an increase in water content in the sub-asphalt layer can decrease the soil stiffness and cause pavement deflection. This deflection can damage the surface in different ways, depending on the temperature, the asphalt characteristics, the age, the repetitions and the loads weight. However, there is one problem which affects pavements universally: the infiltration of water through the pavement brings plastic material into the subgrade or the sub-base of the pavement. Furthermore, estimates of the water content in sub-asphalt soils are necessary to determine the performance of pavement drainage systems (Al-Qadi et al., 2004). Only a few techniques have been used to monitor the water content in sub-asphalt soils in the past two decades. The sub-asphalt water content is often estimated via gravimetric sampling, time domain reflectometry, neutron probe logging and measuring the capacitance or resistance of devices. These methods are accurate, but they also have many disadvantages: it is often necessary to constrain traffic; they are expensive and projects can be time-consuming; the
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
methods are invasive and assessments of the moisture content in a large area, such as several kilometers of road, are often unreliable. Many authors measure the moisture content using GPR, which is a non-destructive technology. With GPR it is possible to collect data quickly on the road and obtain the volumetric water content of soil in unsaturated porous media, such as sub-asphalt soil (Benedetto and Pensa, 2007). This utility of GPR has been demonstrated for numerous applications in the time domain, based on an evaluation of the dielectric permittivity (Davis and Annan, 1989). Assuming that the porous media is a mixture of three phases (solid, water and air), and assuming that the dielectric constant of water is significantly different than that of solid materials and air, it is expected that the dielectric constant of the mixture is dependent on the water content. The relationship between the dielectric constant of a soil and its volumetric water content has been extensively studied in the past. Various empirical correlations have been proposed, like the commonly used theory suggested by Topp, which is supposedly valid for any type of soil (Topp, et al., 1980). Reviews of the various theoretical models are available (Friedman, 1998; Grote et al., 2002, 2003; Hubbard et al., 2002; Huisman et al., 2003; Robinson et al., 2003; Serbin and Or, 2003). Another theoretical approach that relates the soil water content to the soil permittivity is based on dielectric mixing. It uses the volume fractions and the dielectric permittivity of each soil constituent to derive an approximate correlation, using a self-consistent approximation that represents the medium with the multi-indicator mode (Fiori et al., 2005). These aforementioned correlations and models used to evaluate the water content in a porous medium are based on estimations of the dielectric permittivity. The value of the permittivity is generally extracted from GPR measurements that compute the delay time of reflections once a value for the velocity propagation of the wave in the medium is determined (Benedetto and Benedetto, 2002; Benedetto, 2004). In some cases, the dielectric permittivity is estimated from the amplitudes of the transmitted and reflected signals (Al-Qadi et al., 2004). In any case, these methods require calibration steps because the signal velocity of propagation cannot be assumed a priori; in fact, it depends on the characteristics and conditions of the materials. A more efficient and self-consistent approach is based on the GPR processing in the frequency domain. Werts et al. (2001), basing on the Debye model and using time domain reflectometer in a band between 3 and 316 MHz, observed that the dielectric permittivity is influenced by the frequency. Lambot et al. (2004); 2006) considered the dependence of the imaginary part of the dielectric permittivity from the frequency to investigate the subsurface electric characteristics. Relating to the water content estimation, they found very consistent results using a local linear approximation in the 1–2 GHz band. In particular they modeled the GPR response in frequency and time domain using Green's function. The relative dielectric permittivity was inversely estimated as a function of nine different water content levels. These estimated values fit very well both TDR measurements and soil-specific empirical model predictions (similar to Topp's equation). Oden et al. (2008) have calibrated and validated a new model for measuring the electrical properties of soil. The algorithm estimates the shallow soil properties using the early-time arrivals, i.e. the arrivals recorded before subsurface reflections arrive (Pettinelli et al., 2007). The amplitude and shape of the early-time arrivals change with soil permittivity, conductivity, and antenna standoff. In this case the main innovation is using a non-linear inversion algorithm in the frequency domain. Basically this algorithm compares the GPR response to a catalog of Finite-difference time-domain (FDTD) simulations of early-time waveforms to estimate soils parameters. This paper aims to present an innovative, high-performance method that does not need calibration to estimate the moisture content of a porous medium. This method, unlike the others, does not estimate the dielectric permittivity of unsaturated soil but directly the water content by frequency analysis. The starting point is to assume
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that the water droplets in the medium scatter the electromagnetic (EM) waves (Drude, 1902), thereby shifting the frequency of the waves (Bekefi and Barrett, 1987); an example of this phenomenon is when atmospheric particles scatter sunlight, shifting the color of the sky from blue to red during sunset (Bohren and Huffman, 1983). Such an approach focuses only on the water content, which is independent from the solid and air phases. One new aspect of the proposed method is that the volume fractions of the three phases in the medium are not accounted for. A shift in the frequency distribution of the reflected signals has been observed in the past, but the cause of the shift was not identified or investigated. In 1983 Narayana and Ophir (Narayana and Ophir, 1983) analyzed ultrasonic waves reflected by normal and fatty livers; they noticed that different frequencies were attenuated in different media. In particular, they suggested that the observed nonlinear behaviour of the reflected waves in fatty livers was due to Rayleigh scattering: the Rayleigh scattering was due to the fat globules, which exhibit fourth-order frequency dependence. More recently, Ho et al. (2004) observed a frequency shift while detecting different shapes and sizes of buried mines. This paper is able to improve on the effectiveness of GPR measurements. 2. Theoretical background 2.1. Rayleigh scattering It is well known that an EM wave passing through a medium deviates from a straight trajectory by one or more localized nonuniformities. This general physical process is called scattering. When an EM wave is affected by only one localized scattering center the process is called single scattering; otherwise, when scattering centers are grouped together, the EM wave may scatter many times, which is known as multiple scattering. In general the wave propagation in dielectrics is discussed by the well-known Fresnel theory. It assumes space is divided into two regions, or stratified media, separated by a surface. A first region contains the wave source; the wave is propagated into the second region passing through the surface. This is applied to GPR inspection, but any rigorous analytical approach should be very approximated because the media encountered in the second region is very heterogeneous, anisotropic and asymmetric in the spatial scale of soil particles and dispersed water. In the case of GPR, there are multiple scattering events for impulse propagation in a three-phase porous medium comprising numerous different materials, typically air and water. When the dimensions of the non-uniformities that cause the scattering are much smaller than the wavelength of the wave, the process is described as Rayleigh scattering. In this paper Rayleigh theory is used to explain a new method applied to geophysical measurement of moisture content in porous media. As it will be discussed later this approach introduces the measurement of the moisture content from frequency spectra analysis without any calibration of the system, which is always required when moisture content is calculated from the signal amplitude or signal processing in time domain. From a practical point of view this is a relevant point of innovation for engineers and practitioners. The intensity I of the EM wave scattered by a single particle for a beam of unpolarized waves with a wavelength λ and intensity I0 is given by (Mie, 1908):
IðθÞ = I0
!2 2 2 1 + cos θ 2π 4 n −1 d 6 ; 2 2 λ 2 2R n +2
ð1Þ
where R is the distance from the observer to the particle, θ is the scattering angle, n is the refractive index of the particle and d is the diameter of the particle.
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The angular distribution of Rayleigh scattering, governed by (1+ cos2θ) term, is symmetric in the plane normal to the incident direction of the wave; thus, the forward scattering is equal to the backwards scattering. Integrating over a sphere surrounding the particle gives the Rayleigh scattering cross section (Chakraborti, 2007):
σs =
2π5 d6 3 λ4
n2 −1 n2 + 2
!2 :
ð2Þ
From Eq. (2) it is evident that the refractive index plays an important role. 2.2. Derivation of the refractive index Assuming the following constitutive equations, →
→
→
D = ε0 E + P
ð3:1Þ
→ → B = μ0 H + M
ð3:2Þ
under the hypotheses of amagnetic medium, linear polarization, absence of free charge, null current density, the following equation derives from Maxwell equations for propagation in a medium:
ð4Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi c 1 + χ = εr μr = : v
Δε ; 1 + jντ
ð6Þ
where
where the refractive index n is given by: n=
The dielectric permittivity of a three-phase medium plays the most important role in determining n. Considering that the dielectric permittivity is 1 for air, approximately 3 to 6 for solid particles and 81 for water, the value of εr for a given medium is strongly influenced by the moisture content (Kyritsis et al., 2001; Sengwa and Soni, 2006). Moreover, water molecules are dipoles that can be oriented by an external electrical field (Fig. 1). If this electric field varies with a significantly long period, then the dipoles have the time to change charges direction and the physical process of dipolar polarization is observed. The time needed for dipoles to change their orientation is called the Debye relaxation time (Agmon, 1996; Barbero and Lelidis, 2008; Beneduci, 2008). The change to the orientation of the dipoles is opposed by random molecular agitation. If the period of the electric field is 10− 3 to 10− 12 s, the dipoles can be polarized. In the present case, the frequency of the EM field used for GPR is centered at 600 MHz, giving a period of 1.7 × 10− 9 s; this period is long enough to allow for dipole polarization. Atomic and electronic polarizations are not induced in the medium if the period of the electric field is less than 10− 14 and 10− 16 s, respectively. The polarization of a medium implies that the value of the dielectric permittivity of a three-phase medium depends on the frequency ν of the EM wave. The following Debye model will be assumed in this paper, where τ is the relaxation time: εr = ε∞ +
2→
∂ E ∇ E −ε0 μ0 ð1 + χÞ 2 = 0; ∂t 2→
2.3. Dielectric permittivity
Δε = εstatic −ε∞ ð5Þ
In a three-phase porous medium such as soil the value of μr is approximately 1. The assumption of zero electrical conductivity is not valid for unsaturated and saturated soils. But if electrical conductivity is not too high, the effect on the reflection coefficients can be neglected on first approximation. However in this case it will still influence the wave attenuation.
ð7Þ
is the difference between the value of the dielectric constant of the medium observed for a steady EM field and the value for a high frequency field when the medium is totally polarized. Eq. (6) can be written by separating the real and imaginary part of εr as follows: εr = ε∞ +
Δε ντΔε − j 1 + ν2 τ2 1 + ν2 τ2
Fig. 1. Water dipoles surrounding solid particles.
ð8Þ
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
Fig. 2 qualitatively shows how the dielectric permittivity is a function of the frequency. 2.4. Final formulation Eq. (1) can be rewritten considering Eqs. (5) and (8) as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !4 1 + cos2 θ 2πν Δε ε + μ r ∞ c0 2R2 1 + ν2 τ2 0 12 6 μr ε∞ + 1 +Δεν2 τ2 −1 A d : ×@ Δε 2 +2 μ ε +
Iðθ; νÞ = I0 ðνÞ
r
∞
1 + ν2 τ2
ð9Þ
2.5. The relaxation time The relaxation time of a single molecule of water can be calculated according to Stokes law:
τ=
4πηR kB T
3
ð10Þ
where kB is the Boltzmann's constant, η(T) is the viscosity, which varies with the absolute temperature T, and R is the approximate radius of the molecule; the recommended value for R is between 1.4 and 2.8 Å, depending on the temperature. Consequently, the relaxation time of a molecule in free water can vary between 1–10 ps (Weijia et al., 1997). Of course, for the case of water droplets dispersed in a porous medium or for multiple water molecules adsorbed to solid particles by dipolar forces, the inertia of the water dipoles elongates the relaxation time. Something like this was found by Ishida et al. (2000) in the case of Kaolinite, Montmorillonite, Allophone and Imogolite under moist conditions. Analogous results have been found previously for biological materials (Mashimo et aL, 1987). In all these cases the relaxation time can be until 1000 times greater than in pure water. For clayey materials the relaxation time is found to vary to about 30 ns depending on the interfacial polarization (Ishida et al., 2000). Since there is no literature on the exact value of the relaxation time in the case of water dispersed in a soil or in a clayey soil, because it can vary depending on minerals concentrations and polarization according to the range of variability found in the cited literature, its value is a calibrated parameter in the simulations that are presented in the next chapter.
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Simulations have been carried out to evaluate the effect of different parameters on the scattering. Specifically, an EM field with a uniform frequency distribution has been considered; the frequency spectrum is constant over the frequencies ranging from 0 to 1.2 GHz. The value of the relaxation time of the water dipoles in a medium has been approximated as 4 × 10− 9 s. This value is in the range found for clayey minerals (Ishida et al., 2000). Six different moisture conditions have been simulated, ranging from quasi-dry conditions (w0) to high moisture (w5). From the normalized graphs in Fig. 3 it is evident that the scattered intensity depends on the frequency and the moisture. Here the normalized intensities have been plotted because the absolute reflected intensities are significantly affected by the energy absorption in the wetted soil. This makes the frequency shift, which is present in any case, less evident in the graphics. It has been elsewhere demonstrated that as the water content in soil increases more energy is absorbed. It is the obvious consequence of the increasing of the dielectric permittivity of soil when the moisture content increases. Some authors showed that the amplitude of the reflected GPR signal decreases as the soil humidity increases (Pettinelli et al., 2007). From Fig. 3 it is also evident that the scattering effects are more prominent in the central band of frequencies as the moisture increases. In particular, the frequencies between 400 and 800 MHz are highly scattered as the water content in the medium increases. This has interesting consequences for the case where the EM field has a dominant frequency component. In fact, according to the Rayleigh Eq. (12), the different frequency components are scattered with more or less intensity. This produces a noticeable shift to the dominant frequency component as the moisture content changes. Simulations have been carried out using an EM signal with a triangular frequency distribution. The maximum value of the spectrum is at 525 MHz and the spectrum is null for frequency values less than 75 MHz and greater than 975 MHz. These simulations were carried out using the same values shown in Table 1. Fig. 4 shows the results of these simulations. The modulation to the frequency of the spectrum is evident in Fig. 4. In particular, two effects are prevalent: (1) Rayleigh scattering shifts the main frequency component to higher values, and (2) as the moisture increases we observe a shift of the frequency spectrum towards lower frequencies. Of course, the quantitative results depend on the spectrum and other global parameters. Yet, a frequency shift towards lower frequencies is generally observed and induced by Rayleigh scattering.
3. Simulations Eq. (12) shows that the scattered intensity of an EM wave is a nonlinear function of the frequency and the dielectric permittivity. Since scattering is caused by the water present in a medium, more scattering events are expected as the moisture content increases.
Fig. 2. The dependence of the real and imaginary parts of the permittivity on the frequency.
Fig. 3. Normalized scattered intensity versus frequency for different moisture levels.
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Table 1 EM characteristics for increasing moisture levels.
w0 w1 w2 w3 w4 w5
εstatic
ε∞
Water film thickness around particles [μm]
7 12 20 35 40 48
4 4 4 4 4 4
2.0 2.4 2.8 3.0 3.2 3.4
This theoretical prediction has been empirically observed in some experiments that will be described later. The experiments were performed in laboratory under controlled conditions for soil samples with different water contents using GPR. Fig. 5. GPR and laboratory equipment.
4. Experiments and results Ground-coupled Radar antennas (RIS/MF system manufactured by IDS S.p.A., Italy) were used for the GPR analysis. The GPR uses two antennas with central frequencies of 600 and 1600 MHz (Benedetto et al. 2004). The GPR measurements are developed using 4 channels: 2 mono-static and 2 bi-static. The received signal is measured in the time domain every dt = 7.8125 × 10− 2 ns. Only the signal of the mono-static channel 600 × 600 MHz was post-processed. The monostatic signal at 1600 Mhz and the two bi-static signals were used for cross checking. The GPR was calibrated in standard conditions (Laboratory temperature 19 °C ± 2.5 °C; relative humidity 45% ± 15%; absolute pressure about 1 atmosphere); the spectra of the reflected signals were measured for metal plates (total reflection) and for a sample of dry road material (without clay) that was previously classified. The samples were in a box 0.40 × 0.40 m and 0.13 m high, so that the tested sample of soil was 0.33 × 0.33 m and 0.10 m thick. It is also possible to arrange thicker samples using additional 5 cm high boxes. In particular the experiment was also repeated for 15 and 20 cm thick samples. The paper focuses on the results obtained for the 10 cm thick samples, but analogous high regression numbers have been found for the other samples as it will be mentioned later. The box was impermeable and electrically isolated and this configuration was applied for all tests (Fig. 5). The bottom of the box is on a metal plate
in order to have a total reflection. The GPR is in contact with the soil surface, so that any edge effects can be considered negligible within the range of the tested thicknesses. Five different soil types were tested: a sandy soil (A), the so called Misto della Magliana alluvial soil with a minimum clay fraction (B), a typical subgrade soil (C0) and two other soil samples (C2) and (C3) containing different percentages in clay content. Porosity and hydraulic permeability are shown in Table 2 for the five cases. The grades of the materials are shown in Fig. 6. These soil samples were first tested in dry conditions. Then, the soil was incrementally moistened in steps of 1% moisture content by weight. For each test the radar signal was post-processed. Low-pass and high-pass electronic filters were used to remove noise from the monostatic 600 × 600 MHz signal. After filtering the signal, a fast Fourier transform (FFT) was employed to extract the frequency spectrum. The peak frequency of the spectrum fP, which is the component of the signal with the largest amplitude, was measured for increasing moisture content. Fig. 7 (A–C) show that the frequency modulates as the moisture content increases. It is evident that the peak frequency systematically moves to lower values for all the tested soils. Fig. 8 shows that the value of fP changes as the moisture content increases. It also shows some small differences in the regressions as the thickness of the samples changes. This negligible effect is reasonably caused by some interference patterns, which are not clearly the cause of the observed frequency dependence. In addition, measurements were performed on the subgrade soil (C0) for different volume fractions of clay. In particular, one sample had 5% of clay in weight (C1) and another had 20% (C2). The mineralogy of the clay that has been used is mainly monmorillonite. The particles are plate-shaped with an average diameter of approximately one micrometer. This mineral is a very soft phyllosilicate that forms in microscopic crystals. The results for these samples are given in Fig. 9; as for samples (A), (B) and (C0), the frequency shifts towards lower values as the moisture content increases.
Table 2 Porosity and hydraulic permeability of soils. Soil Fig. 4. The frequency distribution of the normalized scattering intensity for different levels of moisture content and a triangular frequency spectrum.
A
B
C0
C1
C2
Hydraulic permeability [cm/s] 2 × 10− 2 6 × 10− 5 3 × 10− 4 1 × 10− 5 1 × 10− 7 Porosity [%] 27 28 32 35 39
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
Fig. 6. The grades of the materials tested in laboratory using GPR.
Fig. 7. (A–C). Frequency spectra modulation with the change in moisture content.
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5. Discussion
Fig. 8. Frequency of the spectrum peak fP for increasing levels of moisture content.
From the analyses of the frequency spectra it is evident that as the peak of the frequency shifts, the shape of the spectra also changes with increasing moisture content. To quantify the changes to the shape of the spectra, two parameters were investigated: the normalized second and third order moments of inertia of the area under the spectrum curve. Fig. 10 (A) shows the second order moments for soils A, B and C0 while Fig. 10 (B) gives the results for soils C0, C2 and C3. Also, for the normalized third order moments, Fig. 11 (A) refers to soils A, B and C0, and Fig. 11 (B) to soils C0, C2 and C3. Figs. 10 and 11 show that the moments of inertia change in different ways with the different soil types. For soils A and C0 there is no correlation between the moments of inertia and the water content, but for soils B, C1 and C2 there is a linear correlation, which will be discussed in the next section.
Fig. 9. The frequency of the spectrum peak fP as the moisture increases for soils Ci.
The GPR signals propagate in an unsaturated soil according to the Rayleigh theory of scattering. The droplets of water and the water adsorbed by the soil particles are much smaller than the wavelength of the EM waves. It was shown above that as the moisture content increases, the frequency spectrum shifts towards lower frequencies. These expectations are empirically confirmed by the experimental data. Fig. 7 shows that the frequency spectrum modulation gradually changes as the moisture content changes. Figs. 8 and 9 confirm the expected correlation between the shift of the peak of frequency and the moisture content. As the water content in the soil increases, the dimensions of the droplets increase and the film of water molecules around the solid particles becomes thicker. This produces a new distribution of the scattering centers in the medium, causing the frequency to shift to lower values. The observed correlation can be explained using the Fresnel theory but any generalization from empirical data should consider the possible strong variability of the characteristics of the encountered media. However it is interesting to observe that the following regression law can be proposed to predict moisture content (ω), expressed in %, from the value of the peak of frequency (fP), expressed in Hz: ω = A−fp = B
ð11Þ
where A and B are regression coefficients calibrated from experimental data. Despite the five tested soils are very different in terms of water affinity, the values of A vary from 5.3 × 108 to 7.0 × 108 and the values of B from 1.1 × 107 to 2.3 × 107. The values of the regression coefficients R2 vary between 0.97 and 0.89 as shown in Table 3. Assuming the Eq. (11) as valid for all the tested soils, the values of A and B are in Table 3 and R2 is however considerably high. This approach is very useful because it provides a way to measure the water content only by using an FFT to find the shift to the peak of the frequency spectrum. One of the greatest advantages of this method is that no calibration is needed, unlike methods that analyze data in the time domain, where a preventive evaluation of the propagation velocity of waves in the medium is needed. One application for this method that was tested by the author is road pavement engineering (Benedetto et al., 2009). The water content of the soil beneath the road pavement was evaluated for more than 100 km of road with a longitudinal resolution of 0.1 m, providing 104 GPR signals per kilometer. The results, which are discussed elsewhere, confirm the laboratory outcomes and the effectiveness of the method. There are two theories that accurately show how it could be possible to calculate the water content from the shift of the frequency spectrum. These theories allow to generalise the single scattering to multiple scattering. More generally, there are two theories on wave propagation in randomly distributed particles. One of the theories may be called the “analytical theory,” and the other can be called “transport theory” (Ishimaru, 1977). The analytical theory starts from Maxwell equations or the wave equation where the scattering and absorption characteristics of particles are introduced to obtain differential or integral equations for statistical quantities, such as variances and correlation functions. Of course, such an approach is mathematically rigorous when all of the scattering, diffraction and interference events are included. In practice, considering the heterogeneity of natural systems and the complexity of the phenomena involved, it is impossible to obtain a formulation that completely includes all of these effects. Some theories that yield useful solutions are approximate and only apply to a specific range of parameters. Twersky theory, the diagram method,
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
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Fig. 10. (A,B) Normalized second order moment of inertia vs. water content.
and the Dyson and Bethe–Salpeter equations are examples of analytical theories. On the other hand, the transport theory is not based on Maxwell equations in differential form. Instead, it deals with the transport of energy through a medium containing particles. The development of this theory is essentially heuristic (Ishimaru, 1977). The transport theory was first studied by Schuster, 1905 and is also called the “radiative transfer theory.” The basic differential equation is called the “equation of transfer” and is equivalent to the form of Boltzmann equation (also known as the Maxwell–Boltzmann collision equation) that is used for the kinetic theory of gases and neutrons. The transport
theory is flexible and capable of treating many scenarios. It has been successfully employed for applications including atmospheric and underwater visibility, marine biology, the optics of paper, photographic emulsions and the propagation of radiant energy in the atmospheres of planets, stars, and galaxies. Using stochastic theories and laboratory tests and results, an empirical approach is also possible. A high level of correlation for experimental outcomes and the evident correlation between the water content and frequency spectra suggest that a stochastic approach could be very useful to predict the water content of a soil sample from the frequency shift. This is a new field of research that is
Fig. 11. (A,B) Normalized third order moment of inertia vs. water content.
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Table 3 Values of the regression coefficients in Eq. (11). Parameters
8
A × 10 B × 107 R2
Soils
For all tested soils
A
B
C0
C1
C2
Average regression
5.7 1.1 0.97
7.0 2.1 0.97
6.2 2.3 0.89
5.6 1.7 0.94
5.3 1.5 0.97
5.7 1.4 0.73
actually in progress. The current study also considers how the presence of clay in the soil affects the results. Figs. 10 and 11 show that when the soil contains clay, the shape of the frequency spectrum of the reflected GPR signal changes uniformly as water content increases. When there is no clay, the shape of the spectrum completely changes as the moisture increases to 1%, and there is no correlation between the values of the momentum versus the moisture content. In general it is reasonably due to an increase in the electrical losses as the clay content increases. In particular, the water adheres to the solid particles of the soil in different ways according to the different amounts of clay. When clay particles are present, the water molecules adhere to the surface of the particle by molecular forces. Each water dipole is oriented according to the electrical charge of the clay particle, as illustrated in Fig. 1. The water is tightly bound to the solid particle; as the moisture content increases, the film of oriented dipoles becomes thicker and the external water becomes loosely bound. These layers of adsorbed water consist of arranged monomolecular layers surrounding negatively charged mineral surfaces and additional adsorption water layers that can be tightly or loosely bound (Mitchell, 1992). If the water molecules are fixed to particles in the soil (not necessarily clay) via capillarity, a meniscus forms around single or multiple particles. In this case, the dipoles are randomly oriented due to the random molecular agitation, which is a function of the temperature. This case is schematically shown in Fig. 1. In soil science, capillary water is classified into two layers: inner and outer (Lyon and Buckman, 1937). The inner, slightly diffusive layer is in intermediate contact with the adsorbed water layer and acts as a transitional zone between this layer and the outer capillary water layer. The outer capillary water layer can be defined as loosely bound water that is controlled by surface tension and colloidal forces, while the inner capillary water layer is only controlled by colloidal forces. The amount of capillary water is controlled by the soil texture, soil structure, organic matter and gravity (Lyon and Buckman, 1937). The capillary force is weak compared to the molecular forces caused by the electrical charges of the dipoles. As the EM field from the GPR is applied (Fig. 1), the water dipoles tend to orient according to the oscillating polarity of the field. Since the period of the GPR field is about 10−9 s, the dipoles can change polarization according to the Debye relaxation time. It is possible that the water dipoles are free and not tightly bound to the solid particles. If the water is capillary water, it is expected that all of the dipoles are oriented according to the external EM field. This means that the dielectric characteristics of the medium greatly change for conditions ranging from dry to wet. Also if the moisture content is low (1%), all of the dipoles are polarized. When clay particles are present, producing adsorbed water, the dipoles are oriented and fixed to the solid particles by molecular forces and when the GPR field is applied only the loosely bound water dipoles are oriented. When the water in the soil forms layers around particles, that are thick to 15 ÷ 20 molecules, the water is considered only adsorbed (i.e. Martin, 1960) and it is expected that the dipoles are not polarized by the field at all. If the moisture content increases, the film of water around the solid particles is thicker and the outer dipoles begin to polarize. The result is a low variability of the dielectric properties of the soil with the water content. This molecular model explains the observed regularity of the momentum trend in the case
of soil with clay. The strength of this correlation increases as the fraction of clay in the soil increases. For the correlation between the frequency peak and the moisture content the value of R2 increases from 0.89 (C0) to 0.94 (C2) as the clay content increases from 0 to 5%, reaching 0.97 for a clay content of 20%. In the case of the second order momentum the value of R2 increases from 0.66 to 0.78 as the clay content increases from 0% (C0) to 20% (C2). The value of R2 for soil A is always very low, demonstrating that in this case no correlation exists. This result confirms that clay particles fix water dipoles by molecular forces. This study suggests that this method can be used for determining the presence of clay in soil. This diagnosis could be very useful in many fields; examples include hydraulic engineering, detecting impervious material, road pavement engineering, and checking the presence of plastic soil fractions. 6. Conclusion In this study GPR signals propagate in unsaturated soils and the results are analyzed using Rayleigh scattering. Considering the Fresnel theory we have experimentally showed in heterogeneous and different soils that the scattered waves shift in frequency depending on the moisture content. As expected, it was demonstrated that the shift to the peak frequency provides information on the moisture content of a soil sample. Specifically, the peak of the frequency shifts to lower values as the water content increases. The experimental results confirm these expectations. From these outcomes and according with the theoretical framework, an empirical approach to predict water moisture from frequency analysis has been investigated. The regression coefficients result very promising. Basing on these empirical evidences and grounding on the theoretical framework, the approach introduces the main benefit for geophysical and engineering applications that the method can be applied reliably without any calibration. Further research is needed to clearly define an operational procedure to accurately measure the water content from the shift of the frequency spectrum. To achieve this objective, it is possible to integrate the equations of transfer from radiative transfer theory in a random media, or it is possible to predict the water content using a stochastic approach. The latter approach seems to be very promising due to the high level of correlation between the measured parameters. The capability of detecting clay fractions in soil has also been investigated. It is evident that clay particles are able to orient and fix water dipoles, reducing the polarization of water under an external EM field. References Agmon, N., 1996. Tetrahedral displacement: the molecular mechanism behind the Debye relaxation in water. Journal of Physical Chemistry 100 (3), 1072–1080. Al-Qadi, I.L., Lahouar, S., Loulizi, A., Elseifi, M.A., Wilkes, J.A., 2004. Effective approach to improve pavement drainage layers. Journal of Transportation Engineering 130 (5), 658–664. Barbero, G., Lelidis, I., 2008. Debye's relaxation frequency: a poor man's approach. Physics Letters A 372 (12), 2079–2085. Bekefi, G., Barrett, A.H., 1987. Waves in dielectrics. 6.5 in Electromagnetic Vibrations, Waves, and Radiation. MIT Press, Cambridge, MA, pp. 426–440. Benedetto, A., 2004. Theoretical approach to electromagnetic monitoring of road pavement. Proc. 10th Int. Conference on Ground Penetrating Radar. Delft. The Netherlands. Benedetto, A., Benedetto, F., 2002. GPR experimental evaluation of subgrade soil characteristics for rehabilitation of roads. Proc. IX International Conference on Ground Penetrating Radar. Santa Barbara. California. USA. Benedetto, A., Pensa, S., 2007. Indirect diagnosis of pavement structural damages using surface GPR reflection techniques. Journal of Applied Geophysics 62, 107–123. Benedetto, A., Benedetto, F., De Blasiis, M.R., Giunta, G., 2004. Reliability of radar inspection for detection of pavement damages. International Journal of Road Material and Pavement Design, Hermes Science 5 (1), 93–110. Benedetto, A., D'Amico, F., Fattorini, F., 2009. Measurement of moisture under road pavement: a new approach based on GPR signal processing in frequency domain. Proc. Intern. Workshop Adv. Ground Penetrating Radar, May 2009 Granada, Spain. Beneduci, A., 2008. Which is the effective time scale of the fast Debye relaxation process in water? Journal of molecular liquids 138 (1–3), 55–60.
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35 Bohren, C.F., Huffman, D., 1983. Absorption and scattering of light by small particles. John Wiley, New York. Chakraborti, S., 2007. Verification of the Rayleigh scattering cross section. American Journal of Physics 75 (9), 824–826. doi:10.1119/1.2752825. Davis, J.L., Annan, A.P., 1989. Ground-penetrating radar for high resolution mapping of soil and rock stratigraphy. Geophys. Prospect. 37, 531–551. Diefenderfer B. K., Galal K., Mokarem D.W. (2005). Effect of subsurface drainage on the structural capacity of flexible pavement, VTRC 05-R35. Project 66818: pp. 29. Drude, P., 1902. The theory of Optics. Longmans, Green, and Co, New York, pp. 268–396. Fiori, A., Benedetto, A., Romanelli, M., 2005. Application of the effective medium approximation for determining water contents through GPR in coarse-grained soil materials. Geophysical Research Letters 32, L09404. doi:10.1029/2005GL022555. Friedman, S.P., 1998. A saturation degree-dependent composite spheres model for describing the effective dielectric constant of unsaturated porous media. Resources Research 34, 2949–2961. Grote, K., Hubbard, S., Rubin, Y., 2002. GPR monitoring of volumetric water content in soils applied to highway construction and maintenance. Leading Edge Exploration 21 (5), 482–485. Grote, K., Hubbard, S., Rubin, Y., 2003. Field-scale estimation of volumetric water content using GPR groundwave techniques. Water Resources Research 39 (11), 1321. Grote, K., Hubbard, S., Harvey, J., Rubin, Y., 2005. Evaluation of infiltration in layered pavements using surface GPR reflection techniques. Journal of Applied Geophysics 57, 129–153. Ho, K.C., Gader, P.D., Wilson, J.N., 2004. Improving landmine detection using frequency domain features from ground penetrating radar. Proceedings. 2004 IEEE International Geoscience and Remote Sensing Symposium, IGARSS '04, 3, pp. 1617–1620. Hubbard, S., Grote, K., Rubin, Y., 2002. Estimation of nearsubsurface water content using high frequency GPR ground wave. Leading Edge of Exploration Society of Exploration Geophysics 21 (6), 552–559. Huisman, J.A., Hubbard, S.S., Redman, J.D., Annan, A.P., 2003. Measuring soil water content with ground penetrating radar: a review. Vadose Zone Journal 2, 476–491. Ishida, T., Makino, T., Wang, C., 2000. Dielectric-relaxation spectroscopy of kaolinite, montmorillonite, allophane, and imogolite under moist conditions. Clays and Clay Minerals 48 (1), 75–84. Ishimaru, A., 1977. Theory and application of wave propagation and scattering in random media. Proceedings Of the IEEE 65 (7), 1030–1061. Kyritsis, A., Siakantari, M., Vassilikou-Dova, A., Pissis, P., Varotsos, P., 2001. Large low frequency dielectric constant exhibited by hydrated rock materials. Proceedings of the Japan Academy, Series A 77B (2), 19–23. Lambot, S., Slob, E.C., van den Bosch, I., Stockbroeckx, B., Vanclooster, M., 2004. Modeling of ground-penetrating radar for accurate characterization of subsurface electric properties. IEEE Transactions on Geoscience and Remote Sensing 42, 2555–2568. Lambot, S., Weihermüller, L., Huisman, J.A., Vereecken, H., Vanclooster, M., Slob, E.C., 2006. Analysis of air-launched ground-penetrating radar techniques to measure the
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soil surface water content. Water Resources Research 42, W11403. doi:10.1029/ 2006WR005097. Lyon, T.L., Buckman, H.O., 1937. The Nature and Properties of Soils. Macmillan, New York. p. 391. Martin, R.T., 1960. Adsorbed water on clay: a review. Clays and Clay Minerals 9 (1), 28–70. Maser, K.R., 1996. Condition assessment of transportation infrastructure using groundpenetrating radar. Journal of Infrastructure Systems 2 (2), 94–101. Mashimo, S., Kuwabara, S., Yagihara, S., Higasi, K., 1987. Dielectric relaxation time and structure of bound water in biological materials. Journal of Physical Chemistry 91, 6337–6338. Mie, G., 1908. Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Annalen der Physik 330, 377. Mitchell, J.K., 1992. Fundamentals of Soil Behaviour, 2nd edn. Wiley, New York. p. 437. Narayana, P.A., Ophir, J., 1983. On the frequency dependence of attenuation in normal and fatty liver. IEEE Transactions on sonics and ultrasonics SU30 (6), 379–383. Oden, C.P., Olhoeft, G.R., Wright, D.L., Powers, M.H., 2008. Measuring the electrical properties of soil using a calibrated ground-coupled GPR System. Vadose Zone Journal 7 (1), 171–183. Pettinelli, E., Vannaroni, G., Di Pasquo, B., Mattei, E., Di Matteo, A., De Santis, A., Annan, P.A., 2007. Correlation between near-surface electromagnetic soil parameters and earlytime GPR signals: an experimental study. Geophysics 72 (2), A25–A28. Robinson, D.A., Jones, S.B., Wraith, J.M., Or, D., Friedman, S.P., 2003. A review of advances in dielectric and electrical conductivity measurement in soils using time domain reflectometry. Vadose Zone Journal 2, 444–475. Saarenketo, T., Scullion, T., 2000. Road evaluation with ground penetrating radar. Journal of Applied Geophysics 43, 119–138. Schuster, A., 1905. Radiation through a foggy atmosphere. Astrophysics Journal 21, 1–22. Sengwa, R.J., Soni, A., 2006. Low-frequency dielectric dispersion and microwave dielectric properties of dry and water-saturated limestones of the Jodhpur region. Geophysics 71 (5), G269–G277. Serbin, G., Or, D., 2003. Near-surface soil water content measurements using horn antenna radar: methodology and overview. Vadose Zone Journal 2, 500–510. Tighe, S., Li, N., Falls, L.C., Haas, R., 2000. Incorporating road safety into pavement management. Transportation Research Record 1699, 1–10. Topp, G.C., Davis, J.L., Annan, A.P., 1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resources Research 16 (3), 574–582. Weihermüller, L., Huisman, J.A., Lambot, S., Herbst, M., Vereecken, H., 2007. Mapping the spatial variation of soil water content at the field scale with different ground penetrating radar techniques. Journal of Hydrology 340, 205–216. Weijia, W., Hongru, M., Wing, Y.T., Ping, S., 1997. Frequency and water content dependencies of electrorheological properties. Physical Review E 55 (2), R1294–R1297. Werts, A.H., Huisman, A., Bouten, W., 2001. Information content of time domain reflectometry waveforms. Water Resourches Research 37 (5), 1291–1299.
Contents lists available at ScienceDirect
Journal of Applied Geophysics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j a p p g e o
Water content evaluation in unsaturated soil using GPR signal analysis in the frequency domain Andrea Benedetto Department of Sciences, Civil Engineering, University Roma Tre, Rome, Italy
a r t i c l e
i n f o
Article history: Received 10 March 2009 Accepted 4 March 2010 Keywords: Ground penetrating radar Moisture content Frequency analysis Rayleigh scattering Road pavement Clay Polarization
a b s t r a c t The evaluation of the water content of unsaturated soil is important for many applications, such as environmental engineering, agriculture and soil science. This study is applied to pavement engineering, but the proposed approach can be utilized in other applications as well. There are various techniques currently available which measure the soil moisture content and some of these techniques are non-intrusive. Herein, a new methodology is proposed that avoids several disadvantages of existing techniques. In this study, ground-coupled Ground Penetrating Radar (GPR) techniques are used to non-destructively monitor the volumetric water content. The signal is processed in the frequency domain; this method is based on Rayleigh scattering according to the Fresnel theory. The scattering produces a non-linear frequency modulation of the electromagnetic signal, where the modulation is a function of the water content. To test the proposed method, five different types of soil were wetted in laboratory under controlled conditions and the samples were analyzed using GPR. The GPR data were processed in the frequency domain, demonstrating a correlation between the shift of the frequency spectrum of the radar signal and the moisture content. The techniques also demonstrate the potential for detecting clay content in soils. This frequency domain approach gives an innovative method that can be applied for an accurate and non-invasive estimation of the water content of soils – particularly, in sub-asphalt aggregate layers – and assessing the bearing capacity and efficacy of the pavement drainage layers. The main benefit of this method is that no preventive calibration is needed. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Measuring the water content of soils is important for applications such as flood defense, agriculture, determining the geomorphologic stability of slopes, construction, and finding the bearing capacity of structural foundations. Moreover, the variation of the water content in space cannot be neglected for most of these applications. In fact, it has been demonstrated that different spatial distributions of the moisture content produce different effects. Some examples include run-off generation for basins with spatially varying saturation zones (Weihermüller et al., 2007), foundations of structures with variable moisture content (Diefenderfer et al., 2005) and non-homogeneous moisture distributions in the soil beneath road pavement (Benedetto et al., 2004; Grote et al., 2002, 2003; Maser, 1996; Saarenketo and Scullion, 2000). It is well known that the conditions of the pavement influence the safety of driving (Tighe et al., 2000). A significant percentage of accidents are caused by surface deformations, cracks and potholes that induce an unexpected acceleration on a vehicle and reduce the effective friction between the tires and the pavement. Such road
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damage is often caused by a decrease in the bearing capacity of the sub-asphalt soils (Diefenderfer et al., 2005; Grote et al., 2005). The bearing capacity is defined as the ability to carry a defined number of repetitions of a set of loads. The bearing capacity of the sub-asphalt soil is greatly affected by the soil's water content and soil suction, and it can be measured indirectly using a falling weight deflectometer. It has been widely demonstrated that an increase in water content in the sub-asphalt layer can decrease the soil stiffness and cause pavement deflection. This deflection can damage the surface in different ways, depending on the temperature, the asphalt characteristics, the age, the repetitions and the loads weight. However, there is one problem which affects pavements universally: the infiltration of water through the pavement brings plastic material into the subgrade or the sub-base of the pavement. Furthermore, estimates of the water content in sub-asphalt soils are necessary to determine the performance of pavement drainage systems (Al-Qadi et al., 2004). Only a few techniques have been used to monitor the water content in sub-asphalt soils in the past two decades. The sub-asphalt water content is often estimated via gravimetric sampling, time domain reflectometry, neutron probe logging and measuring the capacitance or resistance of devices. These methods are accurate, but they also have many disadvantages: it is often necessary to constrain traffic; they are expensive and projects can be time-consuming; the
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
methods are invasive and assessments of the moisture content in a large area, such as several kilometers of road, are often unreliable. Many authors measure the moisture content using GPR, which is a non-destructive technology. With GPR it is possible to collect data quickly on the road and obtain the volumetric water content of soil in unsaturated porous media, such as sub-asphalt soil (Benedetto and Pensa, 2007). This utility of GPR has been demonstrated for numerous applications in the time domain, based on an evaluation of the dielectric permittivity (Davis and Annan, 1989). Assuming that the porous media is a mixture of three phases (solid, water and air), and assuming that the dielectric constant of water is significantly different than that of solid materials and air, it is expected that the dielectric constant of the mixture is dependent on the water content. The relationship between the dielectric constant of a soil and its volumetric water content has been extensively studied in the past. Various empirical correlations have been proposed, like the commonly used theory suggested by Topp, which is supposedly valid for any type of soil (Topp, et al., 1980). Reviews of the various theoretical models are available (Friedman, 1998; Grote et al., 2002, 2003; Hubbard et al., 2002; Huisman et al., 2003; Robinson et al., 2003; Serbin and Or, 2003). Another theoretical approach that relates the soil water content to the soil permittivity is based on dielectric mixing. It uses the volume fractions and the dielectric permittivity of each soil constituent to derive an approximate correlation, using a self-consistent approximation that represents the medium with the multi-indicator mode (Fiori et al., 2005). These aforementioned correlations and models used to evaluate the water content in a porous medium are based on estimations of the dielectric permittivity. The value of the permittivity is generally extracted from GPR measurements that compute the delay time of reflections once a value for the velocity propagation of the wave in the medium is determined (Benedetto and Benedetto, 2002; Benedetto, 2004). In some cases, the dielectric permittivity is estimated from the amplitudes of the transmitted and reflected signals (Al-Qadi et al., 2004). In any case, these methods require calibration steps because the signal velocity of propagation cannot be assumed a priori; in fact, it depends on the characteristics and conditions of the materials. A more efficient and self-consistent approach is based on the GPR processing in the frequency domain. Werts et al. (2001), basing on the Debye model and using time domain reflectometer in a band between 3 and 316 MHz, observed that the dielectric permittivity is influenced by the frequency. Lambot et al. (2004); 2006) considered the dependence of the imaginary part of the dielectric permittivity from the frequency to investigate the subsurface electric characteristics. Relating to the water content estimation, they found very consistent results using a local linear approximation in the 1–2 GHz band. In particular they modeled the GPR response in frequency and time domain using Green's function. The relative dielectric permittivity was inversely estimated as a function of nine different water content levels. These estimated values fit very well both TDR measurements and soil-specific empirical model predictions (similar to Topp's equation). Oden et al. (2008) have calibrated and validated a new model for measuring the electrical properties of soil. The algorithm estimates the shallow soil properties using the early-time arrivals, i.e. the arrivals recorded before subsurface reflections arrive (Pettinelli et al., 2007). The amplitude and shape of the early-time arrivals change with soil permittivity, conductivity, and antenna standoff. In this case the main innovation is using a non-linear inversion algorithm in the frequency domain. Basically this algorithm compares the GPR response to a catalog of Finite-difference time-domain (FDTD) simulations of early-time waveforms to estimate soils parameters. This paper aims to present an innovative, high-performance method that does not need calibration to estimate the moisture content of a porous medium. This method, unlike the others, does not estimate the dielectric permittivity of unsaturated soil but directly the water content by frequency analysis. The starting point is to assume
27
that the water droplets in the medium scatter the electromagnetic (EM) waves (Drude, 1902), thereby shifting the frequency of the waves (Bekefi and Barrett, 1987); an example of this phenomenon is when atmospheric particles scatter sunlight, shifting the color of the sky from blue to red during sunset (Bohren and Huffman, 1983). Such an approach focuses only on the water content, which is independent from the solid and air phases. One new aspect of the proposed method is that the volume fractions of the three phases in the medium are not accounted for. A shift in the frequency distribution of the reflected signals has been observed in the past, but the cause of the shift was not identified or investigated. In 1983 Narayana and Ophir (Narayana and Ophir, 1983) analyzed ultrasonic waves reflected by normal and fatty livers; they noticed that different frequencies were attenuated in different media. In particular, they suggested that the observed nonlinear behaviour of the reflected waves in fatty livers was due to Rayleigh scattering: the Rayleigh scattering was due to the fat globules, which exhibit fourth-order frequency dependence. More recently, Ho et al. (2004) observed a frequency shift while detecting different shapes and sizes of buried mines. This paper is able to improve on the effectiveness of GPR measurements. 2. Theoretical background 2.1. Rayleigh scattering It is well known that an EM wave passing through a medium deviates from a straight trajectory by one or more localized nonuniformities. This general physical process is called scattering. When an EM wave is affected by only one localized scattering center the process is called single scattering; otherwise, when scattering centers are grouped together, the EM wave may scatter many times, which is known as multiple scattering. In general the wave propagation in dielectrics is discussed by the well-known Fresnel theory. It assumes space is divided into two regions, or stratified media, separated by a surface. A first region contains the wave source; the wave is propagated into the second region passing through the surface. This is applied to GPR inspection, but any rigorous analytical approach should be very approximated because the media encountered in the second region is very heterogeneous, anisotropic and asymmetric in the spatial scale of soil particles and dispersed water. In the case of GPR, there are multiple scattering events for impulse propagation in a three-phase porous medium comprising numerous different materials, typically air and water. When the dimensions of the non-uniformities that cause the scattering are much smaller than the wavelength of the wave, the process is described as Rayleigh scattering. In this paper Rayleigh theory is used to explain a new method applied to geophysical measurement of moisture content in porous media. As it will be discussed later this approach introduces the measurement of the moisture content from frequency spectra analysis without any calibration of the system, which is always required when moisture content is calculated from the signal amplitude or signal processing in time domain. From a practical point of view this is a relevant point of innovation for engineers and practitioners. The intensity I of the EM wave scattered by a single particle for a beam of unpolarized waves with a wavelength λ and intensity I0 is given by (Mie, 1908):
IðθÞ = I0
!2 2 2 1 + cos θ 2π 4 n −1 d 6 ; 2 2 λ 2 2R n +2
ð1Þ
where R is the distance from the observer to the particle, θ is the scattering angle, n is the refractive index of the particle and d is the diameter of the particle.
28
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
The angular distribution of Rayleigh scattering, governed by (1+ cos2θ) term, is symmetric in the plane normal to the incident direction of the wave; thus, the forward scattering is equal to the backwards scattering. Integrating over a sphere surrounding the particle gives the Rayleigh scattering cross section (Chakraborti, 2007):
σs =
2π5 d6 3 λ4
n2 −1 n2 + 2
!2 :
ð2Þ
From Eq. (2) it is evident that the refractive index plays an important role. 2.2. Derivation of the refractive index Assuming the following constitutive equations, →
→
→
D = ε0 E + P
ð3:1Þ
→ → B = μ0 H + M
ð3:2Þ
under the hypotheses of amagnetic medium, linear polarization, absence of free charge, null current density, the following equation derives from Maxwell equations for propagation in a medium:
ð4Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffi c 1 + χ = εr μr = : v
Δε ; 1 + jντ
ð6Þ
where
where the refractive index n is given by: n=
The dielectric permittivity of a three-phase medium plays the most important role in determining n. Considering that the dielectric permittivity is 1 for air, approximately 3 to 6 for solid particles and 81 for water, the value of εr for a given medium is strongly influenced by the moisture content (Kyritsis et al., 2001; Sengwa and Soni, 2006). Moreover, water molecules are dipoles that can be oriented by an external electrical field (Fig. 1). If this electric field varies with a significantly long period, then the dipoles have the time to change charges direction and the physical process of dipolar polarization is observed. The time needed for dipoles to change their orientation is called the Debye relaxation time (Agmon, 1996; Barbero and Lelidis, 2008; Beneduci, 2008). The change to the orientation of the dipoles is opposed by random molecular agitation. If the period of the electric field is 10− 3 to 10− 12 s, the dipoles can be polarized. In the present case, the frequency of the EM field used for GPR is centered at 600 MHz, giving a period of 1.7 × 10− 9 s; this period is long enough to allow for dipole polarization. Atomic and electronic polarizations are not induced in the medium if the period of the electric field is less than 10− 14 and 10− 16 s, respectively. The polarization of a medium implies that the value of the dielectric permittivity of a three-phase medium depends on the frequency ν of the EM wave. The following Debye model will be assumed in this paper, where τ is the relaxation time: εr = ε∞ +
2→
∂ E ∇ E −ε0 μ0 ð1 + χÞ 2 = 0; ∂t 2→
2.3. Dielectric permittivity
Δε = εstatic −ε∞ ð5Þ
In a three-phase porous medium such as soil the value of μr is approximately 1. The assumption of zero electrical conductivity is not valid for unsaturated and saturated soils. But if electrical conductivity is not too high, the effect on the reflection coefficients can be neglected on first approximation. However in this case it will still influence the wave attenuation.
ð7Þ
is the difference between the value of the dielectric constant of the medium observed for a steady EM field and the value for a high frequency field when the medium is totally polarized. Eq. (6) can be written by separating the real and imaginary part of εr as follows: εr = ε∞ +
Δε ντΔε − j 1 + ν2 τ2 1 + ν2 τ2
Fig. 1. Water dipoles surrounding solid particles.
ð8Þ
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
Fig. 2 qualitatively shows how the dielectric permittivity is a function of the frequency. 2.4. Final formulation Eq. (1) can be rewritten considering Eqs. (5) and (8) as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !4 1 + cos2 θ 2πν Δε ε + μ r ∞ c0 2R2 1 + ν2 τ2 0 12 6 μr ε∞ + 1 +Δεν2 τ2 −1 A d : ×@ Δε 2 +2 μ ε +
Iðθ; νÞ = I0 ðνÞ
r
∞
1 + ν2 τ2
ð9Þ
2.5. The relaxation time The relaxation time of a single molecule of water can be calculated according to Stokes law:
τ=
4πηR kB T
3
ð10Þ
where kB is the Boltzmann's constant, η(T) is the viscosity, which varies with the absolute temperature T, and R is the approximate radius of the molecule; the recommended value for R is between 1.4 and 2.8 Å, depending on the temperature. Consequently, the relaxation time of a molecule in free water can vary between 1–10 ps (Weijia et al., 1997). Of course, for the case of water droplets dispersed in a porous medium or for multiple water molecules adsorbed to solid particles by dipolar forces, the inertia of the water dipoles elongates the relaxation time. Something like this was found by Ishida et al. (2000) in the case of Kaolinite, Montmorillonite, Allophone and Imogolite under moist conditions. Analogous results have been found previously for biological materials (Mashimo et aL, 1987). In all these cases the relaxation time can be until 1000 times greater than in pure water. For clayey materials the relaxation time is found to vary to about 30 ns depending on the interfacial polarization (Ishida et al., 2000). Since there is no literature on the exact value of the relaxation time in the case of water dispersed in a soil or in a clayey soil, because it can vary depending on minerals concentrations and polarization according to the range of variability found in the cited literature, its value is a calibrated parameter in the simulations that are presented in the next chapter.
29
Simulations have been carried out to evaluate the effect of different parameters on the scattering. Specifically, an EM field with a uniform frequency distribution has been considered; the frequency spectrum is constant over the frequencies ranging from 0 to 1.2 GHz. The value of the relaxation time of the water dipoles in a medium has been approximated as 4 × 10− 9 s. This value is in the range found for clayey minerals (Ishida et al., 2000). Six different moisture conditions have been simulated, ranging from quasi-dry conditions (w0) to high moisture (w5). From the normalized graphs in Fig. 3 it is evident that the scattered intensity depends on the frequency and the moisture. Here the normalized intensities have been plotted because the absolute reflected intensities are significantly affected by the energy absorption in the wetted soil. This makes the frequency shift, which is present in any case, less evident in the graphics. It has been elsewhere demonstrated that as the water content in soil increases more energy is absorbed. It is the obvious consequence of the increasing of the dielectric permittivity of soil when the moisture content increases. Some authors showed that the amplitude of the reflected GPR signal decreases as the soil humidity increases (Pettinelli et al., 2007). From Fig. 3 it is also evident that the scattering effects are more prominent in the central band of frequencies as the moisture increases. In particular, the frequencies between 400 and 800 MHz are highly scattered as the water content in the medium increases. This has interesting consequences for the case where the EM field has a dominant frequency component. In fact, according to the Rayleigh Eq. (12), the different frequency components are scattered with more or less intensity. This produces a noticeable shift to the dominant frequency component as the moisture content changes. Simulations have been carried out using an EM signal with a triangular frequency distribution. The maximum value of the spectrum is at 525 MHz and the spectrum is null for frequency values less than 75 MHz and greater than 975 MHz. These simulations were carried out using the same values shown in Table 1. Fig. 4 shows the results of these simulations. The modulation to the frequency of the spectrum is evident in Fig. 4. In particular, two effects are prevalent: (1) Rayleigh scattering shifts the main frequency component to higher values, and (2) as the moisture increases we observe a shift of the frequency spectrum towards lower frequencies. Of course, the quantitative results depend on the spectrum and other global parameters. Yet, a frequency shift towards lower frequencies is generally observed and induced by Rayleigh scattering.
3. Simulations Eq. (12) shows that the scattered intensity of an EM wave is a nonlinear function of the frequency and the dielectric permittivity. Since scattering is caused by the water present in a medium, more scattering events are expected as the moisture content increases.
Fig. 2. The dependence of the real and imaginary parts of the permittivity on the frequency.
Fig. 3. Normalized scattered intensity versus frequency for different moisture levels.
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A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
Table 1 EM characteristics for increasing moisture levels.
w0 w1 w2 w3 w4 w5
εstatic
ε∞
Water film thickness around particles [μm]
7 12 20 35 40 48
4 4 4 4 4 4
2.0 2.4 2.8 3.0 3.2 3.4
This theoretical prediction has been empirically observed in some experiments that will be described later. The experiments were performed in laboratory under controlled conditions for soil samples with different water contents using GPR. Fig. 5. GPR and laboratory equipment.
4. Experiments and results Ground-coupled Radar antennas (RIS/MF system manufactured by IDS S.p.A., Italy) were used for the GPR analysis. The GPR uses two antennas with central frequencies of 600 and 1600 MHz (Benedetto et al. 2004). The GPR measurements are developed using 4 channels: 2 mono-static and 2 bi-static. The received signal is measured in the time domain every dt = 7.8125 × 10− 2 ns. Only the signal of the mono-static channel 600 × 600 MHz was post-processed. The monostatic signal at 1600 Mhz and the two bi-static signals were used for cross checking. The GPR was calibrated in standard conditions (Laboratory temperature 19 °C ± 2.5 °C; relative humidity 45% ± 15%; absolute pressure about 1 atmosphere); the spectra of the reflected signals were measured for metal plates (total reflection) and for a sample of dry road material (without clay) that was previously classified. The samples were in a box 0.40 × 0.40 m and 0.13 m high, so that the tested sample of soil was 0.33 × 0.33 m and 0.10 m thick. It is also possible to arrange thicker samples using additional 5 cm high boxes. In particular the experiment was also repeated for 15 and 20 cm thick samples. The paper focuses on the results obtained for the 10 cm thick samples, but analogous high regression numbers have been found for the other samples as it will be mentioned later. The box was impermeable and electrically isolated and this configuration was applied for all tests (Fig. 5). The bottom of the box is on a metal plate
in order to have a total reflection. The GPR is in contact with the soil surface, so that any edge effects can be considered negligible within the range of the tested thicknesses. Five different soil types were tested: a sandy soil (A), the so called Misto della Magliana alluvial soil with a minimum clay fraction (B), a typical subgrade soil (C0) and two other soil samples (C2) and (C3) containing different percentages in clay content. Porosity and hydraulic permeability are shown in Table 2 for the five cases. The grades of the materials are shown in Fig. 6. These soil samples were first tested in dry conditions. Then, the soil was incrementally moistened in steps of 1% moisture content by weight. For each test the radar signal was post-processed. Low-pass and high-pass electronic filters were used to remove noise from the monostatic 600 × 600 MHz signal. After filtering the signal, a fast Fourier transform (FFT) was employed to extract the frequency spectrum. The peak frequency of the spectrum fP, which is the component of the signal with the largest amplitude, was measured for increasing moisture content. Fig. 7 (A–C) show that the frequency modulates as the moisture content increases. It is evident that the peak frequency systematically moves to lower values for all the tested soils. Fig. 8 shows that the value of fP changes as the moisture content increases. It also shows some small differences in the regressions as the thickness of the samples changes. This negligible effect is reasonably caused by some interference patterns, which are not clearly the cause of the observed frequency dependence. In addition, measurements were performed on the subgrade soil (C0) for different volume fractions of clay. In particular, one sample had 5% of clay in weight (C1) and another had 20% (C2). The mineralogy of the clay that has been used is mainly monmorillonite. The particles are plate-shaped with an average diameter of approximately one micrometer. This mineral is a very soft phyllosilicate that forms in microscopic crystals. The results for these samples are given in Fig. 9; as for samples (A), (B) and (C0), the frequency shifts towards lower values as the moisture content increases.
Table 2 Porosity and hydraulic permeability of soils. Soil Fig. 4. The frequency distribution of the normalized scattering intensity for different levels of moisture content and a triangular frequency spectrum.
A
B
C0
C1
C2
Hydraulic permeability [cm/s] 2 × 10− 2 6 × 10− 5 3 × 10− 4 1 × 10− 5 1 × 10− 7 Porosity [%] 27 28 32 35 39
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
Fig. 6. The grades of the materials tested in laboratory using GPR.
Fig. 7. (A–C). Frequency spectra modulation with the change in moisture content.
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5. Discussion
Fig. 8. Frequency of the spectrum peak fP for increasing levels of moisture content.
From the analyses of the frequency spectra it is evident that as the peak of the frequency shifts, the shape of the spectra also changes with increasing moisture content. To quantify the changes to the shape of the spectra, two parameters were investigated: the normalized second and third order moments of inertia of the area under the spectrum curve. Fig. 10 (A) shows the second order moments for soils A, B and C0 while Fig. 10 (B) gives the results for soils C0, C2 and C3. Also, for the normalized third order moments, Fig. 11 (A) refers to soils A, B and C0, and Fig. 11 (B) to soils C0, C2 and C3. Figs. 10 and 11 show that the moments of inertia change in different ways with the different soil types. For soils A and C0 there is no correlation between the moments of inertia and the water content, but for soils B, C1 and C2 there is a linear correlation, which will be discussed in the next section.
Fig. 9. The frequency of the spectrum peak fP as the moisture increases for soils Ci.
The GPR signals propagate in an unsaturated soil according to the Rayleigh theory of scattering. The droplets of water and the water adsorbed by the soil particles are much smaller than the wavelength of the EM waves. It was shown above that as the moisture content increases, the frequency spectrum shifts towards lower frequencies. These expectations are empirically confirmed by the experimental data. Fig. 7 shows that the frequency spectrum modulation gradually changes as the moisture content changes. Figs. 8 and 9 confirm the expected correlation between the shift of the peak of frequency and the moisture content. As the water content in the soil increases, the dimensions of the droplets increase and the film of water molecules around the solid particles becomes thicker. This produces a new distribution of the scattering centers in the medium, causing the frequency to shift to lower values. The observed correlation can be explained using the Fresnel theory but any generalization from empirical data should consider the possible strong variability of the characteristics of the encountered media. However it is interesting to observe that the following regression law can be proposed to predict moisture content (ω), expressed in %, from the value of the peak of frequency (fP), expressed in Hz: ω = A−fp = B
ð11Þ
where A and B are regression coefficients calibrated from experimental data. Despite the five tested soils are very different in terms of water affinity, the values of A vary from 5.3 × 108 to 7.0 × 108 and the values of B from 1.1 × 107 to 2.3 × 107. The values of the regression coefficients R2 vary between 0.97 and 0.89 as shown in Table 3. Assuming the Eq. (11) as valid for all the tested soils, the values of A and B are in Table 3 and R2 is however considerably high. This approach is very useful because it provides a way to measure the water content only by using an FFT to find the shift to the peak of the frequency spectrum. One of the greatest advantages of this method is that no calibration is needed, unlike methods that analyze data in the time domain, where a preventive evaluation of the propagation velocity of waves in the medium is needed. One application for this method that was tested by the author is road pavement engineering (Benedetto et al., 2009). The water content of the soil beneath the road pavement was evaluated for more than 100 km of road with a longitudinal resolution of 0.1 m, providing 104 GPR signals per kilometer. The results, which are discussed elsewhere, confirm the laboratory outcomes and the effectiveness of the method. There are two theories that accurately show how it could be possible to calculate the water content from the shift of the frequency spectrum. These theories allow to generalise the single scattering to multiple scattering. More generally, there are two theories on wave propagation in randomly distributed particles. One of the theories may be called the “analytical theory,” and the other can be called “transport theory” (Ishimaru, 1977). The analytical theory starts from Maxwell equations or the wave equation where the scattering and absorption characteristics of particles are introduced to obtain differential or integral equations for statistical quantities, such as variances and correlation functions. Of course, such an approach is mathematically rigorous when all of the scattering, diffraction and interference events are included. In practice, considering the heterogeneity of natural systems and the complexity of the phenomena involved, it is impossible to obtain a formulation that completely includes all of these effects. Some theories that yield useful solutions are approximate and only apply to a specific range of parameters. Twersky theory, the diagram method,
A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
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Fig. 10. (A,B) Normalized second order moment of inertia vs. water content.
and the Dyson and Bethe–Salpeter equations are examples of analytical theories. On the other hand, the transport theory is not based on Maxwell equations in differential form. Instead, it deals with the transport of energy through a medium containing particles. The development of this theory is essentially heuristic (Ishimaru, 1977). The transport theory was first studied by Schuster, 1905 and is also called the “radiative transfer theory.” The basic differential equation is called the “equation of transfer” and is equivalent to the form of Boltzmann equation (also known as the Maxwell–Boltzmann collision equation) that is used for the kinetic theory of gases and neutrons. The transport
theory is flexible and capable of treating many scenarios. It has been successfully employed for applications including atmospheric and underwater visibility, marine biology, the optics of paper, photographic emulsions and the propagation of radiant energy in the atmospheres of planets, stars, and galaxies. Using stochastic theories and laboratory tests and results, an empirical approach is also possible. A high level of correlation for experimental outcomes and the evident correlation between the water content and frequency spectra suggest that a stochastic approach could be very useful to predict the water content of a soil sample from the frequency shift. This is a new field of research that is
Fig. 11. (A,B) Normalized third order moment of inertia vs. water content.
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A. Benedetto / Journal of Applied Geophysics 71 (2010) 26–35
Table 3 Values of the regression coefficients in Eq. (11). Parameters
8
A × 10 B × 107 R2
Soils
For all tested soils
A
B
C0
C1
C2
Average regression
5.7 1.1 0.97
7.0 2.1 0.97
6.2 2.3 0.89
5.6 1.7 0.94
5.3 1.5 0.97
5.7 1.4 0.73
actually in progress. The current study also considers how the presence of clay in the soil affects the results. Figs. 10 and 11 show that when the soil contains clay, the shape of the frequency spectrum of the reflected GPR signal changes uniformly as water content increases. When there is no clay, the shape of the spectrum completely changes as the moisture increases to 1%, and there is no correlation between the values of the momentum versus the moisture content. In general it is reasonably due to an increase in the electrical losses as the clay content increases. In particular, the water adheres to the solid particles of the soil in different ways according to the different amounts of clay. When clay particles are present, the water molecules adhere to the surface of the particle by molecular forces. Each water dipole is oriented according to the electrical charge of the clay particle, as illustrated in Fig. 1. The water is tightly bound to the solid particle; as the moisture content increases, the film of oriented dipoles becomes thicker and the external water becomes loosely bound. These layers of adsorbed water consist of arranged monomolecular layers surrounding negatively charged mineral surfaces and additional adsorption water layers that can be tightly or loosely bound (Mitchell, 1992). If the water molecules are fixed to particles in the soil (not necessarily clay) via capillarity, a meniscus forms around single or multiple particles. In this case, the dipoles are randomly oriented due to the random molecular agitation, which is a function of the temperature. This case is schematically shown in Fig. 1. In soil science, capillary water is classified into two layers: inner and outer (Lyon and Buckman, 1937). The inner, slightly diffusive layer is in intermediate contact with the adsorbed water layer and acts as a transitional zone between this layer and the outer capillary water layer. The outer capillary water layer can be defined as loosely bound water that is controlled by surface tension and colloidal forces, while the inner capillary water layer is only controlled by colloidal forces. The amount of capillary water is controlled by the soil texture, soil structure, organic matter and gravity (Lyon and Buckman, 1937). The capillary force is weak compared to the molecular forces caused by the electrical charges of the dipoles. As the EM field from the GPR is applied (Fig. 1), the water dipoles tend to orient according to the oscillating polarity of the field. Since the period of the GPR field is about 10−9 s, the dipoles can change polarization according to the Debye relaxation time. It is possible that the water dipoles are free and not tightly bound to the solid particles. If the water is capillary water, it is expected that all of the dipoles are oriented according to the external EM field. This means that the dielectric characteristics of the medium greatly change for conditions ranging from dry to wet. Also if the moisture content is low (1%), all of the dipoles are polarized. When clay particles are present, producing adsorbed water, the dipoles are oriented and fixed to the solid particles by molecular forces and when the GPR field is applied only the loosely bound water dipoles are oriented. When the water in the soil forms layers around particles, that are thick to 15 ÷ 20 molecules, the water is considered only adsorbed (i.e. Martin, 1960) and it is expected that the dipoles are not polarized by the field at all. If the moisture content increases, the film of water around the solid particles is thicker and the outer dipoles begin to polarize. The result is a low variability of the dielectric properties of the soil with the water content. This molecular model explains the observed regularity of the momentum trend in the case
of soil with clay. The strength of this correlation increases as the fraction of clay in the soil increases. For the correlation between the frequency peak and the moisture content the value of R2 increases from 0.89 (C0) to 0.94 (C2) as the clay content increases from 0 to 5%, reaching 0.97 for a clay content of 20%. In the case of the second order momentum the value of R2 increases from 0.66 to 0.78 as the clay content increases from 0% (C0) to 20% (C2). The value of R2 for soil A is always very low, demonstrating that in this case no correlation exists. This result confirms that clay particles fix water dipoles by molecular forces. This study suggests that this method can be used for determining the presence of clay in soil. This diagnosis could be very useful in many fields; examples include hydraulic engineering, detecting impervious material, road pavement engineering, and checking the presence of plastic soil fractions. 6. Conclusion In this study GPR signals propagate in unsaturated soils and the results are analyzed using Rayleigh scattering. Considering the Fresnel theory we have experimentally showed in heterogeneous and different soils that the scattered waves shift in frequency depending on the moisture content. As expected, it was demonstrated that the shift to the peak frequency provides information on the moisture content of a soil sample. Specifically, the peak of the frequency shifts to lower values as the water content increases. The experimental results confirm these expectations. From these outcomes and according with the theoretical framework, an empirical approach to predict water moisture from frequency analysis has been investigated. The regression coefficients result very promising. Basing on these empirical evidences and grounding on the theoretical framework, the approach introduces the main benefit for geophysical and engineering applications that the method can be applied reliably without any calibration. Further research is needed to clearly define an operational procedure to accurately measure the water content from the shift of the frequency spectrum. To achieve this objective, it is possible to integrate the equations of transfer from radiative transfer theory in a random media, or it is possible to predict the water content using a stochastic approach. The latter approach seems to be very promising due to the high level of correlation between the measured parameters. The capability of detecting clay fractions in soil has also been investigated. It is evident that clay particles are able to orient and fix water dipoles, reducing the polarization of water under an external EM field. References Agmon, N., 1996. Tetrahedral displacement: the molecular mechanism behind the Debye relaxation in water. Journal of Physical Chemistry 100 (3), 1072–1080. Al-Qadi, I.L., Lahouar, S., Loulizi, A., Elseifi, M.A., Wilkes, J.A., 2004. Effective approach to improve pavement drainage layers. Journal of Transportation Engineering 130 (5), 658–664. Barbero, G., Lelidis, I., 2008. Debye's relaxation frequency: a poor man's approach. Physics Letters A 372 (12), 2079–2085. Bekefi, G., Barrett, A.H., 1987. Waves in dielectrics. 6.5 in Electromagnetic Vibrations, Waves, and Radiation. MIT Press, Cambridge, MA, pp. 426–440. Benedetto, A., 2004. Theoretical approach to electromagnetic monitoring of road pavement. Proc. 10th Int. Conference on Ground Penetrating Radar. Delft. The Netherlands. Benedetto, A., Benedetto, F., 2002. GPR experimental evaluation of subgrade soil characteristics for rehabilitation of roads. Proc. IX International Conference on Ground Penetrating Radar. Santa Barbara. California. USA. Benedetto, A., Pensa, S., 2007. Indirect diagnosis of pavement structural damages using surface GPR reflection techniques. Journal of Applied Geophysics 62, 107–123. Benedetto, A., Benedetto, F., De Blasiis, M.R., Giunta, G., 2004. Reliability of radar inspection for detection of pavement damages. International Journal of Road Material and Pavement Design, Hermes Science 5 (1), 93–110. Benedetto, A., D'Amico, F., Fattorini, F., 2009. Measurement of moisture under road pavement: a new approach based on GPR signal processing in frequency domain. Proc. Intern. Workshop Adv. Ground Penetrating Radar, May 2009 Granada, Spain. Beneduci, A., 2008. Which is the effective time scale of the fast Debye relaxation process in water? Journal of molecular liquids 138 (1–3), 55–60.
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