Using Geometry Data from Ground Penetrating Radar to Improve Pavement Layers Auscultation Using Seismic Surface Waves Inversion Method

Cheikh Diallo Diene, Mapathe Ndiaye

Laboratory of Mechanics and Soils Modelisation, University Iba Der Thiam of Thies, Thiès, Senegal.

DOI: 10.4236/ojce.2022.123016                

Abstract

In order to reduce the unknown parameters during the inversion of the dispersion curve in the aim to obtain more precise Vs and V_P profiles, the Multi-Channel Analysis of Surface Waves (MASW) method was combined with the Ground Penetrating Radar (GPR) method. First, a 2D GPR profile was made on the pavement, then 1D MASW profiles spaced by 0.2 m apart in the perpendicular direction and centered on the intersection with the Radar profile. The GPR measurements, made with a 1600 Hz antenna, allowed to calculate the dielectric permittivities then velocities in order to convert the times profiles to depth. Thus, the thicknesses of the layers are directly read on the radar profile. MASW measurements were performed by simulating the Multi-Channel Simulation with One Receiver (MSOR) method in Land Streamer mode. Six 4.5 Hz pointless geophones are connected to the seismograph consisting of an Arduino Due microcontroller and a nano-computer type Raspberry Pi 4. The results of the dispersion analysis showed a fundamental mode located between approximately 70 Hz and 200 Hz and an inverted dispersion, characteristic of pavements with higher frequencies propagating at higher velocities. The results show that the integration of the number of layers and the thicknesses obtained from the GPR measurements in the inversion parameters makes it possible to obtain a more precise Vs and V_P velocity profile. All profiles, seismic and radar, have shown that velocities decrease with depth. The detected heterogeneities appear to be related to differences in water content inside the pavement.

Keywords

MASW, GPR, Auscultation, Route, Elastic Properties, Permittivity

1. Introduction

Pavement auscultation generally involves a series of more or less destructive tests which, in addition to information on the thicknesses of the different pavement layers, are designed to allow an assessment of the conditions of the materials and the quality of the interfaces. These tests with boreholes and cores are long and expensive and their number necessarily limited, which increases the uncertainty on the basic parameters. In addition, coring may damage the taken samples. Road engineers who have for a longtime wanted to inspect the pavement by transparency without destroying it can now do so using several tools such as the surface wave method and the GPR Radar method.

The first uses of surface waves in road auscultation were carried out by the German Soil Engineering Company (GSSM) [1]. Subsequently, Jones, Henklom and Klomp used steady-state vibrators to improve the method of surface waves on pavements [2]. In the early 1980s, several researchers worked on the development and application of the Spectral Analysis of Surface Waves (SASW) method on several pavements divided into flexible and rigid pavements [3] [4] [5], the results were then compared with other independent tests.

Subsequently, significant improvements were made and proved useful for roadside testing [6] [7] with the rise of Multi-Channel Analysis of Surface Waves (MASW) [8] [9] and Multi-Channel Simulation with One Receiver (MSOR) [10] which provided accurate non-destructive estimates for the calculation of the top-layer module of bituminous concrete.

However, the use of the MASW method as a pavement investigation method remains tedious due to several implementation factors; This led to the use of peakless geophones with the Land Streamer acquisition technique [11] [12].

Other difficulties were observed because of the fundamental nature of wave propagation in stratified environments, where rigidity decreases with depth, which is the case with a pavement system. Sezawa (1938) was the first to report the abnormal behaviour of surface waves in this type of medium, and his speculative findings revealed some of the difficulties to come. Choi et al. (2018) later confirmed the possible existence of surface waves in this type of medium.

In recent years, GPR has been shown to be a valuable non-destructive tool for assessing the thickness of the pavement layer [13] [14] [15]. Even better, Emund et al., (2010) conducted a cumulative study between the radar GPR and the MASW method to determine variations in thickness and modulus of pavement layers. At the end of this study, they showed that by using the AASHTO 1993 guide for the design of pavement structures, the difference in module and thickness between the data integrating the GPR results resulted in a difference of almost two inches (5.08 cm) in the required cover thickness. There are also correlations between relative permittivities and compaction parameters of pavement granular materials [16] [17].

The objective of our study is precisely to combine the MASW and GPR methods in order to be able to integrate the thicknesses obtained by Radar auscultation in the model parameters during the inversion of the dispersion curve in order to reduce the unknowns and obtain an accurate and unique V_S and V_P profile.

To achieve these objectives, Radar and MASW measurements will be carried out on the same profile of a road using respectively a GSSI Structure Scan Radar tool and a seismograph specially designed for road testing [12]. The Radar acquisition gives an amplitude profile from which we can calculate the permittivities [18] and deduce the velocities. From the velocities, the axis of the times can be transformed into depth, which allows to know the thicknesses of the layers directly on the profile.

In this article, we will first discuss, some theoretical aspects on radar and surface waves and their use for road layer testing before moving on to experimental measurements and interpretation and finally to a comparative study

2. Ground Penetrating Radar

In order to perform a reliable and non-destructive mean for straightforward road quality control, the use of the GPR is a major asset. It is with this in mind that several researchers have studied backfill construction, in particular the existence of relationships between compaction parameters and dielectric properties [19] [20]. In 2020, the Regional Laboratory for the Road and Road Network evaluated the metrological performance of its Radar systems with a view to better specifying their field of application [21].

In the road field, measurements of the thickness of pavement layers and the detection of irregularities by means of radar were carried out [22]. Interface between bituminous and hydraulic layers of mixed pavement structures [23] was also studied. A further a procedure for the determination of bituminous pavement layer modules from curvimeter lift measurements associated with radar thickness measurements was developed [24]. Subsequently, many researchers [25] [26] reported success in using ground penetration radar (GPR) technology to measure the thickness of the soft pavement layer.

The average velocity of propagation of radar waves in a medium is given as:

$v=\frac{3\times {10}^8}{\sqrt{{\epsilon }_r}}$ (1)

where ${\epsilon }_r$ is the relative dielectric permittivity of the site propagation

The attenuation of radar waves in an environment is usually expressed in dB/m and is written as:

$\alpha =1.69\frac{{\sigma }_e}{\sqrt{{\epsilon }_r}}$ (2)

where ${\sigma }_e$ is the effective electric conductivity of the site

Table 1 gives order of magnitude of permittivity of some materials.

Table 1. Order of magnitude of permittivity of some materials [27].

(*) Natural rock conditions saturated with formation water.

Short electromagnetic waves pass through pavement layers and reflect surfaces or objects that exhibit discontinuities in dielectric properties. Variations in dielectric properties are related, for example, to differences between materials, changes in moisture content or changes in density [28]. The intensity of the reflected pulses is directly proportional to the contrast of dielectric properties between adjacent materials. The reflected pulses are received by the antenna and recorded as waves that are digitized and interpreted by calculating the amplitude and arrival times of each main reflection.

After the GPR method, MASW method is explained.

3. MASW

Surface wave measurements have been continuously improved and have proved useful for roadway testing [6] [7]. In soil mechanics and pavement design, models of materials based on the results of surface wave measurements are beginning to be developed [29] [30] [31] [32]. However, difficulties related to the measurement procedure in pavement seismic testing are always reported.

Today, the MASW method allows an acquisition similar to conventional seismic with the use of several geophones. MASW methods are based on the dispersive nature of surface waves in a layered medium and can be divided into 7 steps (Figure 1). It is often accepted that Rayleigh waves are the predominant waves in sub-surface prospecting, with a penetration depth of about one wavelength [33]. However, this assertion is only valid in a medium where stiffness increases

Figure 1. MASW method process.

with depth [34] [35]. In a medium with an inverted velocity profile (i.e. stiffness decreases with depth) as with road structures, the nature of the propagation of surface waves is more complex. Many studies have shown that the dispersion curve with phase velocity increasing with frequency (i.e. an inverted dispersion curve) is constructed by considering small portions of the higher modes [36] [37] [38]. The MASW approach is thus summed up in a measurement of the experimental dispersion curve of the pavement body and subsequently, define a soil model allowing to find a compromise between the theoretical and experimental dispersion curves, which will make it possible to obtain the variation of the shear velocities of the layers.

The methodology adopted including GPR and MASW is discussed in Section 4.

4. Material and Method

The Radar and MASW measurements were made on a road located inside the Campus of the University of Thies with the following UTM coordinates: −16.960050E and 14.791811N.

First we created a 2D GPR profile. In a second step, we made 1D MASW profiles spaced by 0.2 m in the perpendicular direction and centered on the intersection with the radar profile (Figure 2). 1D MASW profiles are later combined to obtain a 2D MASW profile overlaid with the 2D Radar profile.

For Radar prospecting, the used equipment is a GSSI Radar Structure Scan. It consist of a SIR 3000 connected to an antenna of 1.6 GHz central frequency (cart model 614) (Figure 3).

The radar measurements were carried out in reflection mode which directly provides geometric information.

The permittivity can be calculated according to the reflection amplitudes method [18].

For the paving layer, the relative permittivity is calculated by comparing the amplitude of the reflection on the road surface to the reflection on a metal plate.

${\epsilon }_1={\left(\frac{1+{\rho }_0}{1-{\rho }_0}\right)}^2$ (3)

Figure 2. Layout of GPR, MASW 1D and MASW 2D profiles.

Figure 3. GPR data acquisition with the Radar Structure Scan.

where ${\epsilon }_1$ : dielectric constant of the first layer.

With

${\rho }_0=\frac{A_0}{A_m}$ (4)

A₀: Amplitude of reflection between air and first layer.

A_m: The amplitude of the reflection between the air and a metal plate placed on the pavement.

For the second layer, the relative permittivity can be calculated, but in a slightly more complicated way. We have:

${\epsilon }_1={\left(\frac{1+{\rho }_0^2+{\rho }_1}{1-{\rho }_0^2-{\rho }_1}\right)}^2$ (5)

where ${\epsilon }_2$ : diélectric constant of the second layer.

With

${\rho }_1=\frac{A_1}{A_m}$ (6)

A₁: The amplitude of the reflection at the interface between layer 1 and layer 2.

Finally, for the third layer, the relative dielectric permittivity is calculated as follows:

${\epsilon }_3={\epsilon }_2{\left(\frac{1+{\rho }_0^2+{\gamma }_1{\rho }_1+{\rho }_2}{1-{\rho }_0^2+{\gamma }_1{\rho }_1-{\rho }_2}\right)}^2$ (7)

where ${\epsilon }_3$ : dielectric constant of the third layer.

With

${\rho }_2=\frac{A_2}{A_m}$ (8)

A₂: The amplitude of the reflection at the interface between layer 1 and layer 2

With

${\gamma }_1=\frac{\sqrt{{\epsilon }_1}-\sqrt{{\epsilon }_2}}{\sqrt{{\epsilon }_1}+\sqrt{{\epsilon }_2}}$ (9)

For the MASW survey, a seismograph was developed (Figure 4) consisting of an Arduino Due [39] microcontroller connected to a Raspberry Pi 4 nanocomputer [40]. The Raspberry is used as a real-time data acquisition and visualization interface, while the Arduino acts as an analog-to-digital converter. These receivers are made up of six GD 4.5 Hz geophones connected to each other by a graduated ribbon allowing to control the inter-trace distance and faster acquisition of data in land streamer mode. The recording is triggered by a KY-038 sensor [12].

More details about acquisition parameters are given to Table 2.

Figure 5 presents a schematic diagram of the combination of MASW and GPR methods.

Obtained results will be discussed in the following section.

Figure 4. MASW data acquisition on pavement.

Table 2. Acquisition parameters.

5. Results and Discussions

Raw Radar data are shown in Figure 5.

An important step in processing is the profile time to depth conversion. This requires knowledge of the propagation velocities of the investigated materials. The rate of propagation can be easily estimated from Equation (1) where permittivities are obtained by exploiting Equations (3), (5), (7). The amplitudes at the different interfaces obtained on the radargrams are recorded in Table 3. The velocities obtained are presented in Table 4.

From velocities in Table 4, we can convert the time axis to depth (Figure 6).

After identifying the different interfaces between the layers, the thicknesses can be read directly on the vertical axis on the right (Table 5).

Figure 5. Schematic diagram of the combination of MASW and GPR methods.

Table 3. Amplitudes and permittivities of the different layers of the pavement (A₀: air/pavement interface, A₁: base bearing interface, A₂: base/platform interface, Am: amplitude on the metal plate).

Table 4. Radar velocity of different layers.

Table 5. Thickness of layers.

Figure 6. Raw radar data with metal plate (a) and without metal plate (b).

The MASW data are displayed using the Open Source Geopsy software [40] as a seismogram (Figure 7).

In order to assess the energy range within which an interpretation of the results is possible, we carried out a dispersion analysis (Figure 8). This step with the Geopsy [40] software is performed by introducing the geometry of the MASW profile and applying a linear FK analysis with velocity ranges in the range [0, 1000], and frequency in the interval [0, 800] and a linear sampling step of 100 is applied for both velocity and frequency.

Figure 9 shows a maximum energy between approximately 70 Hz and 200 Hz, corresponding to the fundamental mode, indicating the desired dispersion curve. The dispersion is reversed compared to a normal situation where low frequencies propagate at higher velocities. This reversal is explained by the decrease of velocities with the depth on the pavements. This interval [70 - 200] was confirmed by the work of Park (2018) which showed that it is dependent on the length of the profile and the spread of the geophones. These results are also confirmed at various sites studied by Diene and Ndiaye (2022) with the same acquisition device.

The experimental dispersion curve is then extracted to allow data inversion.

The inversion is done using the integrated Dinver module of Geopsy. The first step is the selection of model parameters including a priori knowledge (Ólafsdóttir, 2016). The layer thicknesses obtained with the Radar auscultation results and

Figure 7. Radar profile as a function of depth.

Figure 8. The Seismograms of the six 1D MASW profiles: MASW1 (a); MASW 2 (b); MASW 3 (c); and MASW 4 (d); MASW 5 (e); MASW 6 (f).

Figure 9. Dispersion curves: MASW1 (a); MASW 2 (b); MASW 3 (c); and MASW 4 (d); MASW 5 (e); MASW 6 (f).

presented in section 5.2 gives the model thicknesses that will be fixed.

The quality of the inversion, the number of iterations, the convergence and the misfit are available on log files. The inversion gives very low misfits values (less than 1%) after a 50 iterations. The good superposition between the theoretical and experimental dispersion curves (Figure 10) confirms the quality of the model obtained after inversion.

Figure 10. Overlay of theoretical and experimental dispersion curves: MASW1 (a); MASW 2 (b); MASW 3 (c); and MASW 4 (d); MASW 5 (e); MASW 6 (f).

The velocity profiles for the investigated sites are shown in Figure 10.

From the data in Figure 11 showing the variations in V_P and V_S velocities, it is

Figure 11. V_P and V_S profiles obtained by inversion: MASW1 (a); MASW 2 (b); MASW 3 (c); MASW 4 (d); MASW 5 (e); MASW 6 (f).

possible to summarise the MASW data according to the position in the 2D profile (Table 6).

Using the MASW (Table 6) and GPR (Table 4) data, we reconstructed the pavement profile using the velocities V_P, V_S and V_GPR (Figures 12(a)-(c)).

The V_S profile, shows that the velocities are maximum (above 850 m/s) in the paving layer. Velocities of 650 to 850 m/s are encountered in the base layer and the lowest velocities (150 to 650 m/s) in the platform.

On the V_P profile, the velocities are high (above 2400 m/s) in the paving layer, moderately high in the base layer (1800 to 2400 m/s) and lower in the platform (below 1800 m/s).

On the radar profile, the velocities are also higher in the paving layer (above 0.09 m/ns) moderately high in the base layer (0.08 to 0.09 m/ns) and lower in the platform (below 0.08 m/ns)

The Vs velocities have an almost homogeneous distribution in the paving layer and platform. They show some heterogeneities in the base layer. The V_P velocities show heterogeneities in the three layers (paving, base and platform). The heterogeneities are most pronounced in the paving layer in the distance intervals [0.1; 0.25] and [0.75; 0.85]. In the base layer, heterogeneities are mainly noted in the distance intervals [0.55; 0.65]. Radar velocities show heterogeneities in the three layers in the distance intervals [0.15; 0.25] and [0.5; 0.9]. Basically, the heterogeneities are noted and more marked according to the profiles in two zones: zone 1 in the range [0.1; 0.25] and zone 2 in the range [0.5; 0.9]

In zone 1 [0.1; 0.25] the heterogeneities appear well on the V_P and V_GPR profiles and a little less on the Vs profile. The decrease of V_P and V_GPR is noted, on the other hand we have a slight decrease then an increase of Vs. The decrease in V_P could be due to a decrease in mechanical properties by a decrease in compactness. This hypothesis can be supported by the decrease in V_GPR due to a higher water content in voids, and the local decrease in Vs due to the difficulty of shear waves to propagate in a wetter environment.

Table 6. V_S and V_P according to the depth and position of the profile

Figure 12. Reconstruction of the pavement using V_S (m/s) (a), V_P (m/s) (b) and V_GPR (m/ns) (c) velocities.

In zone 2 [0.5; 0.9], we generally note an increase in V_S and V_GPR, but we note a decrease in V_P. This could be related to the presence of dry voids.

Based on Figure 11, it should also be added that the MASW method used is more sensitive to V_S variations than to V_P variations due to single value of V_S obtained after inversion. The elastic modules can be estimated from 5300 to 9800 MPa in the bearing layer and from 3100 to 5300 MPa in the base layer.

6. Conclusions

The integration of the number of layers and thicknesses obtained from radar data makes it possible to obtain more precise V_S and V_P profiles from the MASW method. Indeed, these data allow to reduce the inversion parameters.

The obtained profiles show that all velocities decrease with depth. In the case of seismic data, the velocity decreases are due to a decrease in mechanical properties as we move from the paving layer to the base layer and platform. In the case of radar waves, the decrease in velocity is mainly explained by the decrease in water content. The hydrophobic nature of the bitumen in the paving layer, the optimum Proctor compaction of the base layer and the presence of natural water contents in the subgrade could explain this increase in water contents.

The heterogeneities that appear simultaneously on the V_P and V_GPR profiles appear to be related to water-saturated voids, while those that appear on both the V_S and V_GPR profiles would be due to dry voids.

Radar waves propagate in the road layers at velocities almost 2 × 10⁵ times higher than S waves and more than 6 × 10⁴ times higher than P waves. This large difference in velocity is explained by the fact that radar waves are electromagnetic waves propagating by moving electric charges as seismic waves move matter.

Further investigation is needed to understand the role of relative orientation between MASW and GPR profiles in observed heterogeneities.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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