1. Introduction
China has a vast territory, a large population, and an unbalanced distribution of resources and industries. Therefore, China’s railway plays an important role in economic and social development. Subgrade frost heaving is a common geological phenomenon in northern China, and its treatment is the main task of railway maintenance in winter. Frost heaving of the subgrade seriously affects the safety and comfort of train operation. Temperature, soil properties, and moisture content are the three factors of the formation of subgrade frost heaving. The main cause of soil freezing is the moisture content in soil. Therefore, it is crucial to measure the moisture content of railway subgrade quickly and accurately for solving the problem of frost heaving.
Drilling samples can obtain the most accurate information about the subgrade moisture content [
1]. However, this method is time-consuming and expensive for large-scale measurement. Ground penetrating radar (GPR) is a geophysical technique for the non-destructive and efficient detection of shallow layers by electromagnetic (EM) waves, which is widely used in the field of environment and engineering. Using GPR to measure the moisture content has become an important branch of GPR applications [
2]. In recent years, a lot of papers using GPR to measure soil moisture content have been published [
3,
4,
5,
6,
7,
8,
9,
10,
11,
12]. Some of them focus on ground water table measurement. As an example, Tsoflias et al. observe that the radar signal response is correlated to changes in the water saturation of the fracture and provide spatial information about the saturation of the fracture [
5]. Saintenoy and Hopmans study the water table detection sensitivity of GPR and state a power type relationship between the reflected signal amplitude and the slope of the soil retention curve [
6]. Others are concerned about the measurement of soil moisture content. Two review papers are valuable. Huisman et al. (2003) presents the basic theoretical principles of GPR and how they can be used to investigate the spatiotemporal variation of soil water content [
10]. In particular, they propose four categories of methods to determine soil water content with GPR. Klotzsche et al. (2018) provide an update on the review of recent advances in vadose zone applications of GPR with a particular focus on new possibilities, e.g., for multi-offset and borehole GPR measurements [
11].
A large number of GPR applications in measuring soil moisture content has benefited from the research of Topp et al., which established the relationship between the relative dielectric constant and soil moisture content [
13]. It is essential to estimate the velocity of EM waves, since it is directly related to the dielectric constant of medium. The common mid-point (CMP) or wide-angle reflection and refraction (WARR) sounding mode in GPR are primarily used to obtain an estimate of the radar wave velocity versus depth in the ground by varying the antenna spacing and measuring the change in the two-way travel time [
2]. The velocity analysis of CMP gather, coming from seismic exploration, is a common and accurate way to obtain wave velocity. Some scholars have carried out research studies to get a better velocity estimation in GPR. Feng et al. improved the signal to noise ratio by CMP antenna array and data processing technology and obtained a good result in velocity analysis, which they successfully applied to landmine detection [
14]. Liu et al. obtain the EM wave velocity through the envelope velocity analysis method, which can monitor the underground dynamic water level [
15]. Lu described the method to obtain the soil moisture content and monitored the underground water level [
16]. Liu et al. used GPR profiles and moisture content to estimated hydraulic conductivity parameters and accurately distinguished a slight change of groundwater level [
17]. Pue et al. proposed a modified velocity analysis method to successfully estimate depth and propagation velocity with small offset air-coupled GPR configurations by accounting for the refraction at the surface [
18]. Yi et al. proposed a high-resolution velocity analysis by applying the
-1 norm regularized least-squares for pavement inspection [
19]. In recent years, many other related papers have been published to improve the performance of CMP velocity analysis in the estimation of EM wave velocity [
20,
21,
22]. However, there are few research studies that deal with shallow and thin multi-layered structures such as the railway subgrade. In such a case, the reliability of the routine velocity analysis process needs to be retested.
In this paper, we introduce the basic theory used here firstly. Then, two synthetic models are established to simulate the railway subgrade structure and the problems of velocity analysis in a shallow thin layer are analyzed by numerical simulation. After that, the solution of optimal gather is proposed. The proposed scheme is applied to the measured data of railway subgrade, and a long moisture content profile of railway subgrade is obtained. Finally, the polarization features from induced polarization (IP) measurement show that the proposed scheme is reliable in a certain range.
4. Case Study
We measured the GPR data in a certain railway in Heilongjiang, which is the coldest area in China. In
Figure 9, a SIR-20 GPR system that employed the shielded antenna with the central frequency of 100 MHz from GSSI (Geophysical Survey Systems, Inc.) is used in the field survey. The CMP gather is acquired with the initial offset of 0.6 m between the transmitter and receiver. The increment of antenna separation is 0.2 m and the maximum antenna transceiver distance is about 14 m. The parameter setting in acquisition is consistent with that in the model. CMP gathers from 56 mid-points are acquired, and the separation between two adjacent mid-points is 10 m. In order to avoid the influence of sleepers, CMP data are acquired along the outside of the rail (see the photo in
Figure 9).
The preprocessing for the original CMP gathers includes zero-time correction, gain control, and frequency domain filtering.
Figure 10a,b show the original CMP gather acquired at the first CMP point and its profile after preprocessing, respectively.
The CMP gathers acquired at the offset of 0.6 m to 5 m are used in velocity analysis, which is decided from the tests on the model in
Section 3.2.2.
Figure 11 shows the velocity analysis result for the CMP gathers in
Figure 10b. In
Figure 11a, the velocity spectrum shows five energy clusters which are marked by ①–③, ⓐ, and ⓑ. Only the energy clusters labeled ①–③ have corresponding peaks in the average amplitude curve, which is also marked by ①–③ in
Figure 11b, while ⓐ and ⓑ cannot be identified. The hyperbolic trajectories of the signals are plotted according to the velocities picked up from the five energy clusters, as shown in
Figure 12. In
Figure 12a, the hyperbolic trajectories generated by velocities ①–③ correspond to relatively complete hyperbolic events, which are meaningful. On the other hand, the clusters ⓐ and ⓑ, in
Figure 12b, are invalid because they produce trajectories without corresponding hyperbolic events. Therefore, the energy clusters ①–③ are the reflections from the interfaces of the railway subgrade, and we extract the
from them to calculate the
. The
is shown in
Figure 11c, and the moisture content is calculated as shown in
Figure 11d.
As shown in
Figure 11d, the vertical moisture content ranges from 2.24% to 7.1% with depth, and there is no abnormal trend in moisture content change.
Table 2 shows the details of related information from the estimates. The estimated total thickness is consistent with that of the actual railway subgrade structure, but some errors exist in the thickness of each layer. We think that the main reason for these errors is the velocity pick-up errors. It is also related to the resolution provided by the 100 MHz central frequency of the radar antenna, which may have a limitation in detecting thin layers such as in this case.
Figure 13 shows the velocity analysis for another CMP gather acquired at the 27th mid-point. Four energy clusters are considered to be valid, which are labeled by ①–④ in
Figure 13a, and the corresponding wave crests can be found in the average amplitude curve (
Figure 13b). The velocities, 0.2 m/ns (8 ns), 0.186 m/ns (14.5 ns), 0.150 m/ns (34 ns), and 0.135 m/ns (46 ns), are picked up. These velocities (
) are converted to the
, which is shown in
Figure 13c, and four velocity layers are identified. The thicknesses of the first two layers, which are considered as layers of ballast and graded gravel, are accurately estimated. The third layer of medium to coarse-grained sand with the thickness of 0.2 m is not distinguished. A velocity increasing can be found in the fourth layer of the A, B group filling. In
Figure 13d, the profile shows the moisture content of 11.8% in the A, B group filling, and it increases to 27.1% at the bottom of the A, B group filling at the depth of 2.47 m. We direct attention to the abnormal increase of moisture content occurring at the bottom of the A, B group filling layer.
The total of 56 CMPs are acquired with the separation of 10 m between two adjacent mid-points. The velocity spectrum of each CMP gather is calculated by the optimal gather with an offset of 0.6 to 5 m. The valid energy clusters in the velocity spectrum are determined by judging their correspondence with the peak of the average amplitude curves and the events in CMP gathers. The stacking velocities (
) are picked up and converted to interval velocities (
) by the Dix formula. Then, the relative dielectric constant (
) can be obtained by Equation (5)—that is,
. At last, the moisture content can be calculated by Equation (7) of the Topp formula. The moisture content curves from 56 mid-points are interpolated into a profile of moisture content, as shown in
Figure 14a.
In
Figure 14a, high moisture content areas are mainly located at around 130–140 m, 180–190 m, 260–270 m, 310 m, 370 m, 420–450 m, and 520–540 m. There are two known culverts with a size of 4 m × 4 m along this survey line. One is located between 150 and 160 m and the other is at 400–410 m with a depth of about 2 m. The positions of the culverts are marked by white boxes in
Figure 14a. The culverts are filled with air, and their existence affects the moisture estimation of their surroundings. These regions feature large velocities of EM waves, small dielectric constants, and small moisture content.
IP measurements are also conducted along the same survey line. A four-electrode sounding method is used in the IP measurement. In the IP acquisition, current electrodes A and B are stainless steel electrodes, and Pb-PbCl nonpolarizable electrodes are used for the potential electrodes M and N to avoid the charge-up effect. The distance between the electrodes of M and N is fixed to 0.2 m, and the distance between electrodes A to B is gradually increased. These separations are 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 6.0, 7.0, 8.0, 9.0, and 10.0 m, respectively. The IP measuring points are consistent with the mid-points in CMP measurement, and the separation of two adjacent measuring points is 10 m. The polarizability of each measuring point is calculated by Equation (8). These 1D polarizability data are used to create a polarizability profile by interpolation, as shown in
Figure 14b.
In
Figure 14b, there are some anomalies of polarizability whose values are higher than that of the surroundings. Compared with
Figure 14a, it is found that the positions of polarizability anomalies are consistent with those of the abnormal area of moisture content, although the level of polarizability and moisture content are not consistent. For example, there is an obvious high-water content area around 250 m in
Figure 14a, but it shows a polarizability anomaly at the same position, which is weak. In
Figure 14b there is an obvious polarization anomaly at 100–150 m, which is stronger than that seen at 250 m. However, the moisture content evaluated at 100–150 m is lower than that evaluated at 250 m in
Figure 14a.
These observations indicate that the relationship between polarizability and moisture content is complex. There is no doubt that an IP survey can find water. However, the dominant factor controlling the strength of polarizability should be the ion concentration in water, not only the amount of water. Therefore, we do not use the strength of polarization to show the moisture content, since we have no information about the ion concentration in soil solution. We compare the positions of abnormal polarizability with that of moisture content from GPR data. We state that no matter how strong or weak, as long as anomalies of the moisture content and polarizability appear in the same position, they can be considered as representing the same target. As a result, this comparison shows that the moisture content extracted from velocity analysis is reliable in the case of railway subgrade.
5. Conclusions
In this paper, we use GPR to detect the moisture content of railway subgrade. The flow of the processing and interpretation includes: first, to obtain the stacking velocity of each layer of subgrade by the velocity analysis of CMP gathers; second, to convert the stacking velocities into interval velocities by the Dix formula and then calculate the dielectric constant; finally, to obtain the moisture content distribution of subgrade by the Topp formula. In this flow, it is the most important thing to pick up the accurate stacking velocity.
The shallow and thin multi-layers of railway subgrade make CMP gather seriously disturbed by multiple waves and refraction waves, which makes the routine velocity analysis unable to provide accurate velocity. In the railway subgrade case, we propose a solution of the optimal gather from a certain offset range dominated by the primary reflection to calculate the velocity spectrum. The extraction of the valid velocities can be completed by judging their correspondence with the peak of the average amplitude curves and the events in CMP gathers. The proposed optimal gather and interpretation flow are applied to the CMP data acquired at a railway site, and a long profile of moisture content distribution is obtained. IP measurement along the same survey line shows the abnormal regions of polarizability whose positions are consistent with large water content areas extracted from GPR data.
In the field survey, a GPR system equipped with a shielded antenna with a central frequency of 100 MHz is used. This frequency of the antenna has a limitation in the detection of the shallow and thin layer structure of the subgrade. The shielded antenna with the center frequency of 200 MHz may give a better result which is known through numerical simulation (not shown in the text). Unfortunately, we do not have such equipment. However, it is gratifying to see that the results given by this paper show that the antenna with a center frequency of 100 MHz is feasible. In conclusion, the velocity analysis of CMP gathers in GPR has great potential in quantitatively estimating the moisture content of the railway subgrade in the construction and maintenance of railway in cold regions.