**1. Introduction**

The ballast layer plays an important role in keeping the sleepers in the correct position, in supporting repeated train loads, and in transferring the train load to the substructures. It also provides free drainage of water and prevents the growth of vegetation. Sound ballast materials should be strong, stable, and drainable. Railway ballast is subjected to both traffic loads and environmental changes and, as the ballast bed deforms and degrades, it adversely affects the performance of the railway track [1–5].

Ballasts become fouled because of the fragmentation of the ballast materials, the surface infiltration of weathered particles and coal droplets, and the upward migration of fines from the subgrade and sleeper wear [2–4,6]. When fouling becomes severe, excess pore water pressure is generated under cyclic loading that, in turn, degrades the track resiliency and stability in undrained conditions [2,4].

As a result, routine track inspections to access the ballast condition are an important aspect of track operations. Cost-effective tracks are needed as the demand for faster and heavier trains increases. To meet these needs, it is essential to improve the monitoring methods and the assessment of the track performance [1].

Railway track condition assessments mainly consist of monitoring the geometric parameters of the track using inspection vehicles. The geometric parameters are related

**Citation:** Birhane, F.N.; Choi, Y.T.; Lee, S.J. Development of Condition Assessment Index of Ballast Track Using Ground-Penetrating Radar (GPR). *Sensors* **2021**, *21*, 6875. https://doi.org/10.3390/s21206875

Academic Editors: Carlos Morón Fernández and Daniel Ferrández Vega

Received: 11 September 2021 Accepted: 14 October 2021 Published: 16 October 2021

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to the positioning and wearing of the rail [7]. Track geometry deformation (i.e., track settlement) is the final phenomenon, arising because of various causes, such as track stiffness differences and subgrade defects, among others [1,8]. Nondestructive tests are widely used to assess the condition of the ballast and subgrade. Common nondestructive methods are visual inspections, the light-falling weight deflection method (LFWD), and electromagnetic methods (e.g., GPR) [1,2]. A lightweight deflectometer (LWD) involves dropping a known weight from a specified height onto a circular plate over soil and measuring the vertical surface deflection and the impact load. The LWD can also be used to determine the stiffness of the track [7,9,10].

Ground penetrating radar (GPR) is currently used more often to assess track ballast conditions. GPR uses electromagnetic signals to detect subsurface features, into which it transmits the electromagnetic pulses into the ground and measures the reflected signals. The changes in the dielectric properties of different materials and, hence, the layers, alter the electromagnetic wave propagation. Such a feature, along with its ability to acquire high-speed data without disturbing train operations, makes GPR a desirable inspection tool [2,5,6,8,11,12]. Nevertheless, GPR is not yet used in a systematic manner for railway track characterization or rehabilitation planning [8], one of the reasons being the lack of a simple and reliable method. With regard to this concern, numerous studies have been carried out. This study has been conducted with the aim of resolving this issue as well.

Conventional GPR analysis primarily involves the interpretation of the signal in the time domain, and is generally performed in specific locations or for a particular purpose, such as subgrade characterization or fouling detection [2,8,13]. Interpreting radar profiles is still a challenging and time-consuming task that, therefore, requires significant experience by GPR experts. Furthermore, there are no potent procedures to find the level and type of fouling quantitatively. Recently, many studies have focused on identifying the thicknesses and fouling levels of railway ballast by means of a frequency-domain analysis, in addition to a time-domain analysis [2,8,11,13–17].

Fontul et al. [8] attempted to identify infrastructure changes by adopting short- and long-sliding windows. For these sliding windows, they calculated the area under the signal in the time and frequency domains. The peaks of these areas, and the peaks of the differences of the areas between the short and long sliding windows, were utilized to detect anomalies in ballast tracks.

Anbazhagan et al. [16], and Alani et al. [18], showed that as the fouling level increases, the electromagnetic wave velocity decreases and the dielectric constant increases. De Chiara [19] points out that the presence of moisture can significantly increase the dielectric constant of a medium. In addition, they showed that the dielectric permittivity can vary, not only according to the frequency of the GPR, but also according to the antenna configuration of the device.

Roberts et al. [20] adopt a void-scattering amplitude envelope approach to assess the condition of the ballast. After comparing the energy between the clean and fouled sections, they showed that the loss of energy is higher in fouled ballast, as it has fewer void spaces.

Most GPR applications achieve the detection and localization of buried features and discontinuities and/or the estimation of the electromagnetic properties of materials by performing signal processing tasks in the time domain. However, time-domain methods do not account for the frequency-dispersive properties of media, and do not consider the signal phase [8]. In the frequency domain, it is also easy to filter out electromagnetic interference.

Various attempts have been made to detect the fouling level of ballast using a frequency spectrum analysis, in which the time-domain GPR data are converted to the frequency domain using the Fourier transform [8,13,21]. Silvast et al. [21] showed that the area of a signal in the frequency domain is higher in clean ballast compared to fouled ballast. Shao et al. [13] used a 800 MHz antennae to evaluate the track at the network level. They proposed an automatic ballast condition assessment method using the maximum peak in the frequency domain.

Birhane et al. [11] developed a 500 MHz GPR device (referred to as a KRRI GPR device). The device has eight channels and can eliminate sleeper noise at the GPR surveying stage. In addition, an algorithm that automatically detects the thickness of the ballast layer was developed. It was found that the caliber of the thickness detection algorithm differed in the clean and fouled ballast sections of the track.

In summary, although various studies have found correlations between GPR parameters, such as the dielectric permittivity and the area of the frequency spectrum and the fouling level, there are no potent procedures by which to ascertain the level of fouling. The determination of the level and type of fouling of the ballast layer from GPR analysis remains challenging.

This paper aims to assess the fouling level of the ballast using both time- and frequencydomain parameters. The correlation of the fouling level of the ballast with the time- and frequency-domain parameters, such as the dielectric permittivity, signal strength at the bottom ballast boundary where materials change into reinforced trackbed or sublayer soil, scattering of the ballast thickness values, and the area of the frequency spectrum, is investigated thoroughly.
