# Categorization of the Condition of Railway Embarments Using a Multi-Attribute Utility Theory
## Methodology
### Selection of Attributes
#### 2.2.3 Attributes 3-5: A GPR Investigation Data  
To obtain GPR data relevant for the proposed methodology, a multi-antenna set-up should be implemented. The reason for this is that higher frequency antennas emit electromagnetic waves with a shorter pulse wavelength, therefore enabling the detection of smaller features and providing a high-resolution profile of the ballast bottom and data for analysis of ballast fouling. On the other hand, lower frequency antennas are used to locate potential anomalies in the sub-ballast and embankment fill. The investigation set-up should include both ground-coupled/lower frequency and air-coupled/higher frequency units. A high-frequency antenna (at least 1 GHz) is used to investigate shallow features such as ballast pockets and ballast quality (fouling), which represent Attribute 3 and Attribute 4, respectively. Lower frequency antennas, for example up to 400 MHz (depending on the height of the investigated embankment), should be used to map deep irregularities within the sub-ballast and embankment material, labeled as Attribute 5. When a ballast penetrates into the lower layers, a depression beneath the ballast layer is formed and referred to as the 'ballast pocket' (Figure 1). Usually, the formation of ballast pockets occurs together with fouling, since during penetration fine grained material intermixes with the clean ballast. When the GPR trace propagates through the clean ballast layer, significant signal scattering occurs, leading to higher signal amplitudes (Figure 1a). Within the sub-ballast layer, the signal is attenuated. By combining the phase and manual layer pick method, the contact between the ballast layer and sub-ballast layer can be determined in a semi-automatic manner. During the determination of the ballast depth, it is important to properly evaluate the value of the dielectric constant of the ballast, since this value affects the depth of the ballast bottom. After the ballast bottom has been marked on the radargram by manual and phase picking (Figure 1b), the depth of the ballast bottom can be easilyobtained. Results are extracted in the form of a report containing information on trace number, profile distance, trace amplitude, two-way travel time, and depth to the ballast layer bottom. On the Croatian network, the normal ballast depth is 0.5 m (0.30 m below the sleeper bottom, with the addition of sleeper thickness, since the reference investigation surface is top of the sleeper). Therefore, Attribute 3 is defined as the measured thickness of a ballast layer in excess of 0.5 m. If the measured ballast depth is 0.5 m, there is no ballast pocket present. The overall steps for the determination of the ballast depth for a provisional 100 m long section of a railway line are shown in Table 1. It is recommended to utilize signal trace separation of maximum 5 cm, leading to 20 traces/m of the investigated line, in order to have a better insight into the position of the layer bottom. The results can be evaluated on each 1 m of the investigated line, that is for every 20 th signal trace. After determination of measured depth for each trace, an averaging procedure for the whole investigated section follows. \(\Delta\)d\({}_{\text{max,i}}\) is determined by the same methodology as given in Table 1, and it represents the line section with the highest average measure depth (\(\frac{\Sigma\,\text{d}_{\text{measured,max,i}}}{100}-0.5\) m). From the data used to formulate the approach, the maximum ballast layer depth measured is assigned a quantification starting value (QSV) of 1, while a ballast layer of 0.5 m is assigned a value 0. The rest are calculated as follows:  
\[\text{QV}_{\text{C3,i}}=\frac{\Delta\text{d}_{\text{i}}}{\Delta\text{d}_{ \text{max,i}}}, \tag{3}\]