*2.2. Selection of Attributes*

The aim of the proposed methodology is to improve the process of prioritization of multiple assets by taking into account multiple attributes. The model makes use of existing data available from railway agencies and improves the quality of information by including the results of non-destructive GPR inspection results. Therefore, the attributes which represent historical performance (maintenance data), experts' judgment on the condition (visual inspection), and GPR inspection results are selected. In total five attributes are selected, and the quantification of each attribute is in the range 0 to 1. For each of the attributes, it is important to define the so called 'quantification starting value' (QSV), since it provides clear quantification procedure, making the decision-making process fully transparent and well followed. All other quantification values (QV) are evaluated in respect to QSV.

### 2.2.1. Attribute 1: Maintenance History

One of the useful indicators about the actual performance of the infrastructure is information on the frequency and extent of past maintenance. For embankments, the main regular intervention performed is ballast tamping, while ballast cleaning or renewal interventions are performed occasionally [11]. In this work, the frequency of tampering activities is taken into account as the relevant attribute. From the whole data set, a maximum number (fmax,t/y,i) of tampering per year is assigned a quantification starting value (QSV) of 1, while the no-tampering events per year ge<sup>t</sup> the quantification value 0. Intermediate values are calculated as follows:

$$\text{QV}\_{\text{C1,i}} = \frac{\text{f}\_{\text{t}/\text{y,i}}}{\text{f}\_{\text{max,t}/\text{y,i}}} \, ^\prime \tag{1}$$

where C1 represents Attribute 1, QVC1 represents the quantification value of Attribute 1, and ft/y,<sup>i</sup> represents the tampering frequency per year for an observed section of a railway line, while fmax,t/y,<sup>i</sup> represents the tampering frequency per year for the most tampered section along the investigated railway line.

#### 2.2.2. Attribute 2: Visual Assessment of External Irregularities

Visual inspections of railway embankments are performed by experienced engineers, with the overall aim of recording visible irregularities along the line. The engineers' remarks about the observed irregularities, as well as detailed photo-documentation, are used to define Attribute 2. It has to be noted that it is very challenging to quantify the irregularities due to their different nature and impact on the overall embankment condition as well as their extent. For example, a logical question could be, would a section with two small landslides observed have a higher QV value than a section with a single larger landslide? To overcome these issues, a percentage of length of irregularity extent in comparison to total section length is defined as the relevant quantifiable attribute. The following irregularities should be considered:


From the whole data set, the maximum number of irregularities (Vmax,RI,i) per section is assigned a quantification starting value (QSV) of 1, while 'no visible irregularities' is assigned a value 0. The rest are calculated as follows:

$$\text{QV}\_{\text{C2,i}} = \frac{\text{V}\_{\text{IR,i}}}{\text{V}\_{\text{max,IR,i}}} \, \text{} \tag{2}$$

where C2 represents Attribute 2, QVC2 represents the quantification value of Attribute 2, and VIR,i represents the number of visually determined irregularities for an observed section of a railway line, while Vmax,IR,i represents the number of visually determined irregularities for the section with the most irregularities along the investigated railway line.

#### 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.

#### Attribute 3: The Depth of Ballast Layer (Ballast Pockets)

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 easily obtained. 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.

**Figure 1.** Determination of ballast pockets: (**a**) Ground Penetrating Radar trace in case of ballast pocket formation and (**b**) radagram showing the features for the determination of Attribute 3.

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 20th signal trace. After determination of measured depth for each trace, an averaging procedure for the whole investigated section follows.


**Table 1.** Methodology steps for the determination of ballast layer depth.

Δdmax,i is determined by the same methodology as given in Table 1, and it represents the line section with the highest average measure depth ( dmeasured,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:

$$\text{QV}\_{\text{C3,i}} = \frac{\Delta \text{d}\_{\text{i}}}{\Delta \text{d}\_{\text{max,i}}},\tag{3}$$

where C3 represents Attribute 3, QVC3 represents the quantification value of Attribute 3, and Δdi represents the measured value of ballast depth minus the designed depth of 0.5 m for an observed section of a railway line, while Δdmax,i represents the maximum measured value of ballast depth minus the designed depth of 0.5 m for the section with measured maximum ballast depth along the investigated railway line.

#### Attribute 4: Ballast Fouling (Quality of Ballast Layer)

High-frequency antennas are also used for the determination of ballast fouling. Ballast fouling is a direct consequence of the ballast aging process, where fine-grained materials fill the ballast void spaces, leading to track instability with serious implications on track drainage [32]. Even though GPR is commonly used for the inspection of ballast fouling, Panjamani et al. [10] state that there are no robust guidelines to find the degree and type of fouling quantitatively. A good quality, clean ballast is approximately of 30–60 mm size and should be dry. Therefore, GPR signal scattering should be prominent as shown in Figure 1a. However, if the layer is infiltrated with fine-grained materials and consequently with water, more attenuation could be expected (Figure 2a). A fouled ballast does not scatter emitted energy so much, since the air gaps are now filled with smaller grain materials. This principle is widely accepted as a good way to assess the degree of ballast fouling [33]. An example of a clean ballast zone and a fouled ballast zone is given on the radargram in Figure 2b.

**Figure 2.** Determination of ballast fouling: (**a**) Ground Penetrating Radar trace in case of ballast fouling and (**b**) radagram showing the di fference between clean and fouled ballasts.

After basic processing, each GPR trace is extracted from the radargram and subjected to further analysis by using a MATLAB developed code. Several steps are conducted in order to determine a quantifiable value for Attribute 4, relevant for each section of a line. As a first step, a trace is divided into several depth zones, each with a pre-defined depth of 10 cm. The total number of zones (kmax) depends on the overall position of the ballast layer bottom. Next, the maximum amplitude of each depth zone is determined, where an amplitude envelope is constructed by connecting the peaks of the reflections down a trace (Figure 3).

**Figure 3.** Elements of a single Ground Penetrating Radar trace for the determination of ballast fouling.

A lower amplitude value could be associated with a fouled ballast. After determining the amplitude ratio Ai/A0 for each depth zone, an averaging procedure for the whole trace is conducted with the determination of an average amplitude decrease (AAD) ratio for a single trace. From there, ballast fouling (%) is determined for a single trace, followed by the calculation of average ballast fouling for the whole investigated section. The overall steps for the determination of a ballast fouling percentage for a provisional 100 m long section of railway line are shown in Table 2. It is recommended to utilize signal trace separation of maximum 5 cm (horizontal resolution), leading to 20 traces/m of the investigated line, with each trace divided into at least 512 samples (vertical resolution). For the ballast fouling evaluation, each signal trace should be analyzed.

**Table 2.** Methodology steps for the determination of ballast fouling.


BQmax,i is determined by the same methodology as given in Table 2, and it represents the line section with the highest average fouling percentage. A non-fouled ballast (clean-ballast) has a 0% fouling degree (QSV of 0). A QSV of 1 is attributed to the section with highest fouling degree, while the rest are calculated as follows:

$$\text{QV}\_{\text{C4,i}} = \frac{\text{BQ}\_{\text{i}}}{\text{BQ}\_{\text{max,i}}},\tag{4}$$

where C4 represents Attribute 4, QVC4 represents the quantification value of Attribute 4, and BQi represents the value of ballast fouling (in %) for an observed section of a railway line, while BQmax,i represents the value of ballast fouling for the section with the lowest quality/maximum fouling of ballast along the investigated railway line.

Attribute 5: Irregularities in Sub-Ballast and Embankment Fill

Although Selig and Waters [34] note that degradation mostly a ffects the ballast layer, it is important to map and detect defects in the sub-ballast and subgrade layers. In this case, lower frequency antennas are used to locate anomalies in the sub-ballast and embankment fill (voids, animal burrows, water erosion channels, etc.). Reflections of the emitted waves occur when the signal reaches boundaries and/or anomalies at larger depths. The presence of irregularities results in specific signal trace peaks (Figure 4a). If the anomaly is in the form of a void within the investigated layers, for example, animal burrows, it shows in the radargram in the form of a hyperbola (Figure 4b). The parameters of these hyperbolas are commonly determined by utilization of generalized Hough transform or, recently, by utilization of neural network tools to reduce the analysis time [35].

**Figure 4.** Determination of deeper irregularities: (**a**) Ground Penetrating Radar trace in case of deep irregularity presence and (**b**) radagram showing the detected hyperbolic phenomena.

(**a**) (**b**)

From the whole data set, the maximum number of deep irregularities ( Dmax,IR,i) per section is assigned a quantification starting value (QSV) of 1, while 'no deep irregularities' is assigned a value 0. The rest are calculated as follows:

$$\text{QV}\_{\text{C5,i}} = \frac{\text{D}\_{\text{IR,i}}}{\text{D}\_{\text{max,IR,i}}} \text{},\tag{5}$$

where C5 represents Attribute 5, QVC5 represents the quantification value of Attribute 5, and DIR"i represents the number of deep irregularities for an observed section of a railway line, while Dmax,IR,i represents the number of deep irregularities for the section with the maximum number of irregularities along the investigated railway line. These values are determined based on a visual assessment of each radargram, by counting the number of hyperbolic phenomena for each investigated section.

#### *2.3. Implementation of Multi-Attribute Utility Theory*

To e ffectively implement MAUT into a methodology for railway embankment condition assessment, several steps need to be considered. A detailed description of the mathematical basis of the MAUT approach is presented in [36–38]. After the selection and determination of the quantification values of the attributes (QVC) using Equations (1)–(5), the following step includes calculation of the utility function values for the selected '*n*' number of attributes (five attributes are proposed in the paper) and ' *m*' number of alternatives. An alternative (S) is defined as 'a sub-section of pre-defined

length'. In this case, 100 m long sub-sections were considered, which determine the resolution for categorization. Any other resolution length, adapted to the character of specific problem and to the needs of infrastructure managers, can also be considered.

The overall MAUT problem can be expressed by an *m* × *n* decisional matrix, having the form as shown in Table 3.


**Table 3.** The Multi Attribute Utility Theory matrix for railway embankment condition assessment.

The normalized utility function values can be determined using the following equation:

$$\overline{\rm U\_i}(\mathbb{S}\_{\mathbb{I}}) = \frac{\rm QV\_{C,i}(\mathbb{S}\_{\mathbb{I}})}{\sum\_{j=1}^{m} \rm QV\_{C,i}(\mathbb{S}\_{\mathbb{I}})} \, ^{\prime} \tag{6}$$

where 

Ui Sj —normalized utility function value for Attribute *i* and Alternative *j*

Sj—Alternative *j*, subsection of 100 m in length; j = 1, 2, ... , m

*m*—number of alternatives

QVC,i—quantification value of Attribute *i*; i = 1, 2, ... , n

*n*—number of attributes

> The sum of all utility function values for a specific alternative is equal to 1:

$$\sum\_{i=1}^{n} \overline{\mathbf{U}\_{i}}(\mathbf{S}\_{i}) = 1. \tag{7}$$

The next step in the implementation of MAUT includes the evaluation of the importance of each selected attribute. To do this, a grading scheme is established, where the grading of importance of each attribute for the embankment condition assessment is conducted by attributing a grade ranging from 1 (negligible importance) to 10 (extremely important). This information was collected using a questionnaire completed by experienced engineers working in the field of infrastructure management. The determination of each attribute's importance is thus by nature subjective, reflecting the experience and risk acceptance of the engineers in question. After determining mean values and standard deviations of the assigned grades, a weight of importance for a specific attribute can be calculated by:

$$\mathbf{w}\_{\mathbf{i}} = \frac{\mathbf{Q} \mathbf{V}\_{\mathbf{C},\mathbf{i}}}{\sum\_{\mathbf{i}=1}^{n} \mathbf{Q} \mathbf{V}\_{\mathbf{C},\mathbf{i}}} \,' \tag{8}$$

where

wi—weight of importance for Attribute *i*

> The sum of all weight values for all attributes is equal to 1:

$$\sum\_{i=1}^{n} \mathbf{w}\_i = 1\,\text{.}\tag{9}$$

Finally, the overall utility function values U(Sj) for each alternative are calculated by combining the calculated utility functions (Equation (6)) and the weight of importance (Equation (8)):

$$\mathbb{U}\left(\mathbb{S}\_{\mathbb{I}}\right) = \sum\_{i=1}^{n} \mathbb{w}\_{\mathbb{I}} \cdot \overline{\mathbb{U}\_{\mathbb{I}}}(\mathbb{S}\_{\mathbb{I}}).\tag{10}$$

where

USj —the overall utility function value for Alternative *j*

After the overall utility function is calculated for each alternative, the development of a final ranking list is completed as follows. A classification list is developed for five (5) categories ranging from an embankment in a very poor to very good condition. The appropriate MAUT condition for each category is shown in Table 4. The list is color-coded in order to be easily comprehensible for railway infrastructure managers.


**Table 4.** Categorization representation with Multi Attribute Utility Theory conditions.

A higher value of overall utility function for a specific alternative reflects a larger number of visible as well as deeper (GPR) anomalies, larger ballast depth, lower ballast quality, and more tampering activities per year.
