*3.2. Data Acquisition Procedure*

As a starting point in the categorization procedure, each SC provided information on the tamping frequency for the railway lines under their supervision. The tamping activities are usually determined solely on the basis of visual assessment and periodical measurements of the track level. In the study area, the tamping frequency was provided for the year prior to the in-situ assessment which followed.

The next step included expert visual assessment of the sections and the performance of ground-penetrating radar (GPR) investigations. The visual assessment included walking along the selected line sections and recording of detailed photos and video-documentation along with textual description of each phenomena, including its shape, extent, and the potential nature of the irregularity. The assessment was done by a multidisciplinary team consisting of railway inspectors, geotechnical engineers, and geologists.

The GPR investigation methodology included a multi-channel approach in order to detect the phenomena which are defined as attributes for methodology of embankment categorization (Figure 6). For the purpose of distance measurements during data acquisition, a distance measuring instrument (DMI) was attached to the survey wheel of a specially constructed bogey which housed the GPR equipment. In this study, the signal trace separation was 5 cm, leading to 20 traces per m of investigated track. The rapid nature of GPR testing was essential, since the investigations were conducted during the day with minimal line closure as requested by infrastructure managers.

**Figure 6.** Conduction of GPR investigations.

## *3.3. Results and Discussion*

The terminology used in this section includes the following terms: 'line' as the railway line, 'section' as part of the line under investigation, and 'subsection' is a 100 m length of the investigated line. Therefore, for the total of 181.1 km of 18 investigated sections on 18 different railway lines, we had 1811 subsections, which were analyzed and represented the alternatives for the implemented multi-attribute utility theory model. Taking into consideration that sections selected for investigation were part of different lines, the analysis for 18 sections were done independently, bearing in mind that maintenance on those sections would also be performed independently. Sections differed from 1.0 km of length, which had 10 alternatives (10 subsections of 100 m length) to the largest one, which was 31.3 km long and consisted of 313 alternatives. This division was done in agreemen<sup>t</sup> with the Supervision Centers, since it was rational to separately evaluate these groups, rather than implementing categorization procedure for all the lines together. The division will enable infrastructure managers' better insight into the condition of each section within the relevant line, where a subsequent resource optimization can be conducted.

As a first step in implementing the developed methodology in the case study, attributes were evaluated for all alternatives within each section. The quantification values were determined as given by Equations (1)–(5). An example of attribute evaluation is given for a 1000 m long section, divided into 100 m subsections, in Table 5.

Next, a multi-attribute decision-making problem was expressed by an *n* × *m* decisional matrix, *n* being the number of attributes (5 in our case) and *m* being the number of alternatives within one section. Considering the 18 investigated lines, the alternatives were divided into 18 groups (*k* = 1, 2, ... , 18), leading to the formation of 18 *n* × *m* decisional matrices, the smallest one being 5 × 10 and the largest one being 5 × 313. As a first step in calculating the overall utility function of each alternative UiSkj , the normalized utility functions were determined using Equation (6). For example, the normalized utility function value for the GPR fouling Attribute (QVC4) and Alternative (S15) which stands for 'fifth alternative within the first section' was calculated as:

$$\mathbf{U}\overline{\mathbf{U}}\mathbf{s}\_{5}^{1}\mathbf{(}=\frac{\mathrm{QV}\_{\mathrm{C4}}\mathrm{(S}\_{5}^{1}\mathrm{)}}{\sum\_{j=1}^{m}\mathrm{QV}\_{\mathrm{C4}}\mathrm{(S}\_{j}^{1}\mathrm{)}}\tag{11}$$

with

$$\sum\_{i=1}^{5} \overline{\mathbf{U}\_i} \Big( \mathbf{S}\_5^1 \Big) = 1. \tag{12}$$

Further, to define the importance of each of the five attributes in the overall embankment categorization procedure, a developed questionnaire was used to obtain information from experienced experts working in the railway maintenance sector. To overcome the mentioned subjectivity aspect, a questionnaire was delivered to 12 experts, and the results are given in Table 6.


**Table 5.** An example of attribute evaluation from one of the sections.

**Table 6.** Mean values, standard deviations, and calculated weight of importance for attributes.


Taking into consideration the mean and standard deviation (SD) data from Table 6, the weight of importance for each attribute could be calculated. For example, the importance of ballast fouling Attribute (C4) was calculated using Equation (8):

$$\text{BW}\_{4} = \frac{\text{QV}\_{\text{C4}}}{\sum\_{\text{i=1}}^{5} \text{QV}\_{\text{C,i}}} = \frac{8.70}{9.30 + 5.60 + 8.40 + 8.70 + 6.30} = 0.227.\tag{13}$$

The sum of all weights of importance concerning attribute parameters, based on Equation (9), equals 1:

$$\sum\_{i=1}^{5} \mathbf{w}\_i = 0.243 + 0.146 + 0.219 + 0.227 + 0.164 = 1.\tag{14}$$

Finally, the overall utility function values U(S<sup>k</sup> j ) for each alternative was calculated by combining five weights of attribute importance with the normalized utility functions for the five (*n)* attributes and the (*m)* alternatives of specific section using Equation (10). The overall utility function values give the ranking for each alternative. For example, it is calculated for the fifth subsection within the first section:

$$\mathbb{U}\{\mathbf{S}\_5^1\} = \sum\_{i=1}^5 \mathbf{w}\_i \cdot \overline{\mathbf{U}\_i}\{\mathbf{S}\_5^1\}.\tag{15}$$

After the overall utility function was calculated for each alternative within each section (railway line), the development of the final ranking list followed. A classification scheme, as shown in Table 4, was assigned to each subsection and the results are presented in the form, shown in Figure 7, for a 500 m length where the overall condition of the embankment was in the range from very poor to adequate and a second 500 m section where the overall condition of embankment was in the range from adequate to very good.

**Figure 7.** A graphical representation of: (**a**) a 500 m long line section with very poor to adequate condition and (**b**) a 500 m long line section with adequate to very good condition.

The implementation of the multi attribute utility theory thus provided classification of the condition for the investigated railway embankments. The overall classification results, given in Figure 8, represent the summation of classification results for lines selected by each Supervision Center (SC), as well as averaged values, in the form of an overall utility function—an overall percentage graph.

As it can be seen from Figure 8, the categorization results show that most of the investigated embankments, 41.8%, are in an adequate condition and that 33.7% of the embankments are in poor condition, while 12.6% are in a very poor condition. On the other hand, 10% of the investigated embankments are in good condition, with only 1.9% is in a very good condition. The categorization results are consistent for line sections within each Supervision Center. The described procedure of implementing MAUT for railway embankment categorization gave the solid basis for decision-makers to plan further detailed investigation works and monitoring programs as well as remediation measures.

**Figure 8.** Overall utility function—overall percentage categorization summation results.
