*2.1. Materials*

The composition of the concrete mix intended for the track slab has been designed on the basis of the method of three equations in accordance with the requirements set out in the technical documents [23–26]. In the further part of the article, cement concrete intended for the track plate is marked with the symbol Z1.

Due to the fact that block supports are prefabricated elements and the design of the concrete mix is a trade secret, the components of concrete intended for block supports were selected on the basis of information obtained from the manufacturer of the ÖBB-PORR system and analogies to the requirements set out in "the Technical Conditions for the Execution and Acceptance of Prestressed Concrete Sleepers and Turnouts Id-101" [27]. In order to analyze the strength parameters in concrete intended for block supports, an additive in the form of fibers was used. Concretes in the further part of the article will be marked as:

Z2—concrete with the addition of steel fibers, Z3—concrete with the addition of polymer fibers, Z4—concrete with the addition of glass fibers, Z5—reference concrete, without the addition of fibers.

For concrete mixes, fine aggregate 0/2 from the Zabiny mine (Mor ˛ ˙ ag, Poland) and granite coarse aggregate with fractions 2/8 and 8/16 from the Graniczna mine (Strzegom, Poland) were used. The concrete mix intended for the Z1 track slab was made using CEM I 42.5 N/NA cement from the WARTA company (Tr˛ebaczew, Poland), while CEM 42.5 R cement from the CEMEX company (Warsaw, Poland) was used to make the concrete mix intended for Z2–Z5 block supports. The properties of the cements used are shown in Table 1. Design assumptions for concrete mixtures are listed in Table 2 and laboratory prescriptions in Tables 3 and 4.


**Table 1.** Properties of cements.


**Table 2.** Assumptions for concrete mixes.

**Table 3.** Concrete mix design for track slab (Z1).


**Table 4.** Design of concrete mix for block supports.


The dosage of fibers in individual mixtures meets the requirements specified by the manufacturer and the standard provisions [28,29].

In the concrete mix intended for block supports Z2, steel fibers for concrete were used, from the Siatpol company (Majdan Stary, Poland) with a length of 50 mm in the amount of 25 kg/m<sup>3</sup> of concrete mix. The concrete mix intended for Z3 block supports uses Polyex Duro polymer fibers from the Astra company (Straszyn, Poland) with a length of 25 mm, in the amount of 4.5 kg/m<sup>3</sup> of concrete mix. The Z4 blend uses CemFil Hp Macro glass fibers from the Serra-Ciments company (Barcelona, Spain) with a length of 36 mm in the amount of 1 kg/m<sup>3</sup> of concrete mix. The dosage of the fibers was based on the manufacturer's recommendations and the standard provisions [28,30]. The parameters of fibers used are summarized in Table 5 and shown in Figure 1.

**Table 5.** Parameters of fibers.


**Figure 1.** Fibers used: (**a**) steel, (**b**) polymer, (**c**) glass.

### *2.2. Research Methods*

The first study that was carried out was the study of the consistency of the concrete mix. The consistency of the mixture was determined by the Abrams cone fall method. The consistency test was carried out in accordance with PN-EN 12350-2:2011 Concrete mix tests—part 2: Consistency testing by the cone fall method [31].

Another test was the compressive strength test of cement concrete samples. This test was performed on cubic samples with dimensions of 150 mm × 150 mm × 150 mm in accordance with the provisions of PN-EN 12390-3:2019 Concrete tests—Part 3: Compressive strength of samples for testing [32]. Due to the possibility of random results, the number of samples to be tested was determined in accordance with PN-EN 206:2014 Concrete— Requirements, properties, production, and conformity [23]. The test was carried out with the use of the FORM TEST MEGA 6 3000-150 testing machine (Figure 2). Concrete samples after the compressive strength test are presented in Figure 3.

**Figure 2.** Sample during compressive strength test.

**Figure 3.** Concrete samples after compressive strength test.

The next study aimed at determining the parameters of the designed cement concretes was the study of the frost resistance of concrete. This test was carried out by the usual method in order to verify the degree of frost resistance F assumed at the design stage of the mixture. However, this degree in the assumptions corresponds to the N index, which is equal to the number of expected years of use of the structure. The usual method makes it possible to take into account the degree of internal destruction of concrete, characterized by the decreased strength of the sample, as well as the external destruction, determined by the loss of mass of the sample. The frost resistance test was carried out in accordance with PN-88/B-06250:1988 Ordinary concrete [33]. The test was carried out with the use of the TOROPOL K-15 testing machine. Samples prepared for frost resistance testing in this device are shown in Figure 4.

**Figure 4.** Samples prepared for frost resistance testing.

In order to determine the physical parameters of the designed cement concretes, a study of the elastic modulus was carried out. Cylindrical samples with a diameter of 150 mm and a height of 300 mm were prepared for the study. The study of elastic modulus was carried out using two methods. The first method consisted in determining the modulus of elasticity using the resonant method. In this method, the modulus of elasticity is determined by the propagation of the waves in the sample. Vibrations are caused by hitting a ball of a properly selected diameter on the base of the cylinder. Based on the measured wave, the device determines the frequency of vibrations and the modulus of elasticity of the tested material. This test is a non-destructive test of the element under study. The test was carried out with the use of the JAMES INSTRUMENT V-E-400 testing machine (Figure 5). In the second method, tests of the elastic modulus were carried out in accordance with PN-EN 12390-13:2014 Concrete tests—Part 13: Determination of the secant modulus of elasticity at compression [34]. The test was carried out with the use of the FORM TEST MEGA 6 3000-150 testing machine (Figure 6).

**Figure 5.** Resonance testing of the modulus of elasticity.

**Figure 6.** Testing of the secant modulus of elasticity at compression.

The main part of the experimental research was to determine the impact of the stiffness and strength of block supports on the strength of the entire ballastless surface, and thus on the strength of the track plate made of cement concrete. According to the adopted model, there are tensions of concrete in the track plate. At the same time, under the block supports, the forces from the wheeled vehicle cause the concrete to stretch downwards, and in the middle of the length of the slab the phenomenon of lifting the slab is triggered. The plate load model adopted for the cross-sectional test is shown in Figure 7.

**Figure 7.** Load distribution model adopted for the test.

Due to the research possibilities, in order to check the tensile strength when bending the track plate with embedded block supports, a laboratory sample constituting 30% of the actual dimensions was prepared. The dimensions of the sample on which the tests were carried out were 100 mm × 150 mm × 750 mm and were adapted to the forms equipped by the laboratory. Figure 8 shows a diagram of the test samples, and Figure 9 shows the sample.

**Figure 8.** Cross-section of the laboratory sample (dimensions are described in mm).

**Figure 9.** Laboratory sample prepared for testing.

The tests (Figure 10) were carried out for all cement concretes Z2–Z5 intended for use in block supports. The load was applied in the middle of the block supports so as to map the forces occurring in the structure. The support points were taken at a distance of 5 cm from the edge of the sample. The adoption of such a spacing of supports was aimed at recreating the variant of the destruction of the substructure during the operation of the railway line.

**Figure 10.** Sample in the test machine (in a model: red arrows—forces generated by the vehicle wheel, green arrows—reaction forces generated by the machine support).

This destruction consists in settling or washing the foundation from the central part of the support. The stress value of the samples is based on the following formula.

$$
\sigma\_{\mathcal{S}} = \frac{\mathbf{P} \cdot \mathbf{z}}{2 \cdot \mathbf{W}\_{\mathcal{S}}} \tag{1}
$$

where:

P—force acting on the sample (kN), z—distance of force from the support—0.05 m, *Wg*—index of the bending strength of the rectangular cross-section relative to the vertical axis.

Another test aimed at determining the strength of block supports on the strength of the entire surface was to check the strength of the longitudinal section. The purpose of this test was to check the load capacity in the direction along the track, derived from the axle load of the bogie of the AEG12X locomotive, with a spacing of 2.60 m. The axle load of the locomotive is 210 kN. The plate load model adopted for longitudinal section testing is shown in Figure 11.

**Figure 11.** Scheme of loading the railway surface with a locomotive.

In order to check the tensile strength when bending along the surface, samples measuring 10 × 15 × 100 cm were prepared. The construction of the surface was made on a scale of 0.3. It is therefore the same scale factor as in the case of cross-sectional testing. In addition to the limited availability of large molds for making samples, the choice of scale factor in this study was dictated by the capabilities of the strength testing machine. Additionally to the limited availability of large molds for making samples, the choice of scale factor in this study was dictated by the capabilities of the strength testing machine. Figure 12 shows the designed test sample with dimensions in cm. In addition, Figure 13 shows the prepared sample for testing.

**Figure 12.** Diagram of the test sample—dimensions are expressed in cm.

**Figure 13.** Prepared sample for bending strength testing.

A sample after the bending strength testing is shown in Figure 14 (test machine is shown in Figure 10).

**Figure 14.** Sample after bending strength testing—dots were used to register the movement of the sample with the PHANTOM MICRO LC310 camera—not described in this article.

The research was carried out for four types of block supports. The load was applied, as in the previous test, in the middle of the block supports. Support points are adopted at a distance of 5 cm from the edge. The stress values in the samples were determined in the same way as in the previous test, i.e., according to Equation (1).
