**1. Introduction**

Composite materials belong to an exceptional group because it is difficult to control grain distribution in the material being formed. The most characteristic example of such a composite is concrete, the most broadly used among them in the construction industry. Tests of this material concern both spatial structure (porosity, tightness, pore, and grain distribution) and its basic parameter, that is, compressive strength. Modifications of this composite aim at the improvement of its homogeneity [1–4].

The industrial floor belongs to those building structures in which concrete should be of the highest quality in the top layer because it is exposed to considerable abrasion, local pressure, impacts, etc. Often, the top layer of the concrete floor quickly crumbles (Figure 1) and strength testing using sclerometric methods does not confirm the concrete class determined on control samples [5].

**Figure 1.** Example of crumbling on the top layer of concrete industrial floor: (**a**) General view; (**b**) close-up of cracked surface.

Strength tests on borehole material of small diameter and height, cut out from various depths, indicate often considerable weakening of concrete in the top layer compared to strength determined on samples cut out from a deeper layer. This problem was noticed in the European standard [6], highlighting that in the top layer, compressive strength can be lower than in the bottom layer by as much as 25%. However, the given value is based on tests of samples from a height not lower than 50 mm. Excessive reduction of samples is not acceptable due to the thickness of the maximum aggregate fraction. Practically, it can be assumed that minimum samples are 50 mm high and before cutting off of the top layer approximately 60 mm high. Compressive strength determined on such samples using the destructive method refers to concrete at a depth of 30 mm from the floor top. Many things indicate that most of the unfavorable phenomena accumulate in this 30 mm small layer. Tests on this type of structure should focus first on this layer. Since in the available scientific literature, there are few test results concerning distributions of compressive strength across the thickness of industrial floors in thin cross-sections taking into account the top layers, the authors of this study undertook this task. Recent articles [7–9] shows that acoustic non-destructive methods are suitable for testing concrete strength and heterogeneity. The concrete strength tests presented in this article were performed using the ultrasound method using spot heads. The ultrasonic wave velocities were correlated with the results of destructive tests. The obtained results from tests concerning strength distributions of floors were arranged by types. Additional characteristics of concrete were proposed based on the strength change rate using mathematical bases of quality evaluation.

### **2. Literature Review**

In calculation theories, concrete is usually treated as a homogeneous entity, specified often as quasihomogeneous, at least in the macroscopic sense. The question of the actual heterogeneity of concrete remains open for several reasons. The most important reason is that the accepted test methods do not favor recognition of its heterogeneity. According to the binding standard [10], they are conducted on big material samples: cubes with dimensions 150 mm × 150 mm × 150 mm or cylinders with a diameter of 150 and a height of 300 mm, which blur porosity changes at the height of sample elements.

The heterogeneity of strength for elements with a large height dimension, such as pillars and vertical partitions formed in the built-in position, was the subject matter of a publication. Research showed a weakening of concrete in their horizontal cross-sections along with an increase in the measurement height. Tests conducted during the period from 1962 until 1978 in Japan [11] on concrete elements 4 m high formed in the built-in position indicated a 10% to 20% strength increase in the bottom zone and a 10% to 30% strength decrease in the top zone versus middle cross-sections. Giaccio and Alberto Giovambattista [12] showed a 30% reduction of concrete compressive strength in a water dam

formed in a vertical position along with an increase in the measurement height. The water draining capacity measured experimentally in concrete used to form these elements was more than 10%.

Khatib and Mangat showed that the cement pastes formed horizontally can have the pore volume twice as large near the top layer than near the bottom layer. Pores near the top layer are also considerably larger (from 46% to 98% of pores above 0.1 μm) than pores near the bottom layer (from 38% to 80% respectively) [13]. The weakening of concrete structures in top cross-sections along the direction of forming and strengthening in lower cross-sections is effected mainly by: the designed aggregate composition, type and quality of cement, quantity of fly ash, consistency of the concrete mix, use of chemical additions binding water, and the vibration method applied to the formed concrete element. The intensity of water drainage from the concrete mix and the rate of desegregation of its components depends on these factors. This phenomenon is called 'bleeding' [14–17]. It is a spontaneous process that is the result of the difference in densities between the binding agent, aggregate composition, and water. In the technical literature [18,19], depending on the type and method of making the elements, two types of bleeding are distinguished:


Topics regarding strength distribution at the height of stocky cross-sections formed in a vertical position are researched, described, and characterized in the technical and scientific literature. Superficial bleeding, the homogeneity characteristics of near-surface structures, and strength distribution for concrete floors in thin layers are not topics broadly described in the scientific literature. Information about mathematical criteria used to describe strength variability in industrial floors is also missing. Cases of superficial damage to the floors which are the subject of this study are frequent, therefore the authors undertook such research.

### **3. Materials and Test Methods**

The research project assumed that the analysis would be carried out on samples from borehole materials taken from various regions of the country to avoid any potential material-related errors connected with, for example, the aggregate source. The floors were constructed of concrete class C25/30 and C30/37. Borehole materials with diameters 80 and 100 mm were provided, 6 pieces from each tested floor. They came from floors that were not superficially hardened, from floors with surface hardened using mineral agents and also with resin flooring (Figure 2).

**Figure 2.** Borehole materials from the tested floors: (**a**) cracked surface; (**b**) hardened surface without damage; (**c**) resin flooring on concrete.

The hardened layer in certain areas of the halls became loosened which is regarded as an emergency condition (Figure 3).

**Figure 3.** Tested borehole material from floors with a hardened top layer with damage: (**a**) cracked surface; (**b**) loosened surface.

The presented damage indicates substrate hardening of low strength (weak concrete).

The compressive strength of concrete samples in their various cross-sections was determined with the use of the non-destructive method calibrated with the destructive tests of the samples. This type of examination is being widely used for the range of building materials, such as concrete, wood, steel, ceramics, and for the diagnostics of building structures [20–25]. Tests were carried out with the use of the ultrasound method based on longitudinal wave velocities [26]. Dependencies between ultrasonic pulse velocity (*UPV*), elastic modulus (*E*), and Poisson's ratio (ν) were researched and described [27,28]. Passing wave velocity (*CL*) is proportional to the square root of the dynamic modulus of elasticity (*Ed*), and inversely proportional to the square root of its density (ρ) in Equation (1):

$$C\_L = (E\_d/\rho \cdot (1 - \nu\_d)/(1 + \nu\_d) \cdot (1 + 2\nu\_d)))^{1/2} \text{ (km/s)}\tag{1}$$

In Equation (1), ν*d* is the dynamic Poisson's ratio. The dependency in Equation (1) applies to homogeneous and isotropic materials. Concrete is a heterogeneous material. High attenuation in concrete limits the *UPV* method to low frequencies (up to 120 kHz). Under this condition, ultrasounds do not interact with most concrete inhomogeneities [29] and it can be regarded as a homogeneous material [30]. Scientific literature shows a strict relationship between concrete compressive strength (*fc*) and *UPV* [27,28,30–36]. This dependency is also described in standards [7,37,38]. Komlos and others [36] stated that UPV non-destructive method of strength testing requires the calibration with the results of destructive tests. Authors research conclusions are the same [36,39]. In the presented research, UPV tests were performed using Unipan 543 tester (company, Warsaw, Poland) and spot heads with frequency 40 kHz. The test stand used to measure ultrasonic wave velocity on the tested concrete borehole material is presented in Figure 4. The results of spot heads testing are presented in the studies [35,39,40].

At the beginning of the tests, the borehole materials were first cleaned and dried to air-dry moisture according to the standard [6]. Testing cores were stored in laboratory conditions for 14 days before the tests. Then, in the first stage of the tests, ultrasound test planes were marked along the borehole materials (by height) at a distance of 10 mm from each other. In the marked planes, the velocity of ultrasonic wave transmission was tested in two directions, I and II, perpendicular to each other (Figure 5).

**Figure 4.** Test stand for measuring ultrasound velocity.

**Figure 5.** Location of the measurement planes at borehole heights—1st stage of the tests.

In subsequent batches, the top zone of the floor at the thickness of 3–4 cm was examined in more detail. The planes in which measurements were conducted were compacted, at first every 5 mm, and in certain series every 2 mm (Figure 6).

Such densely located planes for measurement of the ultrasonic impulse were possible because the diameter of the ends of the spot heads used was only 1 mm (Figure 7).

**Figure 6.** Location of the measurement planes at borehole height—2nd stage of the tests.

**Figure 7.** Spot heads with exponential waveguide where the surface area of contact with concrete is 0.8 mm2.

Boreholes were cut thus obtaining samples with ϕ = *h* (length equal to their diameter). To the pulse velocity determined in the middle of each sample height, compressive strength determined on the strength machine as a relation of destructive force *P* (N) to the surface area of cross-section *A* (mm2) of Equation (2) was assigned:

$$f\_{\mathbb{C}} = P\% \text{ A (MPa)} \tag{2}$$

Destructive strength *fc* (MPa) and mean ultrasonic wave velocities *CL* (km/s) from two testing directions (Figure 5, cross-sections, directions I and II), specified in the middle of the height of the cylindrical sample were the basis for determination of the dependency between ultrasonic pulse velocity and concrete strength for the given series of samples. Scaling curves established hypothetically were used to convert the rate of ultrasound wave in the given cross-section at the borehole height into concrete compression strength in this cross-section. The selection of the dependency *fc-CL* was made

independently for each of the tested concretes taking into account different aggregate, different cement, different additions, and also different conditions of execution not known in detail.
