*2.4. Experimental Procedure*

The study was conducted on 90 concrete cores with a diameter of 74 and 94 mm, extracted from different elements of different structures (Figure 1). The elements include the raft foundation, columns, beams, and reinforced concrete walls. After the extractions of the cores, the processing was conducted in accordance with Romanian Norm NP 137 [12]. The specimens were cut at both ends with a wet diamond disk and then dry air stored in laboratory conditions T: (21 ± 3) ◦C and RH: (50 ± 5)%, in accordance to Romanian Norm NP 137 [12]. The core specimens were cured for five days before weighting and UPV testing. This conditioning was performed to avoid that the humidity resulting from the wet cutting would affect the UPV data. Figure 1 presents the concrete sample after specific cutting and conditioning and before the destructive testing.

**Figure 1.** Concrete core specimens.

The as-received state density was determined with respect to SR EN 12390-7 [58] by specimens air-dry curing and then their measuring (diameter and height, for volume calculation), followed by their weighting. Then, the specimens were tested via UPV with a Tico Proceq device equipped with 54 kHz transducers (Figure 2). The coupling agent for the transducers was Vaseline. The last step was testing destructively the specimens, in compression. This procedure was conducted with respect to SR EN 12390-3 [59] which stipulates the curing and the testing conditions: the recommended dimensions of the concrete cores, the air-dry exposure, the preparation, and positioning, etc., as well as the loading rate. The destructive testing was conducted with a hydraulic press at a loading rate of 0.6 MPa/s.

**Figure 2.** UPV testing.

Figure 3 presents the flowchart of the proposed method, consisting of the sequence of the major considered steps, in terms of experimental testing (black curve contour) and the corresponding parameters (light blue contour) determined by using the previously collected data.

**Figure 3.** Flowchart of the presented method.

#### **3. Results and Discussions**

#### *3.1. Proposed Method Compared to DT*

For a more accessible interpretation of the results, the core specimens were divided into four groups. The considered division criterion is the value of compressive strength (fis) determined via the Destructive Method, as follows:


The theoretical methods for assessing the concrete air-dry density and compressive strength, for the four considered groups of specimens, were statistically evaluated with respect to the experimental and reference procedures, in terms of coefficient of variation (CoV), and also the accuracy (Ac).

CoV is defined by Everitt [60] by the means of Equation (11), as the ratio between the standard deviation (σ) and the mean value (μ) of the group of specimens where applied.

$$\text{CoV} = \frac{\sigma}{\mu} \tag{11}$$

where: CoV—coefficient of variation (%); σ—standard deviation; and μ—mean value.

The air-dry density and compressive strength (measured and predicted) were also analyzed in terms of accuracy, defined in accordance with ISO 5725-1 [61] as the ratio between the predicted value (result of the proposed method) and the "true" value, provided by the reference method. Accuracy was calculated by the use of Equation (12).

$$\mathbf{A\_{c}} = \frac{\text{Predicted value}}{\text{Measured value}} \cdot 100 \tag{12}$$

where: Ac—accuracy (%).

Table 1 presents the air-dry density values for each of the four specimen groups, determined by using both methods: the experimental method, (comprises specimens' measurement and weighing) and the Salman theoretical method (based on UPV individual values) [56]. The accuracy was calculated by using as input data the mean values recorded for each of the four groups of core specimens.



Figures 4 and 5 present a graphical representation of the mean values and accuracy of measured and predicted density. With an accuracy ranging between 98% and 99%, the theoretical Salman method [56] for determining the density via UPV testing proves to be a viable approach. This conclusion is also supported by the CoV values, ranging from 1.3% to 2.7% for the reference method (experimental measurements) and presenting

a more compact range of smaller CoV values, from 0.4% to 0.8%, for the theoretical, Salman approach.

**Figure 4.** Air-dry density, mean values.

**Figure 5.** Air-dry density, the accuracy of the NDT method with respect to the reference.

Table 2 presents the results of compressive strength for each of the four core groups, determined by both methods: the proposed method (UPV testing and interpretation via moduli of elasticity) and the reference, destructive testing.


**Table 2.** Compressive strength.

In terms of compressive strength, which is the main focus of the study, a graphical representation of the mean values and accuracy for each of the four groups is presented in Figures 6 and 7. The specimens sorting into four distinct groups function of the compressive strength, as previously specified, was considered proper for a better understanding of the phenomenon and to facilitate the data processing and the scattering of results. The wide range of values for the DT compressive strength (fis) can be noted, with a minimum of 15.8 MPa and a maximum of 38.9 MPa. Additionally, the corresponding values for the NDT testing (fc) range from 15.1 MPa to 37.0 MPa (Table 2).

**Figure 6.** Compressive strength, mean values.

The accuracy of the proposed method for compressive strength determination via UPV and moduli of elasticity was also calculated using Equation (12), with respect to the mean values for each of the four groups of core specimens, presented in Table 2. The obtained results proved to be satisfactory, as the variation is very small with respect to the DT, regardless of the wide range of values. This conclusion is also supported by the CoV values (Table 2), ranging from 4.7 to 6.8% for the reference method and offering a similar compact range of values from 7.7 to 10% for the proposed method.

**Figure 7.** Compressive strength, the accuracy of the proposed method related to the reference.

Furthermore, when analyzing each group, it can be noticed that for groups 1, 2, and 4, the theoretical compressive strength, evaluated via the proposed method, tends to be a little overestimated with respect to the reference (2.8, 2.7 and 0.9%, respectively), while in the third group there is a clear match of the values.

Figure 7 graphically presents the accuracy evaluation, in terms of mean values. It can be noticed that the values are ranging from 93 to 94%.

As presented in Figure 7, the precision of this method in terms of Ac reaches 93% for the first two groups, 94% for the third group, and 92% for the fourth group. Considering all the values, the mean value of the precision is up to 93%.

Figure 8 presents a graphical representation of the correlation between experimentally determined compressive strength (fis) and predicted compressive strength (fc) is presented.

**Figure 8.** Correlation between experimental and calculated compressive strength.

A good correlation is achieved between the two sets of values. The coefficient of determination r2, which is a statistical indicator of the quality of the theoretical model, is in this case equal to 0.78.
