**1. Introduction**

Non-destructive testing methods (NDT) are essential tools in estimating concrete properties (mechanical or physical). A comprehensive analysis of the mechanical properties is useful in the process of structural optimization, as well as in terms of budget efficiency.

In the case of Reinforced Concrete (RC) structures, one of the key properties is the compressive strength. An investigation from this point of view can provide an overview of the structural integrity of a building. Such an analysis helps civil engineers in optimizing the process of structural intervention by deepening the understanding of how the building works from the structural point of view and also considering the concrete mix design and

**Citation:** Bolborea, B.; Baera, C.; Dan, S.; Gruin, A.; Burduhos-Nergis, D.-D.; Vasile, V. Concrete Compressive Strength by Means of Ultrasonic Pulse Velocity and Moduli of Elasticity. *Materials* **2021**, *14*, 7018. https://doi.org/10.3390/ma14227018

Academic Editor: Jie Hu

Received: 3 November 2021 Accepted: 17 November 2021 Published: 19 November 2021

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the associated physical, mechanical, and durability characteristics. Therefore, the interventions can be targeted on those elements that have a deficient behavior, which can induce negative effects into the structure [1–7].

Traditionally, the concrete compressive strength is determined through destructive testing (DT) which is considered the most reliable testing, and thus been referred to as the reference method. In DT, there are identified three possible situations:


In the first situation, this testing is performed in order to evaluate or calibrate different mixing sequences of concrete mixture [8,9]. The samples collected on the construction site during the concrete casting are usually considered in cases of new buildings, to assess and confirm the concrete class [10] or to check compressive strength at intermediate specific terms (identity tests at 1 day, 2 days, 7 days, etc.). In the case of existing buildings, DT is performed by extracting concrete cores from certain concrete elements, such as columns, beams, slabs, diaphragms, etc., and then subjecting them to a compressive load until failure [11]. The preparation of the cores is made with respect to specific regulations and procedures in order to ensure the necessary testing accuracy [12].

According to [13,14] the analysis procedure depends on the amount of available information regarding the existing structure to be evaluated: information about the construction geometry, elements detailing, and material type determine the appropriate Knowledge Level (KL) of the structure under study. There are considered to be three KLs, defined as follows: KL1—limited, KL2—normal, and KL3—full, and to each of them is assigned a Confidence Factor (CF): (CFKL1 = 1.35; CFKL2 = 1.20; and CFKL3 = 1.00). The confidence factor is used as a correction factor for incomplete knowledge and level of uncertainty [11]. To reach a superior level of confidence (KL3 level, for instance), a large number of cores must be extracted from the structure, which can cause several inconveniences such as they can be time- and resource-consuming and also affect the structure itself due to specimens' extraction. Furthermore, the compressive strength may vary within the same element, due to the specific heterogeneity of concrete [15].

NDT represents a possible, viable alternative, mainly in terms of cost efficiency and also as they are fast in delivering results. However, NDT techniques measure indicators that are sensitive to a specific concrete property. For example, the ultrasonic pulse velocity and rebound hammer are sensitive to mechanical properties such as the compressive strength and porosity of concrete [16]. Another major problem pointed out by Angst [17] is the fact that the relation between mechanical properties and measured indicators is not constant. This is attributed to several causes, strongly connected to concrete physical characteristics (its specific heterogeneity, the porosity, water content, aggregate maximum dimension, etc.) and also to element exposure, measured data accuracy, and limited number of measurements.

Over the years, several NDT methods have been developed with the main purpose of estimating, as correctly as possible, the mechanical properties of materials and elements. A short overview of the NDT methods used on concrete structures is presented thus:


the concrete strength on a depth of 2–3 cm, this being the reason why it should be combined with other methods that tests the concrete elements in depth [19].


The most used NDT methods, for estimating concrete compressive strength, are the Schmidt rebound hammer, the ultrasonic pulse velocity, and the sonic rebound (SonReb) which consists of a combination of the first two methods. Făcăoaru et al. [26] developed and described the procedure which consists of applying some correctional factors based on cement type and dosage, granulometry and type of aggregates, and concrete age. SonReb has a high degree of efficiency and is still used worldwide, successfully, in estimating concrete compressive strength. Still, one of the most important disadvantages of the method is its requirements of mix design information regarding the evaluated concrete; in the case of older structures this information is not always available, which may lead to unprecise results. The viability of the method should also be verified on various types of concrete mix design developed with different additions, waste, or by-products (mineral, rubber, plastic, glass, etc.), which gained large diversity in recent years due to environmental protection requirements and Circular Economy implementation [2–4].

Researchers tried to develop various relationships between the measured indicators and the mechanical properties of concrete, by using different techniques, such as response surface (RS) [27–34], data fusion (DF) [35–37], and artificial neural networks (ANN) [38–43]. The empirical relationships developed over the years have a different structure: linear (LN) [40,41], polynomial (PL) [44,45], and power (PW) [46,47]. Sbartai et al. [34] report a satisfactory level in predicting concrete properties based on ultrasonic pulse velocity, ground penetration radar (GPR), electrical resistivity measurements, and data interpretation through the means of the response surface. However, when the data is interpreted with the help of ANN, the results have a higher rate of predictability. Asteris et al. [40] developed and optimized an ANN that considers the ultrasonic pulse velocity and Schmidt rebound hammer as the input values needed in order to estimate the concrete compressive strength. Based on the statistical parameters employed to evaluate the performance, the developed ANN model proved to have high efficiency in estimating the compressive strength, both when applied on its own database and also applied on other databases of

different researchers. Khademi et al. [41] compared different techniques used to predict the 28 days compressive strength of concrete. In their mentioned study, a multiple linear regression (MLR), an artificial neural network, and adaptive neuro-fuzzy inference system models (ANFIS) were implemented with the purpose of finding the most accurate method of estimating concrete compressive strength. It was concluded that both ANN and ANFIS models can predict the concrete compressive strength more accurately than MLR, which proved to be unreliable. This is due to the fact that these models consider the non-linear correlation between the variables used as input data. It was also concluded that the accuracy of prediction is influenced by the number of input variables.

Breysse concluded [16] that a universal law between NDT and concrete compressive strength does not exist, despite the fact that many authors tried to find one.

This paper aims to present a methodology in estimating the concrete compressive strength by using ultrasonic pulse velocity as the only on-site testing method and a series of mathematical relations connecting the UPV with the moduli of elasticity (dynamic and static) and finally with the compressive strength.

#### **2. Materials and Methods**

#### *2.1. The Destructive Method (DT)*

This method is considered to deliver the most reliable results regarding the concrete compressive strength and, in this study, all results are reported to this method, considered to be the reference one. Consequently, the precision rate of the proposed method is also established with respect to the DT, as reference base of evaluation. DT consists of extracting concrete cores from the existing elements, cores which are then subjected to a series of laboratory processing and conditioning after which they are subjected to compression load until failure. The resulting compressive bearing capacity (fcar) is corrected by a series of coefficients described in Equation (1) provided by Romanian Norm NP 137 [12], thus resulting in the equivalent concrete compressive strength (fis).

$$\mathbf{f\_{is}} = \mathbf{a} \cdot \mathbf{b} \cdot \mathbf{c} \cdot \mathbf{e} \cdot \mathbf{g} \cdot \mathbf{d} \cdot \mathbf{f\_{car}} \tag{1}$$

where: fis—equivalent concrete compressive strength (MPa); a—coefficient that takes into account the influence of the core diameter; b—coefficient that takes into account the height/diameter ratio; c—coefficient that takes into account the influence of the degraded layer; e—coefficient that takes into account the nature of the leveling layer; g—coefficient that takes into account the humidity of the concrete core; d—coefficient that takes into account the position and diameter of the reinforcement bars; and fcar—resulted compressive bearing capacity (MPa).

As mentioned in the previous paragraph, destructive testing inflicts damage on the tested element; therefore, the number of cores must be maintained to a minimum in order to preserve the structural integrity of the element. For this reason, it is possible that the obtained values, calculated on an insufficient number of specimens, namely extracted cores from a designated element or assembly, do not reflect the overall value of the compressive strength of the targeted element. Additionally, in some cases, the extraction of the concrete core itself can prove to be difficult or even impossible to perform due to technological conditions such as the position of the designated element in the structure, the possibility to fix the drilling machine in order to extract the concrete core, etc.
