## 2 Methods Used for Determining the Compressive Strength of Concrete
### Non-Destructive Testing of Concrete
#### 2.2.2 Non-Destructive Ultrasonic Pulse Velocity Method (UPVM)  
With UPVM, it is possible to be performed periodic or continuous measurements for the same test points throughout the service period of a reinforced concrete structure, and there is the possibility of automating the process and detecting damages. Non-destructive UPVM uses the propagation of ultrasonic waves introduced into concrete [2; 4; 13; 21; 28; 29; 30; 31]. These consist of longitudinal, transverse and surface waves. Longitudinal waves have the highest velocity. Devices using this method consist of two transducers (a transmitter and a receiver), a high-frequency signal generator, a device for amplifying signals from the receiver and a display for visualizing the results [3]. They are used to measure the time the ultrasonic pulses take to pass from the transmitter to the receiver; knowing the distance between them, the velocity of the ultrasonic signal can be calculated. With this method, the probabilistic compressive strength, homogeneity and the probabilistic modulus of elasticity of the concrete, as well as the presence of cavities, internal defects, cracks and changes occurring over time in the characteristics of concrete, etc., can be determined. A disadvantage of using UPVM is the difficulties associated with the inhomogeneity of the concrete, which must be taken into account in the measurements. The speed of the ultrasonic signal is influenced by the characteristics of the concrete components [4; 22; 30] and its dependence on them is very complex (involving the size and type of coarse aggregate, the class of cement and water-cement ratio). These characteristics include the age, the moisture content of the concrete, the presence of cracks, concrete delamination, the temperature, the length of the signal path, the contact between the transducers and the surface of the structure, the presence of reinforcement, etc. The influence of these factors has been studied by many researchers [3; 22; 30] and they clearly indicate the need to establish correlations between ultrasonic pulse velocity measurements and standard destructivetests of specimens, prepared on the day of laying the concrete mix in the reinforced concrete elements, or cylindrical cores taken from existing reinforced concrete structures. More than 70 models (linear, power, exponential, polynomial and miscellaneous) are known in the scientific literature, expressing a relationship between the compressive strength of concrete and the ultrasonic pulse velocity [1; 6; 20; 26]. The probabilistic compressive strength of concrete in this study was determined using each of the following two approaches:  
* Approach 1: the dependence of \(\mathrm{f_{c,UPV,app1}}\) on the velocity of the ultrasonic signal \(\mathrm{V_{UPV}(km/s)}\) was calculated with the following formula [3; 22; 33; 32]: \[\mathrm{f_{c,UPV,app1}}=\mathrm{c.V_{UPV}^{3,75}},\] (1) where \(\mathrm{c}\) is a factor. * Approach 2: dependence of \(\mathrm{f_{c,UPV,app2}}\) on the weight per unit volume and dynamic modulus of elasticity of concrete, which were determined based on the velocity of the ultrasonic signal. In [20], a methodology is presented for determining the probabilistic compressive strength of concrete in existing reinforced concrete structures using UPVM and equations that relate the velocity of the ultrasonic pulse to the dynamic and static modulus of elasticity and from there to the compressive strength. \[\mathrm{f_{c,UPV,app2}}\;=\;\left(E_{\mathrm{c,s}}^{2}200\right)\cdot\left[2,1.10^{5}\cdot(\gamma_{\mathrm{c}}/2,3)^{1.5}\right]^{2}, \tag{2}\]  
where \(\gamma_{\mathrm{c}}\) is the air-dry density of concrete (in kg/m) and \(\mathrm{E_{c,s}}\) is the static modulus of elasticity of concrete (in MPa).