## 1 Introduction  
The transverse deformation analysis of structures is usually limited to obtaining Poisson's ratio, which is only applicable to the range of elastic concrete behavior. At the same time, for compression, this range can reach half of the concrete strength. Consequently, the elastic compressed concrete stage is an essential part of concrete behavior investigations [1]. However, according to modern design codes, the elastic stage is limited to about 40% of its strength [2, 3]. Further concrete behavior is characterized by elastic-plastic deformations, which can be graphically represented by a convex square parabola relative to the deformation's axis. If instead of a square parabola, a sinusoidal approximation is used, the difference in potential energy is about 7% [4]. The relationship between stresses (\(\sigma_{c}\)) and strains (\(\epsilon_{c}\)) in compressed concrete is characterized by the following three parts [1]:  
* A linear part from 0 to 0.5\(f_{ck}\), where \(f_{ck}\) is concrete strength;
* A convex parabolic part bound by \(f_{ck}\);
* A descending branch. * Deformations range from 0 to 0.5%, from 0.5 to 2%, and from 2 to 3.5% in the first, second, and third parts, respectively. This relationship was proposed to describe the behavior of normal-strength concrete (NSC) up to class C60. High-strength concrete (HSC) represents classes C70-C90 [2] and exhibits mainly elastic behavior with weakly expressed elastic-plastic deformations [5]. For the more accurate identification of HSC non-elastic deformations, the use of transverse deformation graphs of the compressed specimens was proposed [6]. At the same time, an additional important factor affecting compressed concrete behavior is the specimen's loading rate [7; 8; 9]. The loading rate used in the present research was selected according to standard requirements of modern codes. Following [10], it is recommended to load a concrete specimen at a rate within (0.2... 1.0) MPa/s; according to [11], the recommended rate is (0.25 \(\pm\) 0.05) MPa/s. However, at such loading rates, longitudinal deformations, even for NSC, mainly exhibit elastic behavior [7; 8; 9]. Twenty-two cylindrical NSC specimens were tested under uniaxial loading [7]. The specimen diameters were between 10 and 80 cm, and their heights were from 20 to 320 cm (which corresponds to a real column length). The specimens were loaded at a rate of about 0.1 MPa/s. The obtained \(\sigma_{c}\) vs. \(\varepsilon_{c}\) relationships, when \(\sigma_{c}\) was the compressed concrete stresses and \(\varepsilon_{c}\) was the longitudinal deformations, were characterized by an almost linear performance up until specimen failure. Similar results were obtained for uniaxial loaded 15 \(\times\) 30 cm cylindrical specimens made of steel fibered reinforced concrete with a strength of 27.6 MPa [8]. In this case, the loading rate was 1.3 mm/min (which corresponds to about 0.1 MPa/s). Comparable results were obtained for twenty-six cylindrical NSC specimens loaded at a rate of (0.25 \(\pm\) 0.05) MPa/s [9]. It was shown that in certain cases, particularly in steel-fibered high-strength concrete (SFHSC), transverse deformations efficiently indicate elastic-plastic concrete behavior, which is less pronounced when longitudinal deformations are used [6]. A corresponding theoretical model for the type of transverse cracks and their development as well as a consequent scheme for specimen failure was proposed. Following this concept, the transverse crack development process can be divided into three stages:  
* Linear specimen behavior;
* Nonlinear specimen behavior;
* Ultimate limit state (ULS). The first stage continues until the initiation of cracks (\(\epsilon_{trans}\leq\varepsilon_{ct\;ul}\)), where \(\varepsilon_{trans}\) is the transverse deformation value, and \(\varepsilon_{ct\;ul}\) is the ultimate elastic transverse deformation. At this stage, the cylindrical specimen's cross section is nondamaged and has an original circular shape.