## 1 Introduction  
Concrete is the most popular construction material in the world, but its known disadvantages are low tensile strength, brittleness, and limited crack resistance [1]. Many experimental studies demonstrate that adding steel fibers can improve the mechanical properties of concrete [2, 3]. Steel, basalt, polypropylene, glass, and other types of fibers are used in the concrete industry [4]. The addition of fibers improves the concrete properties and makes its use in modern construction more effective. As is known, creep and shrinkage are two properties that increase the deformations in reinforced concrete (RC) structures under long-term loads [5]. Even without considering the effects of fibers, the mechanical behavior of reinforced concrete (RC) structures is complex due to effects such as shrinkage, creep, and cracking [6]. Additional deformations in RC structures during the lifetime period (commonly 50 years) due to creep are about three times higher than the elastic ones. Therefore, the concrete creep problem is one of the important aspects that are given special attention in modern codes [7, 8, 9, 10, 11] for the design of RC structures at the serviceability limit state (SLS). Experimental results on the creep of high-strength concrete (70 MPa) and normal-strength concrete (40 MPa) were presented [12]. It was reported that creep strains of high-strength concrete are smaller than those of normal-strength concrete at all stress-strength ratios. The relation of creep to stress-strength ratio was found to be linear for the two grades of concrete. A theoretical method to derive the concrete creep from the compressive creep test results was developed [13]. Three types of high-strength concrete were cast for the creep tests. The results demonstrated that concrete creep without considering the stress relaxation effect decreases by 4.3\(\sim\)11.0% when 6.7\(\sim\)13.1% of the applied stresses relax during the creep tests. A software based on finite element methods was adopted to test available creep models [14]. A comparison of numerical and experimental results has shown that the algorithm can be used to model the creep of high-strength concrete if the material properties are previously experimentally assessed. Although wide research on concrete creep was carried out during the last century, design codes still include experimentally based empirical coefficients. Definitions of elastic and plastic potentials of a system were given for linear and non-linear creeps [15]. It was concluded that concrete creep deformations are one of the indicators for RC structures' repairing efficiency and/or necessity. The long-term deflections predicted by the creep models in different design codes have a big difference [16]. Experimental results of creep strains in the high-strength concrete Sutong Bridge were compared with those obtained according to ACI 209 and other models [17]. A creep analysis method was proposed, and parameters in the fib MC 2010 creep model were calibrated according to a long-term loading experimental investigation of a prestressed concrete beam [18]. It was reported that the numerical results are in good agreement with the experimental ones. An experimental study was carried out to investigate the creep deformations of fiber-reinforced concrete (FRC) beams under loading level \(P_{s}\)/\(P_{0}\) higher than 80% (\(P_{s}\) and \(P_{0}\) are the loads at reloading and before unloading, respectively) [19]. The beams' deflection, crack width, and propagation were measured and analyzed. It was concluded that the obtained results form a basis for modeling creep with respect to material parameters and testing conditions. Results of experimental investigations, focused on the long-term behavior of cracked steel fiber-reinforced concrete structures, were described and discussed [20]. The influence of the initial crack opening and stress levels on flexural creep was studied. One hundred and twelve prismatic specimens were extracted from a steel fiber-reinforced panel and submitted to four-point bending tests.