# Cracking Behavior of Fiber-Reinforced Concrete Beams Made of Waste Sand
## 1 Introduction  
In recent decades, the search for and use of sustainable materials with increasingly enhanced properties has become a trend. This trend spans various fields of science and includes numerous materials, particularly concrete, which is the most widely used material in construction [1, 2, 3, 4, 5, 6]. Unfortunately, the brittleness of concrete increases as its strength rises. The higher the strength of concrete, the lower its plasticity. This relationship has a significant disadvantage. A compromise between these two contradictory properties of concrete can be achieved by adding fibers. The main purpose of using steel fibers in concrete elements, aside from improving mechanical properties, is to limit cracks arising under the influence of external and internal loads [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. One of the parameters describing the formation of cracks in \"small beams\" made of fiber-reinforced concrete is the so-called crack resistance index (minimum value 1) [18]. This index is the ratio of the energy absorbed (the area under the force-displacement curve) during a given deformation to the energy associated with the occurrence of the first crack. It determines the ability of an element to absorb loads within aspecific deformation range [19]. This index is compared with that of a perfectly elastic material, which has values of 5, 10, 30, or 100 for I\({}_{5}\), I\({}_{10}\), I\({}_{30}\), and I\({}_{100}\), respectively [18; 20]. Another parameter used to describe the cracking state in \"small beams\" made of fiber-reinforced concrete is the moment of the appearance of the first crack [21; 22]. This moment is most often determined based on the load-strain relationship at the point where the curve deviates from the straight line. Most standards contain this interpretation (ASTM C 1018 [21], NBN B 15-238 [23], JCI Standard SF-4 [24]) and recommendations (CUR, DBV) for testing fiber-reinforced concrete \"beams\", regardless of their size. Numerous studies have verified the calculation methods included in the standards [16; 25; 26; 27; 28; 29; 30; 31; 32]. Unfortunately, these methods are not applicable to the calculation of full-size elements, such as beams with longitudinal reinforcement and steel fibers, because it is often not possible to clearly define the cracking moment based on the load-deflection relationship [33]. There are also established methods for calculating the cracking limit state for reinforced concrete beams with the addition of steel fibers [34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49]. Most of these methods consider the static equilibrium of forces in a beam fragment before and after cracking. Differences in the individual methods include, among others, how the cooperation between reinforcing bars and fiber-reinforced concrete is taken into account, as well as the assumptions regarding different boundary properties of the cracked and non-cracked cross-sections. This study presents the results of tests on the cracking limit state of reinforced fiber-reinforced concrete beams made from waste sand, which continue the investigations presented earlier in articles [50; 51]. The average crack spacing (\(\mathrm{s_{rm}^{\mathrm{Exp}}}\)) and crack widths (\(\mathrm{w_{k}^{\mathrm{Exp}}}\)) determined in the tests were compared with the values obtained using the method in the previous EC2 standard [52], the [PERSON] proposal [41], its modification [53], and the current EC2 standard [54]. The aggregate used in the study was waste sand generated from the hydroclassification process. This is a process of obtaining coarse aggregate by washing it out of deposits. The effect of using the hydroclassification process on natural aggregates is that it leaves heaps of washed sand devoid of coarse fractions. The excavations created in this way should undergo costly reclamation. An alternative to reclaiming former excavations may be the possibility of using waste sand as an aggregate for concrete.