**1. Introduction**

Concrete belongs to the class of brittle and barely deformable materials; therefore, it is susceptible to scratching and cracking. The addition of, for example, steel fibres to such materials allows us to obtain higher plasticity and cracking resistance properties. Fibre-reinforced concrete was first used 140 years ago when, in 1874, Bernard submitted his first patent application for steel fibre-reinforced concrete. Since that time, attempts have been made to both evaluate the impact of the fibres on concrete properties [1–9], as well as distribution of fibres in the concrete [10–12]. Fibre-reinforced concrete has, therefore, become an alternative to ordinary concrete.

The fibre-reinforced concrete filling, just as in the case of ordinary concrete, is a fine and coarse aggregate selected based on a continuous grading curve. Aggregate deposits occur in the Pomeranian area in Poland, in the form of a mixture of fine and coarse aggregates. The high demand for coarse aggregate has contributed to the development of a technique of its sourcing by washing it out from its deposits. This technique is called hydroclassification. The application of hydroclassification of natural aggregates results in the build-up of dumps of washed-out sand, from which coarse aggregate fractions have been eliminated. Such created excavations must be subjected to costly reclamation operations. An alternative for reclaiming these excavations is through the possibility to use waste sand as a valuable construction material. Due to the shortage of coarse aggregate in

**Citation:** Lehmann, M.; Głodkowska, W. Shear Capacity and Behaviour of Bending Reinforced Concrete Beams Made of Steel Fibre-Reinforced Waste Sand Concrete. *Materials* **2021**, *14*, 2996. https://doi.org/10.3390/ ma14112996

Academic Editor: Krzysztof Schabowicz

Received: 27 April 2021 Accepted: 27 May 2021 Published: 1 June 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the north region of Poland, a concrete composite has been developed [11,13,14],included in which is the fine aggregate (i.e., waste sand). In the analysed fine aggregate cement composite, the coarse aggregate was substituted with steel fibres, in order to create steel fibre-reinforced waste sand concrete (SFRWSC).

The subject matter of our analysis is, therefore, the novel steel fibre-reinforced waste sand concrete. This novel fibre composite material, featuring high compression and tensile strength, was designed based on a fine post-production waste aggregate. The research work described in [12,14,15] stated that a fibre composite based on waste sand containing 1–1.5% steel fibres has the best physicochemical properties. If the steel fibre content exceeds 1.5%, some tested material features decrease or improve insignificantly. Therefore, the addition of steel fibres in excess of 1.5% makes the resulting concrete hardly usable, due to material workability, its mechano-physical properties, and cost. A steel fibre content equal to 1.2% seems to be the best possible option, considering the fundamental properties that the structural composite should have. The residual strength values of SFRWSC with a steel fibre content of 1.2%, defined in the EN 14651 standard [16], have been classified in accordance with Model Code 2010 [17] as class 7b, which means that this material is suitable for the manufacturing of structural elements, and traditional reinforcement may be reduced. A feature distinguishing the analysed SFRWSC is its ability to resist higher shear forces, compared to concrete without fibre reinforcement. An increase in the shear capacity may lead to a reduction of traditional shear reinforcement or the complete abandonment of such reinforcement, due to shear capacity at small loads.

Analysing the state-of the-art in the field of shear fibre concrete elements, the first works were started in the 1970s. Batson, in [18], published the results of research on the influence of the shape, quantity, and dimensions of fibre reinforcement on shear force. Based on these studies, he concluded that the stirrups can be replaced by round, flat, or crimped steel fibres, which effectively influence the shear capacity of the support areas. In 1986, Sharma [19] conducted research and confirmed the beneficial co-operation of fibres and stirrups meanwhile, in 1987, Narayanan and Darwish published a study [20] considering beams with crimped fibre content, different degrees of main reinforcement, and varying *a*/*d* ratio. The shear problem in fibre-reinforced elements is still relevant and remains of experimental research. You et al., in their work [21], presented the results of an experiment carried out on rectangular beams, considering the use of fibre reinforcement with and without stirrups. Their research showed that the shear load capacity increases significantly with increasing fibre content, and the addition of an appropriate percentage of fibres can change the failure mode from brittle failure at shear to a ductile mechanism. The stirrups can be partially replaced by steel fibres and the combination of steel fibres and stirrups showed a positive effect on the mechanical behaviour of the composite. Similar conclusions have been reached by Ding et al. [22] and Li et al. [6]. Zhao [23], in his work, additionally characterized the effect of fibres on the reduction of diagonal cracks and strain after cracking. Analyses of the level of the scale effect by fibres in the shear load capacity [24]. Reviews of the state of knowledge of fibre-reinforced shear elements have been presented in the manuscripts [25,26], among others. Although the shear issue has been dealt with in numerous papers, there is still a need for further research, in order to analyse this issue in a more insightful way.

Knowledge of the bahavior and failure of reinforced concrete structures is of great technical and economic importance. Experimental testing of such components is laborious and costly. Therefore, the possibilities of numerically analyzing the work of reinforced concrete elements are often used, e.g., with the help of the Finite Element Method (FEM). In addition, along with the development of new materials and research methods, intensive scientific work is carried out on the use of numerical methods for modeling physical processes, development of material damage to destruction, modeling of ultra-high performance concrete, reinforced concrete shells and walls or structure strengthening [27–30]. The problem of shear in reinforced concrete beams [31,32] and in fiber-reinforced beams [33–35] is also subjected to numerical modeling. Talavera-Sanchez et al. [33] presented the test

results of 16 beams with various parameters, including steel or macro-synthetic fibers, the presence or absence of transverse reinforcement, different shear-to-depth ratios, and different transverse reinforcement values. In numerical modeling was used the nonlinear finite element analysis following the smeared crack approach and a total strain-based crack material model. Numerical modeling has shown that the nonlinear finite element model can predict the behavior and strength of beams with transverse reinforcement with high accuracy. For members without transverse reinforcement, the shear capacity is acceptable, but some doubts remain unclear as these beams have large critical diagonal crack failure. In the manuscript of Amin and Foster [34] comparison of full scale SFRC beams ATENA 2D smeared crack models were described. The ATENA 2D integrated with a constitutive law derived after an inverse analysis from prism bending tests. The numerical model is validated against experimental results obtained. Authors analyzed experimental and numerical shear strength, deflection and diagonal crack pattern. It was shown that numerical model compared well with the experimental data in capturing the linear and non-linear responses of the beams. Some studies also concerned beam sections other than rectangular ones, and Baross and his team [35] dealt with modeling of T-sections. The studies of fiber-reinforced concrete T-beams damaged due to shear were analyzed in comparison to various numerical models, i.e., smeared crack model, discrete crack model, concrete damage plasticity model, and lattice discrete particle model. The models were analyzed in terms of deflection, strain and diagonal cracking. The authors obtained results with different accuracy in relation to the experimental results, stating that for the lattice discrete particle model, the best means of agreement are obtained.

The research work published in [12,15,36] concluded that SFRWSC without steel fibres behaves like ordinary concrete in bent elements provided with conventional reinforcement. The addition of steel fibres considerably improves the flexural capacity of such elements, thanks to which, the reduction of conventional reinforcement due to bending moment is possible. The addition of steel fibres also limits the width of cracks perpendicular to the element axis. These properties provide a possibility to use this material in the production of structural elements such as flooring slabs, beams, or coatings. Thanks to its mechano-physical properties, SFRWSC may, in some cases, serve as a substitute for ordinary concrete.

Considering the abovementioned achievements to date, the objective of the research presented in this paper was to show that the novel SFRWSC, with 1.2% fibre content, could be used for the production of reinforced concrete elements that are subject to bending functioning under shear force. To date, no research work has been performed on reinforced concrete elements made of SFRWSC that are subjected to bending by a transversal force. Therefore, an assumption was made, namely that steel fibres used as reinforcement can contribute to an improvement of the shear capacity of such elements. Another objective is to prove that, by using steel fibres, conventional shear reinforcement can be reduced, as well as reducing the diagonal crack width.

The design of fibre-reinforced concrete cross-sections functioning under shear force is still an unexplored issue [37,38]. The first design methods were based on experimental tests and had a limited scope of application. After the publication of two European standards— RILEM -TC-162-TDF [39] and Model Code 2010 [17]—the dimensioning of fibre-reinforced concrete cross-sections functioning under shear force has been standardised. However, the authors of many scientific papers [40–43] evaluating the shear design methods described in the above-named standards have stated that there were significant differences between the experimental and computed values. Therefore, the next objective of this research work is the evaluation of the shear design fibre-reinforced elements, based on the Model Code 2010 [17] and RILEM TC-162-TDF [39] standards, in terms of the possibility to use the methods for shear design of SFRWSC elements subject to bending. It should be noted that by using waste aggregate as a full-value construction material for the production of the tested SFRWSC, these studies are in line with the global trends related to sustainable development of the environment.
