**2. Test Materials**

The reinforced concrete beams to be tested for shear capacity were made of SFRWSC containing 1.2% steel fibres, in relation to the volume of composite material [44].SFRWSC is a novel structural material, in which the used aggregate is a post-production waste. In the analysed composite, the used aggregate was sand of 4 mm granularity, which is a waste material of aggregate mines located in northern Poland (the Pomeranian region). In this area, a significant part of the output is subjected to the process of hydroclassification, which results in 80% sand and only 20% coarse aggregate. This disproportion leads to the situation where most of sand remains unused, in numerous dumps located near the aggregate mines (Figure 1).

The postulate to somehow utilise remaining waste sand dumps constitutes a worldwide tendency, consistent with Sustainable Ecological Development [45–49]. Similar phenomena of excessive sand fractions can be observed in other parts of the world, such as the Middle East or in North Africa [50]. Figure 2 presents waste sand grading curves appointed by various authors. These curves only insignificantly differ from one another, despite the fact that the sand used in these studies originated from various aggregate mines located in northern Poland. This indicates that all these deposits are post-glacial or fluvioglacial residues, developed in the same period [12,51,52].

The used fine aggregate complied with the requirements formulated for mineral aggregates recommended for ordinary concrete manufacturing. The content of mineral dust in the aggregate was below 3%, which allowed for it to be classified in the *f3* category, based on the PN-EN 12620 standard [53].

Sand obtained from the hydroclassification process performed in the Mineral Raw Materials Mine in Podwilcze, Białogard Commune, was used (1570 kg/m3), together with Portland cement CEM II/A-V 42,5R (420 kg/m3), silica dust (21 kg/m3), superplasticiser FM series [54] (16.8 kg/m3),and tap water (160 kg/m3), in order to form the test elements. The fibre reinforcement comprised steel hook-end fibres (Figure 3) in the amount of 1.2% (94 kg/m3) and with *l/d* ratio *λ* = *l/d* = 62.5 (*l* = 50mm, *d* = 0.8mm) [55].The steel fibres had ITB technical approval No. AT-15-295/1999 [56], in accordance with the PN-EN14889-1 standard [57].

**Figure 2.** Grading curve of used aggregate and grading curves of other Pomeranianaggregates used in different research programs [13,51,58]. Reproduced with permission from ref. [52]; published by Middle Pomeranian Scientific Society of the Environment Protection, 2017.

**Figure 3.** Fibre dimensions and close-up look.

The fine aggregate composite matrix was designed through application of an analytical and experimental method. Modification of its composition by addition of silica dust and superplasticizer allowed us to obtain a*w/c* = 0.38 ratio. The fibres were placed in the composite mix at random. The technical characteristics of the steel fibres used in the tests are presented in Table 1.

The conditions of SFRWSC composing, care, and testing have been broadly described previously [11–13,51]. The mechano-physical properties of the analysed fibre composite with ordinary concrete are detailed below.


**Table 1.** Technical characteristics of the steel fibres used in the tests ([55,56]).

\*—cut crack width according to PN-EN 14651 standard method [16].

When considering fibrecomposite structural elements, one should first of all take into account the method of their design. For a designer of building structures, a standarddefined property is necessary, which determines the material's ability to transmit tensile stresses after cracking, as provided by the manufacturer. Over the past 20 years, several proposals for a quantitative description of the behavior of cracked fiber-reinforced concrete under tensile conditions have been developed. The most common method for describing this property is given in the RILEM TC-162-TDF [39] recommendations. This method has been included in the European standard EN 14651 [16] and in the Model Code 2010 [17]. It consists of an experimental measurement of the relationship between the crack width (CMOD) and the load force on the bar in the middle of its span. The CMOD–Force relation determined as a result is used to define the so-called residual strengths: *f <sup>R</sup>*,1, *f <sup>R</sup>*,2, *f <sup>R</sup>*,3, and *f <sup>R</sup>*,4. The values of the residual strengths obtained in our tests are presented in Table 2. They denote the values of the tensile stresses in the cross-section for a given width of the CMOD crack, equal to 0.5, 1.5, 2.5, and 3.5 mm, respectively. The values of these strengths serve as the basis for the dimensioning of structural elements.

The Load– CMOD diagram resulting from residual strength test is depicted in Figure 4.


**Table 2.** Mechano-physical properties of the analysed fibre composite with ordinary concrete [12,14,51,59].

**Figure 4.** Load—CMOD relation for SFRWSC. Reproduced with permission from ref. [59]; published by Middle Pomeranian Scientific Society of the Environment Protection, 2015.

For easier interpretation of the test results, the graph boundaries (solid lines) and the mean force dependence on CMOD (dotted line line) are shown. The diagram shows a decrease in the destructive force as the CMOD value increases after the appearance of the first crack. The shape of the graph in Figure 4 indicates that the tested fibrocomposite shows the post-crack softening (pcs) feature. The obtained results clearly indicate the ductile nature of the SFRWSC with 1.2% fiber content. In accordance with the guidelines of the Model Code 2010 standard [17], the class of the tested SFRWSC was designated as 7b. It should be noted that the obtained values of the coefficient of variation (*ν*) given in Table 2, unlike the *ν* indices for the other properties of this material, are large. Unfortunately, tests of residual strength carried out with the use of beam elements are usually burdened with a large spread, amounting to an average of 20% [68] due to small bending areas in the beams, which has been confirmed in [69], among other works. Residual strength tests and their results have been discussed, in more detail, in [12,59].

It can be seen from Table 2 that SFRWSC with 1.2% steel fibre content has better or similar properties as ordinary concrete. The properties of this composite comply with the requirements formulated for structural materials; therefore, it may serve as a substitute for ordinary concrete. Partial substitution of concrete by the proposed fine aggregate composite with fibre reinforcement, featuring the same or better properties, provides a perfect solution for those regions that are short of natural coarse aggregate deposits. This will allow for regional aggregates to be used in a sustainable manner. Such actions will also contribute to the gradual depletion of sand dumps (Figure 1).

#### **3. Methodology of Research and Test Elements**

The test elements used in the shear capacity test are described in Figure 5 and Table 3. Additionally, test elements in form of cylinders (150 × 300 mm) and beams (150 × 150 × 700 mm) were made, in order to determine the fundamental properties of the proposed SFRWSC (Table 3).

**Figure 5.** Specification of tested beams.



Composite properties:

*fc* = 52.6MPa, *fct* = 3.3 MPa, *fcf* = 64.4 MPa, *f <sup>R</sup>*<sup>1</sup> = 9.27 MPa, *f <sup>R</sup>*<sup>2</sup> = 8.80 MPa, *f <sup>R</sup>*<sup>3</sup> = 7.87 MPa, *f <sup>R</sup>*<sup>4</sup> = 6.98 MPa, *Ecm* = 36.7 MPa Steel properties: *fy* = 529 MPa, *ft* = 650 RMPa, *Es* = 200 GPa, *fyw* = 584 MPa, *ftw* = 615 MPa

In order to ensure shear failure a relatively large number of rebars was used in the tension face (2#20 and 2#16. In order to avoid the arch effect and the significant impact of the longitudinal reinforcement on the shearing force, shearing section *a* (Figure 5) was determined in such a way that the shear *a/d* ratio was about 3. In B and BF series beams, reinforcement was intentionally located in the compressed area (2#12), due to its significant impact on the shear capacity. Such prepared beams were stored, until tested, for 28 days at 20 ± 2 ◦C temperature and 100% relative humidity conditions. After 30 days, the beams were loaded. The stand used for shear capacity testing of SFRWSC beams is presented in Figures 6 and 7.

**Figure 6.** Schematic of experimental setup [44].

The beams were tested using specially designed experimental setup, in the configuration of a reversed freely supported beam (Figure 6). The beams were loaded at a constant speed of ~4 kN/min, until failure. Two measuring techniques were used in the test: The SAD-256 data acquisition system (APIG Ltd., Łód´z, Poland) (Figure 7a) and the Aramis 4M system (GOM Ltd., Braunschweig, Germany) (Figure 7b). Measurements were performed periodically at 0.5 Hz frequency, from the moment of load application until beam destruction. The SAD-256 sensor arrangement used for the measurement of surface deformation of one beam side (Figure 7b) was designed in such a way that the recording

of deformations in the diagonal crack area was possible. The width of the cracks that were diagonal and perpendicular to the element axis, deformations of the second beam side surface, and deflections were measured using the Aramis 4M software (GOM Ltd., Braunschweig, Germany). To measure deformations of shear reinforcement, strain gauges were used, which were glued to the vertical parts of stirrups before concreting. Six strain gauges were used for each beam (i.e., three for each shear area). The beam loading force was recorded by a force sensor, located over the hydraulic jack, with 0.66 mV/V sensitivity. The beam span (Table 3) was selected in such a way that the shear failure at the first or second support could be recorded by the Aramis 4M (GOM Ltd., Braunschweig, Germany). Considering the adopted static arrangement, beam shear failure could occur within the first or second support area. For this reason, the beams were tested in two stages. In the first stage, the beam was subjected to loading until shear failure occurred. Then, the test was stopped, and the beam load reset. A steel corset, made of steel sections pulled into place by bolts (Figure 8), was put onto the failed shear area. The corset was intended to resist transversal forces in the fractured shear area in the second stage of the test. The beams with the steel corset were loaded until the second shear area failed.

**Figure 7.** Stand for shear capacity testing of bend elements: (**a**) Beam side surface tested using SAD-256 system; and (**b**) beam side surface tested using Aramis 4M system [44].

**Figure 8.** Beam reinforced with steel corset after the first testing stage.
