Introduction. One of the priorities of the strategy of scientific and technical development of the Russian Federation is to counteract man-made, biogenic, sociocultural and other sources of danger to society and the economy [1]. The most important task of environmental safety is the development of processes and techniques [2], resource conservation [3], and complex processing of man-made materials [4], obtaining products with high performance characteristics on their basis [5].

Transdisciplinary approaches provide a new level of development of building composite mixtures. For progress in this area, it is important to move away from the current templates of designing building materials [6]. To reduce the complexity of recipes and the cost of components, it is necessary to use data from various sciences: materials science, physics, chemistry, geology, nanotechnology, etc. In addition, certain operational characteristics can be assigned to the new composite [7].

Improvement of physical, mechanical, operational, protective and environmental properties of modern modified composites is based on:

It is known that the economic efficiency of projects is largely determined by the use of high-tech building materials [9]. Modern composites have good prospects in industrial and civil construction [9]. They are often used for unique projects and objects that are operated under various conditions [10].

When producing the materials described above, one of two innovative strategies is usually used:

It should be noted that the regulatory framework governing construction design does not contain recommendations on the use of man-made waste as fillers for concrete. Promising approaches are discussed in the literature. As a rule, this concerns the comprehensive processing of used tires, as well as fibrous materials — man-made waste from the production of mineral wool [13]. However, both of these solutions have not been sufficiently studied and tested in practice.

The possibility of using carbon black and TFM waste should also be mentioned. However, even in this case there are no adequate scientific conclusions that would prove the practical feasibility of introducing such composites into construction practice [14].

The objective of the presented work was to study and design unreinforced and hybrid-reinforced fibergeopolymers using the FEM. Within the framework of this study, two problems were solved: design of hybrid-reinforced fibergeopolymers and analysis of beams made from them by the FEM. This was required to reach the stated goal, as well as in general for the creation of sustainable building materials.

Materials and Methods. The binding base for the production of fibergeopolymers was sintered particles (beads) extracted from waste basalt wool — technogenic fibrous materials (TFM). A combination of sodium silicate and sodium hydroxide solution was used as an alkaline activating liquid. Polyfractionated quartz sand with a specific gravity of 2.67 acted as a fine filler. The maximum size of the coarse aggregate used in this study did not exceed 12 mm, which increased the workability of concrete. The fiber from the metal cord of waste tires was heat-treated and cut. The fiber from TFM was obtained through grinding basalt wool. The authors found that sometimes the actual technical properties of the fibers differed from those declared by the manufacturers, and these actual parameters are given in Table 1.

The behavior of 1,000×200×100 mm beams made from hybrid-reinforced fiber-geopolymers was studied. They were analyzed by the FEM in bending and shear. The deflection of geopolymer concrete beams was calculated to prevent unacceptable deformations and provide normal operation of structures. The FEM is suitable for computer processing, it can be used to solve problems in solid mechanics, fluid mechanics, heat transfer and vibrations.

Research Results. Compositions of sustainable fibergeopolymer mixtures have been developed, which show satisfactory workability characteristics (Table 2). Workability provides high-quality, safe transportation of the geopolymer mixture to the place of installation.

The composites were cured for 28 days under normal, unintentionally specified conditions. Their final mechanical properties were summarized in Table 3. High values of compressive strength (up to 46.67 MPa) and bending strength (up to 10.19 MPa) were shown. An extremely important difference in the ratio of bending and compressive strength for the studied and traditional materials was established — 1:4 and 1:10, respectively. High modulus of elasticity (more than 25 GPa) is especially important for designers and engineers, since it determines the ability of the material to resist deformation, i.e., the strength and stability of building structures. In Table 3, the compositions with the best characteristics are highlighted in color.

The statics problems were solved by the FEM. The sequence of analysis in the Ansys software environment is described below.

For the modeling, a geopolymer beam with three degrees of freedom at each node was used. It moved and was elastically deformed in x, y, z directions.

Modulus of elasticity of concrete:

(1)

where Ec — short-term static modulus of elasticity, MPa; — compressive strength, MPa.

Poisson's ratio is usually less than 0.5. In [15], the values from 0.18 to 0.24 are given, while in [16], the figures are from 0.23 to 0.32.

Meshing is based on the geometry of the structure. Visualization of the bending analysis in Ansys is shown in Figures 1–11.

Comparison of the experimental and theoretical results of deflection is given in Tables 4, 5 and Figures 12–17. Geopolymer concrete is an elastic-plastic material, therefore the stress-strain graph is nonlinear.

Thus, the finite element modeling of beams made from mono-reinforced and hybrid-reinforced fibergeopolymers has shown good convergence of experimental and theoretical results, which allows for the efficient design of structures from the developed materials and the prediction of their operational characteristics.

Discussion. The most noticeable discrepancy between the results of experiments and calculations (45%) was found for FGP-2 at a load of 20 kN. At 15 kN, the difference was 38%. However, in this and the following cases, it is important to emphasize the low absolute values. At 20 kN, a deflection of 1.45 mm was theoretically assumed, but the experiment showed 2.64 mm. The corresponding data at 15 kN were 1.14 and 1.84. At other loads, the difference was significantly smaller. For FGP-3, the maximum discrepancy was recorded at minimum loads: 40% at 5 kN and 39% at 10 kN. If we are talking about absolute figures, then in the first case, the calculation is 0.42 mm, the experiment is 0.70 mm. In the second case, 0.95 mm and 1.56 mm, respectively. For FGP-1 and FGP–1 (1%), the maximum discrepancy did not exceed 27%, and at low loads. At loads of 5 kN, the theoretically obtained deflection indicator for FGP-1 is 0.35 mm, established empirically — 0.48 mm. The difference is 27%. At a load of 5 kN for FGP-1 (1%), the calculation shows a deflection of 0.47 mm, the experiment — 0.64 mm. The corresponding data for 10 kN are 1.05 and 1.44. The difference in both cases is 27%. For other loads, it is significantly less.

Let us also note the cases of the best convergence of the calculation and experimental data. For FGP-1, this is 8% (load — 35 kN), for FGP-2 — 11% (50 kN), for FGP-3 — 7% (38 kN), for FGP-1 (1%) — 3% (30 kN).

The results of the study of hybrid-reinforced fibergeopolymers allow us to state that the most significant discrepancy between theory and experiments is recorded at minimum loads (in this case, 5 kN). Thus, for HFGP-1, it is 46.2% (calculation shows a deflection of 0.14 mm, experiment — 0.26 mm). The corresponding difference for HFGP-2 is 43.8% (0.18 mm and 0.32 mm), for HFGP-3 — 43.3% (0.17 and 0.30). At other loads, the discrepancies are smaller.

The best agreement between calculations and experimental results for HFGP-1 is 1.85%. This figure is recorded at a load of 72 kN (theory — 5.85 mm, experiment — 5.96 mm). The smallest discrepancy, obtained when modeling the deflection for HFGP-2, is 9.12% (63 kN, 5.58 mm and 6.14 mm, respectively). For HFGP-3 — 0.80% (55 kN, 4.98 mm and 5.02 mm). As noted above, extremely minor discrepancies in absolute figures should be taken into account. Both individual and generalized data are of interest for design and engineering practice. This is confirmed by the visualization of the results of the work — the curves in Figures 12-20 are similar or coincide in numerous cases.

Conclusion. Innovative components for the production of sustainable building materials have been obtained [17]. Ecological compatibility is due to the fact that an alternative to cement is used [18], and this provides a significant reduction in greenhouse gas emissions. The design of hybrid-reinforced fibergeopolymers makes it possible to obtain high strength values — both in compression (from 46 MPa) and in bending (from 10 MPa). When using hybrid fiber, it is possible to reach bending and compression strength at the level of 1:4, and this is several times higher than for unreinforced Portland cement concrete [19]. The modulus of elasticity of more than 25 GPa shows good resistance of the material to deformations, which has a positive effect on the strength and stability of building structures [20]. The finite element analysis of hybrid-reinforced fibergeopolymer beams confirmed the experimental results obtained [21].

The three main research results are described below.