## 2 Materials and Methods
### Methods
Figure 9: Dependence of tensile strength in bending (\(R_{btb}\)) of prism concrete samples with dimensions of 100 \(\times\) 100 \(\times\) 400 (mm) on the percentage of coconut fibers. at around 1.75%; at dosages from 2% to 2.5%, axial compressive strength was similar to compressive strength decreases. Figures 9 and 10 demonstrate that the flexible strength and axial tensile strength curves were similar, and the maximum values, as in the case axial compression, were fixed at a dosage of coconut fibers of 1.75% by weight of cement. Figures 11-13 show the results of a study of dispersed coconut fibers on the concrete strain characteristics. Figures 11 and 12 show that the nature of the change in breaking strains in axial compression and axial tension depending on the percentage of fiber reinforcement was similar to the behavior of SC. The maximum values of compressive and tensile strains were observed with coconut fiber of 1.75 % _wt_. Figure 13 illustrates that a more significant increase in the elastic modulus was observed at a percentage of dispersed reinforcement with coconut fiber from 1.25% to 1.75%; the maximum value of the elastic modulus was recorded at a dosage of 1.75% and amounted to 36.8 GPa, and at a fiber dosage of 2% it dropped to 34.6. In general, in the range from 0% to 1.75%, a stable increase in the elastic modulus was observed, the values of which, respectively, ranged from 31.8 GPa to 35.2 GPa. The relations of SC of concrete on the content of coconut fiber were approximated by the \"saturation\" function (1), which has shown itself well [59] in problems of analyzing the properties of concrete in the structural modification of mortar with additives of various types [53; 58]  
\[Y=C_{0}+Ax^{b}(\sin\omega x+\varphi) \tag{1}\]  
Here \(Y\) is the mechanical property, \(C_{0},\ A,b,\omega,\varphi\) are constants, and \(x\) is coconut content. The saturation function (1) has specific physical meaning as follows: Coefficient \(  
\[\varepsilon_{b}=\ 2.14\ +\ 0.60\times\ x^{0.715}\times\ \sin(0.95x\ +\ 0.32),\ R^{2}=0.918 \tag{6}\] \[\varepsilon_{bt}=\ 1.28\ +\ 0.41\times\ x^{0.822}\times\ \sin(1.05x\ +\ 0.20),\ R^{2}=0.965\] (7) Figure 5.0  
From Figures 7-13 and Equations (2)-(8), it can be seen that the concrete strength in compression with the optimal percentage of coconut fiber of 1.75% compared to ordinary concrete was 26% higher. The axial compressive strength became larger by 24%, tensile strength and flexible strength increased by 42%, and axial tensile strength increased by 43%. Thus, samples with a reinforcement percentage of 1.75% demonstrated the highest SC. An increase in the reinforcement proportion more than 1.75% up to 2.5% led to the opposite trend, that is, to a decrease in strength indicators. This may occur due to the formation of voids in concrete due to an excessive amount of fibers, \"an increase in the water demand of the concrete mixture, which is consistent with studies\" [5; 36]. The effect of the proportion of FDRC with coconut fibers on SC and strain characteristics of concrete prototypes are shown in Table 5 and are presented as proportions compared to the control composition, that is, ordinary concrete without fibers. During the analysis of the concrete mechanical characteristics, dispersed reinforcement with coconut fiber constructed several dependencies on the impact of the amount of FDRC on its strength properties, the results were compared with those obtained on the control composition, which had a significant influence on the concrete SC, not only of the fiber reinforcement itself with coconut fibers, but also of its quantity in relation to the mass of cement. It was found that an increase in the SC of concrete along with the higher percentage of fiber reinforcement was observed until the point of 1.75% fiber amount. Thus, it was determined that dispersed reinforcement with coconut fibers in an amount of 1.75% by weight of the binder made it possible to obtain a higher SC of FRC and was optimal.