# Enhanced Performance of Concrete Dispersedly Reinforced with Sisal Fibers
## 3 Results and Discussion  
Study of the Effect of Dispersed Fiber Reinforcement with Sisal Fibers on the Physical, Mechanical and Deformation Characteristics of Normal Weight Concrete at Different Percentages of Fiber Reinforcement  
To predict the mechanical properties of fiber-reinforced concrete with sisal fibers, the Halpin-Tsai model was used. The equations for this model are as follows:  
\[K_{c}=K_{m}\left[\frac{1+\xi\;\zeta\;V_{f}}{1+\eta\;V_{f}}\right]\text{, here }\eta=\left[\frac{\left(K_{f}\Big{/}K_{m}\right)-1}{\left(K_{f}\Big{/}K_{m} \right)+\zeta}\right] \tag{2}\]  
Figure 4: Scheme of testing a sample for determining the axial tensile strength: (1) active capture, (2) sample. where \(K_{c}\) represents effective mechanical properties of fiber-reinforced concrete; \(K_{f}\) and \(K_{m}\) are the mechanical properties of fiber and concrete, respectively; \(V_{f}\) is the volume of the fiber fraction; \(\zeta\) is a geometric coefficient taking into account the loading conditions (uniaxial, biaxial, multiaxial). The results of experimental studies of the effect of the percentage of fiber reinforcement with sisal fibers on the strength characteristics of concrete are shown in Figures 5-8. Figure 5: Results of experimental studies of the compressive strength \(R_{b,cub}\) of concrete samples in the form of cubes with different percentages of reinforcement with sisal fibers. Figure 6: Results of experimental studies of the axial compressive strength \(R_{b}\) of concrete samples in the form of prisms with various percentages of reinforcement with sisal fibers. The graph in Figure 5 shows the compressive strength (\(R_{b}\)) of a sisal fiber-reinforced concrete as a function of the percentage of fiber reinforcement. The effect of a sisal additive on the strength and deformation properties of concrete is described by the saturation function, which is suitable for assessing the effect of nano-modifying additives and demonstrates the best results in terms of the coefficient of determination, and also expresses the best physical meaning. Cubic strength is approximated by a formula with a coefficient of determination of 0.917. \[R_{b,cube}=48.8+10.302\times x^{0.858}\times\sin(2.0\,x+\,0.15),\,R^{2}=0.917 \tag{3}\]  
Figure 8: Results of experimental studies of the axial tensile strength \(R_{bt}\) of concrete samples in the form of prisms with various percentages of reinforcement with sisal fibers. Figure 7: Results of experimental studies of tensile strength in bending \(R_{btb}\) of concrete samples in the form of prisms with various percentages of reinforcement with sisal fibers. where \(x\) is the amount of sisal, %. Figure 6 shows the axial compressive strength \(R_{b}\) of concrete as a function of the percentage of sisal fiber reinforcement. The axial compressive strength of test samples of concrete with different amounts of sisal fibers is described by a formula with a coefficient of determination of 0.966. \[R_{b}=34.6+9.335\times x^{0.764}\times\sin(2.01\,x+0.119),\quad R^{2}=0.966 \tag{4}\]  
It can be seen that Equations (3) and (4) adequately reflect the ascending branch of the increase in strength and the descending branch of the decrease in strength from an excessively large number of sisal fibers. Figures 5 and 6 show that samples with 1% sisal fibers by weight of cement showed the highest compressive strength. A further increase in the percentage of reinforcement led to the formation of voids in concrete, which reduced its compressive strength, which is consistent with the works of other researchers [11; 16; 19; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 33; 35; 39; 41; 42; 43; 45]. The results of the study of the compressive strength of samples showed that the compressive strength of samples with fiber dispersion reinforcement with sisal fibers at an optimal dosage of 1% compared with conventional concrete was 22% higher, and the axial compressive strength increased by 27%.