*4.2. Elastic Modulus*

The elastic modulus experiment results indicated that the elastic modulus showed insignificant differences with the fiber volume fraction; its value remained ~28 GPa. This was in contrast to the compressive stress experiment results. However, as shown in Figure 5, the strain at peak stress showed significant differences with increasing fiber volume fraction. These results implied that the energy absorption capacity improved as the fiber volume fraction increased.

**Figure 5.** Strain at peak stress.

Figure 6 shows the elastic modulus estimation curve using the compressive stress as presented in KCI 2012 [30] and ACI 318 [31] and the compressive stress and elastic modulus with respect to the fiber volume fraction. The elastic modulus with respect to the fiber volume fraction measured in this study satisfied the lower limit of the elastic modulus estimation curve. This seemed to be because the elastic modulus prediction equation suggested in KCI 2012 [30] and ACI 318 [31] estimated the elastic modulus using only the compressive stress and unit weight.

**Figure 6.** Correlations of compressive stress and elastic modulus between KCI 2012 [30] and ACI 318 [31].

#### *4.3. Poisson's Ratio*

Poisson's ratio of conventional concrete is known to be 0.16–0.20; that of fiber-reinforced high-strength concrete is expected to be higher. Figure 7 shows Poisson's ratio with respect to the fiber volume fraction of SIFRCCs. As with the elastic modulus experiment results, Poisson's ratio showed insignificant differences with the fiber volume fraction. The average Poisson's ratio was ~0.3; this was much higher than that of conventional concrete and was similar to that of steel. This was because the high-strength filling slurry matrix improved the interface adhesion between the matrix and the steel fibers. SIFRCCs showed homogeneous behavior owing to its high fiber volume fraction; this could suppress brittle fracture, a disadvantage of conventional concrete, and provide sufficient energy absorption capacity.

**Figure 7.** Correlation between compressive stress and Poisson's ratio with respect to fiber volume fraction.

#### *4.4. Stress-Strain Relationship*

The stress-strain experiment results of SIFRCCs with respect to the fiber volume fraction showed relatively high strain values for all variables compared to that of conventional concrete, with a strain of 0.008 or higher at peak stress. Figure 8 shows the results for the fiber volume fraction of 6%. In this case, the post-peak behavior exhibited a strain hardening behavior. Even after the elastic section in the stress-strain curve, it showed ductile behavior characteristics like those of metal. This showed that as in the experimental results obtained with high Poisson's ratio, the specimen exhibited sufficient energy absorption capacity even after the peak stress owing to its high fiber volume fraction. Figure 9 shows the results for the fiber volume fraction of 5%. As in the previous case, the post-peak behavior exhibited a strain hardening behavior in the plastic section of the stress-strain curve. Figure 10 shows the results for the fiber volume fraction of 4%. Unlike in the previous two cases, the post-peak behavior exhibited a strain hardening behavior to some degree in the plastic section of the stress-strain curve and a strain-softening behavior in the end. This was because the low fiber volume fraction of 4% produced only a small amount of fiber reinforcement that decreased the resistance to the expansion force in the vertical direction of the specimen axis. Figure 11 shows the results for the stress-strain curve with respect to fiber volume fraction.

**Figure 8.** Stress-strain curve for the fiber volume fraction of 6%.

**Figure 9.** Stress-strain curve for the fiber volume fraction of 5%.

**Figure 10.** Stress-strain curve for the fiber volume fraction of 4%.

**Figure 11.** The stress-strain curve with respect to fiber volume fraction.

Table 5 lists the experimental results for maximum strength, elastic modulus, and strain at peak stress; these are generally used to define the stress-strain curve of the SIFRCCs. The relative error of compressive strength in the average value of the experimental results for each variable with respect to the fiber volume fraction was lower than 10%. The stress-strain experiment results revealed insignificant differences in the elastic modulus with the fiber reinforcement amount. This suggested that fiber reinforcement had no effect on the elastic modulus owing to the use of the same filling slurry matrix regardless of the fiber volume fraction.


**Table 5.** Experimental results for compressive behavior characteristics with respect to the fiber volume fraction.

However, the strain at peak stress also increased with the fiber volume fraction. In contrast to the above-mentioned compressive stress experiment results with respect to the fiber volume fraction, the compressive stress for the fiber volume fraction of 6% increased slightly by approximately 1.11 and 1.27 times compared to those for fiber volume fractions of 5% and 4%, respectively. However, the strain at peak stress for the fiber volume fraction of 6% increased significantly by 1.51 and 2.67 times compared to those for fiber volume fractions of 5% and 4%, respectively. The compressive fracture patterns obtained by performing the compressive behavior experiment, shown in Figure 12, indicated that the strain increased further as axial cracks in the specimen were restrained. This characteristic of the strain increase rate was considered to be caused by the restraining effect of the high fiber volume fraction, in which many steel fibers resisted the expansion force generated vertically to the specimen axis and thereby caused longitudinal split cracks. Moreover, the steel fiber reinforcement effect served to increase the size of the peak stress and the strain at peak stress in all compressive stress areas.

**Figure 12.** Compressive fracture pattern with respect to fiber volume fraction.
