## 4 Results and Discussion
### Compressive Performance of Fiber Reinforced Geopolymer Concrete
#### 4.1.3 Elastic Modulus and Poisson's Ratio  
The behavior of a structure as well as its elastic deformation could be affected by many factors, and elastic modulus is one of the most important factors. This value of polypropylene fiber and hooked end steel fiber-reinforced geopolymer concrete is illustrated in Figure 13. In terms of specimens using the same 0.5% volume fraction of polypropylene fiber, the values of elastic modulus were the highest and most similar--about 25-26 GPa. These values were the maximum elastic modulus, and they decreased as the volume fraction increased at 1.0% and 1.5%.  
Figure 13 also describes the compressive performance with hooked end steel fiber-reinforced geopolymer concrete through elastic modulus E. This modulus had the greatest value at specimens using 1.0% and the smallest value at specimens using 1.5%. The greatest modulus obtained at specimens using 1.5% fiber was 31.56 GPa. By comparing two series specimens, it can be seen that the higher elastic modulus was always measured at specimens reinforced with hooked end steel fiber.  
For ordinary concrete, Australia standard (AS) 3600 [28] proposed Equation (2) to calculate the elastic modulus based on compressive strength, where \(\mathrm{E_{c}}\) is the elastic modulus, \(\mathrm{f_{cm}}\) is the mean compressive strength, and \(\rho\) is the unit-weight of geopolymer concrete at about 2.35 ton/m\({}^{3}\).  
\[\mathrm{E_{c}}=\rho^{1.5}\times(0.024\sqrt{\mathrm{f_{cm}}}+0.12)\ (\mathrm{MPa}) \tag{2}\]  
Figure 12: Stress–strain relationship. (**a**) At a volume fraction of 0.5%; (**b**) at a volume fraction of 1.0%; (**c**) at a volume fraction of 1.5%.  
Figure 13: Elastic modulus.  
For geopolymer concrete without fiber, [PERSON] [6] also presented the following equation to determine the elastic modulus:  
\[\text{E}_{\text{C}}=2707\sqrt{\text{f}_{\text{cm}}}+5300\ (\text{MPa}) \tag{3}\]  
Table 7 and Figure 14 present a comparison of the elastic modulus between measured values from this study, and those of ordinary concrete and geopolymer concrete were calculated from Equations (2) and (3). The elastic modulus of fiber-reinforced geopolymer concrete obtained from this study iwa smaller than those of ordinary concrete. The difference was about 4.3%-23.6%. However, compared with non-fiber geopolymer concrete calculated by Equation (3), the measured modulus was greater than 9%-23.4%.  
Another parameter obtained from compression test was the Poisson's ratio, which was also shown in Table 6. Figure 15 describes the value of the Poisson's ratio with four types of polypropylene fibers and hooked end steel fiber and three dosages of fiber. With series P1 and P2 cast with polypropylene fiber, the Poisson's ratio had a range of 0.129-0.152. Additionally, specimens generated with hooked end steel fiber had higher values from 0.140 to 0.163. Compared with previous studies [6] about non-fiber geopolymer concrete, this ratio also range  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Specimen** & **Compressive Strength (MPa)** & **Measured E (GPa)** & **AS3600–E (GPa)** & **Hardjito–E (GPa)** \\ \hline P1-05 & 43.33 & 26.10 & 31.67 & 23.12 \\ P1-10 & 36.18 & 25.37 & 30.12 & 21.58 \\ P1-15 & 32.45 & 23.09 & 29.25 & 20.72 \\ P2-05 & 38.59 &