# Mechanical Properties of Desert Sand-Based Fiber Reinforced Concrete (DS-FRC)
## 3 Results and Discussion
### Uniaxial Compression Properties of DS-FRC
#### 3.4.3 The Uniaxial Compression Toughness  
The compression toughness was proposed to evaluate the compression deformation performance of DS-FRC. Currently, there are no uniform evaluation standards for the compression toughness of high ductility cementitious composites. Therefore, the area under the uniaxial compression stress-strain curve was used to evaluate the compression toughness and deformation performances of DS-FRC in this study, according to [PERSON] and [PERSON] (2016). The performance parameters are shown in Table 5, such as the cracking stress, the cracking strain, the post-crack strain energy density, the equivalent compression strength and the post-peak toughening index of fiber. It is noted that the cracking point was determined as the proportional limit point of uniaxial compression stress-strain curves. The cracking point considered the relation between DS-FRC and ideal elastoplastic materials. In this point, the covered area under the compression stress-strain of DS-FRC was no more 10% than that of the ideal elastic material. The cracking point (referring to the proportional limit point of the compression stress-strain curve), the cracking strain energy density and the equivalent compression strength were calculated, according to Equations (1)-(3). \[\frac{A_{\text{FRC}}-A_{e}}{A_{\text{FRC}}}=\frac{\int_{0}^{\epsilon_{0}} \sigma(\varepsilon)\text{d}\varepsilon-\frac{1}{2}\sigma_{0}\varepsilon_{0}} {\int_{0}^{\epsilon_{0}}\sigma(\varepsilon)\text{d}\varepsilon}\leq 10\%, \tag{1}\]  
\[A_{\text{rp}}=\int_{0}^{\epsilon_{0}}\sigma(\varepsilon)\text{d}\varepsilon -\int_{0}^{\epsilon_{0}}\sigma(\varepsilon)\text{d}\varepsilon, \tag{2}\]  
\[f_{\text{eq,n}}=\frac{A_{\text{rp}}}{(n\!-\!1)\varepsilon_{0}}. \tag{3}\]  
In the above equations \(\sigma_{0},\varepsilon_{0}\) are cracking stress and cracking strain, and \(\sigma,\varepsilon\) are the stress and strain at a certain point. \(A_{\text{FRC}},A_{\text{e}}\) are cracking strain energy density absorbed by DS-FRC and ideal elastic material, respectively; n is the constant, which is 3 or 5.5; \(A_{\text{rp}}\) is absorbed strain energy density after initial cracking; \(f_{\text{eq,n}}\) is the equivalent compression strength. It was observed that there was no particularly significant post-peak ductility in DS-FRC, and the slope of compression stress-strain curves quickly dropped to the horizontal trend after the ultimate compression stress. Therefore, the value of n was defined as 3 or 5.5 to evaluate the post-peak strain energy density and the equivalent compression strength of DS-FRC, according to [PERSON] and [PERSON]. The post-peak toughening index of fiber was calculated to quantitatively evaluate the post-peak toughness performances of DS-FRC. The point corresponding to the ultimate compression stress was defined as the limit of energy absorption. The post-peak fiber toughening index was obtained by Equation (4). \[RT_{\text{f}}=\frac{A_{\text{3u}}-A_{\text{u}}}{A_{\text{u}}}. \tag{4}\]\(A_{\text{u}}\) is the absorbed post-peak strain energy density corresponding to \(\varepsilon_{\text{u}}\), and \(A_{\text{3u}}\) is the value corresponding to 3\(\varepsilon_{\text{u}}\). As is shown in Table 5, the ratio of \(\sigma_{0}\) and \(\sigma_{\text{u}}\) was in the range of 0.39-0.49. Compared with the ordinary concrete, the proportional limit is slightly raised. It is observed that the fiber post-peak toughening effect is not obvious with the \(RT_{\text{f}}\) of about 1.0, which is in agreement with the relatively rapid drop of the compression stress-strain curves after \(\sigma_{\text{u}}\). Under the different W/B (see NO.1, 2, 3 and 4 of Tables 4 and 5), it was found that the \(RT_{\text{f}}\) ranged from 1.0 to 1.5 and slightly increased with the increase of \(\sigma_{\text{u}}\). Besides, the relation between \(\sigma_{\text{u}}\) and \(A_{\text{np}}\) was discussed with the increase of compression strengths.