## 3 Results and Discussion
### Quantitative Analysis of Test Results
#### 3.5.3 Uniaxial Compressive Toughness  
As can be seen from Table 4, the uniaxial compressive toughness of RC was reduced by 51.8% compared to NC. The uniaxial compressive toughness of recycled concrete increased with the increase in the volume content of steel and polyvinyl alcohol fibre, with the uniaxial compressive toughness of recycled concrete increasing by 39.04-206.43%, compared to RC. When 1.0% steel fibre by volume and 0.2% polyvinyl alcohol fibre by  
Figure 16: Fibre characteristic value and Poisson’s ratio.  
Figure 15: The function of fibre characteristic value, elastic modulus, and uniaxial compression strength.  
volume were hybrid, the uniaxial compressive toughness increased by 109.57% and 188.08% compared to steel fibre or the polyvinyl alcohol fibre single admixture. Thus, this mixing plan is a superior combination for improving uniaxial compressive toughness of recycled concrete. The non-linear regression analysis was used to obtain Equation (8). Figure 17 shows the relationship of fibre characteristic values, peak strain, ultimate strain, and the uniaxial compression toughness index. The test points were less discrete from the spatial curve, while the uniaxial compressive toughness increased with the increase in the fibre characteristic value, and the larger the ratio of ultimate strain to peak strain of the concrete specimen, the higher the uniaxial compressive toughness, as shown in Figure 17.  
\[\text{TI}=0.208\Big{(}\frac{\varepsilon_{\text{max}}}{\varepsilon_{0}}\Big{)}^ {1.762}(1+0.22\lambda_{\text{sf}})\Big{(}1+0.08\lambda_{\text{pf}}\Big{)} \tag{8}\]  
Equation (8) shows that both steel fibre and polyvinyl alcohol fibre can improve the uniaxial compressive toughness of recycled concrete, and steel fibre was more effective in improving the uniaxial compressive toughness of recycled concrete compared to polyvinyl alcohol fibre. The elastic modulus, the Poisson's ratio, and the uniaxial compression toughness index calculated by Equations (6)-(8) were compared with the measured values in Table 5.  
Figure 17: The relationship of fibre characteristic value, peak strain, ultimate strain, and uniaxial compression toughness index.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{2}{c}{\(\boldsymbol{E_{c}\) (GPa)} } & \multicolumn{3}{c}{\(\boldsymbol{\
u_{t}}\)} & \multicolumn{2}{c}{\(\boldsymbol{TI}\)} & \multirow{2}{*}{**Relative**} \\  & **Calculated** & **Measured** & & & & & **Calculated** & **Measured** \\  & **Value** & **Value** & & & & **Value** & **Value** & **Value** & **Error (\%)** \\ \hline RC & 21.83 & 22.75 & \(-4.00\) & 0.219 & 0.220 & \(-0.60\) & 0.259 & 0.211 & 22.77 \\ RS-1 & 19.70 & 18.60 & 5.87 & 0.208 & 0.204 & 1.85 & 0.315 & 0.294 & 7.13 \\ RS-2 & 17.35 & 14.87 & 16.67 & 0.197 & 0.182 & 8.14 & 0.464 & 0.452 & 2.68 \\ RS-3 & 15.46 & 15.32 & 0.95 & 0.186 & 0.195 & \(-4.66\) & 0.571 & 0.647 & \(-11.71\) \\ RP-1 & 21.04 & 24.07 & \(-12.58\) & 0.209 & 0.219 & \(-4.30\) & 0.302 & 0.265 & 13.86 \\ RP-2 & 21.39 & 18.45 & 15.96 & 0.200 & 0.201 & \(-0.29\) & 0.359 & 0.329 & 9.03 \\ RP-3 & 20.17 & 20.87 & \(-3.32\) & 0.191 & 0.187 & 2.28 & 0.535 & 0.580 & \(-7.74\) \\ RSP-1 & 17.86 & 16.98 & 5.16 & 0.182 & 0.179 & 1.52 & 0.531 & 0.566 & \(-6.09\) \\ RSP-2 & 16.93 & 18.57 & \(-8.83\) & 0.180 & 0.187 & \(-3.53\) & 0.967 & 0.948 & 2.00 \\ RSP-3 & 14.60 & 15.99 & \(-8.70\) & 0.178 & 0.177 & 0.67 & 0.978 & 0.962 & 1.69 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The relative error between the calculated value and the measured value.  
Considering the discrete nature of the concrete, except for individual groups where the relative errors between the calculated and measured values exceeded 20%, the relative errors between the calculated values and the measured values were relatively small. Thus, Equations (6)-(8) can accurately calculate the elastic modulus, the Poisson's ratio, and the uniaxial compression toughness of steel-polyvinyl alcohol fibre-reinforced recycled concrete.