## 3 Experimental Results and Discussion
### Complete Stress-Strain Curves  
Stress-strain behavior is one of the most important features in evaluating the mechanical characteristics of the materials. Therefore, the complete stress-strain curves under uniaxial compression were obtained and plotted in Figure 5. Due to the intrinsic randomness and complexity of CA mortar, there was a certain variance among those full curves measured under the same loading conditions.  
In detail, assume \(\sigma_{i}\)= \(\sigma_{i}(\varepsilon)\) represents the \(i\)-th full curve measured in the experiment. According to the statistics theory, the average curve (mean stress \(\overline{\sigma}(\varepsilon)\)) and the standard deviation \(STD_{\sigma}(\varepsilon)\) are capable of representing the integral trend and the variability for the experimental results. By adopting the following equations, the resulting mean stress-strain curve and the standard deviation curve are plotted in Figure 5b.  
\[\overline{\sigma}(\varepsilon)=\frac{1}{N}\sum_{i=1}^{N}\sigma_{i}(\varepsilon) \tag{4}\]  
\[STD_{\sigma}(\varepsilon)=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}\left[\sigma_{i}( \varepsilon)-\overline{\sigma}(\varepsilon)\right]^{2}} \tag{5}\]  
where \(\overline{\sigma}(\varepsilon)\) and \(STD_{\sigma}(\varepsilon)\) denote the mean stress and the standard deviation corresponds to the strain \(\varepsilon\), respectively. \(N\) denotes the total number of stress-strain curves, and \(\sigma_{i}(\varepsilon)\) denotes the stress corresponding to the strain \(\varepsilon\) in \(i\)-th stress-strain curve.  
The complete stress-strain curves are plotted in Figure 5a, in which the nonlinearities of the stress-strain behaviors are fully captured while some researchers focus on discovering certain mechanical behaviors (e.g., strength, Young's modulus) [11; 22; 48; 59; 60]. The corresponding average curve and standard deviation curve generated by Equations (4) and (5) are illustrated in Figure 5b. In Figure 5c, the mean and mean \(\pm\)STD. curves are obtained. It is observed that the CA mortar shows apparent stochastic responses during the uniaxial monotonic compression test. In Figure 5a, it is found that the peak stresses in the stress-strain curves are varied from approximately 14.44 MPa to 17.65 MPa, with the corresponding strains of 0.0077 and 0.0073. In Figure 5b, the peak stress \(\sigma_{p}\) in the  
Figure 4: Secant modulus of CA mortar specimens: (**a**) secant modulus; (**b**) mean and STD. of secant modulus; (**c**) Mean \(\pm\) STD. of secant modulus.  
mean stress-strain curve is 15.23 MPa with a corresponding strain of 0.0064, and the residual stress \(\sigma_{s}\) is found to be around 6.01 MPa. Moreover, in the standard deviation curve, the peak stress is 1.83 MPa with a corresponding strain of 0.0037. It is also noted that, the strain corresponding to the peak stress is significantly larger than that in the mean stress-strain curve. In Figure 5c, it is shown that, in the ascending branch, the area enveloped by the mean \(\pm\) STD. of the stress-strain curve is less than that in the descending post-peak (softening) branch, which reveals a smaller degree of variation appeared during the early loading stage.  
Figure 5: Complete stress–strain curve of CA mortar: (**a**) Stress–strain curves of CA mortar specimens; (**b**) Mean and standard deviation for stress–strain curves; (**c**) Mean \(\pm\) STD. for stress–strain curves.