# Mechanical Performance of Confined Autoclaved Fly-Ash-Brick Masonry Walls under Cyclic Loading
## 2 Axial Compression Test of Autoclaved Fly-Ash-Brick Columns
### Stress-Strain Curve  
The stress-strain curves of the autoclaved fly-ash-brick short column with M7.5, M10, and M15 mortar strength obtained from the test are shown in Figure 5. The constitutive relationship of the autoclaved fly-ash-brick short column was analyzed using the dimensionless stress-strain curve in which dependent variable \(x=\varepsilon/\varepsilon_{0}\) and independent variable \(y=\sigma/\sigma_{0}\) by normalization [25; 26], as shown in Figure 6. \(\sigma_{0}\) indicates the peak compressive stress, and \(\varepsilon_{0}\) denotes the peak compressive strain.  
The experimental results showed that the cracking and failure processes of the brick specimens were similar. From the experimental phenomenon and normalized stress-strain curve of the autoclaved fly-ash brick, a large difference in the curve trend was observed between the upward and downward sections. The constitutive curve should include the elastic-limit, peak, anti-bending, and other numerical points. [PERSON] et al. [23] investigated a no-tension material using the non-linear stress-strain law in compression, and the constitutive relationship was obtained, as expressed in Equation (1). [PERSON] et al. [27] carried out many axial compression tests to study the compression constitutions of a common brick, and the constitutive relationship was obtained, as expressed in Equation (2). [PERSON] et al. [28] conducted a brick-masonry test to obtain a geometrical model for the uniaxial cyclic compressive behavior of brick masonry, which determined several focal points in the uniaxial stress-strain plane based on the geometrical properties of the experimental cyclic stress-strain curves, as expressed in Equation (3). With reference to the literature [23; 27; 28]), the current study presented a simple form of autoclaved fly-ash-brick constitutive relationship that is beneficial for model convergence. The ascending segment of the curve adopts a quadratic parabolic form, which includes the elastic-limit and peak points of the stress. The drawdown segment of the curve satisfies the boundary condition in a fractional form, including the peak, anti-bending, and convergence points of the stress. The stress-strain relationship of the autoclaved fly-ash-brick short column is modeled using test data, as expressed in Equation (4).  
The correlation stress-strain curves obtained from other studies in the literature and the test points are shown in Figure 7. The constitutive curve proposed in this study was consistent with measured data. In the numerical model, the constitutive relationship expression is simplified, which is beneficial for numerical analysis calculation. The other constitutive relationship curves show relatively high performance, and the test-data points basically fall below the curves, indicating that these curves are not suitable for describing the compressive stress-strain characteristics of the fly-ash-brick masonry.  
\[y=6.4x-5.4x^{1.17} \tag{1}\]  
Figure 4: Failure of the autoclaved fly-ash-brick column.  
\[y=\left\{\begin{array}{ll}\dfrac{x}{0.2+0.8x}&x<1.0\\ 1.2-0.2x&x\geq 1.0\end{array}\right. \tag{2}\]  
\[y=2x-x^{2} \tag{3}\]  
\[y=\left\{\begin{array}{ll}\dfrac{1.93x-1.02x^{2}}{0.76x-0.66}&x<1.0\\ \dfrac{0.76x-0.66}{1.48x^{2}-2.38x+1}&x\geq 1.0\end{array}\right. \tag{4}\]  
Figure 5: Stress–strain curves.  
Figure 6: Dimensionless stress–strain curves.  
Figure 7: Correlation curves.