# Mechanical Performance of Confined Autoclaved Fly-Ash-Brick Masonry Walls under Cyclic Loading
## 3 Numerical Simulation Analysis and Verification  
### The Numerical Model of Assembly Autoclaved Fly-Ash-Brick Wall  
In order to simplify the construction process and shorten the construction period, two new types of template block were designed to replace steel or wood templates for the constructional column and ring beam [29], which are shown in Figure 8. The constructional column and ring beam blocks were constructed in the wall, in which the concrete was poured into the hole and the rebar was placed in the internal groove to build the constructional column and ring beam. The autoclaved fly-ash-brick was used as the wall material. The advantages of such block templates are that they can be the permanent part of the columns or beams and work with the concrete poured inside them. A typical model of assembly autoclaved fly-ash-brick masonry wall is shown in Figure 9. All dimension units are millimeters unless otherwise stated.  
To generate an idealized numerical model and analyze the structural system, the macro-scale approaches of masonry walls were adopted in the numerical simulation [30]. The assembly wall models were established by numerical software ABAQUS, in which the C3D8R and T3D2 elements were selected to simulate the concrete, brick, and steel reinforcement, respectively [31], as illustrated in Figure 10. The units were meshed as 4 mm \(\times\) 2 mm \(\times\) 2 mm (length \(\times\) width \(\times\) height), in which the influence of the mesh density on the bearing capacity was small. The penalty stiffness value was \(5\times 10^{5}\) N/mm\({}^{3}\), and the influence of the penalty stiffness was negligible in analyzing the structural aseismic performance [32]. The concrete damage plasticity model was selected to simulate the nonlinear behavior of the masonry blocks, and the \"embedded\" command was used to simulate the interaction between the concrete and steel. The ring beam and constructional column blocks and cast-in-place concrete were two separate parts connected by the binding command. The constitutive model of autoclaved fly-ash-brick was obtained from the test, while the constitutive model of the new type of blocks was obtained from other researchers [8; 32; 33], the constitutive relations and curves of which are presented in Equations (5)-(8) and Figure 11, respectively.  
Figure 8: Specification and dimension diagram of new-type assembly blocks: (**a**) constructional column block; (**b**) ring beam block.  
Figure 9: Reinforced masonry blocks.  
The compression constitutive relation of the assembly concrete blocks in the constructional columns and ring beams is expressed as follows:  
\[\frac{\sigma}{\sigma_{c}}=2\frac{\varepsilon}{\varepsilon_{c}}-\left(\frac{ \varepsilon}{\varepsilon_{c}}\right)^{2}\ \ \varepsilon\leq\varepsilon_{c} \tag{5}\]  
\[\frac{\sigma}{\sigma_{c}}=-0.16\frac{\varepsilon}{\varepsilon_{c}}+1.16\ \ \ \varepsilon_{c}<\varepsilon\leq 4\varepsilon_{c} \tag{6}\]  
in which \(\sigma\), \(\varepsilon\), \(\sigma_{c}\), and \(\varepsilon_{c}\) are the stress, strain, peak stress, and peak strain, respectively, under uniaxial compression. According to GB50003-2011 [25], the strain \(\varepsilon_{c}\) was 0.0022 and the ultimate strain \(\varepsilon_{u}\) was 0.0034.  
The tension constitutive relation of the assembly concrete blocks, which used the concrete damage plasticity model, in the constructional columns and ring beams is as follows:  
\[y=1.2x-0.2x^{6}\ x\leq 1 \tag{7}\]  
\[y=\frac{x}{\alpha_{t}(x-1)^{1.7}+x}\ \ x>1 \tag{8}\]  
in which \(x=\varepsilon/\varepsilon_{t0}\) and \(y=\sigma/f_{t}^{*}\) is the correlation parameter of the uniaxial tensile stress-strain curve, \(f_{t}^{*}\) is the uniaxial tensile strength value, \(\varepsilon_{t0}\) is the tensile strain value corresponding to \(f_{t}^{*}\).