# Mechanical Performance of Confined Autoclaved Fly-Ash-Brick Masonry Walls under Cyclic Loading
## 3 Numerical Simulation Analysis and Verification
### Verification of Assembly Masonry Wall Model  
A low-cyclic loading test of the full-scale assembly using an autoclaved fly-ash-brick masonry wall was carried out in a structural laboratory to study the seismic responses of the brick masonry wall. By contrasting and analyzing the assembly masonry wall adopted by the above constitutive models and cyclic-load testing results, the purpose was to verify  
Figure 11: Constitutive curves of new-type blocks: (**a**) compression constitutive curve (**b**) tensile constitutive curve. Figure 10: (**a**) Wall numerical model; (**b**) wall mesh. the correctness of the wall models' parameters. The parameters of the test wall are shown in Table 2 and the detailed diagram of the assembly of the masonry wall is shown in Figure 12. The test wall consisted of four parts: ring beam, constructional column, brick wall and base beam. All the brick walls were constructed by autoclaved fly-ash-brick with typical size of 240 mm \(\times\) 115 mm \(\times\) 53 mm and 10 mm thickness cement mortar. The base beam were made of concrete which was installed together with brick masonry part by using epoxy mortar. The elastic modulus value of the autoclaved fly-ash-brick was measured by the secant modulus of 0.4 \(\sigma_{0}\) (peak compressive stress) on the stress-strain curve in the micrometer from Figure 9. Material properties of masonry unit and mortar were measured from the material property tests, as listed in Table 2. The test setup is shown in Figure 13a. The base beam was constrained by four screws in the vertical direction and two jacks in the lateral. In order to keep compressive loadings uniform and vertical, steel rollers were placed between ring beam and transfer beam with equal distances. The test wall was subjected to vertical load and cyclic lateral load until the wall was damaged. Before the application of the lateral loadings, the compression load was firstly applied to 0.60 MPa, and remained constant towards the end of the test. During the test, the cyclic lateral loadings were controlled by force initially and by displacement after cracking occurred. The initial displacement of the crack occurred defined as \(\Delta\)cr, and the lateral loading scheme for the cyclic tests is shown in Figure 13b. The maximum displacement value was 20 mm, or the bearing capacity of the wall corresponded to 85% of the ultimate load. The test wall was constructed with the same geometry, brick arrangement and material properties as the numerical wall model. The numerical wall model was constructed into four parts, same as the test wall. The compressive pressure of 0.60 MPa was used in the cyclic-loading test. The loading system of the numerical wall model was the same as that of the test wall. For the model validation, the maximum displacements recorded in tests were loaded for the corresponding numerical models. The assembly autoclaved fly-ash-brick wall was simulated numerically to obtain the load-displacement skeleton curves and the ultimate loads of the test wall, as shown in Figure 14 and Table 3. The diagram of equivalent plastic strain and fracture distribution of the walls are shown in Figure 15. According to GB50003-2011 [25], the shear strength of masonry \(V_{0}\) is calculated:  
\[V_{0}\mathrm{=}\left(f_{v}+\alpha\mu\sigma_{0}\right)A \tag{9}\]  
in which \(f_{v}\) is the design value of shear strength for the masonry wall, \(\alpha\) is the modified coefficient, \(\mu\) is the correction factor under shear compression load, \(\sigma_{0}\) is the compressive stress and \(A\) is the cross sectional area of a masonry wall. The equivalent plastic strain (PEEQ) represented the deformation caused by unit load which changed along the diagonal of the wall. From Figures 14 and 15, the distribution of it was the same as the X-type crack caused by shear failure of the wall under cyclic loading.