# Retrofitting Masonry Walls against Out-Of-Plane Loading with Timber Based Panels
## 4 Numerical Study
### Numerical Simulation of Small-Scale Test on a Masonry Prism (MP) Specim  
#### 4.2.1 Development of the Masonry Prism Model  
The tested plain and retrofitted masonry prisms were modelled in FE to analyse further the efficiency of the proposed timber masonry retrofit technique. The model adopted was based on the micromodel technique developed in ABAQUS. The model was created with all the components in the four-point loading test properly modelled to obtain the best accurate results from the FE analysis. Table 5 summarises the material properties of all components, including those for the anchor connectors and OSB timber panels that were included for the retrofitted models. Two different models were created for the plain and retrofitted MP, and the models were labelled as MP00-NM and MPOSB-NM, respectively. MP00-NM comprised three components; brick unit, mortar and steel plate for load and support application. The brick unit (215 \(\times\) 102.5 \(\times\) 65 mm) and mortar joint (10 mm thick) were modelled as 3D deformable parts and meshed with a hexahedral 8-node linear brick, reduced integration and hourglass control (C3D8R) which has an improved convergence. The steel plate for load and support application (5 mm thick) was modelled using a 3D discrete rigid element and discretised by rigid element R3D4 to represent a part that is much stiffer (deformation negligible) than the masonry prism. For MPOSB-NM, two additional parts, an 18 mm-thick OSB timber panel and anchor rod, were modelled as 3D deformable parts and meshed with a hexahedral 8-node linear brick (C3D8R). The OSB timber panel and brick units were drilled at the connection locations, as done in the experiment to apply the retrofit to the MP. The process to build the full model requires that an appropriate interaction and constraints between model components be implemented to represent the relationship between each element in the model. In the micromodelling strategy employed, the brick-mortar bond interface was not specified separately, so the brick continuum and mortar continuum were merged to assume a perfect bond, as shown in Figure 13(a). In order to place the loading at the front face of the model, the surface of the steel plate was tied to the surface of the brick at the third and seventh course using tie constraints (Figure 13(b)). Similarly, the steel plates were tied to the top and bottom brick or OSB timber at the back of the MP model for the retrofitted MP, as shown in Figure 13(c), for the support application. The use of tie constraints ensured that the steel plate could not slip from the brick unit or the OSB timber panel during the analysis. In addition, frictional, normal hard contact was specified between the surface of the OSB timber and MP model, as shown in Figure 14. For this analysis, the friction coefficient was taken as 0.5, which is a typical coefficient of friction between timber and brick. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Mass** & **Young** & **Poisson** & **Compressive** & **Timile** & **Tensile** \\  & **Density (\(\gamma\))** & **Modulus (E)** & **Ratio (\(\mu\))** & **MPa** & **MPa** & **Energy (\(G_{\gamma}\))** & **Strength (\(f_{\gamma}\))** & **Fracture** \\  & **g/mm\({}^{3}\)** & **MPa** & & **MPa** & **N/mm** & **MPa** & **Energy (\(G_{\gamma}\))** \\ \hline \hline   Brick unit & 2.2 \(\times\) 10\({}^{-3}\) & 32.47 \(\times\) 10\({}^{3}\) & 0.26 & 87.91 & 29.01 & 5.93 & 0.11 \\   Mortar joint & 2.17 \(\times\) 10\({}^{-3}\) & 19.85 \(\times\) 10\({}^{3}\) & 0.20 & 7.10 & 1.90 & 0.23 & 0.02 \\   OSB panel & 0.65 \(\times\) 10\({}^{-3}\) & 3.50 \(\times\) 10\({}^{3}\) & 0.24 & 6.60 & 0.86 & 1.85 & 0.32 \\   Anchor & 7.85 \(\times\) 10\({}^{-3}\) & 210 \(\times\) 10\({}^{3}\) & 0.30 & & Assumed to be linear elastic & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Input material properties of components obtained via calibration.