## 2 Tilting Tests on Perforated Dry-Masonry Walls  
This section briefly describes the experimental campaign: for a detailed description, the reader is referred to the two companion papers [22; 27], which review the experimental study and detail the numerical approach used to model them, respectively. The campaign consists of seven small-scale walls, later referred to as wall design (WD), with different block arrangements (Figure 1) tested on a tilting table and proposed by different competing teams. The walls were built using the same bricks (length \(\times\) height \(\times\) width = 25 mm \(\times\) 5.5 mm \(\times\) 12 mm) of density \(\rho\) = 1800 kg/m\({}^{3}\) and had identical dimensions (length = 0.2 m and height = 0.148 m). Finally, their design had to fill two constraints (Figure 1):* Having unperforated external edges (two sides and top).
* Having at least 30% of voids inside the structure.  
With this in mind, the objective of the design was to reach the maximum resistance to tilting tests, leading to a void ratio very close to 30% for all designs (max 31.5% for wall designs WD 2 and WD 5). Table 1 summarises the collapse tilting angles of each configuration. Tests have been repeated three times, and the coefficient of variation is also indicated in the results. The friction coefficient has been evaluated to \(\mu\) = 0.5 in the original study. The authors also noticed that the blocks were not geometrically perfect [22], which led to some refinements in the numerical paper [27].  
A numerical limit analysis program (with associative and non-associative flow rules) was used to model the experiments [27]. Firstly, assuming blocks as perfectly rectangular, the model largely overestimated the experimentally obtained capacities. The authors then conducted a parametric analysis on the friction coefficient, installation defects (misalignment of bricks) and geometric imperfections of bricks (corner rounding). Indeed, concerning the last point, They noticed that the real contact area was much smaller than the entire block surface, with an averaged reduction of 60%. While the first two had a negligible influence on the numerical results for most tests, the last one had a significant effect. However, from the results, different levels of geometrical imperfections (characterised by different reduction in the contact areas) for each wall design (WD) were necessary to approximately fit the experimental results, while the bricks were the same for the experimental campaign. Therefore, the following sections of the paper focus on discrete element simulations of the same experimental campaign. Therein, the joint stiffness parameters are assumed to account for the blocks' geometrical imperfections.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **WD 1** & **WD 2** & **WD 3** & **WD 4** & **WD 5** & **WD 6** & **WD 7** \\ \hline Collapse tilting angle \(\theta\) (\({}^{\circ}\)) & 18.3 & 7.8 & 19.8 & 16.8 & 7.8 & 7.8 & 18.6 \\ \hline Coefficient of Variation (\%) & 4.7 & 3.2 & 6.2 & 8.1 & 16.8 & 6.0 & 7.1 \\ \hline \end{tabular}
\end{table}
Table 1: Experimental collapse tilting angle for each wall design (WD) [22]. The coefficient of variation is also depicted.  
Figure 1: Seven wall geometries tested on a tilting table and respective teams, adapted from [22]. The external boundaries (length and height) of each wall design (WD) are the same.