## 5 Code Aspects and Masonry Structures with Soft Joints
In Figure 12, it is noted that the DLS tilting angle is very small for low contact stiffness. In fact, all WDs follow a similar hyperbolic tangent trend, with three main different groups. WD 1 and WD 3 form the first one with the highest global stiffness in the low stiffness range resulting in smaller drifts. This is attributed to the even distribution of voids inside the structure, thus limiting stress concentration and joint rotation/deformation. Then, the second group (WD 4 and WD 7) and the third group (WD 2, WD 5 and WD 6) have the same behaviour at low contact stiffness (up to \(\mathrm{k_{n}=k_{s}=4\times 10^{7}\ Pa/m}\)), while the DLS collapse tilting angles of the second group increase at medium contact stiffness to reach similar values as the first group (WD 1 and WD 3) for joint stiffness of \(\mathrm{k_{n}=k_{s}=1\times 10^{9}\ Pa/m}\). The third group (WD 2, WD 5 and WD 6) always has the smaller DLS tilting angles. Table 4 compares the ratio of (1) the collapse tilting angle and (2) the DLS tilting angle for the simulation using \(\mathrm{k_{n}=k_{s}=3\times 10^{7}\ Pa/m}\) to the simulation using \(\mathrm{k_{n}=k_{s}=1\times 10^{9}\ Pa/m}\) for the seven WDs. It is shown that using an inaccurate value for the contact stiffness (in this case a larger one) overestimates not only the collapse tilting angle (by an average factor of 1.7, as seen before), but even more the DLS tilting angle ratio, by an average factor of 5.0. This last comment is of particular importance when assessing the seismic capacity of such structures. Although it has been excluded to simplify the parametric analysis, it is stressed that the accurate evaluation of the stiffness parameters concerns both normal \(\mathrm{k_{n}}\) and tangential \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **WD 1** & **WD 2** & **WD 3** & **WD 4** & **WD 5** & **WD 6** & **WD 7** \\ \hline Collapse tilting angle ratio & 1.3 & 1.9 & 1.3 & 1.4 & 2.0 & 2.7 & 2.0 \\ \hline DLS tilting angle ratio & 3.0 & 4.8 & 2.4 & 5.5 & 4.9 & 7.8 & 6.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the collapse and the damage limit state (DLS) tilting angles between simulations with \(\mathrm{k_{n}=k_{s}=3\times 10^{7}\ Pa/m}\) and \(\mathrm{k_{n}=k_{s}=1\times 10^{9}\ Pa/m}\) for each WD. The results are displayed in the form of the ratio between the stiffer to the softer joint stiffness. Figure 12: Evolution of the Damage Limit State (DLS) tilting angle for each wall design (WD) for different joint stiffness value. The drift limit considered here is 1%, i.e., the maximum one from the Eurocode 8 [36]. \(\rm k_{s}\) stiffness. However, as already noticed above, the effect of \(\rm k_{s}\) is relatively small for the studied configurations. As an illustrative example, Figure 13 shows the pushover curves of WD 6 and the DLS associated with a drift limit of 1% for different combinations of \(\rm k_{n}\) and \(\rm k_{s}\). Except for very small \(\rm k_{s}\) associated with large \(\rm k_{n}\), the influence of \(\rm k_{s}\) is again much less important than \(\rm k_{n}\), although always noticeable. This is attributed to the lower tangential contact forces compared to the normal ones as the tilting angles are almost always smaller than 20\({}^{\circ}\) for every WD (tan 20\({}^{\circ}\) = 0.36). Finally, one can argue that the drift limit of 1% for this particular type of soft wall should be revised to account for most of the elastic part of the pushover curves (Figures 9-11). Actually, this drift limit should even depend on the joint stiffness of the assemblage (Figure 12). However, since the other drift limits of 0.5% and 0.75% from the Eurocode 8 are linked to the protection of the non-structural elements bound to the structural shear wall, they should be kept [36]. In addition, it also means that non-structural elements should be avoided on these kinds of very soft walls, as they will break too easily for very small and common earthquakes/loads.