## 6 Conclusions  
This paper presented numerical DEM simulations of seven perforated masonry shear walls taken from an experimental work in the literature [22]. The work stemmed from the inaccurate predictions provided by Limit Analysis [27]. After the description and calibration of numerical parameters (contact points and density), a parametric analysis was conducted on the stiffness parameters. It was found that the tangential stiffness has only a minor effect on the collapse load and is limited to the range of very low stiffness (1 \(\times\) 10\({}^{7}\)-2 \(\times\) 10\({}^{7}\) Pa/m). Classical stiffness values (1 \(\times\) 10\({}^{9}\)-1 \(\times\) 10\({}^{10}\) Pa/m) achieved very similar results to Limit Analysis (either with associative or non-associative flow rule). In this case, the experimental capacity is overestimated by an average of 70%. Using a much smaller value of stiffness, which is classical in rubble masonry assemblages subjected to low vertical stresses and scaled models in the laboratory, DEM predictions were much closer to the results. A value of \(\rm k_{n}\) = \(\rm k_{s}\) = 3 \(\times\) 10\({}^{7}\) Pa/m was enabled to be, on average, only less than 10% different from the experimental failure value. The approach adopted seems more adequate than the one proposed by [27], where different geometrical parameters should be used for each geometrical model to fit the experimental capacity. In general, simulations with classical (1 \(\times\) 10\({}^{9}\) Pa/m) and low stiffness (3 \(\times\) 10\({}^{7}\) Pa/m) values retrieved the experimental collapse mechanisms of the tested walls, though only the  
Figure 13: Influence of the tangential joint stiffness \(\rm k_{s}\) on the pushover curves and Damage Limit States (DLS) of WD 6 for different normal joint stiffness. simulations with low stiffness could reproduce the progressive bending of masonry piers due to the accumulated joint deformation at each masonry course. In real structures, contact stiffness values are available in standards and from testing large scale structures/structural components. The results, particularly when performance based seismic assessment is adopted, are sensitive to the adopted stiffness. Stiffness values must be significantly decreased to reach accurate simulations when a structure is made of dry joints with imperfect blocks, as for the studied dry masonry walls or generally for dry-stone constructions, and particularly in the case of low vertical precompression. In this case, the stiffness parameters must be identified on the model or at least with joint closure tests, since it significantly affects the final capacity and ductility of the system. The error made using too stiff joints (1 \(\times\) 10\({}^{9}\) instead of 3 \(\times\) 10\({}^{7}\) Pa/m) reaches a factor of 1.7 for the collapse load and a factor of 5.0 for the damage limit state (DLS) load based on the acceptable drift of 1% from the Eurocode 8. The present work also highlighted the inadequacy of the drift limits proposed by the Eurocode for this kind of soft assemblage. The latter requires a definition based on the stiffness of the structure, at least for the third category where no non-structural components are linked to the studied structural element. Finally, though standard Limit Analysis (either with associative or non-associative flow rules) seems valid for masonry structures with classical joint stiffness (1 \(\times\) 10\({}^{9}\) Pa/m), it is not applicable as-is for softer joints with lower stiffness values, in which elastic deformation plays a key role in the response. The following are available online at [[https://www.mdpi.com/article/10](https://www.mdpi.com/article/10)]([https://www.mdpi.com/article/10](https://www.mdpi.com/article/10)) 3390/app12042108/s1, Video S1: WD 1, Video S2: WD 2, Video S3: WD 3, Video S4: WD 4, Video S5: WD 5, Video S6: WD 6, Video S7: WD 7. They all represent the numerical simulations (with the displacement maps) for the joint stiffness of \(\mathrm{k_{n}}=\mathrm{k_{s}}=3\times 10^{7}\) Pa/m.