## 4 Results
### Influence of Low Joint Stiffness on the Simulation Results
Each wall design (WD) has been numerically simulated using the following stiffness parameters: \(\mathrm{k_{n}}\) = \(\mathrm{k_{s}}\) = 1 \(\times\) 10\({}^{7}\), 2 \(\times\) 10\({}^{7}\), 2.2 \(\times\) 10\({}^{7}\), 2.5 \(\times\) 10\({}^{7}\), 2.7 \(\times\) 10\({}^{7}\), 3 \(\times\) 10\({}^{7}\), 4 \(\times\) 10\({}^{7}\), 7 \(\times\) 10\({}^{7}\), 1 \(\times\) 10\({}^{8}\), 1 \(\times\) 10\({}^{9}\) and 1 \(\times\) 10\({}^{10}\) Pa/m. For simplicity, the normal stiffness has been kept constant throughout the simulations, though in theory it should be decreased while the model is tilted since the axial stresses decrease. An even better improvement consists of implementing in the numerical model a stress-dependent joint stiffness, but this is out of the scope of the present paper. The collapse tilting angles are represented in Figure 6, in a dimensionless form, dividing the numerical value by the experimental one. In Figure 6, the mean experimental coefficient of variation (CoV) is also represented with the grey shadow for a better appreciation of the quality of the numerical results. On the left side of Figure 6, it seems that joint stiffness higher than \(\mathrm{k_{n}}\) = 1 \(\times\) 10\({}^{10}\) Pa/m would not lead to significant changes in the collapse tilting angle \(\theta\). Four WDs (WD 1, WD 3, WD 4 and WD 7) saturate even before (at \(\mathrm{k_{n}}\) = 1 \(\times\) 10\({}^{9}\) Pa/m) because the failure is already a sliding failure at this stage. On the left side of Figure 6, one can note that at \(\mathrm{k_{n}}\) = 1 \(\times\) 10\({}^{7}\) Pa/m, some WDs (WD 4, WD 6 and WD 7) are not even stable under static vertical loads only. Between these two extremes, collapse tilting angles increase with joint stiffness. In general, one can note that numerical results are very close to the experimental ones when the stiffness ranges between 2.5 \(\times\) 10\({}^{7}\) Pa/m and 4 \(\times\) 10\({}^{7}\) Pa/m for each WD. From Figure 6, the value \(\mathrm{k_{n}}\) = 3 \(\times\) 10\({}^{7}\) Pa/m is excellent for predicting the experimental behaviour accurately. In particular, its accuracy appears to be much better than the one obtained with limit analysis, where different block geometries should be used for each WD to fit the experimental results [27]. Here, the same geometrical, physical and mechanical  
Figure 6: Collapse tilting angle \(\theta\) depending on the joint stiffness parameters (\(\mathrm{k_{n}}\) = \(\mathrm{k_{s}}\)). The trend is monotonous and indicates a strong effect of joint stiffness. parameters are used for each WD, leading to an average error of 7.9%: Table 3 sums up the relative difference between numerical and experimental results for this particular stiffness. The obtained collapse mechanisms for each WD have been compared to the experimental ones (three tests for each WD) in Figures 7 and 8, while the videos of the entire numerical simulations are available in the Supplementary Materials. DEM simulations reproduce the mechanisms well and, in particular, the progressive bending of masonry pairs, which is more accurately modelled than using DEM with large joint stiffness values (Section 4.2) or with Limit Analysis [27] (Figure 4). However, apart from these progressive bending effects and the large differences in capacity found as a function of the stiffness, the failure mechanisms are not significantly affected by the stiffness parameters, as already noticed by other authors for dry-joint assemblies [42]. Given the strong influence of \(\mathrm{k_{n}}\) on the collapse tilting angle \(\theta\) (Figure 6), the less accurate simulation prediction presented for the model WD 6 is not significant (Figure 8). In addition, one could argue that the stiffness in this particular case might be higher than for the other WDs. Indeed, in the bottom part of the wall where most of the deformation occurs (Figure 8), the contacts are half of the time only between two bricks.