## 5 The Step towards Full Dynamic Seismic Assessment Tools
### Comparison of Rocking Analysis Results with Code-Based Assessment Procedures
#### 5.2.1 Masonry Wall Loaded in Its Plane with Openings  
In the case of the in-plane loaded masonry wall with openings, the kinematic constants of the mechanism are first calculated using the Python script in Grasshopper [30]. The kinematic constants are then used to determine the equivalent rocking parameters \(p_{eq}\), \(\bar{\lambda}\) and \(\eta_{\text{COR}}\) defining the rocking equation of motion, which are listed in Table 4. Note that  
Figure 14: Acceleration response spectra (in grey) of the different recorded ground motions used in the analyses for the (**a**) pulse type and (**b**) non-pulse type records. The target spectrum is shown in black (scaled here to \(a_{g}=1.0\) g), while the average of the spectra is indicated in red. Figure 13: Acceleration response spectra (in grey) of the artificial ground motions used in the non-linear dynamic analyses. The target spectrum is shown in black (scaled here to \(a_{g}=1.0\) g), while the average of the spectra is indicated in red. the coefficient of restitution \(\eta_{COR}\) is negative due to one-sided rocking being assumed for this mechanism. In the first set of analyses, the rocking equation of motion was solved by scaling the suite of ground motions to \(a_{g}\) = 0.35 g for both the artificial and recorded accelerograms, as this was the PGA predicted to cause collapse by the displacement-based code approach. In the case of the artificial accelerograms, a comparison between the code-based predictions and those obtained from the rocking analyses revealed the code to consistently be the more conservative of the two (Figure 15, positive polarity indicated in black, negative in white). Specifically, using the actual response spectra for each accelerogram, the code predicted collapse in 70% of the cases (points lying above the solid horizontal line), while the maximum response predicted by the rocking model never exceeded 7.5% of \(\theta_{ov,c}\) or 3% of \(\theta_{ov}\). Similar trends were also observed in the case of the recorded accelerograms. Specifically, in the case of both pulse and non-pulse type motions, the code predicted larger demands than the rocking model in 100% of cases (i.e., all points lying above the dashed line in Figure 16). In the case of pulse-type motions in particular, the code predicted collapse in 54% of the cases, while the maximum response predicted by the rocking model never exceeded 66% of \(\theta_{ov,c}\) or 26% of \(\theta_{ov}\). However, in the case of the non-pulse-type motions, the code only predicted collapse in 26% of the cases, while the maximum response predicted by the rocking model never exceeded 38% of \(\theta_{ov,c}\) or 15% of \(\theta_{ov}\). Nevertheless, in both cases, it can be seen that the code is much more conservative than the rocking model, and that the PGA of 0.35 g is insufficient to cause rocking collapse. Thus, in a second set of analyses, the scaling of the ground motion was progressively increased until complete rocking collapse occurred, with collapse in this case being defined as \(\theta=\pi/2\). As the recorded ground motions are less conservative than the artificial ground motions, only the former are considered. From these analyses, it was found that for the masonry wall with openings, a minimum PGA of 0.50 g is required for at least one record to cause collapse, with the PGA having to be increased to 1.30 g for 50% of the recorded accelerograms (average of pulse and non-pulse type records) to cause complete overturning of the structure (Figure 17), which is 3.7 times higher than the code-based prediction of \begin{table}
\begin{tabular}{c c c} \hline \hline \(p_{eq}\) (s\({}^{-1}\)) & \(\widetilde{\lambda}\) (rad) & \(\eta_{COR}\) \\ \hline
1.55 & 0.20 & \(-\)0.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Masonry wall with openings. Equivalent rocking parameters calculated by the GhPython script. Figure 15: Masonry wall with openings.