# Lateral Capacity of URM Walls: A Parametric Study Using Macro and Micro Limit Analysis Predictions
## 4 Results  
Figure 3 shows parameters' individual effects for both micro and macro LA models. The two formulations show good agreement in terms of both mean and standard deviation values. Figure 3 remarks small differences in terms of horizontal load multiplier for the analysed bond patterns. As expected, the higher friction coefficient tends to increase the horizontal capacity of the in-plane walls but generates more scattered results. Panel aspect ratio (PR = H/B) and the block aspect ratio (BR = b/h) strongly influence the horizontal load multiplier. In both cases, the standard deviation is very sensitive to PR and BR. In particular, higher PR tends to reduce lateral capacity scattering, whereas a higher BR has the opposite effect since it tends to increase the noise in the prediction of both micro and macro LA formulations. The macro and micro LA two-way factor interactions are reported in Figures 4 and 5, respectively. Results are organised into a 4 \(\times\) 4 matrix that is symmetric if one considers the data included in each cell, even though they are plotted by flipping the legends with the horizontal axis to provide broader information to the reader. It is worth underlining the good agreement between macro and micro LA formulations is again confirmed. In macro LA, \(\alpha_{b}\) was set equal for Running and English bonds, so the corresponding mean and standard deviation values are the same. Conversely, the Flemish bond type is computed differently according to the graphical approach represented in Figure 1. Assuming micro LA results as more accurate, the overestimation of lateral capacity for Flemish bond type is generated by an inaccurate evaluation of \(\alpha_{b}\). In fact, micro LA underlines slight differences among the bond types that could not be caught with macro LA. Referring to Figure 4, in macro LA simulations, the effect of the bond patterns tends to decrease by increasing PR and BR, whereas standard deviation values tend to decrease with higher values of PR and increase with higher values of BR, but stays constant with the change in friction coefficient. Micro LA shows a different influence of the bond types (Figure 5), where the two-way interaction with BR, PR, and friction coefficient  
Figure 3: Linear interaction: micro and macro LA. does not provide remarkable differences, highlighting a relatively low influence of the bond type in predicting the lateral capacity of in-plane masonry walls. Referring to the second row of the matrices of both macro and micro LA formulations (Figures 4 and 5), it is worth underlining that the bond type does not produce significant differences in terms of load multiplier predictions, whereas the two-way factors PR-BR and PR-friction coefficient produce remarkable differences, the latter yielding very scattered results. Figure 4: Two-way interaction plots: macro LA. The third row of the matrices shows a good agreement (Figures 4 and 5). In particular, one can note how by increasing BR the prediction tends to be more scattered except in the case of a very slender wall, i.e., PR = 2, or very limited friction coefficient (e.g., \(\mu=0.5\)). Furthermore, analysing the data reported in the third row, one can note that the higher BR generates more friction resistance and produces an increment in terms of lateral capacity. The fourth row of the matrixes represents the two-way factor interactions with the friction coefficient. Overall, the friction coefficient has a much lower influence in terms of mean values; however, the high variation in the results underlines the importance of such a mechanical parameter for assessing the lateral capacity of dry-stack masonry walls. Finally, to conclude the comparisons between the two computational procedures, one should note how macro LA result's trend of varying the friction coefficient is not influenced  
Figure 5: Two-way interaction plots: micro LA. by the value of PR, meaning the two parameters are not correlated. On the contrary, micro LA visualises an evident two-way friction-PR interaction.