# Uncertainties in the Seismic Assessment of Historical Masonry Buildings
## 5 Discussion  
This work highlights the importance of considering all sources of material and modelling uncertainty since rather small differences in the material and modelling parameters led to rather different results. Firstly, differences here could produce a different PGA at failure, which was already visible from the fragility curves. Secondly, they could produce different modes and locations of failure; the difficulty in predicting the correct mode of failure was especially evident for the Holsteiner Hof building, where the probability of out-of-plane and in-plane failures were evenly divided. Furthermore, the in-plane failure modes comprised both shear and flexural failures, with 62% of the in-plane failure modes being flexural, and both the flexural and shear drifts at collapse showing a clear correlation with PGA at failure, together with the Rayleigh critical damping ratio, modulus of elasticity, shear modulus and compressive strength. Although the Holsteiner Hof had a high number of out-of-plane failures, there was no correlation detected between the probability of out-of-plane failures and floor stiffness or floor-to-wall connection effectiveness. This is because the floors of the building span in the y-direction, whereas Figure 11 showed that the majority of out-of-plane failures were located in the second storey walls in the y-direction. Since these walls fail out-of-plane in the x-direction and the timber floor beam span in the opposite direction, the floor-to-wall connection does not influence the out-of-plane failure unless retrofit interventions provide also floor-to-wall connections in this direction. To link our work with previous studies where EFM were used to compute fragility functions without accounting for out-of-plane failures, the stochastic analyses were repeated with the out-of-plane capability of the macroelement disabled and floor-to-wall and wall-to-wall connections modelled as rigid. The Holsteiner models 84 th percentile IDA  
Figure 23: Lausanne Malley model (with out-of-plane disabled and rigid connections) failure statistics: (**a**) In-plane type of failure. (**b**) Failure location. curves are compared in Figure 24. The results in terms of the base shear are almost identical, while the difference in the roof displacements progressed with the PGA increment. Comparison of fragility curves showed that the model with out-of-plane behaviour and non-linear connections was significantly more fragile than the model without out-of-plane behaviour and with rigid connections, having higher probability of failure for each PGA level as shown in Figure 25. The difference was emphasized for lower PGA levels, where a significant occurrence of the early out-of-plane failure was observed. The difference in failure type and location was significantly influenced by the ability of the macroelement to simulate the out-of-plane behaviour and presence of non-linear connections. Whereas the first model failed in flexure in 62% of the cases, the second failed in shear in 64% of the cases. Although failure was still most common to occur in the second storey, having disabled the out-of-plane behaviour and non-linear connections, the number of failures located in the first storey increased. Figure 24: Holsteiner Hof comparison of IDA curves for models with: (i) out-of-plane enabled and non-linear connections, and (ii) out-of-plane disabled and rigid connections, displaying the maximum values of seismic demand parameters: (**a**) Total base shear in x-direction. (**b**) Total base shear in y-direction. (**c**) Average roof displacement in x-direction. (**d**) Average roof displacement in y-direction. A different effect of modelling uncertainties was observed in the Lausanne Malley building, which is tall and slender. As such, it failed out-of-plane 92% of the time. A dominant out-of-plane behaviour is shown in Figure 19, wherein failures were distributed in both directions and scattered through floors, but nevertheless were mostly concentrated in the fifth storey.