# Uncertainties in the Seismic Assessment of Historical Masonry Buildings
## 6 Conclusions  
Scientists and practitioners alike often model unreinforced masonry buildings using the equivalent frame model (EFM) approach. This method is affected by numerous epistemic uncertainties, commonly handled by adopting conservative deterministic values. However, any deterministic approach bears the risk that possible damage and collapse mechanisms are overlooked. Therefore, we proposed a methodology to account for epistemic uncertainties and applied it to two masonry buildings representative of their categories: a stiff monumental historical masonry building, and a tall and slender residential masonry building. Each building was modelled twice --first with the out-of-plane capability of the macroelement used for modelling each wall enabled and with non-linear wall-to-wall and floor-to-wall connections, and then with the out-of-plane capability disabled and rigid connections. We used Latin Hypercube Sampling to create 400 sets of 11 material and modelling parameters, distributed according to normal and lognormal distributions, to account for epistemic uncertainties. Then for each model and each set of parameters, we carried out an IDA in OpenSEES using a newly developed macroelement that can couple in-plane and out-of-plane responses until the building failed or collapsed. Failure mode and location were analysed according to a set of criteria considering the loss of equilibrium due to out-of-plane failure of some element(s) or the progressive loss of lateral force capacity due to in-plane failure of walls. The response of each modelling approach was evaluated in terms of the seismic response parameters--base shear and roof displacement, correlations of seismic response parameters with input parameters, seismic fragility curves, correlations of failure PGA with input parameters, and statistical distributions of failure modes and locations. The factors that clearly impact the failure PGA for each building typology were the material parameters (modulus of elasticity, shear modulus, compressive strength) and the EFM modelling parameters (limit drift values, Rayleigh damping ratio). The floor stiffness and floor-to-wall friction coefficient also impacted the failure PGA if the model developed a dominant out-of-plane failure mode. The floor stiffness was second in importance to the floor-to-wall friction coefficient. A similar effect was observed by [PERSON] et al. [16]. The importance of the floor stiffness is lower than the force capacity of the floor-to-wall connection if the latter is exceeded because the stiffness of the floor cannot be exploited. On the other hand, for PGA levels farther from failure, the floor-to-wall connection force capacity is not exceeded and the seismic response parameters correlate with the floor stiffness. Hence, the floor stiffness has only a large influence on the results, if the connection between floors and walls is effective enough to fully exploit the contribution of floors. In unstrengthened building configurations this force capacity is typically governed by friction  
Figure 27: Comparison of Lausanne Malley fragility curves for models with: (i) out-of-plane enabled and non-linear connections, and (ii) out-of-plane disabled and rigid connections. forces between floor beams and wall and is therefore rather small. While this finding is intuitive, it is often overlooked because the floor-to-wall connection is modelled as perfectly rigid. The effect of the floor-to-wall friction coefficient highlights therefore the importance of modelling the nonlinearity of the connections in historical masonry explicitly. For both the Holstein Hof and Lausanne Malley buildings, disabling out-of-plane behaviour and making connections rigid produced significant differences in the seismic fragility, failure modes and locations. The difference in the seismic fragility was even pronounced for lower PGA levels, which for certain sets of material and modelling parameters, could already produce significant out-of-plane behaviour.