# Uncertainties in the Seismic Assessment of Historical Masonry Buildings
###### Abstract  
Seismic assessments of historical masonry buildings are affected by several sources of epistemic uncertainty. These are mainly the material and the modelling parameters and the displacement capacity of the elements. Additional sources of uncertainty lie in the non-linear connections, such as wall-to-wall and floor-to-wall connections. Latin Hypercube Sampling was performed to create 400 sets of 11 material and modelling parameters. The proposed approach is applied to historical stone masonry buildings with timber floors, which are modelled by an equivalent frame approach using a newly developed macroelement accounting for both in-plane and out-of-plane failure. Each building is modelled first with out-of-plane behaviour enabled and non-linear connections, and then with out-of-plane behaviour disabled and rigid connections. For each model and set of parameters, incremental dynamic analyses are performed until building failure and seismic fragility curves derived. The key material and modelling parameters influencing the performance of the buildings are determined based on the peak ground acceleration at failure, type of failure and failure location. This study finds that the predicted PGA at failure and the failure mode and location is as sensitive to the properties of the non-linear connections as to the material and displacement capacity parameters, indicating that analyses must account for this uncertainty to accurately assess the in-plane and out-of-plane failure modes of historical masonry buildings. It also shows that modelling the out-of-plane behaviour produces a significant impact on the seismic fragility curves. stone masonry; seismic assessment; equivalent frame models; uncertainty analysis; Latin hypercube sampling; incremental dynamic analysis +
Footnote †: journal: Medical  
subjected to the Valle Scrivia Earthquake, 2003, Piemonte, Italy [2]. If numerical models are used for deriving the vulnerability curves, the models must adequately describe the geometry, morphology, connections and support conditions and must balance this with maintaining cost-effective computations that can be applied outside of the academic domain in seismic risk areas worldwide. To face these challenges, different modelling techniques and approaches have been developed to simulate the behaviour of masonry, and these techniques vary greatly in complexity levels and associated computational burden [3,4]. No matter which model is used, the question still remains on the choice of material and modelling parameters. When dealing with uncertainty, it is common to differentiate between aleatory randomness and epistemic uncertainty. Aleatory randomness is the natural randomness in the process, and the epistemic uncertainty stems from limited data and knowledge [5,6]. Different approaches with different levels of complexity were applied by several authors to treat these uncertainties in modelling historical masonry buildings. For example, many Incremental Dynamic Analyses (IDAs) were performed by [PERSON] [7] to deal with both the aleatory randomness stemming from differences in seismic records and the epistemic uncertainty stemming from material and modelling properties. Latin Hypercube Sampling (LHS) was used to distribute the material and modelling properties. The effect of uncertainty on the seismic response parameters was presented in terms of summarized IDA curves and dispersion measurements. The study concluded that epistemic uncertainty did not significantly affect the seismic response parameters in the range farther from collapse, but that the median collapse capacity was reduced when the epistemic uncertainties had been accounted for. [PERSON] et al. [8] dealt with the issues of the knowledge levels and associated values of a confidence coefficient in the assessment method for existing buildings included in Eurocode 8, Part 3 [9].