For seismic vulnerability assessment of buildings one usually relies on the probabilistic seismic demand analysis, where the cloud analysis is a popular method. Within the cloud analysis method, a statistical model is used to predict the demand of the building with respect the intensity of the earthquake ground motion. The data required to fit the model are obtained by running nonlinear, dynamic or static, analy-ses to obtain the demands of the building, known as Engineering Design Parameters (EDPs), when subjected to a suite of seismic ground motions, each represented by their intensity measure (IM). The statistical model predicts the EDP for any IM value, and provides an estimate of the record-to-record variability. In this work, a procedure is presented to extend the application of the Cloud Analysis method by accounting for the record-record variability as well as parameter uncertainties in the model used in the dynamic nonlinear analysis. The case study is a three-bay four-storey RC building, for which is designed to satisfy the seismic Eurocode requirements. The EDP consid-ered is the maximum inter-storey drift, for which is determined by a model developed in the OpenSees software. The uncertain parameters investigated are the compres-sive cylinder strength of the Concrete C30/37 and the yield strength of the Grade S450 Steel of the building. The procedure relies on the Monte Carlo method to propagate the uncertainties from the model parameters to the EDP, and the popular kriging surrogate model will be used to substantially reduce the computational costs associated with run-ning a large number of dynamic nonlinear analyses. A comparison is made between the cloud analysis with and without accounting for these parameter uncertainties. The fragility, typically of interest within performace-based earthquake engineering, will be calculated from the cloud analysis data. |