Probabilistic dynamic analyses of a soil-structure system subjected to a stochastic earthquake Ground-Motion

In this paper, a probabilistic dynamic analysis of a five-storey building subjected to a stochastic earthquake Ground-Motion (GM) is presented. The entire soil-structure system is considered in the analysis. The stochastic GM time-histories are based on a real recorded time history. The probabilistic dynamic analysis is performed using the classical Monte Carlo Simulation (MCS) methodology. As is well known, this method requires a great number of calls of the deterministic model. To overcome the inconvenience of the time cost, a simple deterministic model based on the "macro-element" concept is used. The main advantage of the macro-element is that the time cost for a single deterministic calculation is relatively small and thus, this model is suitable for the probabilistic dynamic analysis. The simulation of the stochastic GM time-histories is done using a fully nonstationary stochastic model in both the time and the frequency domains. This model employs filtering of a discretized white-noise process. Non-stationarity is achieved by modulating the intensity and by varying the filter properties in time. As for the probabilistic analysis, a large number of samples (say 100,000) of the stochastic GM time-histories is generated using Monte Carlo technique. For each sample, a dynamic calculation using the macro-element is performed and the following responses are retained for the probabilistic analysis: (i) the maximum horizontal displacement at the top of the building, (ii) the three maximum displacements of the footing centre, and finally (iii) the three maximum reaction forces at the contact of the soil and the footing. These results are used to compute the statistical moments of the different system responses together with the probability of exceeding of predefined thresholds for these responses