1. Introduction

The numerical Monte Carlo method consists in doing \(\mathit{Ns}\) numerical simulations of the mechanical model in order to evaluate the statistical quantities of the calculation results. The 3 main steps in propagating uncertainties by Monte Carlo simulation are:

• Uncertainty modeling: Generation of a sample of \(\text{Ns}\) realizations of random data as input to the mechanical model (random parameters and stochastic processes),

• The propagation of uncertainties: Calculation of the \(\text{Ns}\) result quantities corresponding to these data,

• The calculation of statistical estimators of the quantities sought: mean, standard deviation, fractions…; evaluation of seismic fragility curves.

As part of a mechanical study with Code_Aster, you can use the distribution functionalities of parametric studies in order to carry out such a probabilistic analysis. Indeed, in the current case where the \(\mathit{Ns}\) prints and mechanical simulations are independent, we can first establish an experimental plan of the case studies to be launched. The \(\mathit{Ns}\) corresponding studies are then launched, and the statistical quantities are calculated by post-processing the results.

The approach and its implementation with*Code_Aster* are described in this document.