Modèles probabilistes et possibilistes pour la prise en compte de l'incertain dans la sécurité des structures

This thesis relates to the analysis of the behavior of the safety of structures, from the point of view of both - probability and possibility - of the modelling of variabilities and uncertainties of the design variables introduced in the limit states. After reviewing the classical expressions about structural safety (semi-probabilistic and probabilistic approaches), the attention is focused on the definition of pre-measures of confidence to estimate the risk of exceeding limit states. Different concepts related to the expression and to the modelling of the uncertainties are reviewed, highlighting the particularities of the measures of possibility and their positionings to the measures of probability. The essential notions of the reliability theory are also reviewed. An analogous approach to the probabilistic theory of reliability is adopted to develop a new theory of reliability. The so-called possibilistic reliability theory adopts a possibilistic approach for modelling the variabilities and uncertainties associated with the structural variables; two important definitions have been given in this study - the possibility of failure and the possibilistic index of reliability. There exist numerous theoretical similarities between the two theories of reliability and one comparison has been presented, in augmenting numerical examples. The theoretical formulations are given for the linear limit states or nonlinear limit states, introducing only distinct and non-inttractive variables modelled by fuzzy intervals. The theoretical developments show a lot of simplifications for calculation, since the determination of the possibilistic index of reliability is reduced to the search of a scalar minimum. It can be realized by the means of the signs rule which principle is detailed and illustrated. An example concerning the calculation of the fatigue life of welded joints, is finally proposed to illustrate the possibilistic reliability approach. Attention has been focused on the modelling of uncertainties, by using the concept ...