1. Introduction

Conventionally, the response of a structure subjected to seismic excitation can be calculated by two approaches:

• calculation of transient dynamics if the excitation is defined by an accelerogram (cf. [R4.05.01]).

• calculation by the classical spectral method if the excitation is defined by an oscillator response spectrum (SRO) (cf. [R4.05.03]).

However, seismic excitation is by nature random. These two methods were not initially planned to take them into account: in one case it is necessary to repeat numerous temporal calculations for different excitations and then make a statistical average (significant calculation cost), in the other case very conservative hypotheses are made by considering means (simple or complete quadratic type for example) for the maximum number of answers.

A probabilistic calculation method, also called « stochastic approach to seismic calculation », has therefore been developed, based on the calculation of the dynamic response expressed in power interspectra from the power spectral densities of the excitation. In particular, this method has the advantage of better taking into account the correlations between the excitations at the various supports of the structure.

The discussion of the various advantages of this method can be further discussed in reference [bib1].

We therefore present the principle of the method and the ratings used from classical approaches, then in the third part we present the probabilistic calculation itself.

Finally, in the fourth part, the various methods for obtaining the excitatory interspectrum will be presented.