Le projet ROS-3D a été réalisé dans le cadre du WEAMEC et avec le financement de la CARENE par l’Université de Nantes
Résumé de la publication
As is well known, the classical Kriging-based probabilistic approaches such as the Active learning method combining Kriging and Monte Carlo Simulations MCS (named AK-MCS method) or the method combining Kriging and Importance Sampling IS (named AK-IS method) involve the construction of a surrogate Kriging metamodel based on the responses of a small design of experiments computed using the mechanical model. This approximate Kriging meta-model is then successively updated via an enrichment process by selecting new training points that are close to the limit state surface using a powerful learning function. The essential issues in these approaches are that both the choice of a ‘best new point’ and the stopping criterion of adding a new training point are defined from the perspective of individual responses, which may lead to some extra evaluations of unnecessary added training points. To overcome this shortcoming, a reliable and efficient probabilistic methodology based on an enhanced Kriging model (called Global Sensitivity Analysis-enhanced Surrogate GSAS modeling) was proposed by(Hu and Mahadevan, 2016). In this method, both the convergence criterion and the strategy of selecting new training points are defined from the perspective of reliability estimate instead of individual responses of MCS
or IS points. A global sensitivity analysis is performed to select the optimal new training point and the convergence criterion is reached based on the desired accuracy of the reliability estimate. This method is applied in this paper in combination with the classical MCS or IS approach in order to reduce the number of calls of the mechanical model with respect to the corresponding classical AK-MCS and AK-IS approaches. It is used for the probabilistic analysis at the ultimate limit state of a strip footing resting on a spatially varying soil. The aim is the computation of the failure probability against soil punching.
The mechanical model was based on numerical simulations using the finite difference code FLAC3D. The soil behavior was modeled using a conventional elastic-perfectly plastic model based on Mohr-Coulomb failure criterion. The soil cohesion c and angle of internal friction j were modeled as two anisotropic non-Gaussian random fields. An anisotropic square exponential autocorrelation function was used for both random fields EOLE methodology was used to discretize these fields. Finally, notice that all the other soil parameters are assumed to be deterministic.
The probabilistic numerical results obtained from the combination of GSAS with either MCS or IS are
compared to those obtained from the AK-MCS and AK-IS approaches. A significant reduction in the number of calls of the mechanical model was observed in both cases where GSAS was introduced in the probabilistic model. It should be noted that the probabilistic models allow one to obtain not only the failure probability but also the reliability index and the corresponding design point. The critical
realization obtained at the design point was shown to be symmetrical with respect to the central vertical axis of the foundation with the weaker soil near the footing, the stronger soil being far from the footing.