Numerical studies of earth structure assessment via the theory of porous media using fuzzy probability based random field material descriptions

Abstract

To account for the natural variability of material parameters in multiphasic and hydro‐mechanical coupled finite element analyses of soil and earth structure applications, the use of probabilistic methods may be effective. Here, selecting the appropriate soil auto‐correlation functions for random field realizations plays an essential role. In a joint study, the general influence of auto‐correlation lengths on the results of strongly coupled models is determined. Subsequently, a polymorphic approach using fuzzy probability based random fields is used to capture the solution space for fuzzy auto‐correlation lengths. To adequately describe the behavior of the soil the theory of porous media is implemented, which uses a homogenization approach for the multiple phases on the soil microstructure. Its foundations and the differentiated methods used for the polymorphic uncertainty quantification are explained in this contribution. Based on two representative examples, the requirements and advantages of a polymorphic uncertainty model are worked out30.

Efficient domain decomposition based reliability analysis for polymorphic uncertain material parameters

“…Epistemic uncertainties are due to limited data and/or the lack of knowledge and can be modeled using intervals or fuzzy variables [4,5]. Realistic uncertainty models can be achieved by combining basic uncertainty approaches to polymorphic uncertainty models, like interval probability-based random variables or fields [6,7]. Various approaches have been developed to remedy high computational costs of reliability analysis: Ranging from efficient failure probability estimation [2,8] to domain decomposition (DD) approaches involving random field material description [9,10].…”

Polymorphic Uncertainty Quantification of Computational Soil and Earth Structure Simulations via the Variational Sensitivity Analysis

“…Monte-Carlo Analyses [1], partly in combination with Random Fields (RF), allow to assess uncertainties in earth structures for diverse applications [2][3][4]. However, the high computational effort due to the large number of simulation runs required, builds a main drawback of this approach.…”