Imprecise random field analysis for non-linear concrete damage analysis

Imprecise random fields consider both, aleatory and epistemic uncertainties. In this paper, spatially varying material parameters representing the constitutive parameters of a dam-age model for concrete are defined as imprecise random fields by assuming an interval valued correlation length. For each correlation length value, the corresponding random field is discretized by Karhunen-Loeve expansion. In a first study, the effect of the series truncation is discussed as well as the resulting variance error on the probability box (p-box) that represents uncertainty on the damage in a concrete beam as a result of the imprecise random field. It is shown that a certain awareness for the influence of the truncation order on the local field variance is needed when the series is truncated according to a fixed mean variance error. In the following case study, the main investigation is on the propagation of imprecise random fields in the context of non-linear finite element problems, i.e. quasi brittle damage of a four-point bended concrete beam. The global and local damage as the quantities of interest are described by a p-box. The influence of several imprecise random field input parameters to the resulting p-boxes is studied. Furthermore, it is examined whether correlation length values located within the interval, so-called intermediate values, affect the p-box bounds. It is shown that, from the engineering point of view, a pure vertex analysis of the correlation length intervals is sufficient to determine the p-box in this context. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper defines imprecise random fields by considering spatially varying material parameters with an interval-valued correlation length and discusses the effect of series truncation and resulting variance error. The study focuses on the propagation of imprecise random fields in the context of quasi brittle damage of a four-point bended concrete beam. It explores how correlation length values affect the p-box bounds and concludes that a pure vertex analysis of the correlation length intervals is sufficient for determining the p-box in this context.