Geostatistical-based enhancement of RFEM regarding reproduction of spatial correlation structures and conditional simulations

Abstract

Engineering always deals with uncertainties, and efforts are needed to quantify them. A probabilistic analysis considers the statistical information of the problem to this quantification. In the geotechnical area, uncertainties play a particular role in structure design because it deals with naturally formed materials. Evaluating spatial variability has become progressively important. However, studies on the correct reproduction of this variability and conditional simulations are limited. In this paper, a geostatistical-based enhancement of the Random Finite Element Method (RFEM) is presented. The main aim of this study is to incorporate an advanced multivariate geostatistical technique (i.e., Turning Bands Co-simulation, TBCOSIM) to reproduce the coregionalization model of soil properties correctly in order to investigate the effects regarding this reproduction. It is illustrated in a real case of soil slope. The results showed that, for the unconditional simulation, the presented approach reached a perfect agreement with the coregionalization model, while the conditional simulation inserted some disturbances to this agreement, but it still satisfactorily reproduced the model. The original RFEM failed to reproduce this structure, leading to lower variances than the presented approach, which would cause a non-conservative design. Furthermore, disregarding the local uncertainty (i.e., the nugget effect) may introduce bias to analysis and, depending on its magnitude, may also lead the conditional analysis to not show a worthwhile reduction in variances of results. Finally, this paper shows that correctly determining the coregionalization model and reproducing it on probabilistic analysis may meaningfully influence the results.