Computational Integrity Analysis: Approaches for Uncertainty Quantification and Visualization

Given the legal requirement in Germany for documenting uncertainty impacts on safety analyses (§11 EndlSiUntV), a systematic investigation of uncertainties in simulation results is imperative. In several projects, including ANSICHT-II [1], MeQUR [2], and ThermoBase we have investigated the forward propagation of input parameter uncertainties through numerical models. Since modeling studies on long-term safety itself, such as on the host rock integrity of repository systems, represent computationally challenging problems, methods for quantifying the uncertainties have been enhanced and adapted to the particular requirements.

This study delineates a two-step process for uncertainty quantification, commencing with variance-based sensitivity analyses to ascertain the significance of individual input parameters on the integrity of the containment-providing rock zone (CRZ). For this purpose, all numerical input parameters are first considered uncertain. Bandwidths for each parameter are estimated using literature values and expert knowledge. Sobol indices are then determined, and key parameters whose uncertainty significantly influences results are identified. Subsequently, these parameters are employed to define a reduced stochastic state space, which is explored through techniques such as Monte Carlo sampling and stochastic collocation. The reduced state space enables comprehensive stochastic evaluations on full-scale models with only a minimal reduction of the total variance.
Within the ANSICHT-II project, criteria in alignment with legal safety requirements were developed to evaluate CRZ integrity in clay rock. These criteria establish a functional relationship between uncertain input parameters and simulation output. The two-staged process is conducted with the ANSICHT NORD model as an example and the integrity of the CRZ described by criteria functions as quantities of interest. 

Specialized software crafted to meet the computational challenges associated with uncertainty quantification in numerical integrity analyses of repository systems were developed. Notably, this is the OpenGeoSys Uncertainty Quantification framework (OpenGeoSysUncertaintyQuantification.jl [3]) in the Julia language. This enables the stochastic postprocessing of such analyses without prior data reduction. Finally, an interactive dashboard designed to provide users with intuitive access to the uncertainty quantification results, thereby enhancing the transfer of knowledge regarding safety-relevant processes in repositories and their inherent uncertainties, is presented.

[1] J. Maßmann, J. et al. (2022). Methode und Berechnungen zur Integritätsanalyse der geologischen Barriere für ein generisches Endlagersystem im Tongestein. Projekt ANSICHT-II. Ergebnisbericht. Bundesanstalt für Geowissenschaften und Rohstoffe (BGR).

[2] Kurgyis, Kata, et al. "Uncertainties and robustness with regard to the safety of a repository for high-level radioactive waste: introduction of a research initiative." Environmental Earth Sciences 83.2 (2024): 82.

[3] Bittens, M. (2024). OpenGeoSysUncertaintyQuantification.jl: a Julia library implementing an uncertainty quantification toolbox for OpenGeoSys. Journal of Open Source Software, 9(98), 6725.