Machine-learning enabled model optimization of an emplacement drift in the context of deep geological disposal

Currently, in the planning phase of a deep geological repository, different closure concepts are modeled using numerical (multiphysical) simulations and manually evaluated based on the objective function. Expert knowledge is required for preselection, which limits objectivity and contrasts with the automated creation and evaluation of various concepts. In the SEMOTI project, we aim to automate an optimization process in the planning phase of a emplacement drift in rock salt using machine learning methods.

Initially, the rock salt parameters are calibrated using experimental data to have a basis for the numerical model in the planning phase. An automated optimization process requires a parameterised model. For the selection of suitable sealing materials, parameterisation is provided by the material parameters. The geometry of the repository and the rock formation can be modeled using parametric splines. The axial permeability of the excavation damage zone (EDZ) serves as the objective function. For this purpose, the constitutive model for rock salt TUBSsalt can be used to obtain an anisotropic permeability depending on damage, fluid pressure and stress state [1, 2].

Training and testing data is generated using numerical simulation software FLAC3D based on the model parameterization [3]. This data is then used to train and test a Gaussian process (GP) based surrogate model. GP is a statistical machine learning technique for the regression of unstructured data with uncertainty quantification [4]. To ensure the surrogate model’s accuracy, the coefficient of determination (R^2) are evaluated. Afterwards global sensitivity analysis is performed using Sobol indices to assess the influence of each input parameter. Finally, the trained surrogate model is optimized using a differential evolution algorithm to determine the optimal parameter values that minimize the axial permeability. Furthermore, an adaptive sampling approach will used to refine the surrogate model by focusing on regions of interest, enhancing model accuracy, efficiency and  optimization speed [5]. 

Monitoring of the emplacement drift during the excavation phase enables automated calibration using a GP-based surrogate model leading to a digital twin, which can be updated efficiently as soon as new monitoring data is available, see [6]

References:

[1] C. Missal and J. Stahlmann. A relation of anisotropic damage and permeability in the edz of drifts in rock salt. Proceedings of the 9th Conference on the Mechanical Behavior of Salt, Hannover, Germany, pages 573–584, 2018.
[2] I. Epkenhans, S. Wacker, and J. Stahlmann. Weiterentwicklung und Qualifizierung der gebirgsmechanischen Modellierung f¨ur HAW-Endlagerung im Steinsalz (WEIMOS)(Verbundprojekt: Teilprojekt D): Endbericht des Teilprojekts. Technische Universität Braunschweig, Institut f¨ur Geomechanik und Geotechnik, 2022.
[3] Itasca Consultants GmbH. Itasca Software 9.0 documentation - FLAC Theory and Backround, 2023.
[4] C. Williams and C.E. Rasmussen. Gaussian processes for machine learning, volume 2. MIT press Cambridge, MA, 2006.
[5] J.N. Fuhg, A. Fau, and U. Nackenhorst. State-of-the-art and comparative review of adaptive sampling methods for kriging. Archives of Computational Methods in Engineering, 28:2689–2747, 2021.
[6] L. Paul, J.-H. Urrea-Quintero, U. Fiaz, A. Hussein, H. Yaghi, H. Wessels, U. Römer, and J. Stahlmann. Gaussian processes enabled model calibration in the context of deep geological disposal. arXiv preprint arXiv:2409.02576,2025.