Automatization of Geomechanical Modeling for Complex Geological Structures Using Isogeometric Analysis

Predictions of the three-dimensional in-situ stress state are crucial for the site selection process for deep geological repositories for nuclear waste and their long-term safety. However, the geological configurations relevant to a potential siting region, such as fault offsets, salt intrusions, and intersecting sedimentary units, create increasing structural complexities. These complexities, especially in the form of intersecting lithological boundaries and interfaces, present significant challenges for the discretization using the Finite Element Method (FEM). In the FEM, lithological boundaries and interfaces are commonly modeled using spline-based representations, which are then geometrically approximated by finite elements. This process introduces an additional layer of geometrical approximations that can lead to discretization errors, mesh distortions, and the need for repeated geometry regeneration when testing different model scenarios.

This study investigates whether the Isogeometric Analysis (IGA) as a discretization method can enhance and facilitate geometric fidelity and contribute to an automated modeling workflow. Unlike FEM, IGA employs the same spline basis functions (e.g., NURBS) for both the geometrical representation and numerical approximation. This direct application of splines eliminates the need for a geometry-to-mesh approximation step, allowing for an exact representation of both lithological boundaries and structural features, such as faults. The workflow for IGA differs from traditional FEM primarily in the preprocessing, solver implementation, and postprocessing stages: geometry is handled directly through control points, spline basis functions replace conventional shape functions, and the numerical solution is stored at these control points before being mapped back to the physical domain. While IGA does not necessitate a separate meshing step, refining the spline representation may still be required.

To evaluate this approach, we begin with a three-layer benchmark model previously used in sensitivity analyses and introduce a fault that offsets the lithological layers. IGA is utilized to compute stress, strain, and displacement fields, with its performance compared to that of the FEM, focusing on the impact of the geometrical approximation. The results aim to illustrate how exact geometrical representation and spline refinement influence stress predictions, particularly in areas where faults or salt contacts create sharp geometrical variations.

This work represents a significant advancement toward a more automated and reliable geomechanical modeling workflow. By reducing the need for manual geometrical regeneration and directly integrating spline-based representations into the analysis, IGA can streamline model scenario exploration and support more consistent gemechanical modeling for repository-scale studies.