Impact of resolution and finite element type in geomechanical-numerical modelling

Due to the limited access to the underground, numerical models are essential in nearly all branches of geosciences to improve the general understanding or to estimate behaviour or properties in applied cases. Complex subsurface structures can be best represented by applying the finite element method (FEM) as it allows unstructured meshes during the discretization of the model geometry. The resulting model quality depends on the resolution of the mesh, the element type (shape), the element order (1^st or 2^nd), or special elements e.g. with reduced integrations points. However, always a balance between the effort of mesh generation, computing time, amount of model runs needed, and the justifiable expense needs to be found. As such factors can’t be tested for each project individually, we will test this with simplified and already existing, purely elastic geomechanical models. The derived conclusion can in turn be utilized to improve the numerical implementation of future studies.

To investigate the impact of a chosen mesh, 2-D models (mechanical in 3-D) are generated based on a cross section. Geologically, the models represent the crystalline basement, several slightly dipping thin Mesozoic sedimentary units, covered by Cenozoic deposits. The goal is, to represent the thin about 10 to 100 m thick Mesozoic units sufficiently well to reliably predict the present-day stress state. Varied within the target units are the mesh resolution, the element type (tetrahedra vs. hexahedra), the element order (1^st and 2^nd) and elements with reduced integration points provided by the used solver. All models are calibrated using in situ stress data from a borehole that is located at the model cross section which results in a best-fit model that minimizes the deviation between modelled and the in-situ stress calibration data by varying the displacement boundary condition of the model. Model results are always compared along the well trajectory using a reference model with a fine mesh resolution. The computational effort will be considered, too. Study results indicate that, flat (brick-like) hexahedrons provide better results than tetrahedrons, taking mesh resolution and computing effort into account. Above a certain level, the number of hexahedrons (fine vs. coarse resolution) in the vertical direction per layer exerts a discernible influence on the results in the proximity to material transitions only. Second order elements provide nearly the same results as first order elements, which means that the extra computational effort is not worth it. Differences due to the usage of special solver-provided elements are neglectable.

Additionally, we tested three site models based on a different model geometry, mechanical stratigraphy, and mesh resolution, by applying the same material properties whenever possible. Most of the observed differences are acceptable and mainly driven by the differences in geometry and the resolution of the mechanical stratigraphy. Deviation of model results is much bigger, when the original material properties (state of knowledge at the time) are applied.