Login
Spatial influence of fault-related stress perturbations in northern Switzerland
Solid Earth
2026
17
1
179-201
Minimum Amount of Stress Magnitude Data Records For Reliable Geomechanical Modeling
Rock Mechanics and Rock Engineering
2026
How the mesh controls accuracy in geomechanical-numerical models
Given that in-situ data of the stress field are limited, geomechanical models are used to receive a continuous prediction of the 3-D stress in the subsurface. For the numerical solution of these models the Finite Element (FE) method is often used as it allows to discretize complex structures using unstructured meshes. Therefore, the results strongly depend on the FE-mesh resolution, the element types, and the element order used. In a comprehensive approach to optimizing a mesh, it is necessary to find a balance between a detailed high-resolution mesh and the resulting computing time or available computing capacity.To investigate such a question an extensive model series that change the model geometry and its resolution is required. However, such test series can only be conducted using simplified models, as the effort involved in producing the FE-mesh would otherwise be too substantial. For this reason, the complexity of a real 3-D structure was reduced to a 2-D profile section. As a template for this approach, we use a geomechanical-numerical model of the siting region of Nördlich Lägern for a deep geological repository for radioactive waste in northern Switzerland. Geologically, it consists of the crystalline basement, south-dipping Mesozoic units, and a cover of Cenozoic deposits. The key purpose of our study is to investigate the impact of the FE-mesh on the predicted 3‑D stress field within the thin stratigraphic units of the Mesozoic. The mesh resolution, element type, element order, and solver-specific elements with reduced integration points are tested. All models are calibrated separately with the same set of in-situ stress magnitude data from a borehole to find the best-fit displacement boundary conditions. All results are also displayed along the same borehole trajectory, which is located exactly on the profile section, in comparison to the available in-situ stress magnitude data. The result shows that horizontally elongated hexahedrons are more suitable for thin layers in comparison to tetrahedron elements; higher order elements also offer little added value in such static case.For our study of Nördlich Lägern we use three different model geometry realizations that resulted from the different stages of the exploration process during the past 15 years. To achieve better comparability, the mechanical properties were also harmonized as far as possible. If almost identical rock properties are used, only small differences in the predicted stress field are visible, mainly in the areas where the stratigraphic boundaries differ between the models. Differences become more significant when the original and deviating rock properties are used. This indicates that the rock properties have a large influence on the model estimates. However, in comparison to predicted bandwidth of the predicted stress field that is controlled by the probability distribution of the rock stiffness in each lithology, the changes to the different model realization are small.
2025
From pointwise in-situ data to stress prediction in 3-D
For a deep geological repository (DGR) for radioactive waste the characterization of the in-situ stress field is critical for the repository design and evaluation of long-term safety. It is crucial to obtain a spatial 3-D description of the stress state (both orientation and magnitudes) in the host rock formation covering the potential repository area, and ideally also in the under- and overlying formations. For the prediction in 3‑D geomechanical-numerical models are used. The geological structure of these models is derived from the interpretation of 3‑D seismic surveys and borehole logs. After assigning the rock properties to the different lithologies, the model is calibrated using in-situ data of the horizontal stress magnitudes. One of the issues encountered during the calibration process is, that stress measurements might sample the mechanical variability of the subsurface units that is not explicitly represented by the geomechanical model. Another one is that stress measurements are typically reported as a best estimate without any uncertainty attached to it.As part of the site evaluation for the final disposal of radioactive waste in Switzerland, three siting regions were explored. Between 2019 and 2022 an extensive and integrated campaign of measurements of the horizontal stress magnitudes was carried out in eight deep boreholes using Micro-Hydraulic Fracturing (MHF) and (dry) Sleeve Re-opening (SR) tests. Out of 139 successful MHF tests, 121 estimates of the magnitude of the minimum horizontal stress Shmin and 65 estimates of the magnitude of the maximum horizontal stress SHmax were obtained. These data are used for the calibration of 3-D geomechanical-numerical models of the three siting regions. To achieve a best-fit with respect to the in-situ stress data, lateral displacements can be determined automatically provided that the problem is an elastically linear system. The models have a lateral side length between 10 and 15 km, represent 17 or 18 lithologies, and contain 6 to 13 faults that are implemented as contact surfaces allowing relative displacement to each other. The resolution in the vertical is at best 5 m and laterally between 50-150 m using up to 8 × 106 finite elements.We show that a best-fit can be achieved with our model workflow and that the prediction of the 3-D stress state in the larger volume is primarily controlled by the variability of the rock stiffness. As the rock stiffness is a probability distribution in each lithological layer, the prediction of the horizontal stress magnitudes in the larger volume is as well. The result of our workflow are bandwidths of the predicted 3-D stress field that can be represented for example with the P05-P95 probability range.
2025
Minimum number of stress magnitude data records for model calibration
Geomechanical-numerical modeling aims to provide a comprehensive characterization of the stress tensor within rock volumes by leveraging localized stress magnitude data for model calibration. This calibration involves optimizing boundary conditions to achieve the closest alignment with in-situ stress measurements from boreholes, which provides magnitudes of the minimum and maximum horizontal stress. However, the high cost of acquiring stress magnitude data often results in sparse and incomplete datasets, potentially hindering meaningful calibration.In this study, we use a comprehensive dataset of 45 stress magnitude data records acquired for the geomechanical characterization of the candidate siting region Zürich Nordost, a potential site for a deep geological repository in northern Switzerland. We demonstrate how the number of available stress magnitude data records influences the accuracy of 3D total stress tensor predictions. To achieve this, we introduce a novel statistical approach that enables the analytical estimation of a large number of model simulations, each calibrated using different numbers of stress magnitude data records. This approach evaluates how the availability of data influences stress predictions across formations with varying rock stiffness by rapidly assessing the stress states associated with numerous combinations of stress magnitude data records.By comparing the resulting stress fields with an increasing number of data records, it is possible to estimate the minimum number of calibration points required to achieve a prediction range comparable to the range expected due to inherent data uncertainties. The results indicate that for the region Zürich Nordost, fewer than 15 data records are sufficient to achieve the same model precision and accuracy, suggesting that additional data would not significantly improve model accuracy.In addition, detailed analysis of the dataset revealed an outlier with respect to our model, linked to a local stiffness anomaly. While this outlier represents a physically valid measurement, it significantly impacts stress predictions when calibration data are limited. However, as the calibration dataset size increases, the influence of the outlier diminishes. Our statistical approach also allows the objective identification of clear outliers within the calibration dataset, which in turn affects the minimum number of data points required for model calibration.These results highlight the importance of dataset size and composition in reducing uncertainties, and providing a framework for optimizing calibration strategies. This study provides valuable insights for subsurface projects, such as energy storage, CO₂ sequestration, deep geological repositories, and geothermal energy, where precise stress predictions are critical.
2025
The Spatial Reach of Faults: How They Shape Regional Stress Fields.
Characterizing the crustal stress field is crucial for understanding global processes like earthquakes and plate tectonics, as well as for local applications such as subsurface storage, geothermal exploration, and nuclear waste repositories. A key challenge lies in understanding how pre-existing geological structures, particularly faults, influence crustal stress distribution. While some studies infer fault impact from variations in stress magnitudes or maximum horizontal stress (SHmax) orientation over large regions, this approach cannot isolate fault-induced perturbations. Generic geomechanical models, though informative, often lack site-specific calibration. The SHmax orientation, systematically documented in databases like the World Stress Map, reflects consistency on large scales due to large-scale tectonic and buoyancy forces but can exhibit significant local rotations due to faults. Accurately modeling these third-order perturbations remains difficult due to computational challenges and the risk of numerical artifacts.The hypothesis in this study is that the impact of local faults with a few tens of meters displacement on the far field in-situ stress state beyond a certain spatial scale might be overstated and overinterpreted by many studies. Here, we use 3-D geomechanical-numerical models that are calibrated against a unique and robust dataset of 45 stress magnitude data records. This dataset was acquired for evaluating the suitability of potential siting regions to build a deep geological repository for high-level nuclear waste in Switzerland. We vary the numerical resolutions and investigate the spatial scale at which faults influence the individual components of the far-field stress tensor and in particular the SHmax orientation. Finally, we compare models with and without faults.Our results reveal that faults of this scale do not have a significant influence on the stress tensor orientation or principal stress magnitudes beyond a few 100s meters distance from the fault. Comparisons between the models reveal that the stress differences are not necessarily controlled by the mechanics of faults. The impact is rather due to lateral stiffness variations and density contrasts due to the offset along faults and lateral juxtaposition of units with contrasting mechanical properties. Small lateral variations could be attributed to the mechanical behavior of faults but these variations are generally less than the stress variations due to uncertainties in the rock property variability.Our findings suggest that faults could have been excluded from the modeling workflow for models that focus on large-scale stress predictions and not on stress changes close to the faults Removing faults from the modeling workflow reduces computational complexity and accelerates the modeling process, without causing any significant differences in the model results at a distance of few 100s meters from the faults.
2025
SpannEnD 2.0 – New insights into the present-day stress of Germany by a new 3D geomechanical-numerical model
For prediction of the short and long-term geomechanical behaviour of a deep geological repository for nuclear waste, the present-day 3D in-situ stress is a key parameter. However, in Germany the knowledge concerning the crustal stress state is still quite low. It is mainly based on data from the World Stress Map (WSM) project providing data of the orientation of the maximum horizontal stress (SHmax) and a new compilation of stress magnitude data providing magnitudes of SHmax and the minimum horizontal stress (Shmin). However, these two databases still provide only unequally distributed data records and in particular horizontal stress magnitude data records are only reliable at a dozen locations all over Germany. Thus, for an in-situ stress field prediction geomechanical-numerical models - calibrated on available horizontal stress magnitudes – are used. They enable a continuum-mechanics based description of the 3D present-day stress state and can resolve lateral and especially vertical variations. Two 3D geomechanical-numerical models of Germany have been published during the initial phase of the SpannEnD project (2018-2022). In the follow-up project SpannEnD 2.0 a new model has been set-up based on a new geological model enabling new insights into present-day crustal stress field of Germany, in particular due to higher vertical resolution. We also use a significantly enlarged stress magnitude database for model calibration.The new 3D geomechanical-numerical model combines information of 27 regional geological models and comprehensive additional data. It comprises 49 geological units parametrized with elastic rock properties (Young’s modulus and Poisson’s ratio) and rock densities. Linear elasticity is assumed and the finite element method (FEM) is used to solve the partial differential equations that describe the equilibrium of gravitational and surface forces. Overall, the model contains ~10 million hexahedral elements providing a lateral resolution of 4 km and a vertical resolution of up to 45 m in the uppermost 5 km. The model results show an overall good fit with stress magnitudes used for calibration indicated by a mean of the absolute stress differences of ~3 MPa for Shmin and of ~5 MPa for SHmax. Furthermore, the results agree well with additional data sets - not used for calibration - e.g., an absolute mean deviation of the orientation of SHmax with regard to WSM data of ~10°.
2025
Embrace the uncertainty – Geomechanical example for the value of uncertainties
The initial in-situ stress state is a key parameter for the evaluation of siting regions for deep geological repositories. To achieve a 3D description of the stress field geomechanical-numerical models are used to extrapolate between a usually small number of in-situ stress measurements and finding a best fit in a model calibration process. However, if all in-situ data points cannot be fitted equally well by the model, the predictive value decreases. Furthermore, this approach neglects that the data records of in-situ stress magnitudes are not data points, but ranges. Each data record is a range of possible values or even a probability distribution of the physical value. As a consequence, the modelled stress field has to be a range as well. Considering the inherent uncertainty of in-situ stress magnitude data a single fit of a model to the observed stress state is usually not meaningful as it can only explain a subset of the data records used for the model calibration. To quantify these uncertainties a range of model results can be used that contain extreme and average cases resulting in a range of possible stress states. However, this range of results also includes extreme and therefore unlikely scenarios and probably overestimates the range of modelled stress states resulting in an unspecific prediction of the stress field. If the in-situ stress magnitude data is provided as a range, this modelled stress range can be refined. Data records that come as a range can be fitted in a model scenario that also agrees with other ranges of in-situ stress magnitude data. At the same time, extreme model scenarios can be identified since they only agree with very few data ranges. This allows to narrow down the range of modelled stress states.The concept is exemplified and its applicability demonstrated using a case study of the siting region Zürich Nordost located in northern Switzerland. Here in the context of the site-selection process for a deep geological repository a 3D geomechanical models has been built and a unique data set of 45 in-situ stress magnitude data records is used for the model calibration. Our results show that using the measurement uncertainties of the in-situ stress magnitude data narrows the modelled stress state range compared to an approach where data records are used as data points only. Thus, we propose that using the ranges of the in-situ stress magnitude data instead of treating them as data points using e.g. their mean value, will increase the significance of 3D geomechanical models.
2025
Faults in geomechanical models – Necessary, nice, or nonsense?
Faults are an important factor for geoenergy applications due to either their sealing or conducting properties or their mechanical behaviour. Consequently, (thermo-hydro-) mechanical numerical investigation of geoenergy applications often include faults in their modelled rock volume. It is often assumed, that faults can significantly alter the far-field stresses, impacting both magnitudes and the orientation. In contrast to the far-field, stress rotations in the vicinity of faults are clearly observed in numerous borehole stress analyses across the world. While an impact of faults on the stress field is expected, the representation of faults in (thermo-hydro-) mechanical numerical models is technically highly diverse. We investigate different methods to incorporate faults in geomechanical-numerical models and the relationship between faults and the stress state on two different spatial scales. (1) The impact of faults on the stress state at distances of several hundred meters to a few kilometres (far-field) is tested. Therefore, faults are modelled with different numerical representations, material properties, fault orientations w.r.t. the stress field, fault width, extent, and boundary conditions. The results show that the impact of faults on the far-field is negligible in terms of the principal stress magnitudes and orientations. Only in extreme cases, stress changes in the far-field (>1km) can be observed, but these are not significant considering the general uncertainties in stress field observations.(2) Stress changes within the fault zone are investigated, too. Particularly, the material contrast between the intact rock and the damage zone and fault core is regarded. This contrast can be responsible for a dramatic change in the stress tensor, observed as a rotation of the principal stress axes. In general, the change in the stress field increases with increasing stiffness contrast. The orientation of the fault w.r.t. the background stress field and the relative stress magnitudes, particularly the differential stress, lead to further stress changes. A small angle between the fault and the maximum principal stress axis and a small differential stress promote stress changes.The study indicates that the impact of faults on the stress field is mostly limited to the fault’s near-field. These models provide an upper limit of stress changes, as several factor which alter stress changes (joints, viscosity etc.) are not included. However, the stress changes depend on the acting processes and material properties. Furthermore, for models used for site investigation, the implementation method and the mesh resolution can play an important role. All these factors need to be considered when planning the setup of a model with faults and their implementation.The work was partly funded by BGE SpannEnD 2.0 project, the Bavarian State Ministry of Education and Culture (Science and Arts) within the framework of the “Geothermal-Alliance Bavaria” (GAB), and the DFG (grant PHYSALIS 523456847).
2025
Global Sensitivity Analysis to Improve Geomechanical Stress Characterizations Using Physics-Based Machine Learning Models
Robust predictions of in-situ stress states are essential for the safety assessment and long-term stability of nuclear waste disposal sites. However, these predictions are inherently uncertain due to the variability in geological parameters and material properties as well as uncertainties of model calibration data. Thus, a large number of model simulations would be required for a complete investigation of the model uncertainties which is not feasible due to required high numerical resolution with several million discretization points. An alternative to classical full order solutions is to develop surrogate models that run much faster but perform with similar precision.We propose to use a machine learning-aided methodology to set up and solve these surrogate models. Specifically, we use the non-intrusive reduced basis (NI-RB) method. The resulting surrogate models are 5-6 orders of magnitude faster compared to the initial full-order model which allows an extremely fast computation of many models with different parameters. The initially required full order geomechanical simulations are conducted using GOLEM, based on the MOOSE framework (a multiphysics simulation platform).For our case study, we use benchmark models and a simplified model inspired by the potential siting area Nördlich Lägern for high-level nuclear waste in northern Switzerland. Preliminary results indicate that our surrogate model accurately replicates the findings of the full order solutions while significantly reducing computational costs. We primarily focus on global sensitivity analyses to identify the most critical parameters impacting the stress field. Our study explores seven scenarios for surrogate modeling, each focused on different model parameters. The first five scenario examine boundary conditions, rock properties (density, Poisson ratio, Young’s modulus), geometrical features and combinations of the three, using a benchmark model to demonstrate general implication for geomechanical studies. For these scenarios, we change between two to thirteen parameters. The sixth scenario uses the simplified study based on the Nördlich Lägern, adjusting 15 parameters (Young’s modulus of each lithological layer) illustrating the potential for future real-case applications.We show an additional seventh scenario that integrates comprehensive fault considerations, including parameters such as geometry, geographical location, dip angle, and strike direction. These factors are vital in the context of subsurface engineering studies, as they significantly influence the stress fields and the overall stability of the geological formation. A thorough understanding of fault characteristics is paramount for assessing potential risks and ensuring long-term safety and structural integrity.The results demonstrate that the surrogate models are much faster but keep a similar precision as the full order solution. This shows the potential of surrogate modeling for rapid uncertainty quantification in geomechanics, offering a useful tool for assessing nuclear waste disposal sites, but also different applications like, for example, geothermal exploration.
2025