The ZNO study region is located in the northern Alpine Foreland of northern Switzerland, approximately 30 km NNE of Zurich (Fig. 2). It is close to the SW of Germany, where pre-Mesozoic basement rocks locally outcrop (Nagra, 1984, 2002a). The geological evolution of this region was influenced by the development of a WSW–ENE striking Permo-Carboniferous basin (Gorin et al., 1993; Mccann et al., 2006; Nagra, 2014), formed in response to the Variscan orogeny and subsequent post-orogenic transtensional processes (Nagra, 1991; Marchant et al., 2005).

During the Mesozoic, a sequence of sedimentary successions was deposited on top of the Variscan basement. This depositional process was prominent, especially from the Early to Middle Jurassic due to a combination of regional tectonic subsidence and sea level change (Coward and Dietrich, 1989; Nagra, 2024c). The sedimentary rocks were originally deposited directly on the ocean floor as a result of the landmass corresponding to the present day northern Switzerland being submerged in a broad and shallow epicontinental marine setting (Jordan, 2008; Reisdorf et al., 2011). The Opalinus Clay formation, deposited during the Jurassic Period of the Mesozoic Era, is of particular importance as it has been selected as the host rock for Switzerland's DGR. Factors contributing to the effectiveness of Opalinus Clay as a long-term geological barrier are its favorable mineralogy and associated low permeability, and good sorption and self-sealing properties (Nagra, 2001, 2002b, 2008).

At the late Cretaceous and onset of the Cenozoic, the Alpine orogeny, formed by the collision of Adriatic and Eurasian tectonic plates, led to a significant tectonic activity in the European northern Alpine Foreland (Illies, 1972; Schmid et al., 1996, 1997; Cloetingh et al., 2006). This resulted in the formation of basement-rooted, NNE-striking normal faults, forming the Upper Rhine Valley in combination with the uplift of the Black Forest and Vosges Mountain Massifs. The formation of the flexural Molasse Basin during the Late Oligocene to Early Miocene is a result of downbending of the European plate, in response to the orogenic loading of the Alps, and caused a gentle dip from north to south in the Mesozoic strata (Sinclair and Allen, 1992; Kempf and Adrian, 2004; Sommaruga et al., 2012). In our study region, the Mesozoic strata gently dips SSE (Fig. 3). In the Late Miocene, continued Alpine deformation propagated into the northern Foreland, resulting in the formation of the Jura Mountains and their associated fold-and-thrust belt, primarily further to the west, and reactivating the pre-existing basement structures (Diebold and Noack, 1997; Burkhard and Sommaruga, 1998; Laubscher, 2010). These tectonic processes, along with the glacial–interglacial cycles during the Pleistocene (Fiebig and Preusser, 2008; Preusser et al., 2011), have established the present day geological and stratigraphic setting in the region.

The reference model (REF model) is rectangular, spanning 14.7km E–W×14.8 km N–S laterally, and extending to a depth of 2.5 km below sea level (b.s.l.). The upper boundary is defined by the local topography. In the siting region, SHmax orientation is 170±11° according to the BO and DITF observations from the boreholes, in agreement with the regional trend (Nagra, 2013; Heidbach et al., 2025b). To align the model geometry with the SHmax orientation, the entire model domain is rotated by 10° counterclockwise from geographic north, such that its sides are parallel and perpendicular to the mean SHmax orientation (Fig. 2).

The present day geomechanically relevant layers were constructed using SKUA-GOCAD v19 software. Successive lithologies with comparable mechanical properties were combined (Table 1), eventually leading to 14 geomechanically different units in the REF model (Fig. 3). A total of seven faults and flexures, named Neuhausen, Uhwiesen, Wildensbuch, Marthalen-Rafz Flexure, Rheinau, D2, and Trüllikon, were implemented in the model (Fig. 2). These structures are modeled as contact surfaces, weakly interpreted from the regional 3D seismic sections, and are highly simplified for ease of implementation in the model. Here, simplification means merging much smaller segments interpreted on 3D seismics into larger, continuous fault planes to represent what is, in reality, a volumetric fault zone structure (Nagra, 2024a) (Figs. 2 and 3).

Both Neuhausen and Uhwiesen faults dip at 60° toward the northeast, while the others are vertical. Neuhausen is the only fault that has a stratigraphic offset, with a vertical displacement of approximately 50 m at the base of the Mesozoic units that decreases towards the surface (Nagra, 2002a, 2008, 2024d). The Marthalen-Rafz Flexur and Wildensbuch Flexur are monoclines that dominate the overlying Mesozoic strata in the siting region through a step-like bending rather than a discrete break in an otherwise dipping strata (Madritsch et al., 2024; Nagra, 2024c). Other than the Neuhausen fault, the remaining faults and flexures show no clear displacement but are included in the model as they represent the first-order geological structures of the ZNO siting region.

Removing the fault implementation from the 3D models allows us to use different model discretization strategies, which in turn significantly accelerates the model setup and stress prediction workflow. Using two different discretization strategies, we developed three additional fault-agnostic 3D geomechanical numerical models. The reference model and the three fault-agnostic models are then compared to quantify the spatial influence of faults on the far-field stress state. In our study, the time required to build a model was reduced from approximately two months for the reference model, the model that includes contact surfaces, to just two days for the fault-agnostic models.

The standard procedure discretizes each geomechanical unit individually using the definition of its top and bottom interface surfaces, and later connected by matching the nodes along the common interfaces. Each element of the unit is assigned to the appropriate mechanical properties (Fig. 4a) directly from the stratigraphic definition. While this approach results in a smooth unit boundary, it requires substantial manual effort and is particularly time-consuming when working with models containing many geomechanical units.

In order to simplify the setup and discretization procedure of the fault-agnostic models, we use ApplePy (Automatic Partitioning Preventing Lengthy Manual Element Assignment), a Python-based tool that automates the discretization and element property assignment process (Ziegler et al., 2020). The entire model volume is discretized in a single step as a largely homogeneous mesh, ignoring both lithological interfaces and fault structures. ApplePy uses the depth values of the stratigraphic boundaries to decide which element belongs to which lithological unit/geomechanical unit (Fig. 4b). Although this approach introduces step-like transitions at unit boundaries which looks optically unrealistic, it significantly reduces the meshing time, especially for large or complex models, like the REF model without compromising the stress prediction capability of the final 3D geomechanical numerical models, as discussed in Sect. 4.

Building on the discretization strategies described in Sect. 3.1, three fault-agnostic 3D geomechanical numerical model realizations were developed. The three fault-agnostic 3D geomechanical numerical models follow the general model workflow of the REF model, i.e., the model parameterization and calibration are the same (Sect. 2.2), along with the same model extents (Sect. 2.1). They are calibrated to the same dataset of 45 horizontal stress magnitude measurements used for calibrating the REF model. The only differences lie in the model discretization strategies (Sect. 3.1) and finite element resolution. Out of these three models, one is set up using the standard procedure, and two are set up using the ApplePy procedure. Table 2 presents the technical details on the number of elements and spatial resolution of each model used, along with the corresponding best-fit displacement boundary conditions obtained after applying FAST Calibration tool. The brief description of the three fault-agnostic models is:

REF-NF model: Derived directly from the REF model with identical geometry, mesh and mechanical property assignments but with faults removed. Contact surfaces are eliminated, and opposing nodes are equivalenced, except for the Neuhausen Fault, where a 50 m lithological offset prevents node equivalencing. In this case, slip is prevented by assigning an artificially high friction coefficient of 50.

The resulting predicted stress magnitudes from all the model realizations are presented together with the measured Shmin (red bars) and estimated SHmax (blue bars) magnitude ranges along the TRU1-1 and MAR1-1 borehole trajectories in Fig. 5. In general, the predicted horizontal stress magnitudes from the REF model align reasonably well with the measured stress ranges across different geomechanical units. However, some discrepancies are present, particularly in the Klettgau and Bänkerjoch formations, where the REF model underestimates Shmin magnitudes, and in the Schinznach formation, where Shmin magnitude is overestimated. These deviations arise because, for the model calibration, the REF model uses P50 (median) horizontal stress magnitude values despite the MHF tests resulting in ranges (red and blue bars in Fig. 5). Therefore, the stress predictions may vary from the assumed P50 value at a particular point in the subsurface. The vertical stress magnitude (SV) is calculated from the weight of the overlying rock mass, considering the densities of the individual lithologies. From Fig. 5, it can be seen that SV increases linearly with depth.

The predicted results from all the model realizations, regardless of fault implementation or exclusion, also align well with the measured horizontal stress magnitude ranges along both borehole trajectories across different geomechanical units, and are consistent with the REF model. Minor but negligible differences of <1 MPa in the SHmax magnitudes can be found at ∼475 m (t.v.d) along the TRU1-1 borehole and at ∼250 m (t.v.d) along the MAR1-1 borehole in the AP and AP-H models (Fig. 5). This is likely due to a high stiffness contrast between the Cenozoic sediments (E= 15 GPa) and Felsenkalke + Massenkalke (E= 31 GPa) units, the transition boundary of which is differently discretized due to ApplePy usage. A similar difference can be found at the Zeglingen Fm. (E= 36 GPa), Kaiseraugst Fm. (E= 23 GPa) and the Dinkelberg, Weitenau Fm. and Crystalline basement (E= 34 GPa), which is also due to the widely varying stiffness contrasts.

Stiffer formations such as the Schwarzbach-Villigen Fm., Zeglingen Fm., and the basement have broader stress ranges in the measured data due to their statistically larger stiffness variability, while weaker formations like the Opalinus Clay exhibit narrower, more consistent stress distributions. Moreover, stiffer layers shield the weaker layers above and below, reducing stress variability in these formations. In short, Fig. 5 clearly indicates that the differences between the profiles from all the models are smaller than the measurement errors, represented by the length of the horizontal red and blue bars, and that the differences between the fault agnostic models and the REF model are insignificant. The variation of SV magnitude with depth is consistent across all the model realizations, with differences <0.05 MPa observed between the models using ApplePy and the standard procedure.

The AP and AP-H models yield identical results. This indicates that increasing model resolution would not significantly improve stress predictions in our study and that the resolution of the AP model is already sufficient. This rules out resolution effects within the ApplePy models on the predicted stress magnitudes with respect to the REF model.

To better quantify the impact of faults on stress, we interpolated the results of the four models on a SW-NE oriented horizontal line at 300 m (b.s.l.) crossing five of the seven faults (Fig. 10a–c). To improve readability, the results from the AP model were not plotted, as it is clear from Figs. 5, 7, and 9 that the AP and AP-H model results are almost identical.

The SHmax and Shmin magnitudes of different model realizations largely overlap each other along the horizontal line. A difference of ∼0.5 MPa is observed in SHmax magnitude (Fig. 10b), and ∼1 MPa is observed in the Shmin magnitudes (Fig. 10a) between the REF model and the fault-agnostic models, within ∼500 m of the faults. However, these differences are less than the widths of the stress magnitude data, which in turn, represent the uncertainty of the measurements (Fig. 5). In general, the horizontal stress magnitudes from the REF model have an abrupt change in the vicinity of the faults, deviating from the continuous trend followed by other model realizations. The differences in the SHmax magnitudes reduce to <0.2 MPa beyond a distance of about 500 m from the fault. The differences in the Shmin magnitudes follow the same pattern as the SHmax magnitude, and also reduce beyond a distance of about 500 m away from the fault.

Similarly, the SHmax orientation of the REF model shows negligible deviations of <2° in the undisturbed rock volume, away from the faults, and a deviation of 2–6° up to 1 km from the modeled faults (Fig. 10c). According to the quality ranking scheme of the SHmax orientation from the World Stress Map, the A-quality data, data of the highest quality, has a standard deviation of ±15° (Heidbach et al., 2025a). Even SHmax orientations derived from the DITF and BO in the MAR1-1 and TRU1-1 boreholes exhibit standard deviations of approximately ±11°. Considering this, the orientation deviations seen in Fig. 10c are not resolvable and well below the uncertainties of the in situ indicators.

Near the Neuhausen fault, there is a localized abrupt change in the horizontal stress magnitudes within ∼100 m on either side of the modelled fault for all the model realizations. An important observation is that this abrupt change occurs not only in the REF model but also in the models without any faults. These stress changes are primarily controlled by the lateral stiffness contrasts due to the offset and not by the mere presence of the faults.

Overall, the differences are <0.2 MPa in stress magnitudes and <2° in SHmax orientations beyond 1 km from the fault, which is far less than the uncertainties of the horizontal stress magnitude data from the MHF and the SR tests, as well as the stress indicators for the SHmax orientation from the boreholes. Even in a conservative approach, it is clear that the effect of faults on the stress field is within about 1 km from the fault core. This conclusion aligns with the findings by Reiter et al. (2024), who, through generic model studies, found that significant stress changes due to faults only occur within a distance of a few hundred meters, partly up to 1 km next to the fault.

The SHmax orientation is the most widely available characteristic of the reduced stress tensor. It is also the easiest to analyze because it can be averaged and visualized with respect to the fault on stress maps (Fig. 1) (Yale et al., 1993, 1994; Yale and Ryan, 1994; Yale, 2003; Rajabi et al., 2017c; Heidbach et al., 2018). The SHmax orientation can be determined from different stress indicators, such as from direct borehole-based indicators, earthquake focal mechanisms, geological indicators, or passive seismic methods (Amadei and Stephansson, 1997; Zang and Stephansson, 2010; Heidbach et al., 2025a). Among these, direct borehole-based indicators such as borehole breakouts (BOs), drilling-induced tensile fractures (DITFs), and hydraulic fracturing (HFs) are commonly considered to be the most reliable (Bell, 1996a; Zang and Stephansson, 2010).

In the ZNO study region, 11 SHmax orientation data records are available from HFs, DITFs, and BOs. The mean SHmax orientation from these data is 170° with a standard deviation of ±11° (Nagra, 2024d, c; Heidbach et al., 2025b). The individual standard deviation of each data record is between ±9 and ±19°, indicating that rotations <±11° cannot be resolved. As the differences between the REF model and the three fault-agnostic models, as displayed in Fig. 9, are smaller than ±10°, the potential impact cannot be resolved with any stress indicator. Furthermore, most of the rotations observed are located close to the fault. At a distance of 1000 m from a fault, the rotation is <±2° and thus clearly below the uncertainties of any measurement.

The stress regime of the rock volume, by itself, would not have an influence on the SHmax orientation. A rotation of SHmax orientation would primarily be driven by the horizontal differential stresses, i.e., the greater the horizontal differential stresses, the lesser the possibility of any rotation in the SHmax orientation (Bell, 1996a; Yale, 2003; Reiter et al., 2024).

The 1 km spatial distance limit can also be confirmed by viewing the SHmax orientation from the boreholes in correlation with their distance from the nearest faults. The TRU1-1 borehole is less than 1 km from the Neuhausen fault. Similarly, the MAR1-1 and RHE1-1 boreholes are closest to the Rheinau fault. The average SHmax orientation from the BO, DITF, and HF is ∼165° along the TRU1-1 borehole, ∼175° along the MAR1-1 borehole, and ∼172.5° along the RHE1-1 borehole (Nagra, 2024d, c). Comparing the SHmax orientation values from these three boreholes to the regional SHmax orientation value of 170±11° already strengthens the argument that the faults have minimal effects on SHmax orientation even at a distance of less than 1 km.

In geomechanical modelling, the fault strength is commonly characterized by its friction coefficient (μ) and cohesion (Brandes and Tanner, 2020). In most geological settings, the friction coefficient varies between 0.6 and 1.0 in reservoirs with depths where normal stresses are <200 MPa on a pre-existing fracture plane (Byerlee, 1978; Zoback and Healy, 1984). In stark contrast, significantly lower friction coefficient values are found in geological settings with extremely weak lithologies, overpressured fault cores, and in faults with very large offset and/or high slip rates (Morrow et al., 1982, 1992; Di Toro et al., 2011; Hergert et al., 2011; Li et al., 2022). Cohesion varies with different lithologies, but for pre-existing faults, it is commonly assumed to be zero. In general, the value of the friction coefficient varies between 0.4 and 0.8, and is standardly taken as 0.65 (Hawkes et al., 2005; Kohli and Zoback, 2013). In northern Switzerland, taking the lithology and the geological setting into consideration, the values of apparent fault friction coefficient also range from 0.6 to 1.0, and very rarely to 0.4 (Kastrup, 2002; Viganò et al., 2021). Kastrup (2002) states that the apparent fault friction value of 0.2 is extremely rare in Switzerland and only occurs at depths of more than 10 km.

We investigate the effect of varying the friction coefficient of the contact surfaces on the predicted in situ stress state and recalibrate the REF model with a different friction coefficient. The results of stress magnitudes and orientation from friction coefficients 0.2, 0.4, 0.6, and 0.8 are compared to the friction coefficient of 1.0, the value we use in the REF model (Fig. 11). We see that changes in friction coefficient do not significantly affect our model results beyond lateral distances of 1 km. Even within 1 km from the faults, the horizontal stress magnitudes have observable variations of <1 MPa and <5° for the SHmax orientation variations. These variations reduce to <0.25 MPa in both minimum and maximum horizontal stresses, and <2.5° in the SHmax orientation beyond 1 km from the faults. The maximum variations, still far less than the uncertainties in the in situ stress data of the stress magnitudes and resolvable SHmax orientations, occur at a friction coefficient of 0.2. For the other values of the friction coefficient, the results are very much comparable to the REF model, with a friction coefficient of 1. This is to show that changing the friction coefficient has a negligible effect on the predicted stresses in our model. Minor amounts of slip, in the order of a few tens of cm, occur along the faults in the REF model during the application of boundary conditions. However, the stress change along the fault due to this slip is expected to be far less than the much larger background stresses and the differential stresses. Therefore, the minor slip occurring along the contact surfaces does not influence the overall stress field analysis.

These findings are in line with the results from the generic studies by Homberg et al. (1997) and Reiter et al. (2024), who studied the impact of variable friction coefficient on astress tensor and found that lower values of friction coefficient lead to a higher stress perturbation near the modelled fault. This is also seen in Fig. 11 and is because of possible decoupling at the fault and consequently a better dissipation of stress at the faults, facilitated by lower friction coefficients. The studies also showed that this effect is limited to a distance of 1 km from the fault zone.

Faults in the REF model are represented as contact surfaces, a common and effective approach for large-scale geomechanical simulations. Using contact elements to model faults seems to be a reasonable simplification for large, field-scale reservoir models, where the actual width of the fault core is much smaller than the overall size of the model. Hence, contact surfaces are computationally efficient for reservoir-scale models where actual fault zone widths are negligible compared to model dimensions (Caine et al., 1996; Treffeisen and Henk, 2020). Since our interest is on reservoir scale, alternative fault representation using, e.g. continuous rectangular finite element grid, or a continuous curvilinear finite element grid in a homogenized continuum (Henk, 2009, 2020) is not used in our study. Furthermore, the results from Treffeisen and Henk (2020) and Reiter et al. (2024) show that the stress and strain perturbations from different technical fault implementations vary only within a few tens to a few hundred meters from the fault representation. As we focus only on the far-field stress state, it can be safely assumed that the choice of fault implementation approach does not significantly affect the far-field results.

Although a numerical value does not exist for what is universally defined as far-field stresses, our model indicates that at a distance of >500 m from the faults, the impact of the faults on the stress field is clearly smaller than the uncertainty of the model itself and smaller than the expected variability of the stress field. As seen in Fig. 10, the influence of faults on the stress field is limited to within 1 km from the contact surfaces. Beyond this distance, the choice of the fault representation approach would have no significant impact on the predicted in situ stress state.

In the REF model, the faults, represented by contact surfaces, are simplified and a unified representation of numerous small fault patches that were interpreted from the 3D seismic interpretation. This simplification is necessary for an easier and reasonable representation of fault structures and the consequent computational simulation feasibility of the model. However, the reality is more complex. In the subsurface, faults often occur in clusters and display heterogeneous geometry, composition, and structure (Tanner and Brandes, 2020). Large faults are often accompanied by zones of secondary faults, which can extend the spatial influence of faults on the stress state. Small fault segments of the primary fault and the associated secondary faults can lead to a higher stress concentration along the fault surfaces, complicating the interaction between faults and the in situ stresses (Jones, 1988; Maerten et al., 2002). A single fault may also have complex geometry with multiple bends (Saucier et al., 1992; Roche et al., 2021), increasing its influence on stresses compared to the planar faults.

Our study focuses on a reservoir scale, in the order of a few km, to predict present day stress variation in the area of interest. While seven faults were implemented in the REF model, many more fractures or joints exist in reality but cannot be resolved at our current lateral resolution of approximately 70–100 m, and the available structural geological data. Including these would significantly increase the element count and computational demand, far beyond the scope or need of most studies. It is important to emphasize that the focus of our results is only the far-field present day stresses, and in an intact and undisturbed rock volume.

While previous studies have documented significant stress rotations near fault tips, they also emphasize that these perturbations are typically localized, rarely extending beyond a few hundred meters from the termination point (Homberg et al., 1997; Nicol et al., 2020). Our findings are in general agreement with this observation. In our model, fault tips ending within the Mesozoic sediments indeed exhibit localized stress concentrations and enhanced stress rotations. However, because these effects are spatially restricted, they do not significantly alter the regional stress field predicted by the fault-agnostic models at distances greater than a few 100 m from the structural discontinuities.

Extreme cases exist where large-scale faulting separated the crust into distinct fault blocks, each having an independent SHmax orientation between adjacent fault blocks of the same field (Yale et al., 1994; Yale and Ryan, 1994; Bell, 1996b; Kattenhorn et al., 2000; Hergert and Heidbach, 2011; Hergert et al., 2011; Li et al., 2019; Qin et al., 2024). While complex stress patterns and large SHmax rotations have been reported for major fault systems such as the Møre–Trøndelag Fault Complex and the San Andreas Fault, these systems differ fundamentally from the Alpine Foreland Basin in terms of tectonic setting, fault displacement magnitude, and fault frictional properties (Zoback et al., 1987; Pascal and Gabrielsen, 2001; Roberts and Myrvang, 2004). In particular, the large offsets and anomalously low friction coefficients reported for these systems are not representative of the fault conditions in northern Switzerland. But, as seen in our study region, if the Mesozoic sediments are not massively faulted or fractured, have sufficiently large differential stresses, and are located in an intraplate Foreland Basin setting, it could be expected that the impact of faults on the stress state would only be within 1 km from the fault zone. However, further investigation is needed for other geological settings, with different lithologies such as salt domes, anhydrite, or crystalline rock formations, or regions where faults exhibit more complex geometry with more curvature/bends, or with extremely large total offsets and high slip rates, to confirm the broader applicability of our results.