The safety case for a deep geological repository in Switzerland: radiological consequence analysis and study of the barrier efficiency

Geological repositories for radioactive waste are sited and designed to provide a set of natural and engineered barriers that isolate the waste from the human environment and contain its associated radionuclides. Nonetheless, some release of radionuclides from a geological repository cannot be excluded over the Time frame of hundreds of thousands of years during which the waste presents a potential hazard. Thus, radiological consequence analysis is a key element of the post-closure safety case for deep geological repositories and provides essential insight into the efficiency of the multi-barrier system. This paper presents the current methodology and selected results of the radiological consequence analysis for a combined repository for high-level waste and low- and intermediate-level waste in an Opalinus Clay rock formation hundreds of metres below ground at a proposed site in Northern Switzerland. Deterministic and probabilistic simulations are performed to evaluate radionuclide transport, barrier efficiency, and associated uncertainties. Radionuclide migration in the liquid phase is modelled for a wide range of potentially safety-relevant radionuclides, while gas-phase transport focuses on C-14 released as methane under two-phase flow conditions. Results show that calculated dose rates are several orders of magnitude below Swiss regulatory protection criterion, demonstrating a large safety margin. Long-lived, weakly sorbing radionuclides, particularly I-129, dominate the calculated dose in a reference safety scenario that corresponds to the expected evolution of the repository and in a range of other scenarios, while most other radionuclides are effectively retained within the engineered barriers and the Opalinus Clay host rock. Probabilistic analyses and sensitivity studies identify key parameters controlling radionuclide release. Overall, the analysis confirms the robustness of the multi-barrier system and provides improved understanding of the Swiss deep geological repository system.

Disposal of radioactive waste in deep geological repositories is a widely recognised strategy for the long-term management of radioactive waste. Although they differ in detail, all such repositories are sited and designed to provide a set of natural and engineered barriers that isolate radionuclide waste from the human environment and contain its associated radionuclides. Nonetheless, some release of radionuclides from a geological repository cannot be excluded over the time frame of hundreds of thousands of years during which the waste presents a potential hazard. Thus, radiological consequence analyses are needed which evaluate the potential radiation dose to individuals arising from a deep geological repository in all potential scenarios leading to radionuclide release.

International practice requires that radiological consequence analyses be conducted in accordance with the specific repository concept, the available site and system data, the stage of project development, and the applicable national regulatory framework. Some studies support preliminary pre-siting safety assessments and the development of assessment methodologies and computational tools, such as those reported in NWS (2016), NUMO (2021), Finsterle et al. (2021), Mariner et al. (2015), and Jang et al. (2024). Other analyses have been undertaken for hypothetical repositories at assumed sites to support repository concept development and site selection, including Sillen and Marivoet, 2002 and Nagra’s earlier safety assessment (Nagra, 2002). In contrast, site-specific radiological consequence analyses form part of the safety cases supporting licensing applications, as demonstrated by the national programmes of Posiva (2021), SKB (2010), SKB (2022), and Andra (2026).

In Switzerland, the National Cooperative for the Disposal of Radioactive Waste (Nagra) is responsible for the planning and implementation of a repository for all Swiss radioactive waste. Currently, a combined repository is foreseen for high-level waste (HLW) and low- and intermediate-level waste (L/ILW) in an Opalinus Clay rock formation hundreds of metres below ground at a proposed site in Northern Switzerland. Nagra’s most recent radiological consequence analysis forms a key element of its post-closure safety case that supports the general licence application process for the repository and also serves as an important tool for improving understanding of behaviour of the repository over time, which is essential for guiding future project development.

Compared with current international practice, the following novel aspects of Nagra’s analysis can be highlighted: A combined probabilistic and deterministic simulation strategy is adopted to strengthen uncertainty management. Probabilistic sensitivity analysis is used to identify the most influential parameters, improve understanding of system behaviour, and define a bounding case for comparison with the regulatory dose rate limit using pessimistic values for the sensitive parameters. This integrated approach provides a stronger safety argument than relying exclusively on either probabilistic or deterministic analyses.

The migration of gaseous carbon-14 is systematically evaluated for all safety scenarios using a state-of-the-art numerical modelling approach, providing a comprehensive assessment of this potentially important release pathway.

Three-dimensional modelling of two-phase flow using so-called “macro-elements”, which substantially reduces computational requirements while maintaining simulation accuracy. This approach enables large-scale probabilistic analyses without compromising the quality or comprehensiveness of the simulation results.

Furthermore, in accordance with the recommendations of the international PAMINA project (Performance Assessment Methodologies in Application to Guide the Development of the Safety Case; Galson and Richardson, 2011), complementary safety indicators (such as radiotoxicity) are evaluated alongside the conventional radiological dose rate, thereby increasing confidence in the overall safety demonstration.

The analysis presented here is based on a provisional design for the combined repository in which high-level waste (HLW) and low- and intermediate-level waste (L/ILW) are emplaced within spatially separate sections of the repository. HLW consists of both spent fuel (SF) and vitrified high-level waste from reprocessing (RP-HLW), Guillemot et al. (2026). Both these waste types are packaged in steel disposal canisters. These canisters are emplaced coaxially in horizontal drifts within the Opalinus Clay, with the space around the canisters filled with compacted bentonite buffer material and subsequently sealed. In the L/ILW section, which also includes alpha-toxic waste (ATW), waste packages are placed in disposal containers that are emplaced in caverns and backfilled with a cement-based mortar. The repository concept is described in detail in Smith (2026).

The analysis encompasses a broad range of cases that cover a set safety scenarios leading to radionuclide release, including a reference safety scenario corresponding to the expected evolution of the repository and its geological setting, several alternative safety scenarios, and a series of “what-if?” cases. Details of scenario development can be found in Javanmard (2026). Most of the cases analysed for the safety case are documented in Nagra (2024e) apart from analyses addressing future human actions (reported in Nagra (2024g)) and a specific set of “what-if?” cases related to repository excavation (documented in Nagra (2024f).

This paper focuses on the radiological consequence analysis for the reference safety scenario and selected cases for the alternative safety scenarios and “what-if?” cases. It provides insight into the applied methodology and the post-closure radiological safety of the Swiss deep geological repository.

Overall analysis strategy for the safety scenarios

For the reference safety scenario, a single deterministic reference case, denoted by “RS-RC” in the radiological consequence analysis, is defined based on the reference conceptualisation discussed in Javanmard (2026). Uncertainties in the input parameters are generally quantified in terms of reference value and associated bandwidths and probability distributions. The complete set of parameter values, uncertainty ranges, and probability distributions is documented transparently in the digital enclosures of Nagra (2024e). The underlying data sources are referenced accordingly, including Glaus et al. (2024) for the diffusion database and Miron et al. (2024) for the sorption database.

The reference case is calculated using reference parameter values. This case is analysed in greater detail than others to improve understanding of repository system behaviour and the efficiency of the engineered and geological barriers.

Additional calculations are performed to identify, illustrate, and quantify the effects of uncertainty in parameters controlling radionuclide retention and transport within the repository barriers.

Probabilistic calculation comprising multiple realisations, in which all relevant parameters are randomly sampled from predefined probability distributions. These distributions are derived from assessments of parameter uncertainty and are used to quantify uncertainty ranges in the calculated radiological consequences and to support global probabilistic sensitivity analysis. 4,000 Monte-Carlo simulation realisations were performed to account for parameter uncertainty in the radiological consequence analysis. Correlation coefficients are applied as sensitivity measures, including the Pearson correlation coefficient, the Spearman correlation coefficient, and the modified EASI sensitivity Index (Plischke, 2010; Plischke, 2012).

The strategy of treating parameters in the probabilistic simulations needs to be defined jointly by the data producers and users: Parameters supported by extensive datasets (uncertainty mainly with aleatoric nature) are described using fitted probability density functions, e.g., diffusion coefficients (Glaus et al., 2024)

Parameters mainly with epistemic uncertainty are assigned uniform or log-uniform distributions e.g., rate of the gas generation (Nagra, 2024d)

Some parameters are decided to be fixed at their pessimistic (e.g., HLW canister lifetime Nagra, 2024a) or best estimate values (e.g., repository layout Nagra, 2023).

The decision and the comprehensive set of the parameters is documented in appendices in Nagra (2024e).

A set of deterministic calculation cases in which each parameter identified as highly sensitive in the sensitivity analysis is assigned its most pessimistic value within its respective probability distribution. It should be noted that these pessimistic bounding values typically lie in the tails of the respective parameter distributions—for example, the highest effective diffusion coefficients given by Glaus et al. (2024), and therefore represent values with a low probability of occurrence. Consequently, the simultaneous occurrence of all pessimistic bounding values is extremely unlikely and may be regarded as a hypothetical combination.

Despite this, it is appropriate and conservative to include such a bounding case within the framework of the reference safety scenario. The deterministic bounding case complements the probabilistic analyses by strengthening confidence in the safety conclusions and addressing the practical limitation that probabilistic simulations, despite using a large number of realisations, cannot fully sample the high-dimensional input parameter space. Furthermore, defining the bounding case on the basis of the system understanding gained from the probabilistic sensitivity analysis provides a transparent and technically justified rationale for the selection of pessimistic parameter values. This approach addresses the regulatory expectation of demonstrating a clear basis for the definition of a bounding case, as required by the Swiss regulation (ENSI, 2018).

Throughout this paper, the term “conservative” is used to describe assumptions or model configurations that are expected to yield calculated dose rates higher than those that would occur under realistic conditions. For alternative safety scenarios and the “what-if?” cases, simulations are performed in a deterministic manner to evaluate their radiological consequences.

Transport pathways of the radionuclides

The analysis considers two principal pathways for radionuclides to migrate from the repository to the surface environment: Liquid-phase transport, in which radionuclides are released as dissolved into porewater in contact with the waste packages and are subsequently transported by aqueous diffusion and, where porewater or groundwater flow occurs, by advection.

Radionuclide migration in the gas phase, in which gaseous radionuclides mix with and are transported by repository-generated bulk gases under two-phase flow conditions.

The source term for the radiological consequence analysis is based on Nagra’s waste inventory database, which is described in Guillemot et al. (2026). The database provides the waste inventory, radionuclide composition, and radionuclide release characteristics used in the analysis. Only the information most relevant to the present study is summarized here.

According to the current repository concept (Smith, 2026), HLW will be encapsulated in carbon steel disposal canisters. The canisters are assumed to provide complete containment for the first 10,000 years after repository closure (Diomidis et al., 2026). Following canister failure, a fraction of the radionuclides contained in the spent fuel is assumed to be released instantaneously, represented by the instant release fraction (IRF), whereas the majority remains incorporated within the fuel matrix and is released congruently as the matrix dissolves. The congruent release fraction (CRF) is modelled using dissolution rates under the relevant geochemical conditions. Radionuclides contained in RP-HLW are assumed to be released congruently, controlled by the dissolution rate of the glass matrix under repository conditions. Because the canisters are assumed to maintain complete containment during the first 10,000 years after repository closure, the elevated temperatures resulting from the decay heat of the HLW (Papafotiou et al., 2026) do not affect radionuclide transport and therefore do not need to be taken into account in the radiological consequence analysis.

The L/ILW comprises a wide range of organic and inorganic waste materials. For the purposes of the radiological consequence analysis, radionuclides contained in L/ILW are conservatively assumed to be released instantaneously following repository closure, compared to the current system understanding that the L/ILW emplacement caverns will stay unsaturated for very long time (Martin et al., 2026). The only exception is carbon-14 (C-14), whose release is coupled to the degradation of organic materials and the corrosion of metallic components. The corresponding release model described by Guillemot et al. (2026) is incorporated into the analysis. The treatment of C-14 is presented in greater detail in Nagra (2024i) which significantly reduces the conservatism associated with C-14 releases compared with previous safety assessments.

The majority of radionuclides are expected to be transported in the liquid phase, including the radionuclides belonging to the 4N–4 N + 3 decay chains (the relevant radionuclides are listed in Tables A3.1-9b in Nagra (2014), together with a broad range of fission and activation products. Approximately 60 radionuclides (listed in Appendix H of Nagra, 2024e) identified as potentially safety-relevant are considered in the current radiological consequence analysis for the liquid phase transport.

Only a limited number of radionuclides are gaseous under expected conditions or can form volatile species. Screening indicates that C-14 released in the form of methane is the only radionuclide relevant for gas-mediated transport (Nagra, 2024i) Other potentially gaseous radionuclides are not safety-relevant, due either to their high solubility under repository conditions (e.g., I-129 and inorganic C-14) or their short half-lives (e.g., H-3 and Rn-210). Consequently, both deterministic and probabilistic calculations addressing gas-mediated radionuclide transport only consider C-14 in the form of methane.

Model abstraction and computer codes for radionuclide transport in the liquid phase

For liquid-phase transport, radionuclide migration from the emplacement rooms in the containment-providing rock zone (CRZ) is assumed to occur predominantly in the vertical direction, as the previous analyses have demonstrated that lateral transport along the tunnel system is negligible (Nagra, 2024h). The definition and functional role of the CRZ are described by Wüst et al. (2026). The CRZ comprises the sequence of the rock formations located between the Malm and Keuper aquifers, extending from the Marly Malm (MM-2) to the Dolomitic/Sandy Keuper (DK1/SK) units (Figure 1). The emplacement level of the repository will be located approximately at the centre of the Opalinus Clay formation, providing substantial geological barriers both above and below the disposal horizon for radionuclide transport.

To simulate radionuclide migration from the repository to the surface environment in the liquid phase, the model domain is divided into the near field and the geosphere. The near field comprises either an individual SF or RP-HLW disposal canister and its surrounding bentonite buffer, or

an individual L/ILW emplacement cavern.

Model for the HLW nearfield

The high-level waste nearfield model is developed using the information in Diomidis et al. (2026), including the dimension of the HLW canisters, the geometry of the HLW drifts.

The near-field radionuclide release rates from SF and RP-HLW are computed using the STMAN code (Robinson, 2022). The analysis focuses exclusively on transport processes occurring after canister breach. However, radionuclide decay is also accounted for in the source term during the period in which the canisters remain intact. The canisters are centrally positioned within the emplacement drifts and will not undergo significant displacement, because of the homogeneous mechanical loading from the surrounding bentonite buffer (Diomidis et al. (2026). Owing to this radially symmetric geometry, near field transport of HLW can be represented using one-dimensional radially symmetric model. The conceptual model for an HLW emplacement drift section containing a single HLW disposal canister is illustrated in Figure 2a.

The model domain thus consists of: the radioactive waste (either SF or RP-HLW);

a water-filled reservoir corresponding to the void space inside the canister;

the surrounding bentonite buffer, represented by two or more concentric units with potentially different properties; and

a part of the surrounding host rock

The void space inside the disposal canister is assumed to become instantaneously water filled upon canister breaching. Radionuclides and stable isotopes are released from the waste packages into this reservoir and are assumed to be uniformly distributed.

Chemical interactions between the tunnel lining, the canister, and the bentonite buffer, as well as thermal effects, can lead to mineral alteration of the bentonite in the vicinity of both contact surfaces. Although such interactions will have just minor impact on the transport process of radionuclides (Diomidis et al., 2026), this alteration is conservatively represented by assigning modified properties to a “degraded bentonite buffer” unit.

Owing to the very low hydraulic conductivity of the saturated bentonite and the absence of discrete water-conducting features intersecting the emplacement drifts, nuclide transport within the drifts and their immediate surrounding is dominated by diffusion. The host rock is represented using a linear geometry and is connected to the outer boundary of the cylindrical drift model. The radionuclide release rate from the bentonite buffer multiplied by the number of disposal canisters serves as the source term for the geosphere model.

Inclusion of the surrounding host rock in the near field model domain enables a reliable estimation of radionuclide fluxes across the drift–host rock interface.

Model for the L/ILW nearfield

Papafotiou et al. (2026) conclude that no safety-relevant interactions are expected between repository sections. Consequently, radionuclide transport in the L/ILW repository is modelled independently from the HLW section. According to the preliminary repository design (Nagra, 2023) and the information briefly given in Martin et al. (2026), all emplacement caverns have identical size and exhibit bilaterally symmetrical. This allows the application of a two-dimensional, bilaterally symmetric model (Figure 2b).

Radionuclide transport in the L/ILW near field is simulated using the VPAC code (Holocher et al., 2008). The model explicitly represents the following domains: concrete disposal containers containing the radioactive waste;

the cementitious backfill of the emplacement caverns;

the construction concrete and the cavern lining; and

a portion of the surrounding host rock

For radiological consequence analysis, the first three components are homogenised as a single cementitious porous medium with effective properties. As in the case of the HLW near field, inclusion of the surrounding host rock in the near field model domain ensures a robust estimation of radionuclide fluxes across the cavern–host rock interface.

The combined radionuclide release rates from the HLW and L/ILW repository sections into the host rock constitute the source term for the geosphere model.

Model for the geosphere

The modelling for the geosphere part is based on the geological condition in Nördlich Lägern site which is briefly introduced in Wüst et al. (2026) and in more detail in Nagra (2024c). Geological information taken from the Geosynthesis (Nagra, 2024c) is refined through local geological characterisation (Nagra, 2024b) of the potential repository zones. This process provides an abstraction of geological formations and facies into rock units with similar transport properties. As illustrated in Figure 1, this abstraction includes simplifications of local “layer-cake” models for performance assessment (PA) and radiological consequences analysis (“SA and PA model units”).

The geosphere domain above and below the repository or repository section is represented by two vertical stacks of rock units, one above and one below repository level. These stacks comprise the Opalinus Clay host rock and the surrounding confining units. Liquid-phase radionuclide transport in the geosphere is simulated using the PICNIC-TD code (Robinson and Chittenden, 2022). In this framework, each rock unit within the stacks is represented by a discrete vertical model “leg”, and the legs are connected in series (see Figure 3).

As stated in Wüst et al. (2026), the EDZ around the emplacement rooms is expected to undergo resealing, ultimately reaching properties comparable to the undisturbed Opalinus Clay. Nevertheless, a slight increase in hydraulic conductivity - on the order of less than one to two magnitudes is expected (Nagra, 2024h). For this reason, the EDZ is explicitly included in the modelling.

Zero-radionuclide concentration boundary conditions are imposed at the upper and lower boundaries of the geosphere model. For diffusion-dominated transport, this assumption is conservative, as it corresponds to unlimited flow rate in the bounding deep aquifers. At the horizontal leg representing the Keuper aquifer (“Leg KAL” in Figure 3), a prescribed Darcy flow rate and a free-release (open) boundary condition are applied. The length of the Keuper aquifer is set to 1m, which is a conservative simplification for the horizontal transport within the Keuper aquifer, which in the reality should have several kilometers until its exfiltration point into the biosphere (Nagra, 2024c).

The diffusive properties considered in the modelling for the dissolved radionuclides (excluding the gaseous C-14, which is discussed in the next section) assume a fully saturated porous media. Because the HLW canisters are assumed to provide complete containment during the first 10,000 years after repository closure, the effect of decay heat on radionuclide transport is neglected. The effective diffusion coefficients provided in the database (Glaus et al., 2024) are for the reference temperature of 25 °C. These values are corrected to the local temperature of each rock unit before being used in the transport simulations. Based on the effective diffusion coefficient, D e T 0, at a reference temperature T 0, the coefficient can be corrected to account for the actual (absolute) temperature, T, of the rock by means of the Arrhenius law: where EA is an activaion energy of the temperature effect and R is the universal gas constant.

The temperature of each rock unit is determined from its depth, and the corresponding temperature-corrected effective diffusion coefficient is assigned to that unit in the transport model. For diffusion in the near field, the temperature correction is based on the temperature at the mid-depth of the Opalinus Clay. Radionuclides released through vertical and horizontal model boundaries are assumed to be transported instantaneously to the biosphere. The transport times within the aquifers bounding the CRZ are conservatively neglected (Nagra, 2024c).

As described in Javanmard (2026), potentially hydraulically active confining units (PHAU) located above or below the Opalinus Clay host rock are considered in alternative safety scenarios. For the Haberstal site, three upper confining units (CM: Calcareous Malm, CD: “Calcareous Dogger” and SCD: Sandy-Calcareous Dogger) and two lower confining units (CL: Calcareous Lias and DK2: Dolomitic Keuper) are identified as potential PHAUs.

In the calculation cases addressing these scenarios, PHAUs are represented as horizontal legs to account for potential horizontal advective groundwater flow connecting to regional aquifers. The implementation of this conceptual model with two PHAUs is shown in Figure 4. Depending on the magnitude of the horizontal water flow, a portion of the radionuclide flux will be diverted into the PHAUs and transported advectively, while the remainder continues to diffuse vertically through the model.

Further horizontal transport in the PHAUs is conservatively omitted; rather, radionuclides that enter the PHAUs are assumed to be transported instantaneously to the biosphere. In the reality, there is no evidence showing any connection between these formations with the regional aquifers (Nagra, 2024c). The radionuclide release rates via the PHAUs are summed together with the radionuclide release rates from the upper and lower boundaries to obtain the total release rate from the geosphere.

Model abstraction and computer codes for gaseous radionuclide transport

A macroelement modelling approach is used to simulate the migration of C-14 released as methane from the waste forms under two-phase-flow conditions, using the TOUHG3-EOS75R computer codes (Zhang et al., 2025). Macroelements provide a 3D modelling approach encompassing the entire repository system. Meshing of each macroelement is performed using an unstructured grid. The geometry of the repository is abstracted based on the description and the repository configuration in Nagra (2023). However, to accelerate the simulation speed, the number of the numerical elements was significantly reduced by simplifying the similar and (quasi) symmetrically positioned repository structures along with the surrounding rock to representative 3D macroelements. Two broad types of macroelements are implemented: tunnel elements (incl. waste emplacement rooms and service tunnels) and shaft elements.

An example of the tunnel elements is the macroelement for the L/ILW emplacement caverns. Instead of explicitly meshing and modelling all L/ILW emplacement caverns, each with its surrounding EDZ and geosphere, the macroelement representing the L/ILW emplacement caverns covers only a rectangular domain between a single cavern and a cavern adjacent to it, with vertical boundaries parallel to the caverns consisting of a symmetry plane passing through the cavern axis and a second symmetry plane parallel to this, at the half-axial distance between the caverns. Element volumes and cross-sectional areas between elements of the mesh are then scaled by a factor of 7 (the number of caverns) times 2 (to account for symmetry) to represent the entire set of L/ILW emplacement caverns. The same principle is also applied to the macroelements for the service tunnels and the HLW emplacement rooms.

Another type of the macroelement is designed for shaft. Shaft elements are discretised as 2D radial-symmetric grids with vertical axes. The shafts themselves are laterally surrounded by the EDZ in the host rock.

Macroelements (both tunnel and shaft) include the host rock (including the EDZs) and its confining units above and below the structures.

The extensive properties of the macroelements, such as volumes and source terms, are multiplied by the respective number of aggregated structures, whereas the intensive properties/states, such as temperature, material properties and pressure gradients, remain unscaled. The macroelements are linked together at the interface of the individual structures and the surrounding EDZ to allow for two-phase flow between the macroelements and hence allow for hydrogen and C-14 methane release to transfer along repository structures. The rock parts of the adjoining macroelements are not connected, which reflects the expectation that advective C-14 transport mainly occurs in a plane perpendicular to the tunnel axis.

As shown in Figure 5 for the macroelement model of combined repository, HLW and L/ILW repository sections share a common central area with three access shafts. The macroelements representing the L/ILW and HLW emplacement drifts and caverns are connected to the seal macroelements, which are in turn connected to branch tunnel macroelements. These are connected, via a series of macroelements, to a macroelement representing the three shafts, with their corresponding seals.

Fixed pressure/temperature and zero radionuclide concentration boundary conditions are assigned at the top and bottom of each macroelement.

The impact of repository-generated heat and gas is simulated from the time of backfilling of the emplacement drifts and caverns. Two sources of gas generation are considered: Gas generation from the corrosion of construction materials, which is computed using the gas generation tool described in Nagra (2024d), and which is assumed to occur within all repository structures, apart from the V3 shaft seals, where reinforcement installations are assumed to be removed prior to seal construction.

Gas generation due to the corrosion/degradation of waste and waste packages, which is also computed with the gas-generation model described in Nagra (2024d).

The main gases produced in the L/ILW emplacement caverns under the reducing conditions expected to be established shortly after cavern closure are hydrogen (H 2), methane (CH 4) and carbon dioxide (CO 2). CO 2 is, however, dissolved and consumed by carbonation of cementitious materials. H 2 and CH 4 remain in the gas phase due to their relatively low solubilities in water. The main gas produced in the HLW emplacement drifts under the reducing conditions expected to be established shortly after drift closure is hydrogen (H 2). Hydrogen is also the main gas produced in the underground tunnel system and access structures. After canister breaching, the organic C-14 from the spent fuel and structural materials is assumed to be released as methane.

In the two-phase flow model, hydrogen (H 2), methane (CH 4) are considered as gaseous components. Methane acts as the carrier gas for gaseous radioactive C-14. Gas dissolution between the gaseous and aqueous phases is described by Henry’s law (Oldenburg and Pruess, 1995): where P g ĸ is the partial pressure in the gas phase of component ĸ, H g w ĸ is Henry’s constant, and χ w ĸ is the mole fraction of component ĸ in the aqueous phase.

Individual phase fluxes are given by a multiple form of Darcy’s law (Jung et al., 2018): where v β is the Darcy velocity (volume flux) of phase β, K is the intrinsic permeability, K r β is the relative permeability of phase β, u β is the dynamic viscosity, ρ β is the phase density, and g is the gravitational acceleration vector

The phase pressure is given by

Where P the reference phase pressure and P c β is the capillary pressure of phase β.

In addition to advective transport, the model accounts for diffusive transport. The diffusive mass flux is expressed as: where ∅ is the porosity, d β ĸ is the molecular diffusion coefficient for component ĸ in phase β, and τ 0 τ β is the effective tortuosity factor, comprising a porous medium dependent factor τ 0 and a saturation dependent factor τ β. χĸβ is the mass fraction of component ĸ in phase β.

For partially saturated porous media, the effective diffusivity of hydrogen and methane is scaled using the Millington and Quirk model (Millington and Quirk, 1961) where ∅ is the porosity, S β is the saturation of the phase β.

The parameter values used in the simulations are documented transparently in the digital enclosure of Nagra (2024e). The diffusion coefficient of methane in groundwater is taken from the site-specific diffusion data base (Glaus et al., 2024), ensuring consistency with the diffusion coefficients adopted for the radionuclide transport models described in Section 2.3 of this paper.

Deep aquifers represent the upper and lower boundaries of the model, where a constant temperature, zero H 2 /C-14 concentrations and hydrostatic pressure conditions are assumed to be maintained throughout the simulation. Also consistent with the assumption adopted for the radionuclide transport in the liquid phase, any C-14 released to the deep aquifers is considered to be conveyed instantaneously to the biosphere. Accordingly, transport time within the aquifers is conservatively neglected.

It is well recognized that numerical modelling requires simplifications, assumptions, and abstractions to represent complex natural and engineered systems. A transparent demonstration of the rationale and justification for these modelling abstractions is essential to enhance stakeholder confidence in the modelling results. In the present analysis, the applied model simplifications and abstractions are well understood, systematically evaluated, and documented in the appendices of Nagra (2024e).

Use of biosphere dose conversion factors

Biosphere conversion factors are used (BDCF) to convert the radionuclide flux (in Bq/a) to dose rate (mSv/a). Details of the biosphere modelling used to derive the BDCFs are provided by Brown et al. (2026).

The effective dose rate (in mSv/a) is obtained by multiplication of the BCDF in Sv/Bq for each radionuclide by its corresponding release rates (in Bq/a) to the surface environment, and subsequently summing the contributions over all radionuclides.

In addition to the calculation of dose rate, the safety and behaviour of the disposal system can further be illustrated using a range of additional, complementary safety indicators, which include: Hypothetical dose rate due to radionuclide fluxes (radioactivity flux) from different components or parts of the repository system over time, which are converted to hypothetical dose rates by multiplying the total flux rate of radionuclides with their corresponding BDCFs (the same process as the calculation of individual effective dose rates mentioned above).

Radiotoxicity in individual repository system components, as functions of time, which is compared with the initial radiotoxicity of the emplaced waste inventory. Radiotoxicity (RT), in units of Sieverts, is calculated from the activity A i t [Bq] of a nuclide i at a time t and the ingestion dose conversion factor F i [Sv/Bq] (ICRP, 2012) of the nuclide i:

Fate of radionuclides and barrier efficiency in the reference case

Figure 6 presents the total dose rates for the entire repository, as well as the contributions from the HLW and L/ILW repository sections, together with the dominant radionuclide in each case. The total dose rate from the entire repository reaches 1.5 × 10 −4 mSv/a at 1 million years, which is about three orders of magnitude below the protection criterion of 0.1 mSv/a given by ENSI (2023), indicating a substantial safety margin. The total dose rate continues to increase slightly thereafter, reaching a maximum of 2.0 × 10 −4 mSv/a at around 4.5 million years.

Release from the HLW repository section, as well as from the repository as a whole, is dominated by I-129. In contrast, Cl-36 is the dominant radionuclide for releases from the L/ILW repository section during the first one million years. At later times, the long-lived I-129 becomes the dominant contributor also for the L/ILW section.

Figure 7a illustrates the evolution of the radiotoxicity of the different components within the repository system. The coloured curves represent the distribution of the radionuclides, expressed as radiotoxicity, among the various components of the repository system over time. The dashed black curve shows the total radiotoxicity of the repository system. The total radiotoxicity decreases with time as a result of the radioactive decay. For comparison, the figure also includes the radiotoxicity associated with a hypothetical repository in which the disposal drifts are filled with ore from the Cigar Lake uranium deposit.

Throughout the first million years after repository closure, most of the radionuclides remain confined within the spent fuel matrix (yellow curve) and the vitrified high-level waste (red curve), reflecting the high stability of these materials. Following canister breach 10,000 years after closure, radionuclides from the IRF of the spent fuel are rapidly released into the bentonite buffer and subsequently into the Opalinus Clay. This results in a sharp breakthrough at around 10,000 years, as indicated by the violet, pink, blue and brown curves in Figure 7a.

These radionuclides are transported diffusively in the surrounding rock formations, where many are strongly retarded within the Opalinus Clay. After the IRF release phase, the radionuclides from the spent fuel matrix and RP-HLW are released congruently with the degradation of these waste forms (CRF). Key elements such as Th, Np, U are largely immobilized through sorption or precipitation processes in the bentonite buffer and in the Opalinus Clay.

As a result, radionuclide retention within the buffer and the host rock is very effective, leading to radiotoxicity levels in the confining geological units (grey curve) that are several orders of magnitude lower. Consistent with the results shown in Figure 6, the radiotoxicity that migrates into (grey curve) and beyond the confining units (green curve) is dominated by I-129. The dominant contribution of I-129 to the long-term radiological impact of an HLW repository is also a well-established finding in international safety assessment, despite differences in waste inventories, repository concepts, and geological settings. Examples include the assessment of the vertical drift repository concept (Finstlerle et al., 2021), radiological consequence analyses for repositories in Skandinavien countries (Posiva, 2021; SKB, 2022), and the French CIGÉO project (Andra, 2026) in clay formation with geological conditions are broadly comparable to those in Switzerland. The importance of I-129 arises from its very long half-life (1.57E+7 years), weak sorption in different types of engineered and geological barriers of the repository, and the absence of solubility limitations under repository conditions.

To further illustrate the fate of I-129, Figure 7b presents the radiotoxicity distribution in the repository system. Owing to the low dissolution rate of the spent fuel, the majority of the I-129 remains immobilised in the waste matrix (red curve) throughout the assessment period. The fraction that is released from the waste diffuses through the engineered and natural barriers. The absence of the violet (precipitated I-129) and pink curves (sorbed I-129) confirms that I-129 undergoes negligible sorption and precipitation during the transport. Nevertheless, the combination of the waste matrix (red curve), other engineered barriers (blue curve), and CRZ (brown and grey curves) provides sufficient retardation to delay the breakthrough of I-129 into the surrounding aquifers over very long timescales.

In previous radiological consequence analysis, e.g., Nagra (2014), dissolved C-14 was identified as one of the more relevant radionuclides during the early post-closure period. For the present assessment, Nagra performed a comprehensive re-evaluation of the C-14 source term (Nagra, 2024i) substantially reducing the conservatism of earlier assumptions. As a result, dissolved C-14 no longer represents a significant contributor to water-mediated radionuclide transport or to the associated radiological consequences.

For the radiological consequence analysis of gaseous C-14, a similar approach is applied to evaluate its fate under reference case conditions. Figure 8a presents C-14 activity fluxes at various locations within the repository and surrounding geological formations, converted into dose rates using the BDCF for C-14. The red curve labelled “from the waste” represents the combined C-14 source term from both the L/ILW and HLW repository sections. The IRF from L/ILW is released immediately upon emplacement, whereas the IRF from HLW is released following canister breach at 10,000 years, resulting in two distinct peaks.

Due to the relatively high permeability of the cementitious materials in the L/ILW emplacement caverns, the backfilled access tunnels, and the gas-permeable seals in the L/ILW section, C-14 is transported predominantly by advection through the repository infrastructure. In contrast, C-14 (mainly in the form of methane) released from the HLW section begins at around 10,000 years and migrates directly into the surrounding host rock, driven by overpressure in the HLW near field. There, it dissolves and subsequently diffuses through the Opalinus Clay towards the model boundaries.

The resulting dose rate is dominated by diffusive transport through the CRZ, as indicated by the curve labelled “from the CRZ” in Figure 8a. The repository is located at considerable depth, where high hydrostatic pressures provide significant gas storage capacity within the pore space of both the repository and the adjacent host rock. Although gas pressure builds up, it remains insufficient - given the effectiveness of the shaft seals - to induce advective gas release via the shafts in the reference case. Consequently, transport along the shafts is also diffusion-dominated, but occurs at significantly lower rates compared to releases through the CRZ, as illustrated by the curve labelled “from the shafts” in Figure 8a.

In addition, Figure 8b illustrates the distribution of C-14, expressed as radiotoxicity in different components within the repository system. The red curve labelled “Waste” shows the activity contained within the waste packages, where most of the total C-14 methane resides (the thick black, dashed curve labelled “Total”) and decays throughout the 1E+06-year time period for assessment. This is because of the low corrosion rate of the activated metals that contain most of the C-14 methane in the source term. The figure also shows how the remaining activity, initially dominated by the IRF from the L/ILW, is initially contained mainly in the emplacement rooms (the dark blue curve), before being distributed throughout the repository system (light blue curves), and, at the same time, entering the host rock Opalinus Clay (yellow curve). The small peak in the dark blue curve at 10,000 years corresponds to the release of the C-14 as IRF from HLW upon canister breaching. Only a small fraction of the total amount of C-14 methane is present in the confining units (grey curve).

Probabilistic simulations and parameter sensitivity

As shown in Figure 9a, the spread in the maximum dose rate resulting from uncertainties in input parameter values spans approximately 1.5 orders of magnitude. In contrast, dose rates associated with gaseous C-14 are generally low, as illustrated in Figure 9b. The highest calculated dose rate within the assessment period of up to one million years is 2.8 × 10 −7 mSv/a, slightly exceeding the assumed significance threshold of 1 × 10 −7 mSv/a.

However, the bandwidth of the maximum dose rate due to uncertainty in the input parameter values spans approximately ten orders of magnitude. This wide spread arises because, in the majority of realisations, gaseous C-14 remains confined to the near field, and transport to the biosphere occurs predominantly by diffusion, resulting in low dose rates. Only a small subset of realisations, corresponding to pessimistic combinations of parameter values, exhibit advective gas breakthrough along the shafts through the shaft seals. These cases lead to comparatively higher peak dose rates. The scatterplots in Figure 9c show that, the highest dose rates are associated with higher shaft seal permeabilities, particularly when combined with high gas generation rates and low Opalinus Clay permeability. Under these conditions, gas transport becomes increasingly advection-dominated, promoting the release of gaseous radionuclides through the shafts and resulting in higher calculated dose rates.

In addition, a parameter sensitivity analysis was conducted to evaluate the influence of input parameters on the resulting maximum dose rate. Tables 1, 2 list the five parameters with the highest sensitivity measures associated with radionuclide release in the liquid phase and gaseous C-14 release, respectively.

The most influential parameter governing radionuclide release in the liquid phase is the dissolution rate of the spent fuel matrix, as shown in Table 1, because it controls the rate of radionuclide release (e.g., the dose-rate dominant radionuclide, I-129) from the waste into the repository system. The remaining four parameters are all associated with diffusive transport process, which is consistent with the low hydraulic conductivity of the rock formations in the CRZ. This sensitivity analysis confirms the system understanding from the reference case: I-129 remains predominantly contained within the waste matrix, while the slow diffusive transport through the CRZ provides the primary delay mechanism for its migration and breakthrough into the biosphere.

For gaseous C-14, Table 2 shows that the sensitivity measures indicate a strong positive correlation with the corrosion and degradation rate and, consequently, with the gas generation rate. This relationship arises because the gas generation rate controls both the rate of gas pressure build-up in the repository near field and the rate at which gaseous C-14 is released from the waste. The permeability of the shaft seal also exhibits significant sensitivity in Table 2, as it governs the potential for advective gas breakthrough.

In addition, because diffusive migration in the CRZ dominates the C-14 migration in most simulation realisations, diffusion-related parameters - such as effective diffusion coefficient of C-14 in the Opalinus Clay and the activation energy governing its temperature dependence - also exhibit notable sensitivity. These parameters, together with the hydraulic permeability of the Opalinus Clay, display opposing Pearson and Spearman correlation coefficients. This behaviour can be explained by the dual role of these parameters: higher diffusion coefficient, activation energy, and permeability of the Opalinus Clay enhance diffusive gas migration within the CRZ, while simultaneously reducing the likelihood of advective gas transport along the shafts. This effect is more strongly reflected in the Pearson correlation coefficient, which is particularly influenced by the higher dose-rate values associated with advective gas transport along the shafts. Consequently, these parameters exhibit a negative Pearson correlation, which primarily reflects those simulation realisations in which advective C-14 transport along the shafts dominates. In contrast, the rank-based Spearman coefficient better captures sensitivities associated with the more numerous low-dose realisations arising from diffusive transport. Accordingly, the positive Spearman correlation primarily represents simulation realisations dominated by diffusive C-14 transport within the CRZ.

The observed divergence between Pearson and Spearman correlations for diffusion-related parameters is therefore consistent with the underlying transport mechanisms.

As described in Section 2.1, deterministic cases are used to evaluate the effects of previously identified sensitive parameters by assigning parameters to the most pessimistic bounding value within their respective probability distributions. Figure 10 presents two examples: the combined pessimistic case for the dose rate associated with dissolved radionuclides (Figure 10a), and the combined pessimistic case for dose rates related to gaseous C-14 methane (Figure 10b). In both cases, a significant increase in dose rate is observed compared with the reference case, thereby confirming the strong sensitivity of the dose rate to these parameters, as already indicated by the sensitivity analysis.

Calculation cases for the alternative safety scenario

A radiological consequence analysis is also performed for the alternative safety scenario discussed by Javanmard (2026).

The following example in Figure 11 considers the “Herrenwis Unit”, which is treated as a potentially hydrogeologically active confining unit (PHAU). When the Herrenwis Unit (corresponding to unit “CD: Calcareous Dogger” in Figure 1) is assumed to be hydraulically connected to the regional aquifer, the transport distance within the confining unit to the biosphere is significantly reduced. Consequently, radionuclides originating from the CRZ reach the biosphere earlier.

Nevertheless, due to the slow release rate from the spent fuel and the strong retention capacity of the Opalinus Clay host rock, the resulting increase in the maximum dose rate (2.5E-4 mSv/a) remains limited compared to the maximum dose rate in the reference case (1.5E-4 mSv/a).

Further analysis on selected “what-if?” cases

As described in Javanmard (2026), numerous “what-if?” cases are also considered in the radiological consequence analysis, several of which are highlighted in Figure 12. Some of these cases involve the transport properties of the CRZ, while others concern the properties of the engineered barriers.

The WI-CRZ-DIFF case, which concerns the diffusion properties of all rock formations within the CRZ, assumes a diffusion coefficient ten times higher than the upper bound value used in the reference safety scenario. This case results in the largest increase in dose rate, underscoring the dominant role of diffusion as the primary transport mechanism.

In the WI-CRZ-NOSORB case, where sorption is neglected in all rock formations throughout the CRZ. As a result, the dose rate also increases because sorbing radionuclides, such as Cs-135, which should otherwise be retained within the CRZ in the other safety scenarios, are released to the biosphere. Consequently, Cs-135 replaces I-129 as the dominant contributor to the dose in this case.

The WI-HLW-DISS case assumes a two-order-of-magnitude increase in the dissolution rate of the spent fuel matrix, leading to a significant rise in the maximum dose rate of nearly one order of magnitude. This increase occurs because the faster dissolution rate of the spent fuel matrix accelerates the release of the dominant radionuclide, I-129.

In contrast, cases involving degradation of the engineered barriers generally have a limited impact on dose-rate evolution. For example, the WI-HLW-CAN case assumes canister failure at 1,000 years after closure instead of 10,000 years, as in the reference scenario. Although this leads to slightly earlier radionuclide release to the biosphere, it does not significantly increase the maximum dose rate. A Similar impact can be also observed in other hypothetical “what-if?” for a hypothetical case in which the sorption capacity of the high-level waste near field is neglected cases concerning for a case in which the diffusion coefficients of the high-level waste near field is hypothetically increased engineered barriers (such as WI-HLW-NOSORB and WI-HLW-DIFF).

Extensive radiological consequence analyses for a deep geological repository in Nördlich Lägern were performed as part of the safety case for the general licence application. The results of all radiological consequence analyses, including uncertainty evaluations and hypothetical “what-if” scenarios, demonstrate a substantial safety margin with respect to the regulatory protection criteria. Owing to the excellent containment and retention capacity of the multi-barrier system, most radionuclides are retained within the engineered barriers or in the surrounding Opalinus Clay host rock throughout the assessment period. Furthermore, the behaviour and fate of radionuclides are well understood.

In addition, assessments of the barrier efficiency and the systematic sensitivity analyses have led to significantly improved system understanding. Key insights include the following: properties related to radionuclide release, such as the congruent release rate from spent fuel, can strongly influence the calculated total dose rate;

transport properties within the CRZ play a critical role in determining the total dose rate, and

The gas generation rates and the two-phase flow properties of shaft seals are important for the migration of C-14 in methane form.