### 6.3.1.3 General corrosion

For copper canisters emplaced within clay buffer materials, oxygen is assumed to be present within the void space in both the buffer and backfill materials after closure of the repository. A pessimistic assumption is that all the oxygen present in the buffer material reaches the canister surface and is consumed uniformly by corrosion (SKB, 2010b; Keech et al., 2020). A more realistic assumption, applied to the Swedish KBS-3 repository design, is that oxygen will also diffuse toward the oxygen-free rock and away from the canister; hence, only approximately 50% may reach the canister surface, which equates to an expected corrosion loss of approximately 17 µm that is bounded at 36 µm. The backfill is estimated to contain a greater amount of trapped oxygen than the buffer owing to its greater total volume; however, it is assumed that a smaller fraction of the oxygen trapped in the backfill would reach the canister. This fraction has been estimated for the KBS-3 design by considering the ratio of the canister diameter in relation to the diameter of the deposition hole, with the assumption that the oxygen is consumed as it diffuses downward by reaction with only the canister lid and the top 10% of the canister height. Under these assumptions, a further corrosion loss of approximately 106 µm is anticipated, which gives a total expected loss of 123 µm (SKB, 2010b). In the Swiss program, the amount of copper corrosion arising from trapped O₂, assuming all the trapped O₂ reacts with the canister to form Cu(I), was estimated at approximately 70 µm (Johnson and King, 2003). No credit was taken for the consumption of oxygen by reaction with steel rock supports, microbial activity, or oxidation of Fe(II), making the approach conservative.

Once the oxygen has been consumed, sulfide will be the primary oxidant remaining in the repository (or, more precisely, copper will corrode with the evolution of hydrogen in the presence of sulfide). An initial inventory of sulfide present as minerals (e.g., pyrite) within the buffer and backfill may dissolve and diffuse toward the canister surface during hydration of the borehole. The corrosion of copper by sulfide will lead to the formation of copper sulfide (Eqs 13, 14), although other reactions are also possible). Sulfide is also produced by microbial activity, as previously discussed.

$$2\text{Cu(s)} + \text{HS}^{-} + \text{OH}^{-} \rightarrow \text{Cu}_2\text{S(s)} + \text{H}_2\text{O} + 2\text{e}^{-} \quad \text{anodic process} \quad (13)$$

$$2\text{H}_2\text{O} + 2\text{e}^{-} \rightarrow \text{H}_2 + 2\text{OH}^{-} \quad \text{cathodic process} \quad (14)$$

The contribution of the sulfide present as pyrite in the buffer can be pessimistically bounded by a mass balance estimate for the residual oxygen. The contribution of the dissolution of pyrite and the diffusional transport of sulfide from the pyrite to the canister surface has been considered a source of corrosion in the KBS-3 repository design (SKB, 2010b); however, an allowance is not currently made for it owing to the low solubility of sulfide in the buffer.

In PA models, the corrosion rate due to the diffusion of corrosive species toward the canister surface is typically treated using the assumption that they react immediately upon contact with the canister surface and that any future reaction rate is unhindered by the formation of corrosion products. In the case of the copper/bentonite system, this assumption is justified by the slow rate of

transport of sulfide in compacted bentonite in relation to the inherent reaction rate of copper with sulfide. Under these conditions, the corrosion reaction is treated as being transport-limited, and the rate of corrosion is proportional to the flux of species reaching the surface (SKB, 2010b). It has been demonstrated that for copper corroding due to reaction with HS⁻, the shift from kinetic limitation to transport limitation occurs at HS⁻ fluxes lower than $2 \times 10^{-12} \text{ mol cm}^{-2} \text{ s}^{-1}$, which is considerably greater than the anticipated long-term sulfide fluxes through an intact bentonite buffer (~$10^{-14} \text{ mol cm}^{-2} \text{ s}^{-1}$) (King et al., 2017b). The lack of impact of corrosion product formation on the subsequent corrosion rate is supported by experimental observations that copper sulfide corrosion product layers are porous and non-protective at the pH and sulfide concentration anticipated within a bentonite buffer (King et al., 2017b; Keech et al., 2020). The mass-transport approach can also be applied to any oxygen that is trapped in the buffer and backfill materials, although in conventional disposal scenarios (effectively sealed DGR tunnels), the treatment based on mass balance is considered both cautious and sufficient. On the other hand, while this approach is still conservative (as the consumption of oxygen by other sources is also not considered), this approach could be used to treat the corrosion of disposal canisters in relevant scenarios, including tunnels that were either deliberately or inadvertently unsealed during the DGR operational period (i.e., while operations in other tunnels are still taking place) or access of glacial melt water (see below) (King et al., 2011).

Corrosion of copper by sulfide transport in groundwater is evaluated by mass-transport limitation. The equilibrium concentration of sulfide in the groundwater is determined by the source (i.e., sulfate reduction by microbial activity) and sink (i.e., oxidation and precipitation with metals) terms (SKB, 2010b). Mass-transport modeling has been used to evaluate the effect of buffer erosion on the sulfide transport from flowing groundwater supplied from a rock fracture to the canister surface for a KBS-3 repository (SKB, 2010b). For an intact buffer and a sulfide concentration of the order of 0.01 mM, corrosion rates lower than 0.001 µm year⁻¹ have been predicted for all conditions modeled, with vastly lower corrosion rates predicted for most cases. Predicted corrosion rates are much higher for a partially eroded buffer, and under the most pessimistic combinations of flow rate and sulfide combination (≥0.161 m/s and 0.12 mM), failure of a canister (taken as 47 mm of corrosion or greater) could occur within $10^5$ years (SKB, 2010b). However, for a more realistic sulfide concentration (0.01 mM), failure is only predicted to occur after approximately 850,000 years, even at a high flow rate of 0.251 m/s (SKB, 2010b). Likewise, similar hydrogeology models are used to evaluate oxygen transport from glacial meltwater. This can be done by assuming an upper limit of oxygen concentration (1.5 mM) in the groundwater that is supplied to the canister surface from a rock fracture intersecting a deposition hole over a fixed exposure period of 1,000 years, resulting in a corrosion loss of less than 6 mm (SKB, 2010b). In the Swiss disposal system, the corrosion loss based on the diffusion of HS⁻ to the container surface has been estimated as 80 µm over $10^6$ years. This is based on reactive-transport modeling of sulfide in bentonite (Cloet et al., 2017).

### 6.3.1.4 Localized corrosion

Pitting of copper canisters is only considered viable during the aerobic early post-closure phase, while conditions are oxidizing, but
water chemistry is still quite dilute as the groundwater will have not yet reached the disposal container (or buffering by the initial porewater still occurs) (RWM, 2016). Based on short-term laboratory testing in simulated DGR conditions and in situ corrosion testing in disposal programs, copper has been shown to exhibit non-uniform general corrosion rather than the formation of discrete “classical” pits that are characterized by a small, fixed anode spatially separated from a supporting cathode. Consequently, the relative non-uniformity in the extent of corrosion across the surface is anticipated to decrease over time (RWM, 2016). Therefore, predictions of pit depths based on the assumption of a fixed anode that corrodes at a greater rate than the mean corrosion rate are unrealistically pessimistic (e.g., empirical pitting factor and extreme-value statistical analysis).

Another form of localized corrosion that has been evaluated in some disposal programs, for example, the Canadian disposal concept, is under-deposit corrosion (Scully and Edwards, 2013). The specific mechanism of concern is a form of crevice corrosion that proceeds underneath a precipitated surface film. The film would act as a selective ion exchange membrane and enable the development of a locally aggressive solution chemistry, forming a permanent anodic region. Such a mechanism would preclude the use of a surface roughening factor to account for local attacks in favor of the more conservative pitting factor (Scully and Edwards, 2013). Localized corrosion, including under-deposit corrosion, has been considered by ascribing a 0.1 mm corrosion allowance to this mechanism on the assumption that anodic and cathodic sites will not remain permanently fixed but will change with time within the overall anodic region (under the deposit) (Scully and Edwards, 2013; Keech et al., 2020). The assumption is underpinned by measurements of the surface profiles produced from the corrosion of copper underneath precipitated films in simulated Canadian repository conditions. The results showed a depth of attack of approximately 50 µm following 18 months of exposure under conditions that were conservative, with respect to oxygen concentration, in comparison to those anticipated during the aerobic phase in the DGR (King et al., 1992; Scully and Edwards, 2013).

#### 6.3.1.4.1 Empirical pitting factor.
Pitting factors for buried copper and copper alloys have been found to vary between 0 and 25 but exhibit a tendency to decrease with time. The longest exposure durations used to determine pitting factors are those of bronze-age artifacts (~3,000 years) reported by (Bresle and Arrhenius, 1983) and gave pitting factors between 2 and 5. These values are broadly consistent with measurements made of buried lightning conductor plates, which exhibited pitting factors of between 0 and 5 following exposures between 50 years and 80 years (Hallberg et al., 1984). Hence, for buried copper canisters, a pessimistic pitting factor of 5 may be assumed (SKB, 2010a). A pitting factor of 5 was applied to give a conservative estimation of the maximum depth of penetration of a copper canister in a Swiss repository due to sulfide flux (Johnson and King, 2003). However, the use of a pitting factor for copper is, in general, considered to be overly conservative when applied to DGR performance assessment. This is due to a shift to less oxidizing conditions (i.e., decreasing concentrations of O₂ and Cu(II)) and the progression of general corrosion into the surface, both of which act

against the separation of anodes and cathodes (SKB, 2010a). Consequently, it is anticipated that a measured pitting factor would decrease with increasing time of exposure, consistent with archaeological observations.

#### 6.3.1.4.2 Empirical extent of surface roughening.
Roughening of ±50 µm has been applied for copper corrosion due to initially entrapped oxygen (SKB, 2010a; SKB, 2010b), based on observations by Brennenstuhl et al. (2002) and Litke et al. (1992). Similarly, in the Canadian system, a corrosion allowance of 100 µm has been assigned to address surface roughening during conditions where the oxygen level is still relatively high (Scully and Edwards, 2013; Keech et al., 2020) and is based on arguments supporting the switching of anodic and cathodic regions (Kwong, 2011).

#### 6.3.1.4.3 Extreme-value statistical analysis.
Pitting data generated by (Bresle and Arrhenius, 1983; Hallberg et al., 1984; Romanoff, 1989) were analyzed by King and Kolář (2000) and King and LeNeveu (1992) and fitted to an extreme-value distribution (Eq. 15). Application of these data to a copper canister in the KBS-3 type repository environment led to the prediction of a 10⁻⁶ chance of a pit exceeding 7.5 mm after 10⁶ years and a 10⁻⁶ chance of a pit exceeding 5 mm after only 10 years (SKB, 2010a).

$$F(x) = \exp[-\exp(-ax + b)] \quad (15)$$

An underpinning observation that indicates that long-term prediction of pit depths making use of extreme-value statistical analysis (and empirical pitting factors) may not be particularly meaningful is that copper will not passivate under anticipated repository conditions, as passivation is required to cause pitting (King and Lilja, 2014). In the early oxic period, where pitting is more feasible, the presence of Cl⁻ ions tends to promote general active corrosion at near-neutral pH, with passivation occurring more readily in more alkaline solutions with a lower salinity (Qin et al., 2017; Briggs et al., 2020). In the long term, corrosion proceeds via the formation of copper sulfide, which has been shown to form porous non-protective films under anticipated repository conditions in Canada, Sweden, and Finland (King et al., 2017b).

#### 6.3.1.4.4 Comparison of corrosion potential to critical potential for localized corrosion.
For copper in neutral conditions, when the oxygen concentration is sufficiently low that hydrogen evolution is the dominant cathodic reaction, the anodic overpotential required to cause pitting is estimated as being approximately 600 mV based on the potential at which copper oxide formation occurs. Pitting of a copper oxide film is expected to occur more readily with increasing chloride concentration and less favorably with increasing HCO₃⁻ concentration due to their destabilizing and stabilizing influence on passivity, respectively (Drogowska et al., 1992). When sulfide is present, the pitting potential of the protective sulfide film was shown to shift in the negative direction with increasing HS⁻ concentration (de Chialvo et al., 1985). For copper in the presence of 0.01 M HS⁻, an anodic overpotential of approximately 200 mV is assumed necessary to induce pitting corrosion based on corrosion potentials reported by Escobar et al. (1999). While pitting of copper oxides and
sulfides has been shown to be possible under certain conditions, the potentials at which such pitting occurs are hundreds of mV more positive than anticipated in repository environments (King et al., 2010).

### 6.3.1.5 Radiation-assisted corrosion

Radiation-assisted corrosion is considered separately for the saturated and unsaturated environment, as the prevalent corrosion mechanisms in each case are quite different. In unsaturated conditions, the major corrosion mechanism considered in safety case assessment is that caused by radiolytically produced nitric acid that arises from irradiation of the humid air trapped within the buffer. Once saturation is complete, radiolysis of the anoxic porewater leads to the production of oxidants, primarily $H_2O_2$, which, in high enough concentrations, can influence the corrosion rate and shift the corrosion potential in the positive direction (King and Behazin, 2021).

#### 6.3.1.5.1 Mass balance of radiolytically produced oxidants.
In the unsaturated phase, the influence of radiolytically generated oxidants on the corrosion of copper canisters within a bentonite buffer has been estimated by calculating the radiolytic yield within a given volume around the canister (liquid or gas phase) and assuming the oxidants produced will react with the canister surface to give a bounding value (SKB, 2010b).

This approach is adopted to take into account the formation of nitric acid from gamma irradiation of the humid air present in the canister-buffer gap during the buffer saturation phase. The total amount of nitric acid generated is calculated from the G-value for $NHO_3$ generation, the total absorbed gamma dose, and the irradiated volume (e.g., a 1 cm gap around the canister) (SKB, 2010b).

Radiolysis of water is considered to form hydrogen and oxidants that will react with the canister material, causing corrosion. It is assumed that there exists a volume around the canister in which all radiolytically generated oxidants will reach the canister surface (e.g., a 5 mm gap around the canister) and that there is a fixed stoichiometric ratio between the moles of oxidant produced and the moles of metal that are corroded uniformly from the surface of the canister (SKB, 2010b). Overall, the effect of radiolysis on copper in the Swedish system (KBS-3 type repository), after taking into account the aforementioned contributions, is approximately 7 nm of corrosion (SKB, 2010a).

A similar approach has been adopted to bound the extent of corrosion that may be experienced by copper due to radiolysis of water in the KBS-3 concept. If it is assumed that all the radiolytically produced oxidants within 5 mm of the canister can reach the surface, and it is also assumed that Cu is oxidized as efficiently as dissolved Fe(II), then approximately 14 µm of corrosion would be expected.

#### 6.3.1.5.2 Reasoned argument for exclusion.
Intact canisters provide shielding against alpha and beta radiation, with only gamma and neutrons penetrating through the walls to cause radiolysis of the porewater and groundwater. Due to the shielding afforded by the canister, the surface radiation dose is greatly attenuated. For the thinner-walled Canadian design, the surface dose rate is approximately 1 Gy h⁻¹ (Keech et al., 2020), whereas the average

surface dose is approximately 0.055 Gy h⁻¹ for the thicker KBS-3 containers. At these dose rates, it is anticipated that there will be no enhancement of the corrosion rate (Pusch et al., 1992; Posiva, 2013). This perspective is supported by King and Behazin (2021), who compared the general corrosion enhancement by gamma radiation at dose rates from 0–20 Gy h⁻¹ and total absorbed doses from 1,000 Gy to 50,000 Gy. At dose rates relevant to repository conditions (<10 Gy h⁻¹), there was either no effect or an inhibiting effect of radiation. There is no consensus within the literature about dose rates >10 Gy h⁻¹, with some studies showing an increase in corrosion and others showing an inhibition of corrosion compared to uninhibited rates. These studies also showed that for all dose rates considered, there was no consistent effect of increasing cumulative radiation dose.

Of the articles considered by King and Behazin (2021), the only studies that demonstrated an increase in corrosion rate due to gamma radiation were conducted at dose rates considerably greater than those anticipated at a copper canister surface during emplacement within a DGR. Moreover, King and Behazin (2021) draw attention to the mechanistic impacts of radiation dose rate on corrosion potential, which supports the suggestion that radiation dose rate is a critical factor in determining the influence of gamma radiation on the corrosion rate of emplaced canisters. Consequently, laboratory studies at dose rates far in excess of 10s Gy h⁻¹ are not expected to accurately simulate the corrosive conditions encountered within a DGR.

### 6.3.1.6 Microbiologically influenced corrosion

#### 6.3.1.6.1 Reasoned argument for exclusion.
It has been shown that microbial activity is suppressed in highly compacted bentonite above a certain density due to the low water activity (≤0.96) (Scully and Edwards, 2013), the high swelling pressure, and the lack of physical space. In the Swedish SR-Site safety case, microbial activity leading to sulfide production via sulfate reduction was not considered within the intact bentonite buffer whose dry density exceeds 1,800 kg/m³ (SKB, 2010a). In the Finnish safety case for the disposal of spent fuel at Olkiluoto, a bentonite dry density greater than ~1,650 kg/m³ was considered the upper threshold for microbial activity (Posiva, 2013). Consequently, microbial corrosion is generally not considered feasible within the bentonite buffer, provided it remains compact and retains its density. Microbial activity is instead considered away from the near-field (e.g., in the backfill) (Johnson and King, 2003; SKB, 2010a; Posiva, 2013; Scully and Edwards, 2013).

#### 6.3.1.6.2 Mass transport.
Corrosion of copper by microbiologically generated sulfide outside of the near-field in a KBS-3 repository environment is pessimistically bounded by the supply of nutrients for microbes (SKB, 2010a). The amounts of nutrients available have been estimated in several ways. The backfill contains an abundance of organic matter, but it would be unrealistic to assume the whole inventory is available for dissolution and could be used to produce sulfide that could reach the canister surface within the lifetime of the repository. Bounding calculations based on 1D diffusion of sulfide formed at the same location as the organic matter predict that only a fraction of the sulfide that could be produced would reach the canister surface within 10⁶ years. A bounding corrosion loss from sulfide in the backfill is obtained
by 1D diffusion modeling using pessimistic values for diffusivity and sulfide concentration (10⁻⁴ M) and applying the assumption that sulfur transported from the backfill is consumed by corrosion of the top 10% of the canister uniformly and gives a depth of penetration of 2 mm (SKB, 2010b). In the Canadian system, a corrosion allowance for microbial activity of 1 mm is considered sufficient, provided the buffer remains intact (Wolfaardt and Korber, 2012; Scully and Edwards, 2013).

The contribution of H₂, generated via anaerobic corrosion of rock bolts and other iron components, to the formation of sulfide via acetogenesis and sulfate reduction has also been considered and bounded for specific repository conditions based on the amounts of steel present (SKB, 2011). If a conservative mass balance approach is adopted that assumes that all of the sulfide produced by acetogenesis reacts with the canister, then an upper bound corrosion loss of 300 µm is obtained (SKB, 2010b).

### 6.3.1.6.3 Empirical rates of sulfide formation.
Another method of estimating bounding rates of sulfide production has been based on experimental studies performed in conditions that are more favorable for microbial activity than expected in a repository environment. The rates of copper sulfide production were measured in different densities of bentonite that were supplemented with lactate to act as a source of organic carbon and nutrients (Masurat et al., 2010). The experimentally determined rates of sulfide production were converted into equivalent corrosion rates, and the wall thickness loss after 10⁶ years was extrapolated linearly to give a pessimistic estimation of thickness loss of about 3 mm (SKB, 2010b).

### 6.3.1.7 Environmental-assisted cracking

#### 6.3.1.7.1 Reasoned argument for nonsusceptibility.
A combination of stress, aggressive ions, and oxidizing conditions are required for SCC of copper to occur. Even in the early oxic period, where temperatures are elevated, it is unlikely that sufficient concentrations of aggressive ions would be available within the KBS-3 type repository. No known mechanistic arguments can justify the assumption that copper cracking could be sustained over the long term in the anaerobic phase of the repository environment (King et al., 2010; SKB, 2010b; Posiva, 2013).

This argument has been further underpinned by experimentally validated mixed-potential modeling of the anticipated E<sub>corr</sub> of copper, evaluated over a repository lifetime based on the interfacial chemistry as predicted by reactive-transport modeling. Modeling of E<sub>corr</sub> and the surface pH demonstrated that a CuO<sub>2</sub>/CuO surface film is not thermodynamically stable, which is a requirement for the SCC of copper (Maak and King, 2006) beyond the initial aerobic period (Posiva, 2013).

In the Canadian concept, SCC is not considered to be likely during the steady-state conditions encountered during deep geological disposal. Specifically, the interfacial pH and corrosion potential are expected to be far from the range in which SCC is a feasible corrosion mechanism, given the lack of aggressive species. Certain species, such as ammonia, nitrate ions, acetate, and sulfides, are known to promote the SCC of copper; however, the concentrations in groundwater are below the threshold levels for which they have been shown to promote SCC. It has been acknowledged that activities such as mining could lead to an increase in such species; however, the increase in SCC susceptibility is

somewhat offset by the presence of Cl⁻, which reduces the risk of SCC by promoting general corrosion (Kwong, 2011).

The risk of gradual embrittlement of copper by long-term anoxic exposure to HS⁻ at concentrations of approximately 10⁻⁴ mol/L has been highlighted as a risk to copper canisters (Scully and Edwards, 2013). However, it has also been argued that HS⁻ transport in bentonite is sufficiently slow that corrosion by sulfide could be transport-limited, resulting in surface or crack tip concentrations approaching zero, assuming that Cu(I) will sequester sulfide by precipitation of CuS₂ (Jacobs and Edwards, 2000). It was similarly concluded that for the KBS-3 concept, the possibility of SCC of copper, even at high sulfide fluxes, is not anticipated, and even if copper were susceptible to SCC in the presence of sulfide, the sulfide fluxes in the repository environment are not at a level that could induce SCC (SKB, 2019).

### 6.3.1.8 Mechanical degradation and combined corrosion-mechanical effects

Several modes of mechanical degradation could potentially affect the integrity of waste containers, specifically fracture, plastic deformation, and creep. Detrimental interactions between mechanical factors and corrosion processes are also possible (Figure 10). These issues have been discussed in detail by King et al. (2016). Fracture processes can be subdivided into brittle fracture, characterized by cleavage or intergranular failure, and ductile fracture, resulting in the typical “cup and cone” dimpled fracture surface. Brittle fracture is normally caused by some form of embrittlement process, such as radiation embrittlement, solute segregation within the metal, or hydrogen embrittlement. Plastic deformation can occur when a metal is overloaded past its yield strength, eventually leading to ductile failure if the load is sufficiently high. This form of failure is avoided in container design by choosing wall thicknesses that are appropriate to the expected loads. If the load tolerance is exceeded, deformation of the container may occur.

Creep involves the slow deformation of a material under the influence of an applied static load below the yield stress. In the case of copper, this problem is ameliorated by the use of oxygen-free, phosphorus-doped copper, which has a higher creep ductility.

It is possible that some forms of corrosion may have an effect on the mechanical performance of the container and vice versa. This includes environmentally assisted cracking, which is considered in the previous section, where the mechanical factors affect the corrosion susceptibility, and conversely, corrosion processes such as general corrosion will cause wall thinning, leading to a loss of wall strength and load-bearing capacity, and hence an increased risk of wall deformation or buckling. These interactions have been examined in detail by King et al. (2016) and are summarized in Figure 10. Other corrosion phenomena of note in this context are hydrogen-induced degradation of mechanical properties because hydrogen may be generated by the anaerobic corrosion of iron or may be present in the geological environment and expansive corrosion due to the formation of a corrosion product with a larger volume than the original metal. The latter effect has been examined experimentally by Smart et al. (2003a) and by comparison to analogs, such as archaeological artifacts (Smart et al., 2003a; Smart et al., 2006b).
<figure><img src="image_16.png" /><figcaption>FIGURE 10
Schematic illustration of the mechanical and material-related factors that could lead to container failure and their relationship to various failure modes (King et al., 2016).</figcaption></figure>

### 6.3.1.9 Prediction of canister lifetimes and implications for PA

At present, the most comprehensive predictions of canister lifetime have been performed for the KBS-3 concept, and

estimates have been made for the maximum corrosion loss that may be caused by each mechanism over a period of $10^6$ years. In the absence of buffer erosion, no single process gives an estimated corrosion loss of greater than a few mm, with the greatest loss
<table><caption>TABLE 3 Comparison of approaches currently taken to account for different types of corrosion in performance assessments for copper canisters by international waste management organizations (blank cells reflect an absence of information within the public domain).</caption><thead><tr><th>Mode of corrosion</th><th>Canada</th><th>Finland</th><th>Sweden</th><th>Switzerland</th><th>United Kingdom</th></tr></thead><tbody><tr><td>Oxidic general corrosion</td><td colspan="5">Mass balance within corrosion allowance</td></tr><tr><td>Radiolysis-induced corrosion</td><td colspan="5">Excluded or mass balance within corrosion allowance</td></tr><tr><td>Sulfide-induced anaerobic corrosion</td><td colspan="5">Mass-transport controlled—key factor driving corrosion allowance</td></tr><tr><td>MIC before buffer saturation</td><td colspan="3">Exclude by reasoned argument</td><td colspan="2"></td></tr><tr><td>SCC</td><td colspan="5">Exclude by reasoned argument</td></tr><tr><td>Pitting</td><td>Fixed corrosion allowance to account for surface roughening</td><td colspan="4">Fixed corrosion allowance to account for surface roughening</td></tr></tbody></table>

estimated to arise from sulfide flux caused by microbiological reduction of sulfate in a buffer on the assumption that all the organic material in the backfill is available to support this process. If the estimated contributions from each process are added together, the total loss estimated over $10^6$ years is less than 5 mm (SKB, 2010b).

For scenarios involving erosion of the buffer by groundwater flow, the maximum predicted corrosion rates are greater than for any other mechanism considered. However, extremely high rates of corrosion are only estimated when the least favorable conditions are assumed (i.e., maximum flow rate and maximum sulfide concentration). When a statistical analysis is performed that considers the range of possible flow rates and the range of possible sulfide concentrations, the likelihood of a canister failing within $10^6$ years can be estimated based on the number of canisters being stored. Application of this methodology estimates that between 0 and 2 canisters would fail within $10^6$ once uncertainties are taken into account (SKB, 2010b).

For the Canadian system, a corrosion allowance of 1.27 mm over $10^6$ years was described by Kwong (2011) and was based on several assumptions that have since been shown to be highly conservative (Keech et al., 2020). In particular, the corrosion allowance is dominated by sulfide corrosion due to an assumed sulfide concentration of 3 ppm (Kwong, 2011), which has subsequently been shown to be considerably higher than what is expected in Canadian deep subsurface water (Keech et al., 2020).

Table 3 summarizes the approaches taken for dealing with the corrosion of copper in performance assessments by various WMOs, according to the various possible corrosion mechanisms for copper.

Confidence in the predictions of the longevity of containers can be increased by reference to results from i) *in situ* corrosion experiments, where the environmental conditions are close to those expected in the real repository, with the exception of the external radiation dose rates, and the temperature, and ii) comparison with natural and archaeological analogs (IAEA, 1989; IAEA, 2005). Natural analogs include geological deposits, for example, native copper deposits (Milodowski et al., 2000; Milodowski et al., 2002), which have been found to exist for millions of years, and archaeological artifacts, such as a bronze cannon (King, 1995) and an iron-copper helmet (Smart et al., 2003b).

## 6.3.2 PA models for steel containers

### 6.3.2.1 Introduction

Carbon steel has been proposed as a canister material for SNF and HLW in several national disposal concepts, including the United Kingdom (RWM, 2016), Belgium (Kursten et al., 2017), France (Andra, 2005), Japan (JNC, 2000) and Switzerland (Patel et al., 2012). Different WMOs specify different alloys for the canister material but in general, low-strength, low-carbon alloys are favored. Carbon steel is a desirable canister material as its corrosion mechanisms are well characterized and predictable, based on decades of research, which enables canisters to be designed with suitable corrosion allowances (RWM, 2016). Moreover, due to the extensive use of carbon steel as an engineering material, it can be readily sourced and fabricated, and it is considerably cheaper than many alternative canister materials such as copper, nickel alloys, and titanium.

Carbon steel has been considered for use with both bentonite and cementitious buffers, as well as crushed rock (RWM, 2016). The high pH environment afforded by a cementitious buffer material supports the formation of a stable passivating magnetite film, which reduces the corrosion rate. However, under repository conditions, anaerobic corrosion of steel (even when passivated) leads to the formation of hydrogen gas, which has the potential to destabilize the surrounding buffer material. There is also concern that the interaction of ferrous ions released by corrosion could adversely alter the characteristics of the surrounding bentonite buffer.

In Switzerland, steel canisters for the disposal of SNF and HLW emplaced within a bentonite buffer have a regulatory lifetime requirement of 1,000 years, with the expectation that 10,000-year lifetimes may be readily achieved (Nagra, 2002), and this is the design lifetime. Similarly, complete containment provided by the Belgian Supercontainer concept is expected to endure for at least 5,000 years (for conditions defined within the design reference scenario), although considerably longer lifetimes are anticipated if long-term corrosion behavior is governed by the uniform anaerobic corrosion rate (Weetjens et al., 2012). In the Czech concept, the double-walled steel canister comprising an inner stainless steel layer surrounded by an outer carbon steel layer is designed to last for a minimum of 10,000 years (Pospiskova et al., 2017), whereas the Japanese concept, which has an inner stainless steel HLW cask surrounded by an outer carbon steel layer focuses on a 1,000 years
lifetime specification but is expected to last considerably longer (NUMO, 2021).

### 6.3.2.2 Atmospheric corrosion

The atmospheric corrosion behavior of steel canisters in air is dependent on the relative humidity; below ~60% RH, the corrosion rate is considered to be extremely low (Nagra, 2002). The presence of hygroscopic salt deposits (e.g., NaCl and CaCl₂) on the canister surface can influence the relative humidity at which corrosion can occur, depending on the chemical composition of the contaminating salt (Schindleholtz et al., 2014). However, due to the elevated temperature within the buffer close to the container surface, the canister is expected to remain dry even when the outer layers of bentonite begin to saturate (Nagra, 2002). Consequently, in the initial dry period, which is estimated to persist for a few decades, the extent of corrosion is expected to be less than 100 µm (Nagra, 2002) and has been accounted for in an Opalinus clay repository by applying a corrosion allowance of <1 mm (Johnson and King, 2008). This value is in broad agreement with atmospheric corrosion rates reported in RWM (2016), which shows that the atmospheric corrosion of embedded iron in subterranean environments is on the order of a few µm a⁻¹. It is anticipated that the atmospheric corrosion of iron will generally form iron (hydr)oxides, and this is not expected to directly undermine the integrity of the containers significantly in environments of limited corrosivity. However, there is uncertainty regarding the impact that the formation of a layer of rust could have on the corrosion performance of a steel container during the long-term post-closure phase (RWM, 2016).

### 6.3.2.3 General corrosion

Following the depletion of oxygen within the repository and a shift to more reducing conditions, the long-term corrosion of emplaced steel canisters is expected to occur as uniform general corrosion under anoxic conditions. In this environment, a corrosion rate of ~1 µm a⁻¹ is anticipated for corrosion occurring in a bentonite buffer (Smart et al., 2011), but there are indications that the rates are even lower if sufficiently long experiments are performed (Diomidis et al., 2023). These rates are within the range reported for natural analogs, which exhibit corrosion rates as low as 0.1 µm a⁻¹ for conditions that are not aerated (Miller et al., 1994). For the Czech concept, uniform anoxic corrosion of the outer carbon steel canister when emplaced in Czech bentonite is assumed to occur at a rate of 5 µm a⁻¹, based on average corrosion rates determined by mass loss over a 4-month period. However, the use of these rates to make lifetime predictions is known to be conservative, as in the same study, a comparison of the total corrosion loss of specimens after 2- and 4-month exposures implied that the instantaneous corrosion rate after 2 months had reduced to less than 1 µm a⁻¹ (Pospiskova et al., 2017).

For concepts involving a cementitious buffer, such as the Belgian Supercontainer concept, the high pH (>13) cement porewater that is anticipated to form upon hydration of the buffer ensures that the steel will passivate by forming a stable magnetite surface film. The passive corrosion rate under these conditions can fall below 0.1 µm a⁻¹ (Weetjens et al., 2012).

In the Japanese disposal concept, the corrosion rate of carbon steel in a bentonite buffer is considered in a range of rock types and groundwater chemistries of varying chloride and carbonate concentrations. Based on laboratory testing, it was found that corrosion rates dropped after 1 year of exposure and remained linear for several years at rates less than 2 µm a⁻¹. Based on these observations, an anaerobic general corrosion rate of 2 mm over the 1,000-year design life can be assumed. However, due to the possibility of uneven corrosion, a 6 mm corrosion allowance is applied based on an assumed pitting factor of 3 (NUMO, 2021).

### 6.3.2.4 Localized corrosion

Classical pitting corrosion of emplaced steel canisters is only considered to be feasible in the early oxic period. The extent of inhomogeneity in the corrosion of carbon steel was evaluated from the results of long-term field burial tests (JNC, 2000). From these tests, it has been highlighted (Johnson and King, 2003) that the pitting was initially characterized by high empirical pitting factors of ~100; however, once general corrosion had reached a depth of ~0.3 mm, pitting factors reduced to ~10. Consequently, a corrosion allowance of 10 mm has been estimated for pitting in the oxic phase of the Swiss disposal concept (Johnson and King, 2003).

The presence of a passivating magnetite film introduces the risk of localized corrosion if a breakdown of the film occurs, particularly in a high pH environment, such as a hydrated cementitious buffer. The propensity for pitting was examined using electrochemical measurements for conditions relevant to the Belgian disposal concept (Kursten et al., 2017) and demonstrated that the pitting potential had a strong dependence on chloride concentration (between 0.01 M and 1 M), with the pitting potential shifted in the active direction at higher chloride concentrations. A similar effect was observed at elevated temperatures, where increasing the temperature from 25°C to 85°C caused a shift in the pitting potential in the active direction. In the most aggressive conditions considered (1 M chloride, 85°C), and taking account of statistical variations in the pitting potential, the lowest potential at which pitting was observed was ~+200 mV vs. the corrosion potential.

In the Japanese concept, pitting corrosion during the long-term anoxic phase is excluded due to the combination of near-neutral bentonite pore water pH, a carbonate concentration of less than 0.5 mol/L, and the absence of strong oxidizing species. However, the non-uniformity of general corrosion is treated with a pitting factor of 3, which considerably increases the level of conservitism in the design. Moreover, treatment of the expected pitting corrosion during the oxic phase by use of a combined mass balance and extreme-value statistical analysis approach is also conservative, leading to an allowance of up to 12 mm (NUMO, 2021).

### 6.3.2.5 Radiation-assisted corrosion

As with the corrosion of copper, radiolysis can lead to the formation of oxidants such as nitric acid during the unsaturated phase and H₂O₂ during the saturated phase, which can lead to an acceleration of the corrosion rate during the period in which the waste form is still sufficiently radioactive. However, because the corrosion rate of carbon steel is greater than that of copper in repository conditions due to the spontaneous corrosion of steel in
<table><caption>TABLE 4 Comparison of approaches currently taken to account for various types of corrosion in performance assessments for iron-based canisters by international waste management organizations (blank cells reflect an absence of information within the public domain).</caption><thead><tr><th>Mode of corrosion</th><th>France</th><th>Belgium</th><th>Switzerland</th><th>Japan</th><th>United Kingdom</th><th>Czechia</th></tr></thead><tbody><tr><td>Anaerobic general corrosion</td><td>Empirical corrosion rate</td><td></td><td>Empirical corrosion rate and pitting factor</td><td></td><td>Empirical corrosion rate</td><td></td></tr><tr><td>Radiolysis-induced corrosion</td><td>Limit dose rate to 10 Gy h<sup>-1</sup></td><td>No effect for dose rate of 25 Gy h<sup>-1</sup></td><td>Design requirement (&lt;1 Gy h<sup>-1</sup>)</td><td>Limit dose rate to 3 Gy h<sup>-1</sup></td><td></td><td></td></tr><tr><td>Localized corrosion</td><td></td><td>Reasoned argument based on passivity of surface film</td><td>Depth-dependent pitting factor</td><td>Mass balance and extreme-value statistical analysis</td><td></td><td></td></tr><tr><td>SCC</td><td>Specify resistant material</td><td></td><td>Exclude by reasoned argument</td><td></td><td></td><td></td></tr><tr><td>MIC</td><td></td><td></td><td></td><td>Corrosion allowance based on mass transport</td><td>Excluded by reasoned argument—negligible rate</td><td></td></tr></tbody></table>

anoxic porewater, the additional oxidation of steel by radiolysis products is small in comparison to the general corrosion loss by water oxidation.

In a series of year-long corrosion tests, Andra investigated the influence of gamma irradiation on the corrosion rate of carbon steel in humid air to simulate conditions arising in the unsaturated phase of a repository. Compared to unirradiated conditions, a gamma dose rate of 80 Gy h⁻¹ was found to increase the corrosion rate, whereas no effect was observed for dose rates of 20 Gy h⁻¹; hence, no influence of radiation is expected at the overpack surface, as the design limits the external surface dose rate to less than 10 Gy h⁻¹ (Crusset et al., 2017).

Gutierrez et al. (2018) consider the influence of radiolysis on corrosion of steel canisters for HLW and SNF to be negligible in the saturated phase, owing to the thickness of the canister walls (14 cm), which provides sufficient radiation shielding to attenuate the initial surface gamma dose to ~0.2 Gy h⁻¹, which is significantly below the critical value expected to increase corrosion (Marsh and Taylor, 1988). Corrosion testing in support of the Czech concept considers surface dose rates approximately ten times greater, at approximately 0.3 Gy h⁻¹ (Pospiskova et al., 2017), but these are still assumed to be too low to significantly accelerate the corrosion process. Similarly, acceleration of corrosion by gamma radiation is eliminated in the Japanese concept by the use of an 80 mm shielding allowance, which is expected to attenuate the surface dose rate to significantly below the threshold of ~3 Gy h⁻¹, which is considered to influence corrosion under relevant conditions (NUMO, 2021). Under conditions relevant to the Belgian Supercontainer concept (i.e., young cement water containing thiosulfate, sulfide, and chloride at 25°C and 80°C), dose rates of up to 25 Gy h⁻¹ had no significant effect on the anaerobic corrosion rate of carbon steel, with rates as low as 0.03 µm a⁻¹ measured by hydrogen gas evolution (Kursten et al., 2017).

### 6.3.2.6 Microbiologically influenced corrosion

As with copper-bentonite systems, the high bentonite density is expected to reduce microbial activity to the extent where sulfate reduction is negligible. Equally, the high pH of the porewater within a cementitious buffer is also expected to restrict microbiological activity to negligibly low levels such that sulfate reduction is only considered in the far-field (Nagra, 2002; Kursten et al., 2017; NUMO, 2021). Consequently, for an intact buffer, the influence of MIC is only attributable to sulfate reduction in the far-field, leading to a sulfate flux through the buffer to the canister surface. This process is the same as that for a copper-based system because the flux is determined largely by the microbial activity and the properties of the buffer material (e.g., pH, thickness, etc.).

Because the anaerobic corrosion rate of carbon steel is greater than that of copper in repository conditions, steel corrosion losses due to a sulfide flux tend to be less significant than general anaerobic corrosion arising from water reduction. As an example, in an Opalinus clay environment, Nagra (2002) considers the extent of corrosion that could occur due to a sulfide flux to the container surface due to microbiological sulfate reduction from outside the buffer to lead to ~0.02 mm of corrosion loss over a period of 10³ years, whereas, the
estimated anaerobic corrosion rate due to water reduction over
this period is 1 mm (Johnson and King, 2003).

### 6.3.2.7 Environmental-assisted cracking

SCC at a weld has been evaluated and deemed unlikely based on
a range of reported studies (JNC, 2000). Nagra (2002) also considers
SCC of welded steel containers to be unlikely owing to the
anticipated pH of the bentonite porewater (~7.3), which is
outside the range at which SCC of steel in $HCO_3^-$/$CO_3^{2-}$ occurs
(i.e., approximately pH 10–11 or approximately pH 6) (Johnson and
King, 2003). Furthermore, if a crack were able to initiate, its growth
is expected to be stifled in a repository environment, owing to the
absence of cyclic loading (Nagra, 2002).

Cracking of carbon steel by SCC and hydrogen embrittlement is excluded by reasoned argument in the Japanese concept. This is achieved by considering the chemical environment, the material properties (e.g., strength of steel), and the expected stress levels. In particular, the use of heat treatments, both on the bulk material and for welds, is expected to largely eliminate tensile residual stresses or reduce them to levels where they are insignificant from an environmental-assisted cracking perspective (NUMO, 2021).

The susceptibility of both plain and welded carbon steel to SCC in high pH (13.6) porewater was investigated for conditions relevant to the Belgian Supercontainer concept. Slow strain rate testing was performed at 140°C in the presence of sulfide concentrations up to 15.6 mM. During testing, the fracture properties of plain carbon steel in the test solution were comparable to that in argon, indicating no susceptibility to SCC. In comparison, welded specimens exhibited a slight reduction in ductility but not to the extent that would constitute a susceptibility to SCC, and this was supported by fractographic analysis of the fracture surfaces, which exhibited ductile fracture features. Hence, it was concluded that carbon steel is immune to SCC in the conditions tested (Kursten et al., 2017).

The risk of hydrogen embrittlement of carbon steel containers was reviewed in the context of the Swiss concept by Turnbull (2009). This assessment concluded that the risk of hydrogen embrittlement and cracking of the carbon steel canisters was minimal.

### 6.3.2.8 Weld corrosion

In the Japanese concept, the risk of weld corrosion is accounted for by allowing an additional 3 mm corrosion allowance for welded regions to account for the possibility of undetected welding defects of up to 3 mm in depth. Preferential weld corrosion is also considered and is mitigated by the use of Ni doping of the weld material.

### 6.3.2.9 Prediction of canister lifetimes and implications for PA

Steel canisters are designed with conservative lifetimes of 1,000 to 10,000 years, which is considerably shorter than that of copper canisters owing to continuous corrosion during anoxic conditions of the order of <0.1 µm a⁻¹ for cementitious alkaline conditions or 1–2 µm a⁻¹ for carbon steel in bentonite (Nagra, 2002; Kursten et al., 2017; NUMO, 2021). However, due to the level of conservativism adopted, it is expected that actual canister lifetimes will far exceed the design life. For example, in the Japanese concept, the overpack is expected to last in excess of 17,000 years, which is far beyond the design life.

Table 4 summarizes the approaches taken for dealing with the corrosion of iron-based canisters in PAs by various WMOs, according to the various possible corrosion mechanisms for steel.

## 7 Summary and conclusion

ConCorD (Container Corrosion under disposal Conditions) is one of the work packages of the European Joint Programme on Radioactive Waste Management (EURAD). Its main aims are:

* to assess the corrosion mechanisms of traditional container materials (i.e., carbon steel and copper) in complex disposal scenarios where the corroding environment is under the influence of irradiation, temporal changes of the near-field environment, or microbial activity,

* to assess the potential of novel materials for optimization of the container performance, and

* to integrate experimental evidence on container degradation into the prediction of container corrosion and lifetime assessment.

The state of the art on these research targets has been summarized as a basis for the development of the ConCorD research activities.

External γ-radiation fields for HLW/SF containers are modest, with a maximum of a few Gy/h or lower, although the total accumulated dose over the lifetime of the container can be several MGy. Past work on the effects of radiation-induced corrosion indicates that the maximum additional wall loss due to radiation is of the order of a few tens of µm, although it is unclear whether predictions of the corrosion allowance should be based on the dose rate or the total dose. Furthermore, relatively few studies of the effects of radiation in representative systems, including the presence of compacted buffer material and of unsaturated (atmospheric) conditions, have been conducted.

For the first few thousand years following emplacement, the container will be exposed to an evolving near-field environment. In addition to the time-dependent decay of the external radiation field, the container will also be subject to a thermal transient, the evolution of redox conditions as the initially trapped atmospheric $O_2$ is consumed, and a saturation transient that affects both the availability of $H_2O$ to support corrosion as well as the external load applied to the container. In turn, the buffer porewater composition and the extent of microbial activity will also change over time. Although the effects of some of these time-dependent environmental conditions have been studied, the work in ConCorD seeks to examine the combined effects of the early transient behavior.

Near-field microbial activity can produce metabolic by-products, such as sulfide, that can lead to corrosion of the container. Although it has been known for some time that microbial activity is suppressed in compacted bentonite buffer material, the underlying physiological cause is uncertain. The activity of anaerobes, such as SRB, may also be suppressed by the presence of residual oxygen “trapped” in the bentonite. Irradiation may affect the viability and survivability of various microbial species.

Of the various candidate container materials, most attention has been paid to the performance of copper and steel. However, there is a
wide range of other materials, both metallic and non-metallic, that exhibit certain advantages and disadvantages as container materials. Ceramics have been considered in several international programs, and work within ConCorD will seek to resolve the long-standing issue of how to join such materials at sufficiently low temperatures that the waste inside the container is not thermally damaged. Coatings, both ceramic and metallic, may offer a cost-effective solution as a corrosion barrier. With the exception of copper coatings, however, the development of coated container solutions is relatively immature. The optimization of existing container designs is also an area of ongoing study, such as the investigation of commercial grades of phosphorus-containing copper as an alternative to the custom grade currently specified for the KBS-3 container.

The outcomes of research in the different areas discussed above and in other areas are ultimately incorporated into the safety case and, specifically, used to support container lifetime predictions. Such information may be used directly in the development and validation of predictive models, either process models focused on specific corrosion processes or performance assessment models aimed at predicting container performance under repository conditions. A range of process and performance assessment models have been developed for both copper and carbon steel containers. Alternatively, the research outcomes may be used more generally as part of the safety case documentation to demonstrate a sound mechanistic understanding of the corrosion processes to which the container will and will not be subject. An important component of the ConCorD project is the implementation of the results of the different experimental activities to improve the overall modeling and lifetime prediction of HLW/SF containers.

## Author contributions

AM: writing-original draft, writing-review and editing. AA: writing-original draft. UA: writing-original draft. AF: writing-original draft. RB-L: writing-original draft. AC: writing-original draft. RG: writing-original draft. JH: writing-original draft. NS: writing-original draft. CP: writing-original draft. KM: writing-original draft. VM: writing-original draft. AI: writing-original draft. AP: writing-original draft. OR: writing-original draft. NF: writing-original draft. AS: writing-original draft. FK: writing-original draft.

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## Funding

The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.

## Acknowledgments

euroad
European Joint Programme
on Radioactive Waste Management

## Conflict of interest

Authors JH, NS, and CP are employed by Jacobs. AI, AP, and OR are employed by Amphos 21. FK is employed by Integrity Corrosion Consulting Ltd.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The handling editor BG declared a shared affiliation with the author AA at the time of review.

The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.

## Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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