Humanity's uranium-238 inventory: A significant and enduring gamma-radiation liability

The radiological hazard model

Figure 1 presents a detailed illustration of the U-238 decay chain. This visualization is traditional for its inclusion of beta and alpha radiation 1 , yet it is a rarity for its inclusion of gamma radiation. The foundation for Fig. 1 stems from a largely forgotten 1980 report that acknowledged the importance of gamma emissions from the U-238 decay chain in understanding radiological hazards of mill tailings, but then focused on off-site short-term risks [8]. The omission of gamma radiation in traditional charts obscures the full radiological risk posed by U-238's decay products. By revisiting and elaborating on this critical but neglected insight, Fig. 1 reframes the U-238 decay chain as a comprehensive radiological hazard model.

Fig. 1.

Central to the issue is the concept of secular equilibrium, a state whereby the activity (rate of decay) of all the decay products matches the activity of the parent radionuclide. This state occurs after a certain amount of time, when a long-lived parent-radionuclide decays into a series of much shorter-lived progeny. The U-238 chain (Fig. 1) consists of 15 members, each with significantly shorter half-lives than U-238. All members of the chain are either alpha or beta emitters. A few of them are also gamma emitters. At secular equilibrium, each curie of U-238 will comprise seven curies of alpha radiation, six curies of beta-, and four curies of gamma-radiation.

Table 1 reports the intensity-weighted energies of the four most significant gamma-emissions. At full secular equilibrium, Bi-214 contributes to nearly 78%, followed by Pb-214 at 20.5%, and Pa-234m at a distant third with 0.91%. Given the extremely short half-life of Pa-234m, equilibrium with U-238 can be considered immediate within the timescales of this study.

Figure 2 plots the approach to secular equilibrium based both on the U-234/U-238 and Th-230/U-238 activity ratios. The two paths join at 600 000 years and then progress in step toward secular equilibrium with their common U-238 ancestor. Achieving full equilibrium requires up to 2 million years. Interim stages of partial equilibrium include 5% (Th-230) or 13% (U-234) at 50 000 years, and 15% (Th-230) or 25% (U-234) at 100 000 years. In turn, calculations show that Th-230 will be quickly in equilibrium with Ra-226, Pb-214, and Bi-214. The Th-230 path is then the privileged path for calculating gamma doses progression.

Fig. 2.

The activity ratio equation used in this study, including for Fig. 2, is obtained in Appendix A and it is based on standard formulations derived from the Bateman equations. However, its application to long-term gamma-hazard modeling of U-238 decay products, particularly in the context of secular equilibrium and dose progression, represents a novel integration into radiological risk assessment frameworks.

U-238 inventory and hazard analysis

The study uses literature data of Humanity's U-238 inventory to recalibrate the full inventory to the year 2022 (Appendix B). The recalibrated figures resolve inconsistencies in the international datasets and provide the foundation for dose progression modeling and hazard assessment across all timescales.

Dose modeling focuses on the approach to secular equilibrium via the Th-230/U-238 path, as calculations show that this route provides a practical and sufficient basis for assessing the gamma radiation hazards of the U-238 decay chain.

To provide a meaningful context for risk assessment, the study uses, as a reference point, the ICRP-recommended public dose-limit of 1 mSv/y from all controlled sources. 1-mSv/y is also the International Commission on Radiological Protection's (ICRP) threshold reference-level for intervention in the case of existing exposure situations [9]. Accordingly, all dose calculations are expressed in units of mSv/y. As detailed in the following section, gamma emissions from the various stocks that constitute Humanity's U-238 inventory will surpass this radiological exposure threshold long before full secular equilibrium is achieved.

Terminology

To capture the unique characteristics and hazards associated with different U-238 stocks, we subdivide the U-238 inventory into three categories: conditioned, tailings, and total-mined. Total-mined is a synonym of Humanity's U-238 inventory.

• – Conditioned U-238 refers to the portion of U-238 that was recovered from the original ore. It exists in retrievable and potentially usable forms, such as low-enriched uranium (LEU), SF, reprocessed uranium (RU), and DU. These materials are stored in various containment structures. Conditioned U-238 amounts to roughly 80.6% of the total-mined U-238 (Appendix B).

• – Tailings U-238 is the U-238 that could not be recovered from the original ore and is now in the mill-tailings. It amounts to roughly 19.4% of the total-mined U-238 (Appendix B).

• – Total-mined U-238 is the sum of conditioned and tailings U-238. It represents the U-238 inventory that has been extracted, processed, recovered, or left behind by human activity. This category captures the combined gamma-radiation liability of all U-238 stocks associated with the nuclear fuel cycle, whether in storage, designated for potential use, or else left in the mill tailings. It is Humanity's U-238 inventory, a term that frames the issue of U-238 management over time as a shared, global responsibility.

Table 2, derived in Appendix B, provides an original and, in the literature, first estimate of the amounts of Humanity's U-238 inventory in each byproduct stream by the year 2022. The three largest stocks are DU (69.24%), tailings U-238 (19.4%), and SF (8.4%). We will concentrate on these for dose modeling.

There is no previous comprehensive inventory of all U-238 stocks together at the same time. Table 2 is obtained in Appendix B based on (a) reported values by the International Atomic Energy Agency (IAEA) and the Organization for Economic Cooperation and Development Nuclear Energy Agency (OECD/NEA) of the LEU and SF stocks worldwide; (b) literature-reported DU/U ratios; and (c) on recalibrating mill-tailings production-data based on the LEU, SF, and DU stocks upon assuming, for the original ore, a world-average value of 0.15 wt% uranium. The data in Table 2 are internally consistent and provide a reasonable estimate of the so-far mined U-238 distribution across its various stocks. Future updates, although they are recommended as further research, should not change this paper's results and conclusions significantly.

Evaluating the gamma liabilities through dose modeling

The “frozen” inventory in Table 2 provides a baseline for understanding the gamma-radiation liability that each U-238 category represents, both separately and globally, as of the year 2022. The calculations of the gamma dose rates are rather straightforward. Namely, we start with previously known activities and/or previously known gamma-dose rates at a given time, then we apply the secular equilibrium equation or the equations for the approach to equilibrium (see Appendix A) to calculate or extrapolate the gamma dose rates at any time. The calculations are highly reliable as they involve only exponential functions and the basic understanding of a decay chain.

The gamma hazard of conditioned U-238

Conditioned U-238 refers to U-238 that was separated from its decay products during the milling process. As a result, all stocks of conditioned U-238 begin from zero in their progression toward secular equilibrium. To manage the intensifying gamma emissions (Fig. 2) over time, each conditioned U-238 stock-type will require increasingly robust containment measures, such as thicker shielding or deeper storage. This holds true also for SF, whose composition 2 is 95% U-238 [7].

For a more specific, quantitative estimation of the strength and progression of the gamma dose from conditioned U-238 over time, consider a sample ²³⁸UO₂-cylinder of 40-cm height and 10-cm diameter. Its surface gamma-dose-rate at 1 million years is known from analyses of industry-provided values [10] and it is approximately 0.82 mSv/h or 7183 mSv/y. This value is 7183 times the ICRP recommended 1-mSv/y yearly-dose-limit.

The value of the gamma dose-rate at 1 million years serves as a basis for recalculating its evolution over time along the Th-230/U-238 equilibrium path (Fig. 2) accounting, as well, for the immediate secular equilibrium between U-238 and Pa-234m. Figure 3 plots the progression of the gamma dose rate between 100 years and 3 million years. The dose rate starts from the baseline, a constant value of 70 mSv/y (0.008 mSv/h) representing the Pa-234m contribution of 0.91% of the full-equilibrium dose rate (see Table 1). It increases slowly over the first 5000 years, or so, then it accelerates to reach 7580 mSv/y by 2 million years, firmly in the deterministic health effects region. Namely, the dose rate increases over 100-fold over 2 million years. Afterwards, it remains at these high levels essentially indefinitely.

Fig. 3.

If the sample was DU conditioned as UO₂ the dose rate would be larger and earlier, because DU includes excess 3 U-234. If DU was conditioned as U₃O₈, which is another oxide form foreseen for the de-conversion and conditioning of DU, the dose rate will not change significantly. Excess U-234 would still be present, and while the U₃O₈ matrix is of a lower density than UO₂, by the same token, it is also less self-shielding. Also, U₃O₈ conditioning would require more containers.

If the reference ²³⁸UO₂-cylinder was broken into a combination of smaller fragments, the total gamma hazard would be larger still, for, while the volumetric density of ²³⁸UO₂ stays the same, smaller fragments are much less self-shielding than larger blocks [10].

A simple calculation reveals the magnitude of the latent gamma-radiation hazard of conditioned U-238. Namely, our reference ²³⁸UO₂ sample weighs 34.5 kg. The total stock of conditioned U-238 weighs 3.6 million tons. The DU, alone, corresponds to 90 million such ²³⁸UO₂ samples. The 400 000 metric tons of RU + SF U-238 correspond to 11.6 million samples. Overall, conditioned U-238 constitutes a major, future gamma-radiation liability that needs preparing for.

The gamma hazard of mill tailings

Complementary to conditioned U-238, the tailings U-238 represents the U-238 fraction that was not recovered during the milling process. Tailings U-238 is in secular equilibrium with its progeny. Meanwhile, the progeny of conditioned U-238, separated from its parent radionuclide during milling, forms a new decay-chain headed by Th-230. This orphaned Th-230 chain (Fig. 1) mirrors the original U-238 chain, sharing the same progeny isotopes. However, it will fade over 700 000 years due to the 75 380-year half-life of Th-230. As a result, the current gamma emissions from mill tailings closely resemble those of total-mined U-238 before milling.

As reported in Appendix C, measurements show that gamma dose-rates near uncovered uranium tailings range from around 7 μSv/h to peaks of 20 μSv/h, with an average dose rate of 10 μSv/h (88 mSv/y). As one cannot assume that currently stabilized piles will stay stable over centuries to thousands of years or longer, this average dose rate is significant. Annual exposure at this dose rate is as follows:

• – Approximately 30 times the average, annual background radiation of 3 mSv from all natural sources globally [16];

• – Almost 90 times the ICRP's public dose-limit of 1 mSv/y from all controlled sources [9].

Given its relationship to the conditioned U-238 chain, the decay of the orphaned Th-230 chain, representing 80.6% of the total dose-rate, will lead to a gradual reduction in gamma emissions (Fig. 4), stabilizing the gamma field of mill tailings by approximately 700 000 years. At that point, the dose rate will derive solely from the tailings U-238, settling at approximately 19.4% its present value. Namely, 17.5 mSv/y for uncovered mill tailings – about 17 times the ICRP yearly, public dose limit – highlighting the persistent hazard posed by mill tailings, especially as stabilization measures degrade or if these sites are repopulated or repurposed for human activity (see next section).

Fig. 4.

The instructive case of long-lived nuclear waste

Vitrified high-level waste (VHLW), produced from immobilizing SF-reprocessing waste in a glass matrix, may contain relatively important concentrations of U-238. The French VHLW program is slated to create over 50 000 standard-size containers of HLW, each container incorporating 2 kg or more of U-238, for a combined, total amount of at least 100 metric tons. It turns out that the gamma dose from VHLW is dominated by the radionuclides in the Np-237 chain until 20–25 million years. Afterwards, as Np-237 decays further, the gamma emitters of the U-238 chain take over, notably, its Bi-214 and Pb-214 emitters. As a result, all French VHLW will not be fit for handling or proximity. Relatively small fragments of VHLW, or a combination of these fragments, may also pose a gamma radiation hazard [10].

The French VHLW case is instructive in that it shows that even a small amount of U-238 – of the order of 100 metric tons spread over 50 000 containers – can constitute an indefinite gamma hazard if the U-238 is sufficiently concentrated.

In this light, it seems prudent to examine the U-238 content of long-lived low- and medium-level waste, especially from such activities as MOX fuel fabrication, as well as in anticipation of potential, repeated reprocessing of uranium fuels in nuclear-fuel-cycles currently under study. Accumulation of U-238 from these wastes in near-surface repositories may result, over time, in direct gamma exposures.

DU contamination from military uses

The use of DU munitions in military conflicts has resulted in U-238 contamination across regions such as Iraq, the Balkans, and Afghanistan. U-238 contamination affects vast areas, spanning tens of thousands of square kilometers [19,20,21,22]. As an example, studies conducted in 2002 in Afghanistan's Jalalabad province revealed uranium concentrations of up to 200 times higher than control populations. Soil samples from bombsites demonstrated uranium levels two to three times above global concentration norms (2–3 mg/kg) as well as water concentrations exceeding World Health Organization (WHO) permissible levels [23]. Given the evidence of man-made U-238 contamination, any other risk will be compounded, in the future, by the gamma-radiation emitted by the U-238 decay chain as it progresses toward secular equilibrium. It is an issue that warrants recognition and comprehensive assessment.

Nuclear weapons testing sites

Atmospheric nuclear weapons tests, conducted throughout the mid-20th century, have contaminated vast regions. Notably, the Nevada Test Site in the United States, which is approximately 3500 km² and one of the largest restricted-access areas in the United States. The Semipalatinsk Test Site, in Kazakhstan, covering 18 500 km² was the primary site for Soviet nuclear weapons tests. Concerning weapons sites, …radioactive residue in some environments may be considerable (para. 33 in Ref. [3]). Besides, on these sites, there likely exist disposal sites of classified materials also containing U-238, such as the Greater Confinement Facility at the Nevada Test Site [24].

Monitoring and remediation efforts for sites contaminated by weapons testing tend to focus on the immediate threats posed by plutonium isotopes and certain fission products [25, 26]. This emphasis is justified due to the high radiotoxicity of plutonium isotopes and their role as tracers for anthropogenic nuclear activities. On the other hand, the presence of these isotopes is also a signature of weapons U-238. Current monitoring efforts eschew the contamination of weapons U-238 and may miss on the future, gradual, and persistent emergence of the gamma hazards from U-238's decay chain.

Contamination around mining and milling sites

For many reasons, enumerated and discussed in Ref. [27], people in uranium mining districts may be exposed to radiation doses from mining, milling, transport of radioactive materials, radioactive dust and contaminated water and foodstuffs. Perhaps the most direct implication of mining and milling residues as a radiation source sufficient to cause human health impacts relates to their reuse for building materials. This has happened in many places around the world: The long half-lives of radionuclides from uranium tailings and the demonstrated risks associated with them have given rise to high levels of concern among the general public and in government – in some places exacerbated by official secrecy and lack of data on health impacts [27]. In spite of the mention of the “long half-lives”, the potential long-term gamma-hazard from the full U-238 chain does not seem to be recognized in the literature.

Containment challenges and management priorities

The analysis of Humanity's U-238 inventory underscores the scale and diversity of its gamma liabilities spanning both short- and long-term timescales. Yet, U-238 stocks are primarily managed with a focus on mitigating contemporary risks. Current containment systems, such as dry cask storage for SF and steel cylinders for DU, are designed with operational lifespans of only 100–300 years [28, 29]. During this period, monitoring and maintenance are necessary [30]. Beyond this period, structural degradation due to corrosion, seismic activity, or climate change threatens their integrity, requiring ongoing maintenance, refurbishment, or replacement. Even millennia of containment efforts would be insufficient, given the longevity of U-238's hazards and the complex protection issues it raises. Furthermore, relying on perpetual human intervention is impractical, given the near certainty of societal discontinuities, including technological regression, resource scarcity, or loss of institutional memory.

Addressing the gamma hazards of U-238's decay chain requires a paradigm shift in how this radionuclide is managed. Key priorities for action include the following:

• – Conduct a comprehensive inventory of U-238 stocks. A transparent and comprehensive inventory of all dispersed and non-dispersed U-238, including within low- and intermediate-level radioactive waste, is essential for effective long-term planning. This inventory would provide a baseline for targeted containment strategies and hazard assessments and should be updated regularly.

• – Integrate gamma radiation into hazard assessments extending beyond immediate concerns. Gamma risks over all timescales must be explicitly incorporated into radiological risk frameworks, including those for emerging nuclear-fuel cycles and legacy waste management. Conventional assessments focusing on alpha radiation and chemical toxicity and focusing on only immediate concerns are insufficient and fail to capture the full scope of U-238's hazards.

• – Develop advanced containment materials research. Self-healing concretes, radiation-shielding polymers, and multilayer barriers could play a useful role mitigating gamma risks for at least over hundreds of years. For DU, the deconversion of DUF⁶ into a chemically stable form like U₃O₈ should be prioritized to reduce chemical and radiological vulnerabilities.

• – Reclassify DU and mill tailings for long-term management. Regulatory frameworks should recognize DU and tailings U-238 as radiological liabilities requiring correspondingly robust management strategies over the long-term. A similar suggestion was made by President Carter's Interagency Review Group in 1979 (pp. 80–81 in Ref. [31]). Current classifications fail to account for their significant gamma risks, leaving them inadequately managed for the future 4

• – Establish mechanisms for intergenerational knowledge transfer. Ensuring that future generations are informed of the persistent hazards of U-238 is vital. Mechanisms such as durable records, institutional knowledge preservation, and public awareness campaigns must be established to maintain continuity in U-238 management efforts. The adoption of an ethical chart [32] to that effect would be a useful start. A methodology is presented in Ref. [33].

• – Promote equitable responsibility. Decision-making should be driven by principles of intergenerational equity. Collaborative efforts, both national and international, should identify the financial and technical burdens of U-238 management. Application of the “Polluter Pays Principle” should ensure that the financial liabilities are shared equitably. Without this, the burden will fall on future generations disproportionately.