SSiC Nuclear Waste Canisters: Stability Considerations During Static and Dynamic Impact

Introduction

High-level radioactive waste (HLW) is mainly a by-product of technical nuclear reactions. It has the highest radioactivity and longest decay time (millions of years with significant radiation). Most HLW (more than 90%) comes from spent nuclear fuel. The deep geological disposal concept is considered without alternatives worldwide. This concept includes the multi-barrier concept, which contains three main elements:

• Canisters: HLW is sealed safely in special long-term safe canisters.
• Engineering barrier: Canisters are embedded into an engineered sealing environment (e.g. bentonite) inside the host rock.
• Geological barrier: Embedded canisters are safely buried underground protected by geological layers.

This concept should work for extremely long time (> 1 Mio. years), so that any critical contact between waste and biosphere is avoided.

Two concepts for canisters exist: corrosion resistant ones and corrosion allowed ones. Corrosion resistance considers attack from water, acid, alkali, salt, radiation, bacteria etc. for a very long time (e.g. resistance > 100.000 years). Allowed corrosion means limited corrosion is accepted and safety is guaranteed only for a certain restricted time span (e.g. about 1.000 years). The central point is to choose most corrosion resistant material while meeting also other criteria. Different countries have developed different philosophies in terms of canister design. So far, the following materials for canisters and over-packs, respectively, are under consideration: stainless steel / carbon steel, nickel alloy, cast iron, pure copper or copper coating, special concretes, aluminum, SiC, ZrC, ceramic coatings.

All the above-mentioned materials and corresponding canister concepts have their pros and cons. For nearly all of them it is critical to proof extreme long lifetime. In terms of resistance and lifetime SiC and SSiC especially, show some remarkable advantages. Already Onofrei et al. [1] studied the leaching characteristics of ceramic canisters. Haslam et al. [2] evaluated corrosion resistance of ceramic coatings thermally sprayed on waste containers in simulated ground water of 90℃. Donald et al. [3] estimated the lifetime of SiC and ZrC coatings for nuclear fuel in TRISO and TRIZO concept for direct geological disposal.

Kerber and Knorr [4] proposed a new concept by SSiC (solid-state pressure-less sintered silicon carbide) encapsulation of HLW. This concept has drawn attention due to the excellent corrosion resistance, low permeability and high mechanical strength of SSiC (see Tab. 1).

Tab. 1: Parameter of SSiC

On the other side, SSiC is a brittle material. Therefore, it is necessary to consider the stability and potential fracturing of SSiC canisters under static and dynamic loading scenarios. This paper considers this problem via numerical simulations concentrating on tensile failure (mode-I crack propagation in terms of fracture mechanics). Unprotected and protected (coated, covered) canisters are investigated. It is not the aim of this study to deliver comprehensive simulations for final canister design, but to provide the order of magnitude of potentially induced impact stresses for different loading scenarios and to document, that proper cover (coating) of SSiC canisters can avoid any kind of mechanical damage during transport, installation and final storage.

Lab testing and numerical calibration of SSiC

Special lab tests like illustrated in Fig. 1 were conducted to determine the tensile strength of the SSiC. This type of test was chosen due to the following reasons: (a) the extremely high strength of the material would make classical tensile tests complicated and (2) this type of tests duplicates very well the real canister situation as hollow cylinder. The tested cylinders are 5 cm in length and have outer and inner radius of 2.5 cm and 2.0 cm, respectively. The small hollow SSiC cylinders were compressed between 2 loading platens until tensile failure initiated at the inner cylinder wall leads to brittle failure. In total five lab tests were conducted, results are presented in Fig. 1. For a hollow cylinder under compressive line loading the following analytical solution developed by Timoshenko exist for the failure load:  

                                                                                                                                                                                                                                                                                                                       (1)

where:

ρ – ratio of inner to outer radius of cylinder

R – outer radius of cylinder

P – tensile failure load

σ_θ – tensile strength

θ – angle.

After conducting the lab tests, equivalent numerical simulations were performed (see Fig. 1). A modified elasto-plastic Mohr-Coulomb failure criterion with tension-cut-off and strain-softening was applied. To duplicate the extreme brittle behavior, after reaching the tensile strength, softening starts immediately and tensile strength is set to zero. The cohesion was deduced from a test with similar material (SiC-N) and set to 4 GPa [5]. Tab. 2 shows the used model parameters. The distinct element code 3DEC [6] was used for the simulations.

Tab. 2 Numerical model parameters for SSiC

According to Fig. 1, the tensile strength of SSiC is somewhere between 150 MPa and 200 MPa. For safety reasons, the tensile strength of SSiC is set to 150 MPa in all further calculations. According to Eq. (1) the failure line load P is determined by tensile strength σ_θ, outer radius R, as well as radius ratio ρ (ρ = r/R). Fig. 2 compares numerical and analytical results for failure load P for different radius ratios and proves that numerical simulations deliver reliable results.

Simulation strategy to consider static and dynamic loading

Different loading scenarios are considered under conservative assumptions. Dynamic loading (impact) is considered for scenarios during transport and installation of the canisters. Static loading via in-situ rock stresses is considered after final placement of the canister. Dynamic loading scenarios comprise two cases: (a) free fall of a canister and (b) rockfall from the roof on the canister. In both cases the considered maximum drop height is 2 m. In case of static loading the maximum disposal depth is 1200 meters below surface with different anisotropic stress ratios (minimum to maximum principal stresses) up to 1:3. SSiC canister and foundation are modelled as elastic material. The falling rock blocks are simulated either as elastic material or as assembly of distinct blocks with calibrated elasto-plastic parameters, which allows to consider the rock disintegration during the impact. Damping was not applied for the dynamic simulations because data are not available, but viscous boundary conditions were applied to avoid unrealistic reflections at the lower bottom of the ground. This makes the simulations once again conservative. The interface stiffnesses at the contact between the colliding parts (e.g. between canister and rock block or ground) are adjusted in such a way, that impact induced stresses reach maximum values (corresponding lab data are not available). So far not explicitly otherwise mentioned the model parameters given in Tab. 3 are applied.  

Tab. 3 Matrix and interface contact parameters

Four different canister types are considered as given by Fig. 3 (left) and Tab. 4. The considered waste canisters are hollow cylinders sealed at one, respectively the two ends using the technique of Rapid Sinter Bonding (RSB) as proposed by Knorr and Kerber [7].

Tab. 4: Dimensions of canisters (see also Fig. 3)

Static loading scenarios

This loading case considers anisotropic earth pressure on completely in a rock mass embedded VW and HTR canisters (Fig. 3 (middle)). Tab. 5 lists all the considered earth pressure constellations in terms of principal stresses (X and Y (both horizontal) and Z (vertical): 1:1:1, 2:1:1, 3:1:1, 2:2:1, 3:2:1, 3:3:1. These constellations cover all typical stress states existing in potential host rocks. The considered maximum principal stress ratio is 3:1. The angle between canister axis and Z-axis is set to 0 °, 30 °, 60 ° and 90 °, respectively. Fig. 4 documents the maximum induced tensile stresses inside the SSiC canisters. The considered depth is 1200 m, and the vertical earth pressure will be about 30 MPa. Overall, in any case the maximum tensile stress in the unprotected canister does not exceed 50 MPa which is significantly below the tensile strength of SSiC, which is 150 MPa. Maximum tensile stress is mainly distributed around the two lids of the canister as shown in Fig. 5. The average stress in the VW canister is bigger than that in the HTR canister. The thickness of the canister is a controlling factor. For the VW canister, the thickness/height ratio is 1/56, while the thickness/height ratio for the HTR canister is 1/22.

Tab. 5 Primary stresses (see Fig. 5 and 6)

Exemplary, for the HTR canister some selected simulations with a buffer sealing (200 mm thick) were performed. As Fig. 6 documents, such a clay (bentonite) buffer can significantly reduce maximum tensile stresses.

Dynamic loading scenarios

Free fall of canister

For impact, drop height and canister positions are the controlling factors. The considered drop heights (distance from the lowest point of the canister to the foundation) are 0.5 m, 1.0 m, 1.5 m, and 2.0 m, respectively. The canister positions during impact (0°, 30°, 60°, 90°) are illustrated in Fig. 3 (right). Fig. 7 shows the maximum induced tensile stresses in the different canisters for different drop height and documents, that peak tensile stresses can very locally reach values considerably higher than the material strength. Therefore, an additional simulation was performed assuming a protective cover (layer) around the SSiC canister. Simulation of a VW canister (drop height 1 m, inclination angle 0°) with soft cover (50 mm thick) confirms significant reduction of maximum tensile stress at the inner boundary of the canister from 1118 MPa (without cover) to 147 MPa (with cover) (Fig. 8).

Free fall of rock blocks

First, preliminary pure elastic simulations using the VW canister were performed. Small rock pieces were considered with weights of 0.5, 1.0 and 2.0 kg, respectively. Drop height is 2.0 m (distance from the lowest rock piece point to the highest line of horizontally disposed canister). Simulation cases 1 to 4 generate dynamic line loads, case 5 to 7 lead to point loads (see Fig. 9 (up)). Fig. 9 (down) shows the maximum induced tensile stresses in a VW canister during impact for seven loading cases. Similar results were obtained for the other canister types. It becomes obvious from Fig. 9 (down), that (a) even small rock pieces produce tensile stresses close to the strength of the SSiC material or even larger ones and (b) point loading loads to significant higher values compared to line loading. 

Such a pure elastic consideration is too conservative, especially because the limited strength of the rock pieces is not taken into account. It has to be expected that extreme high local stresses during impact at point or line contacts lead du massive fracturing of the rock pieces, so that stresses above the rock strength will not be reached. To investigate this phenomenon the rock pieces were set-up by numerous distinct elements, so that fracturing and disintegration can take place if strength of the rock is exceeded. Calibration was performed using typical rock parameters. Fig. 10 shows results from a calibration process for claystone. Fig. 10 reveals, that vertical splitting (tensile cracking) is dominating like typically observed during uniaxial lab tests.

Exemplary, Fig. 11 illustrate the collision process for point load impact. Fig. 12 (up) shows, that the size of the distinct elements, which control the fracturing process in detail, is important to obtain reliable stress values during the impact process. The smaller the elements, the more potential fracture paths. However, it becomes also visible, that below a certain threshold the stresses will not any more decrease. Compared with the pure elastic modelling a significant reduction in induced tensile stresses by a factor of about 10 is observed. In additional model runs also larger rock pieces up to a weight of 512 kg were considered (see Fig. 12 (down)). It again becomes obvious, that distinct element resolution has significant influence on modelling results. To get reliable results for larger rock pieces at least at the contact area higher resolution is necessary. However, one has also to consider that enhanced resolution leads to a progressive nonlinear increase in simulation time.  

The effect of a soft cover was also investigated using the pure elastic approach. Tab. 6 shows simulation results in terms of maximum penetration depth and maximum induced tensile stress. It clearly shows that a soft cover can reduce tensile stresses considerably, so that even for the extreme conservative case of pure elastic interaction, the induced tensile stresses can be brought below the strength of the material, which is about 150 MPa.

Tab. 6: Maximum penetration depth and maximum induced tensile stresses inside a CANDU canister with soft cover of thickness D and Young’s modulus E during pure elastic collision with claystone rock piece (drop height 2 m, loading case 1 according to Fig. 16).

Discussion and Conclusions

SSiC has excellent properties in terms of long lifetime, high strength, low porosity and excellent resistance against radiation, high temperatures and aggressive fluids. In that respect it is superior to other materials under consideration for nuclear waste canisters. As documented, static earth pressure even in case of high anisotropy and unfavorable orientation of the canister in relation to the principal stresses will not reach the high failure strength of SSiC canisters for considered depths up to about 1200 m. However, the very stiff and brittle behavior of SSiC needs some more detailed consideration in case of dynamic impacts. Such worst case loading scenarios like rockfall or free fall of a canister can be investigated via field tests (large scale drop tests) and numerical simulations. Under pure elastic conditions and extreme loading constellations (point and line loads) as well as conservative initial and boundary conditions (stiff foundation, no damping, no protective cover etc.) the dynamically induced tensile stresses inside SSiC canisters can locally and temporarily reach – independent on canister type – maximum tensile stresses beyond the static tensile strength of SSiC. Even if we consider that dynamic strength is somewhat higher than the static one, several constellations might give rise of concern.

One should also take into account, that reaching the failure envelope in pure elastic simulations just indicate, that damage is very likely, however, nothing can be said about extent and type of damage. Therefore, a numerical simulation based safety case should follow two directions: (a) consideration of an additional cover to absorb energy during potential dynamic impact and (b) more realistic modeling (considering of energy absorption during collision, fracture propagation, damping etc.). This paper provides first hints and results how these tasks can be handled. The simulations with soft cover indicate that a cover of about 10 cm with stiffness in the order of about 100 MPa would be able to reduce the dynamically induced tensile stresses so that any failure can be avoided.

The presented dynamic simulations are only a very first step toward a comprehensive numerical safety case. The aim was to show, that the most critical issue of SSiC – the stiff and brittle behavior – can be managed. More realistic numerical simulations should consider the following aspects:

• Incorporation of realistic damping
• Replacement of the elastic models for all components by calibrated elastic-plastic models incl. damage laws
• More profound specification of load scenarios
• Consideration of dynamic material properties

In summary, the conclusion can be drawn, that SSiC is a suitable canister material if a certain soft cover is used during transport and emplacement just in case that unexpected dynamic collisions (rockfall of free fall of canister) occur.

References

[1] Onofrei, M., Raine, D.K., Brown, L. & Stanchell, F., (1985). Leaching studies of non-metallic materials for nuclear fuel immobilisation containers, Proc. Mat. Res. Soc. Symp., Materials Research Society., 44: 395-404

[2] Haslam, J.J., Farmer, J.C., Hopper, R.W., Wilfinger, K.R., (2005). Ceramic coatings for a corrosion-resistant nuclear waste container evaluated in simulated ground water at 90°C, Metallurgical and Materials Transactions., A (36): 1085-1095

[3] Donald W. M., Wen Wua., Francesco, V., (2012). Performance of PyC, SiC, ZrC coatings in the geologic repository, Nuclear Engineering and Design., 251: 102-110

[4] Kerber, A. and Knorr, J., (2013). SiC encapsulation of high-level waste for long-term immobilization, atw 58. Jg Heft 1, January: 8-13

[5] Lee, M.Y., Brannon, R.M., Bronowski, D.R., (2004). Uniaxial and triaxial compression tests of silicon carbide ceramics under quasi-static loading condition, Tech. Rep. SAND2004-6005, Sandia National Laboratory

[6] Itasca (2020): 3DEC Manuals, Itasca Consulting Group, Minneapolis, Minnesota, USA

[7] SiCeram (2018): Deutsche Patentanmeldung 10 2018 114 463.6 „Verfahren zum Verbinden von Bauteilen aus SSiC“, GmbH, Jena, Germany

Acknowledgment

The conduction of the lab experiments by Dr. Thomas Frühwirt (TU Bergakademie Freiberg) is highly acknowledged. The authors would like to express their special thanks to the China Scholarship Council (CSC) for financially supporting the first author’s PhD study in Germany.