Nuclear power and the earthquake “near Vaalputs”

A M5.3-magnitude earthquake recently struck the small town of Calvinia in South Africa. Media reports about this town—one I would love to visit someday, indicate that no one was killed, no structures were damaged, and there were no other major impacts on anyone involved.

Predictably, South Africa’s anti-nuclear group sprang into action, claiming that the radiological waste repository at Vaalputs is “at risk”. South Africa has a radiological waste repository, and the last time I did the calculations, it was large enough to accommodate waste from another 600 nuclear reactors. Although it doesn’t yet store high level waste, the government has been opening up in recent years to build a high level waste repository. Vaalputs is the ideal location, because the water table is 1km below the ground, the risk of corrosion in the desert is negligible and because it barely has seismic activity!

‍

As someone who has actually designed nuclear structures against earthquakes and who is currently working on structural amplifications of certain configurations, I find myself in a position where I must express my dismay at how the media reports on earthquakes and in particular as it relates to nuclear structures. It would only take a bit of communication effort from the nuclear industry to overcome the public ignorance.

Earthquakes, much like the climate, are far too complex to be summarized by a single number. What makes this issue even more problematic is that outdated parameters, such as the Richter scale, are often used despite not having being used by practitioners since the 1970s!

A more accurate measurement is the moment magnitude scale, but even this parameter alone is insufficient. The full earthquake hazard spectrum includes factors such as the strong phase motion, peak ground velocity, acceleration, displacement, and additional markers like the Arias Intensity and the power spectral density function.

When it comes to structures we use frequency domain tool called the Response Spectrum, that is derived using the Fourier and Laplace Transformation of the ground signal. Electrical engineers have an intuitive feel for these concepts, because the techniques that structural engineers use overlap to design for earthquakes with signal processing.

Where we differ is in how we approach these problems: structural engineers think in terms of coupled oscillating springs, while electrical engineers think in terms of resistors, but the underlying mathematics are similar. This overlap also explains why it’s not difficult for structural engineers, particularly those in the energy sector, to comment on basic electricity-related topics—and vice versa.

For those curious, I can refer my readers to the following website if they are interested in the fascinating science of geotechnical engineering, seismology and this technically heavy textbook on structural dynamics.

In simple terms, nuclear structures are designed to withstand earthquakes using Newton’s Second Law. The shear force acting on a structure is equal to its mass times the acceleration (F = m.a). A more advanced method, called modal analysis, is also used that treats the structure like an upside down spring, that is described by an expanded definition of Newton’s first law, called the harmonic oscillating equations. The key to minimizing the acceleration experienced by a structure is to ensure that its natural period does not coincide with the ground motion—a phenomenon known as resonance.

Skyscrapers avoid resonance using tuned mass dampers, while older nuclear plants, such as Koeberg, employ base isolation using seismic bearings that allow for the structure to be isolated from the ground. Modern nuclear plants like the European Pressured Water Reactor, on the other hand, are designed with a thick raft foundation and shear walls that are robust enough to absorb earthquake motion and their geometry is carefully selected to completely avoid resonance. It is the reason for example why the reactors are cylindrical.

Even if this sounds too technical, there’s another straightforward reason why Calvinia’s earthquake was unlikely to impact Vaalputs waste repository: it is called geography. We often forget just how large South Africa truly is. As the map below shows, the Northern Cape Province alone is the size of Germany and half the size of its neighbour, Namibia.

‍

The distance between small town of Calvinia and Vaalputs is 264km by Road, just 120km as the crow flies. This is the same distance as Johannesburg to Rustenburg, or for an International Audience from Santa Barbara to Los Angeles

‍