This is a great question!

From reading the NRC submission, the support structure for the modules is Seismic Category 1 (rated for design basis earthquake). This includes the entire Reactor Building, its foundation, and requirements for the site on which it is built. The reactor building is also designed to withstand an impact from a large commercial aircraft. Note that conjecture that the modules are top-heavy appears to be unfounded given the configuration described in the NRC submission.

Elsewhere in the probabilistic risk assessment, they address a module tipping over if it is dropped in the operating area-- the most probable scenario for a horizontal module.

In the case where the drop causes the containment to be breached and does not permit inflow of water from the pool (ostensibly due to pressure difference) the result is core damage and a release of radioactive contamination to the pool.

I encourage interested readers to look at Chapter 19 of the NRC submission. Much of the document is at a level where a lay engineer can understand it. NB: I am not affiliated with NuScale or the NRC.

Safety on the ground is one thing, the other is whether this sort of design might be used in less-than-earth gravity. We need passive/fail-safe reactors for space and this thing looks like it could fit inside a rocket.

One module weighs 762 tons, which is more than 10X the capacity of Falcon Heavy.

Anything that knocks a fully functional multiple thousands of tonnes of concrete, steel, water and fissile material onto it's side was already going to fuck up your day.

As far as I'm aware we've never had a nuclear reactor go sideways, and it's kinda ludicrous to even ask. It's one of the most massive structures, built on bedrock because it's too heavy to be built on anything else, and even these "small" reactors will be incredibly heavy.

They are vertical cylinders to be suspended vertically in a pool of water, not massive squat objects sitting on bedrock. They are thin and relatively top-heavy. It is not ludicrous to ask what could happen should they not remain as vertical as designed.

From a planning perspective, if verticality is a requirement then that verticality has to be protected as strongly as any other aspect. Any attachment or mounting points that maintain verticality must therefore be earthquake proof. If, as in the pictures, these reactors are held in place from the top, horizontal shaking from even a small earthquake would put massive strain on that joint. It isn't just the long/thin/heavy reactor but all the water sloshing around too. A super-strong joint and maybe something important bends/breaks under load? A flexible joint to allow the reactor to sway? Sway how much? What happens at the travel limit of the joint? Can we risk the reactor contracting its neighbours? These are not trivial engineering questions.

I think they are not trivial but relatively easy parts of the design. I’m sure they can design support structure to withstand whatever arbitrarily large earthquake you throw at it. The structure doesn’t need to be particularly light or compact so there shouldn’t be any design constraints getting in the way of strength. The heat transfer problem is much much harder and they’ve already solved that apparently.

I;m not saying it is impossible, just interesting. One option could be to suspend these reactors on cables from above. That might let them swing around all they want during even a huge quake. The water would act as the dampener. Not much extra engineering required.

I was assuming they'd bury these.

As other Nuke submariners in this thread can attest, there are definitely PWRs designed to tolerate massive rolls and “angles and dangles.” I guess it depends on your definition of sideways.