This sounds almost like Patrick Tilley's Fade-Out (1975), though some of the details are not quite right.
In Fade-Out, an alien ship (the U.S. only observes one, anyway) temporarily wipes out all shortwave radio broadcasts and radars when it enters Earth orbit. After orbiting for a couple of days, visible to radar but completely black in optical wavelengths, it lands in Crow Ridge, Montana (we discover later at least one more ship has landed in Kazakhstan as well) and buries itself in the ground.
Locals find a 1.1km (0.69mi) radius zone where electrical devices are knocked out by current surges from an extremely strong alternating magnetic field. The ship moves underground, then surfaces a spherical section. Periodically the zone of electrical disruption expands by a factor of ten: next 11km, then 110km...
By examining disruptions to the Earth's magnetic field they determine there are 6 of these locations that are reshaping the Earth's magnetic field, although 4 of them are in the ocean.
The alien craft ("Crusoe") changes into the shape of a 60-foot tall (smooth) black pyramid and continues to grow by throwing out blocks horizontally in the cardinal directions; these blocks are described as having steps, though.
The zone of effect expands to cover the entire world, and humanity is faced with trying to retain civilization without the benefit of electricity or anything electrical.