The solution here seems fairly straightforward: don't make the design completely pressure-supported, but include enough weighty structural elements like ribs and beams to make it heavy enough to be a compressive structure again. If you have a rib-like structure on the top side of your dome material, you could even just pile Mars dust and rocks on top of it to keep it in place.

sand/dust blows around into dunes and its dense enough that "close enough" won't hack it. Figure as an engineering 1 sig fig estimate (dry) sand runs around a twentieth of a pound per cubic inch, so 14.7 PSI air would be in compression with around three hundred or so inches of sand evenly spread around the top.

Its a major labor sink to build and maintain and dunes could cause a catastrophic failure. Could make an interesting sci fi novel about "emergency EVA to run bulldozer drones to spread sand to prevent dome collapse".

In the end, rather than the nightmare of making a 3000 meter diameter dome deep enough under ground that dune forces will have no effect (using h-bombs to excavate?), just make thirty 10 meter diameter tunnel boring machines and run them 10 kilometers in different directions.

The linked article's tube tent is not a bad idea for surface greenhouses.

Does it need to be more extensive than "make the very bottom ridge of the dome wider than the dome itself (some kind of "lip") and place it into the groove carved in the rock?

Yes... Remember that there's 1 bar of atmosphere in there. 150 feet (45m) makes for a circle of 140m circumference but 1600m^2 area. Since 1 bar ~= 100_000Pa, each of that square meters has 100KN of upwards force on it, for a sum of 160MN distributed over 140m of circumference or ~1MN per meter. So assuming the mass of the dome is negligible, we're talking about the equivalent strength of holding on to a mass of about 100 metric tons (compared to Earth gravity) per meter of dome. Ie. the amount of support you need per meter is the amount that you would need on Earth to hold up 100 metric tons against gravity. That's about a Boeing 737. Per meter.

That's why the author suggests peridiodic anchors, like an air mattress. As other commenters have pointed out, you don't want the structure to deflate in the event of decomp, so a strut which is useful secondarily in compression is useful here.

Basal fiber is about 3GPa tensile, call it a MoS of 6 for a neat 500MPa working strength.

If you plug int wolfram alpha `1 atmosphere * 1 square meter / 500 MPa` you get 2 cm^2 of support (tethering) per sq m of roof. That's reasonable.

But here's the rub: compressive strength lags tensile strength. Even granite is a mere 130 MPa. So even a strut which has some compression resiliance is not gonna be enough to fully abate a collapse. So it's very likely a Martian structure would have some arc to it, as it both benefits tension under nominal operation and some compression in failure mode, at least long enough to keep pressure from dropping too low.

I imagine rip-stop at all sorts of scales will be implemented. It's not gonna be like an inflatable golf dome.

https://www.engineeringtoolbox.com/compression-tension-stren...

https://en.m.wikipedia.org/wiki/Ultimate_tensile_strength

Steel cable with a diameter of 1inch has a breaking strength of 47 tonnes. Give it a safety margin and assume it can hold 10 tonnes. So you need 10 cables per meter. So I assume in case the "lip" being just a sheet of steel it can be way thinner than 25mm.

https://imgur.com/a/h92bLIp

Sure but you need to be sure that the thing you're attaching it to can hold the weight. Ie. if the martian floor was the ceiling, you'd have to be able to hang a plane off that attachment point without it ripping out.

In other words, your lip needs to be distributing force onto a sufficient volume of ground to make up 100_000 metric tons of martian soil, per meter of circumference.

Actually I think just making the underground part cone-shaped would be much better and simpler solution than that lip.

I'd have thought you'd use pegs (pitons, or piles) as for tents on Earth?