How thick should the roof of a large cave be to safely build a city on top of it?

Fullmetal Alchemist (2003) features a giant (and I mean stupidly big) cave under a large and busy metropolis. Nobody is aware of its existence, which means that at least since the city's founding (let's say 150 years) there must have been no subsidence of any kind.

What little I know of cave-ins tells me this is rather unlikely, but for story-reasons I need to know how shallow I can make it before shit starts falling down.

• The cave is unsupported by any columns, and there is a very large space from the floor to the roof (perhaps 80-100m). The floor diameter is about 2-3km. [pic]

• The cave was formed by wild magic, so the erosion/seepage found in karst caves need not be an issue.

• The time period is equivalent to early 20th century, and there is some light automobile traffic. My admittedly superficial research suggests that foundations in early 20th-century London were pretty shallow, so foundation depth is unlikely to have any impact.

• A river runs around the outskirts but not through it. Earthquakes are unlikely.

• The cave should run deeper than 4m (depth of sewers)

In this admittedly improbable scenario, my question is: What would be the minimum thickness for the cave ceiling so that, assuming ideal geological conditions, there is no risk of collapse under the weight of the city above?

RESEARCH

Sarawak chamber (Malaysia) is the largest known cave room (700x400m) with an unsupported roof span of 300m. No word on roof thickness.

Son Doong Cave (Vietnam) has the largest known passage. According to Wikipedia, it is 4.6 km long, 80m high and wide over most of its length, but over 140m high and wide for part of its length.

A very interesting paper on the small (<11m) man-made caves in the sandstone under Nottingham recommends a depth of >50% of the cave width, which is pretty damn deep. This is for flat roofs in karstic limestone (stronger than sandstone).

posted over 7 years ago

Notiophilus‭

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