People have extracted so much underground water that it affects the Earth's balance.
Most relative clauses start with a relative pronoun, such as "that." What is the subject in the relative clause above? Is it "that" or "it?"
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It's not a relative clause, even if it does start with that. There are better ways to identify relatives.
is a complement clause that's part of the so
This construction has two parts
Either so before adjectives, or such before noun phrases:
So long, so firm, so fully-packed, so free and easy on the draw
Such a nice dog, such a lovely day, such an awful smell
Followed by a tensed that-clause complement to the entire of Part 1,
expressing the result of the degree of the adjective or noun properties discussed:
This hotdog is so long (that) it flops out the end of the bun.
This is such a long hotdog (that) it flops out the end of the bun.
She drank so much water (that) she had to run for the bathroom.
Oh, and the subject of that it affects the Earth's balance is it, a non-relative pronoun that's coreferential with the clause People have extracted so much underground water.
People have extracted so much underground water [that it affects the Earth's balance].
As DW256 says, the bracketed element is not a relative clause but a declarative content clause. Its function is that of 'indirect complement' in clause structure, where it has a resultative meaning. Its subject is "it"
It's called indirect because although it follows the head noun, it is not the head noun that licenses it but the "so" that modifies "much".