Has the illogical "three times bigger" replaced "three times as big" in common usage?
Solution 1:
To Google Ngrams!
While we can't make a claim as to the specific intended meaning, we see that usage of "three times as big" has rapidly declined since the 1940s, while usage of "three times bigger" has simultaneously increased.
It is safe to say that "three times bigger" is acceptable (whatever its meaning), but it has not (yet) replaced "three times as big".