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'Unacceptable': Massive BC Ferries lineups to get to Vancouver Island for the long weekend
(vancouverisland.ctvnews.ca)
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Some quick googling and it seems the crossing length to the island is similar to the crossing of the English Channel (40 - 50km). The Channel tunnel depth is about 115m below sea level, whereas the Straight of Georgia has an average depth of ~150m per Wikipedia. The Channel tunnel cost about 21 billion pounds (~$36billion CAD in 2021 dollars) to complete, so I'd imagine a tunnel to Vancouver Island would be at least the same if not more. Doesn't seem worth it for the size of the population crossing even if it were possible.
The Straight gets over 300m deep in proposed crossing areas, and has hundreds more metres of sediment before hitting bedrock. That depth makes for unprecedented engineering challenges for both tunnels and bridge supports; not necessarily impossible but certainly not financially feasible. A floating bridge in a place with so much wind and waves is similarly unprecented and probably a non-starter due to the shipping traffic.
The BC government has a good overview page about it. They basically suggest that the only thing that has even the slightest chance of working is a submerged floating tunnel, something which has never been attempted.
Make sense, if there is a gap like this between BC/Washington then we would have build it to cut transportation cost.