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Terminal 3 and concourse C are physically separated by an active taxiway. I know what you mean by there is no tunnel like T1, it is done quite cleverly. The road descends below ground as you approach the entrance to the terminal so you are already underground. You do the long walk from Chauffeur drive drop-off to immigration/security and up the escalator.
Did you not say Terminal 1 leads to Concourse C? What has Terminal 3 got to do with Concourse C?