TobyB

You are very narrow minded in your aproach, if you get out of the city with your army overnight you can get a nice head's start and attempt to make it to allied territory, or you can atleast do a pincer night attack, because if you pop up half your army near the enemy camp and give them a nasty surprise and the retreat back through your own gates if you don't manage to rout them, you can at least scare them.

As for the supplies part, it would depend on how well the tunnel entrance is hidden, because I plan to set mine in some wood near the city and one year is a whole lot of time for an besieging army to survive on foraging alone, meaning that the forest nearby would be long deprived of any foodstuffs and they would have to rely on their supply chains or supplies reaped from occupied villages. So if you send out a few bands of trusted and discrete men they might start smuggling in bags of grain or rice or things like that.