I saw this happen the other night so of course I took advantage of it...ended up happening a couple more times after the first, but I tried to exploit it as little as possible...

The originally strategy was to fill the outside of the city with archers and toss a battering ram at the door. When you get the door down 20% or so, the cities troops (depending on how many are there) will rush towards the gate to stop the oncoming attack. My original strat was to weaken the gate to 90% while pelting any troops that would run up, then when I had an opening free from enemy troops, I would knock down the last 10% of the gate and move my Hoplites in (They move so slowly, a direct assault would have had many more casualities). What ended up happening next blew me away.

I got the gate down to about 70% and the enemy general came riding up towards the gate with his cavalry. I assumed that he'd turn tail as soon as he got hit with some flaming arrows. At 90% I moved my ram back and away from the gate, the enemy general literally just stood there right in front of the gates waiting for the rush while 5 troops of archers pelted him down to nothing. He didn't even try to move or make a break for it untill he was down to himself and 1 other horseman in his troop, of course by this time, it's too late to run.

It happened two more times over the next day or so, and I haven't really tried it since I got cavalry. I was playing the Greeks and this happened vs the Macedonian's and again while fighting the scippii.