Humanity Road has detailed updates with extensive links about the situation in Kumamoto.

Also, if you view Kumamoto in Google Maps and turn on the traffic view, you can get a very good idea of the road situation. A few years ago we had a partial Kyushu Highway road collapse after heavy rain, and the situation was similar, with trucks clogging up local main roads when the highway was shut.  Presumably a similar thing is happening there now with supplies to surrounding areas also slowed down by road and rail closures.