Use a hydro jetter with a forward piercing nozzle. The running water will melt away the ice. If you do not have access to a hydro jetter you can fish a garden hose down the drain with a nozzle that sprays a hard stream forward. The garden hose idea only works well up to around 50 ' depending if there is any turns in the line or not. One other way is to get one of them waterfall pumps and enough 3/8" hose to run through the line and a 5 gallon bucket full of warm water. Put the pumping the bucket and feed the 3/8" hose down the line. I learned this last idea from an old well guy, he did this to unfreeze the plastic well pump line between the house and the well head.