PITTSBURGH, December 10--The soft coal miners accelerated their back-to-the-pits movement to such an extent today that the Solid Fuels Administration estimated the nation's production of bituminous fuel had reached 95 percent of the normal daily diggings of 2,200,000 tons.

Joining the miners' back-to-work movement were thousands of others who either had been out of employment or on part time. The mighty steel industry was rapidly gaining momentum as interested supplies of coal put more and more open hearthe and blast furnaces back into operation.

The number of idle among the 400,000 mincrs who ended their 17-day walkout last Saturday was not many more than 10,000 with the largest number reported in the southern Appalachian and Hlinois districts. Some of the mines were still shut down because the miners had not received official return-to-work word from their union chieftain, John L. Lowis, while coal disputes and repairs kept others idle.

As the miners went about the task of supplying fuel for the wheels of American industry again, there was practically no indication there would be any trouble over the strike fines, varying from $1 to $2 daily, assessed against them by operators during the walkout.