Coal shipments in all the producing states - even those in the heart of United Mine Workers-organized coal country - have been steadily increasing since the drop at the start of the 3-month-old coal strike, despite some UMW efforts to block the mining of nonunion coal.

In many instances, the unions have been enjoined by the courts from impeding nonunion mining operations, and they have acceded to the law. In other cases, they have encountered difficulty monitoring the hundreds of remote and widely scattered mines, particularly small ones that dig coal on a casual and occasional basis.

But in some regions, inertia and an unwillingness on the part of union leaders to organize illegal picket lines for fear of legal reprisals is cited by rank-and-file members for the lack at activity at the gates of the mines. It is also credited with keeping relatively peaceful the same coalfields where bloody labor battles have been fought for generations.

"Anytime there has been a strike," said Fred Kelley, president of Local 1702 here, "we've stopped production all around here, and stopped it good. Now we're just sitting around, and the coal is moving out more than ever."

This seepage has mitigated the effect of the strike, and has thus given the Carter administration a point from which to start building production should enough UMW miners return under a Taft-Hartley injunction.

There has been some violence, such as when about 40 pickets armed with rifles and clubs tried to halt a coal train at Kenova, W. Va., Tuesday night, hurling rocks at the caboose and shooting at a coal hopper. Also, occasionally, railroad trestles have been mysteriously set afire and track has been dynamited.

But despite these incidents, millions of tons of coal have been making it to the energy-hungry northeastern states.

More than 1,500 mines were operating in the last week of February, compare with normal the usual 4,873.

Northwithstanding that sharp curtailment, 6.7 million tons of coal were produced that week, nearly half that produced in the comparable period last year, according to Department of Energy officials.

More than 37,000 railroad hopper cars were loaded at the mines and moved out to utility and industrial plants during that strike week.

Moveover, the nonunion mines are working overtime.

Federal energy officials said their production for the last week in February actually exceeded normal capacity for a 5-day week by 1.5 million tons, or 29 percent.

The daily production of 1 million tons from the non union mine is split roughly half west of the Mississippi and half in the East where the UMW's strength is the greatest. In the East, on one day - Feb. 23 - Kentucky led the region with 319,000 tons followed by Virginia with 58,557, Tennessee with 44,579 and Pennsylvania with 39,340.

Nationally, UMW mines, virtually all in the West, where the union is allowing some mines to operate, produced 128,771 tons on Feb. 23. However, non-UMW mines produced 908,968 tons of coal that day.

"They're going full blast, we know that. But there's not much we can do about it," said Eddie Sturgill, UMW International Executive Board member from District 19 in southeastern Kentucky.

In some parts of the country, including Kentucky the union's attempt to slow the flow of coal has been impeded by court injunctions, and the local union leaders say their hands are tied. In some cases, the unions have been restrained from putting more than four pickets at a mine.

"You can't do anything with four pickets. They'll put 10 state troopers around them and the scabs can walk right through," Sturgill said in a telephone interview.

In Ohio, District 6 International Executive Board member Richard Vargo said union members have faced the same obstacles, and that there hasn't been any picketing since the first days of the strike.

But District 31 in this northeastern corner of West Virginia is not under injunction, and some strikers feel there should be picket lines around the nonunion mines.

"They're too damned scared. They're like sheep, and they won't make any decisions that will jeopardize they're jobs," said Local President Kelley. He was referring to leaders in District 31 headquarters in nearby Fairmont.

In the last three summers, during wildcat strikes, District 31 union members picketed and shut down non-union mines that are not being picketed now, Kelley said.

The district's rank-and-file plan to hold a rally today in Fairmont, independent of the leadership, and members said they will discuss the possibility of picketing nonunion mines. They are also going to seek united opposition to returning to work if they are ordered under the Taft-Hartley Act.