The Virginia Highway Department says it is tired of subsidizing Fairfax County's pedestrians and tricycle riders. Hereafter, the department said, it won't accept responsiblility for repairing most new sidewalks in the counties.

"Sidewalk maintenance in Fairfax County is becoming an overwhelming problem," Highway Department Commissioner Harold C. King wrote County Board Chairman John F. Herrity in a toughly worded letter.

In the future, King said, the department will take responsibility only for sidewalks "serving a real public need" and which "are built virtually maintenance-free."

It was unclear what will happen now. "We'll have to work out something," Herrity said. But he wasn't sure what that would be.

King said it would take $22 million to repair the county's 900 miles of existing sidewalks, some of which have disappeared into holes because of erosion and undermining.

But, he said, the financially hard-pressed department can only scrape together $500,000 to $1.5 million yearly for repairs. "We . . . are actually fighting a losing battle and also incurring a very poor public service reputation," King said in his letter.

"Who uses sidewalks?" said Donald E. Keith, the highway department's residentt engineer in Fairfax. "The only people I see using sidewalks in my subdivision [country Club Manor in western Fairfax] are kids on tricycles. Those are pretty expensive sidewalks."

An argument commonly made by homeowners is that sidewalks are an asset to their property and community.

If it is an asset to property, said Keith, the homeowner "should pay for it instead of the traveling motorist."

The highway department's funds come from the 9-cent-a-gallon statewide gasoline tax (it goes to 11 cents a gallon July 1) paid by motorists, who almost certainly don't ride tricycles, the agency feels.

King said that Fairfax is the only suburban county in the state where sidewalks are commonly built. "In my subdivision [Pinedale Farms in Henrico County] there are no sidewalks," King said.

Fairfax board chairman Herrity declared: "We intend to keep on building sidewalks." Furthermore, he said, "I use my sidewalks in front of my house."

Supervisor Marie B. Travesky (R-Springfield), whose district is the fastest growing in the county and has numerous sidewalk problems, including cave-ins, said, "I'm a little upset, but I can understand what they're saying.

"Whole sidewalks and curbs have sunk out of sight," she said. "These are real hazards."

If the state won't accept responsibility for maintaining any more sidewalks, she said she's not sure who would. 'Where would we [the county government] come up with the money?"

According to the highway department's Keith, sidewalk repairs cost $14 a square yard. Repairs that would eliminate erosion problems would cost about 40 percent more, King said in his letter.

The highway department has been routinely accepting sidewalks as long as anyone can remember. "Nobody paid any attention to it before," said Keith.