Thomas R. Monroe, a judge on Arlington's General District Court, is expected to become the second black to sit on Virginia's 113-member Circuit Court bench.

His nomination won approval of Senate Democrats today and his election is expected to be approved by the General Assembly later this week. The only other black circuit court judge in the state is James E. Sheffield of Richmond, who was involved two years ago in celebrated controversy when President Carter failed to win him a federal judgeship.

Monroe has been picked by Arlington Democrats to succeed Charles S. Russell, who was recently elevated by the legislature to the seven-member Virginia Supreme Court. Succeeding Monroe on the General District Court is likely to be Eleanor Spence Dobson, one of three candidates endorsed by the Arlington Bar Association.

Dobson, 55, is a law partner of Sen. Edward M. Holland (D-Arlington) but Holland said today he has abstained from all votes involving her appointment. Dobson will be the first woman judge in Arlington.

Johanna Fitzpatrick, now a Juvenile and Domestic Court Judge in Fairfax, has been nominated by Senate Democrats to become the second woman ever appointed to the Circuit Court bench. Barbara Keenan, formerly a General District Court judge, became the first woman in Virginia on the state's second highest court earlier this year.

Other judicial appointments approved today by the Senate Democratic caucus include:

Quinlan Hancock, an Alexandria lawyer, to the Fairfax Circuit Court, filling one of two new judgeships there created this year by the assembly;

Stewart Davis to the Fairfax General District Court, to replace Keenan;

Gaylord Finch to the Juvenile and Domestic Relations Court, replacing Fitzpatrick.

Although judicial appointments are made by the full General Assembly, the selections are traditionally decided by the majority Democrats meeting in caucus. The House Democratic caucus meets tomorrow on the Northern Virginia appointments.