 Thousands of Union soldiers were killed or wounded in a hopeless frontal assault against the fortified positions of Confederate Gen. Robert E. Lee's army.On May 31, as Grant's army once again swung around the right flank of Lee's army, Union cavalry seized the crossroads of Old Cold Harbor, about 10 miles northeast of the Confederate capital of Richmond, Virginia, holding it against Confederate attacks until the Union infantry arrived.Both Grant and Lee, whose armies had suffered enormous casualties in the Overland Campaign, received reinforcements.