On May 4, 1864, the Federal Army crossed the Rapidan River twenty miles west of Fredericksburg. The next day, Confederate General Robert E. Lee's forces struck the Union army in the Wilderness, opening a month-long campaign of nearly nonstop fighting and staggering casualty totals. After the Wilderness, Lee attempted to block Union General Ulysses S. Grant's southward drive toward Richmond at Spotsylvania Court House, then along the North Anna River, again at Totopotomoy Creek, and finally at Cold Harbor, just eight miles from Richmond. At Cold Harbor Grant's headlong assaults into Lee's line on June 1 and June 3 failed. Undaunted, he marched his army south to Petersburg and began the long process of cutting Richmond's supply lines. Fighting in the thick woods west of Fredericksburg during the Wilderness produced nearly 30,000 casualties but no clear winner. At Spotsylvania Court House, Grant ignored the indecisive results of the Wilderness and pressed southward, and for two weeks close to 200,000 men fought for an advantage. Engagements at the North Anna River and Totopotomoy Creek forced Grant to continue moving to Lee's right as Union forces searched for a way to capture Richmond. Major attacks on the Confederate line at Cold Harbor brought the total number of casualties to around 90,000 men in six weeks of fighting. Grant's failure there turned his attention to Petersburg, ending the overland portion of the 1864 campaign.