Not sure if you after number of assets used or weight of munitions.
Assuming 170 assets at 60 min duration, =3400 per hour,
http://www.nps.gov/frsp/fredhist.htm short answer, but the link is a nice read, 8000 over 2 hours from 150 guns at f-burg would be my first guess as to the heaviest weight of munitions used in the field, siege would be higher overal, but at a lower rate of fire.
Edit, a quick search found this.
http://history.rays-place.com/1st-ct-ha.htm which has some data of intrest.
The first siege operations culminated in the battle of Petersburg mine, July 30th, 1864. On the 31st the great mine explosion occurped, when six tons of powder were exploded directly under the confederate forts near Petersburg. In this siege eightyone guns and mortars were served by the 1st Connecticut Artillery and the 4th New York Artillery, and about seventy-five tons of ammunition, or 3,833 rounds, were fired during the battle; and 225 tons, or 12,229 rounds in the preliminary work. This battle was probably the first in which spherical case shot was used from mortars. The novel expedient of putting thirty 12 lb. cannister shot under the bursting charge of a 10-inch shell, proved very effective.
Immediately after the battle a projected movement of the army of the Potomac necessitated the moving of 52 heavy guns and mortars, with all their ammunitions, etc., with urgent haste from the front of the 5th, 9th and 18th corps, to headquarters, a distance of eight miles. This was accomplished in twenty-seven hours, twenty-two light artillery and mule teams, and one hundred and seventy wagons being employed. The aggregate weight moved was 225 tons, and the work was done by the companies that had served the guns in the action. The enemy, did not discover the movement, which began at midnight of July 30th. The siege now took the form of bombardment, the average weight of metal thrown daily was, August 15th 2 tons; September 7th, 8 tons; October 4th, tons; November 2d, 7 tons; December 2d, 1 ton; January 1st, 6 tons; and February 1st 1 ton; aggregating 793 tons, or 37,264 rounds.
Around Petersburg, sudden artillery battles occurred at all hours of the day and night, often involving the entire line to check an annoying enfilade fire from the left bank of the Appomattox. A 13-inch sea coast mortar was mounted on a reinforced platform car and served on a curve of the railroad track. This novelty was widely known as the Petersburg express. During these operations the siege train was organized as a separate brigade under Colonel Abbott; such additional troops as were needed being temporarily attached. The aggregate number at times exceeded 3,500 men; the train contained 127 guns, 73 mortars, and the line of batteries was miles long. Over 1,200 tons of ammunition, or 63,940 rounds, hauled an average distance of seven miles by wagon, were fired during the siege.