Cant find my copy of Ruppenthal 'Logistics in Overlord'. From memory the discharge across OMAHA Beach in July & August came close to the pre invasion estimates for the Mulberry A. Rear Adm Ellesberg. one of the top USN salvage officers published his account of restoring the badly damaged harbor. The main difference between the July-September harbor & the original planned was the salvaged dock materials were removed to Mulberry B and set up there. Both Mulberrys reduced the dependance on the outer floating breakwater & those pontoons were among the first items to be returned to the UK to salvage the steel. The Gooseberry & Phenix breakwaters were damaged, but still functional. That allowed the steady use of lighter discharge from the anchored cargo ships and ferries to shore. Altogether the open beach intake on Utah Beach and the sheltered Omaha Beach took in enough to sustain a average of 15-18 divisions with corps/army overhead in sustained offensive combat. Some where between 10,000 & 15,000 tons daily. In comparison the port of Cherbourg was restored in latter July to its nominal peace time average of 8,000 tons daily. Additional repair and improvements raised the daily intake to 20,000 tons in August, and a brief surge peak of 25,000 tons in September.
If I can find the books I'll post figures direct from them, including something for the B port.