Air carrier Captain reported a blown pneumatic duct and bleed leak during takeoff which filled the passenger cabin with excessive noise and airborne particulates. Multiple flight attendants calling cockpit during event was distracting and created difficulty communicating with cabin crew on inter-phone to assess situation in cabin and to advise of planned return to field for an overweight landing aircraft.

Narrative

Normal taxi and operations to XXR; takeoff roll normal but at 120 kts we got an EICAS message; caution bleed leak body. I verified and continued as we were well into high speed regime at this point. Once airborne we were alerted by multiple Flight Attendants (FAs) that we had potential smoke/fumes in aft cabin. This issue of multiple FAs calling the cockpit during the high speed regime was distracting and created a subsequent problem that the intercom was effectively blocked by multiple users so we could not communicate at a time when I needed specific information on the nature of the smoke etc. I circumvented this by doing a FA check in call and was able to speak to our purser. They did an admirable job as they had to walk to the aft cabin to speak to their cohorts and calm the passengers down; many were standing up trying to get away from the source of the noise and smoke (dust). We [requested priority handling]. Asked to level off at 5000 ft. and took vectors around for a downwind whilst the (FO) ran the multiple bleed EICAS messages and did an awesome job coordinating with ATC and flying the jet as I juggled Maintenance Control and Dispatch plus the very concerned Flight Attendants.Once we were complete with these; I spoke with Dispatch and asked them to run weights for overweight landing at 509000 lbs. Dispatch did and verified our performance limit was 578000 lbs. We ran the overweight landing checklist; coordinated Brief with FAs and made a PA to passengers. By that time the smoke/dust had dissipated and the noise from the duct had stopped. We flew an ILS XXL flaps 30 approach; smooth landing. Crash rescue were there to meet; inspected the aircraft and cleared us to taxi back to the gate. At same time we coordinated with FAs to make sure there were no further issues in back. We taxied back to gate x. I made a PA to passengers to try and alleviate any stress; especially in the aft section of the aircraft. The gate agents and FAs did a nice job deplaning the aircraft. Mechanics came on and informed us that it was a blown duct and Assistant Chief Pilot Person A came up and asked us some questions flowed by the Chief Pilot.It was only after deplaning and debriefing with our FAs that the extent of the noise and particulates in the air was apparent. The passengers in rear rows XX/XY in the vicinity of the duct were very shaken; O2 was administered to some passengers as they were having trouble breathing. FO did an outstanding job; running checklists; highlighting relevant information; coordinating with ATC; pulling up the overweight checklist and once on ground having situational awareness to pull up tire synoptics for the overweight landing. Couple of small points; having the Chief Pilots office in the cockpit too fast after an event is not helpful; adrenaline is too high and my bad for just not kicking them out. We answered a bunch of questions which in hindsight should have waited until a reasonable time after the event. The mechanics were also very fast to want to get forms filled out but again hindsight should have told them to wait. I should have been with the FAs who needed my attention. I got to them eventually but should have been quicker.