Lewis Hamilton and Fernando Alonso sustained left-rear punctures during FP1 at Interlagos.
Any time lost is particularly critical during a sprint race weekend where there is only one hour-long practice session before parc ferme and qualifying.
Autosport observed on Thursday night that mud had dried in the grooves cut into the track surface. These are designed to carry rainwater off the track to prevent aquaplaning.
The punctures are understood to have been caused by screws and nails, with the teams reporting that most of this debris was to be found in the pitlane.
As such, F1 tyre supplier Pirelli has requested the FIA to clean the circuit.
Pirelli motorsport boss Mario Isola explained: "We had a couple of punctures due to debris and we also found some cuts on the tread. Obviously, we are going to inform the FIA to clean the track.
"I believe the problem is the pitlane more than on track. But we have to pay attention because we had a couple of punctures."
Aston Martin performance director Tom McCullough said that following a Thursday track walk, the team had noted the dirt when feeding back to FIA race director Niels Wittich, as is customary.
He added that two-time champion Alonso reckoned that small stones on the track surface also made it feel as though he had been "sand blasted" and that the AMR23 returned to the pits with wear as a result of the states of the circuit.
McCullough said: "We always walk the track; we always measure the track to understand the grip level and the state of the track.
"It was very dirty as far as the rainwater running across - the mud you can see as you go around. We always report back what we think of the track to the race director. We said it was dirty.
"We didn't actually notice any debris out on track. When Fernando did his first run, the first comments he had were, 'lots of stones. I feel like I've been sandblasted as I'm driving.'
"We could see the front wing; the front of the car had taken a hard hit."
