In the early scenes of the film (that inspired the long-running TV series) we see the "Seaview" being hit by sinking chunks of ice. Any one with brains knows that ice floats! In fact, if it didn't, the whole world would be flooded from the tidal waves caused by all the world's ice sinking!
The falling objects were not blocks of ice, but rather the large pieces of rock which had been frozen inside the glacier and were released during the melting.