Ice dams
An ice dam is not really a roofing failure. It is heat escaping into an attic, melting snow high on the roof, and that meltwater refreezing at the cold eave.
How the water gets in
Melt runs down under the snow until it reaches the overhang, which is not warmed from below and stays at outdoor temperature. It refreezes there and builds a ridge of ice. Water backing up behind that ridge sits on the roof rather than running off, and shingles are designed to shed water flowing downhill, not to hold standing water. It works its way under the courses and into the deck.
What actually fixes it
Air sealing and insulation at the attic floor, so heat stays in the house. Ventilation, so the attic runs close to outdoor temperature and the roof deck stays uniformly cold. Ice-and-water shield membrane at the eaves during a replacement, which does not prevent the dam but does prevent the backed-up water from reaching the deck.
What does not fix it
Chipping at the ice with anything sharp damages the shingles underneath and is dangerous from a ladder in winter. Salt products stain and corrode. Both treat the symptom on a roof that will form the same dam at the next thaw, because nothing about the attic has changed.