I always thought they burst at the point where the water is freezing and expanding. But in fact the damage occurs at a location between the plug of frozen water and a closed valve, because the water pressure increases dramatically as the ice plug increases in length. Pressure can go as high as 25,000 psi !!
https://www.thisoldhouse.com/plumbing/21133681/how-a-frozen-pipe-bursts
https://www.thisoldhouse.com/plumbing/21133681/how-a-frozen-pipe-bursts