suffer significant damage(The Queen of Victoria suffered significant damage while the Sergey Yesenin only suffered minor damage. -- Парому был нанесён значительный ущерб / Паром получил значительные поврежденияyoutube.comART Vancouver)
be badly damaged(о здании: The Guildhall was mostly rebuilt in the 15th century and was restored after being badly damaged in the Second World War.ART Vancouver)