Hadrosaur Tail Injuries
Researchers have long noted pathologies in hadrosaur caudals. Some of these resulted from predation. In 1988, Kenneth Carpenter described mangled neural spines in the tail of a DMNS Edmontosaurus. The damage across several spines, he wrote, "appears to delineate the mouth of a large predator." Presumably it was the contemporary Tyrannosaurus.
The best evidence for Tyrannosaurus preying on hadrosaurs is a tooth, embedded in a caudal centrum of an Edmontosaurus. No doubt, tyrannosaurs chased hadrosaurs and bit their tails to stop them.
Not all of the damage is attributable to predators. The majority of mangled tails resulted from accidents involving other herd members. Mating mishaps appear likely. The position of distorted neural spines suggests males caused the damage while mounting their mates. It seems odd, though, that something as essential as procreation would be routinely injurious. Moreover, it is noteworthy that iguanodonts don't display the same caudal injuries as duckbills. That may be because iguanodonts, unlike hadrosaurs, probably stood and fought (with thumb spikes) instead of fleeing from a predator.
If some damage resulted from trampling, it may provide indirect evidence of predation. Under ordinary circumstances, when a hadrosaur herd was just resting or browsing, accidental stepping on a tail seems unlikely. Hadrosaurs had good vision. Even in crested taxa the view below them (as opposed to above or behind) was unobstructed. Herd members could easily see and avoid the tails of those lying on the ground--the only ones vulnerable to trampling as the stiffened tails were held off the ground when the animals got up. Occasionally, however, things got chaotic. When an approaching tyrannosaur was detected and a herd member sounded the alarm, a common result may have been a stampede. Throwing caution to the wind, some hadrosaurs could've run over the tails of others in a mad scramble to escape. Therefore, some tails showing no evidence of toothmarks or teeth might still testify to the threats duckbills faced in their environments.
References
Carpenter, Kenneth 1988 Evidence of Predatory Behavior in Tyrannosaurus
Hadrosaurs Indiana University Press 2014
Tyrannosaur tooth embedded in hadrosaur centrum.
