What is "run-off canal"?

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Here is my guess, though it would really be best if a civil engineer would step forward and answer your question. ;)

A run-off canal is a water channel such as a stream or small river typically used for the discharge of contaminants. Otherwise, such contaminants discharge from their source by flowing over a surface, for instance, by flowing over land rather than through a canal.

So paving over (that is, enclosing) the Tiber River would have essentially turned it into a sort of hidden canal to be used for the discharge of various kinds of wastes, such as sewage.

I hope this makes some sense to you! :)