Using time field in Eloquent model

I have got a database field containing only a time, it's declared in my migration as

$table->time('time')->default('00:00:00');

Now I want to add a number of seconds to this field using Eloquent, doing something like:

$activetime->time->add(new DateInterval('PT5S'));

(where $activetime is a object of a Eloquent model)

First try on this I got

Call to a member function add() on string

So obviously I have to tell Eloquent that this is not a string but a time. The closest I have got is putting it in protected $dates in the model, but then instead I get

Unexpected data found.

I suspect this is because it isn't really a date but only a time, but I can't seem to find much information about how to handle times. Is there any way of solving this or would I be better off using something else, like dateTime or timestamp (or even an integer for amount of seconds)? What I DO want to record is a users amount of active time for a given date, so for that purpose time seems like the natural choice...

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