There is a piece of ground that gets very muddy after it rains. It also is used as a parking area. The ground gets tire tracks and ruts in it after the rain.

Is the solution just to dump gravel in the area? Just keep dumping gravel until the problem is fixed? Any other ideas?

Thanks,

Glenn

Is it level ground? A depression?

Take a look at this answer:
https://www.askmehelpdesk.com/gardening-plants/adding-drainage-soggy-backyard-55348.html

If it is a parking area and a low spot you need to look into why it is low and what building it up will do as far as drainage,if the entire area is gravel and you have water ponding and you dump more gravel the pond may simply move left right or closer in,survey the field and build up accordingly with a strong base first and a good surface last

The soggy area isn't a depression. The soggy spot and the ground around it is level. There isn't really a place to drain it to.

Remove the top soil which is the soggy part. Lay several inches of coarse gravel then 1/2" gravel with fines.