Concrete needs less cover than plastic or metal but it needs a better bed if it settles too much it will come apart.If if you have any kind of acidic water or acid rain metal wont last very long I've put metal pipe in three times in 35 years at one place the last time used plastic.The new galvanized is about 1/3 as thick as older metal pipe.If it was mine and I could get around 10" of cover I'd use double wall smooth bore plastic you can use one size smaller than corrugated and it will handle the same or more water.The pipe won't come up out of the ground never saw one with enough cover do it in 43 years.1/4 inch fall to the foot minimum.You can cover with whatever you want but seal the end especially the inlet you don't want water flowing under or along the pipe

Last edited by willycc; 01/02/20.