Drain Tile

This winter my draiage pipe for drain tile froze up at the end ... about 10 feet in. This is about 100 feet or so from my house. I dug it all up and im going to slope the pipe more so that water will not it in it. Due to the build of my lot I cannot go much deeper and the last 5-7 feet of the pipe will only be 1 foot or so under the ground.
My questions are : do I need gravel under the pipe? does it do anyhting in this case where its a a solid pipe?
Upon exit of the pipe should I make dig a little run off for the water and fill in with gravel so lawn will not grow in?

The gravel bed under solid pipe is mostly to make is easier to adjust the pitch while you lay the pipe.

You might want to consider a heat tape in the shallow section. It would also help to bury a layer of straw or foamboard over that section.

Grass or no grass is a matter of how much discharge there actually is. Heavy discharge will wash out grass. I like grass but the water will make it's own ditch if there is enough of it. Gravel often ends up spreading where you don't want it.

So basically the gravel under the pipe doesnt really do too much in this case.
Heat tape is not an option, as it is too far from the house.
IF the pipe is at the right angle no water should lay in it anyways. I just dont want the frost to heave the pipe up again so it lays level and water can sit in it.

Frost can move the pipe regardless of if you put a gravel base in or not. 3" of gravel does not do much when the ground is moving 3 or more feet down.

The drain tile catches water as it flows horizontally through the ground. It's not often that the ground will thaw and then freeze in cycles often enough to have a problem. Most drain tile problems come with the use of corrugated flexible tubing which is apt to have low spots and bellies. Using 4" rigid PVC and proper slope makes problems much less likely.

Sounds like I wont waste my time with the gravel then. I am going to dig a ditch for the drain water to drain into after exiting the pipe as the end of the pipe will be still lower then ground level.