I would not use the corrigated pipe with a sock on it at dirt will infiltrate thru the gravel and plug the fabric where water is entering the holes and you are digging it up again. The gravel alone will transport the water and the pipe gives it a quicker path to get away, so you need to protect the gravel too. The same fabric they use on that pipe can be purchased in width. I would dig a trench a min. of 12" wide lay wide fabric in the trench add 6" of gravel then the hard pipe with the holes on the down side, cover the pipe with gravel, 6 to 12 inches above the pipe and wrap with the sides of the fabric. That will protact the gravel from dirt infiltation and will take much, much longer to get plugged. When if ever it does fail and the pipe begins to plug up the hard pipe will give you and opportunity to clean the pipe with out digging it up. All that takes care of the water below the surface and allows you to replace the top soil and grow grass over it. A certain amount of water is on the surface during rain storms so the yard drain is a small man hole concrete with a cast iron grate or one of many plastic units available in the market. Shape the lawn so surface water runs to these man holes. [ame]https://www.youtube.com/watch?v=XmmdGiEh1Mw[/ame] [ame]https://www.youtube.com/watch?v=1UfIgbadQXE[/ame] See the fabric but I would not use limestons as it will pack like concrete and defeat the job over time.