Using sand to fill lawn depressions

I have a large wet area on my lawn and I am currently draining it and this morning after all the rain the trenches seem to be working although i have no pipe or stone in yet.All the grass is dead from water lying on the ground all winter.The problem is the soil is very poor and the tracks left by my ride-on mower were still full of water right next to the drains as the soakage is bad.Will using builders sand fill in these tracks mixed with a little moss peat (sprinkled with grass seed later) or will it just cake into a cement like substance?I was then planning on aerating the soil when i have all done. Regards, Brad