Houston Lawn Problems

I have a problems keeping my lawn watered. It is St augustine grass from sod layed over a clay lot that he builder graded with sand. The problem I'm having is that were the sand was thickest, the water seems to fall away from the roots of the grass is it get dry long looking before the grass just a few feet from it. My yard has green spots with light green patches.
My dad suggested I plug aerate then distribute a light layer of peat moss to fill in the holes with a spongy material that will hold water.
What do you guys think of this? Any other ideas?
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You can try the peatmoss. The ideal situation would be to strip the sod and sand base. Replace the sand with good topsoil - 6 inches deep. Even with aerating and top dressing watering will continue to be a problem.
Derryl

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