I am anti insecticide so I look for solutions that won't do much harm to the beneficial insects in the yard. Is there a chance these are fire ants? The clues are GA, recent rain, and new ant hills. Fire ants in the south usually build a mound like that right after a rain. If they are fire ants, then the product of choice is called Green Light Fire Ant Control with Conserve
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One bag should be a lifetime supply. For a mound that size I would only use a two-finger pinch. Conserve is the active ingredient. It is a disease called spinosad that causes immediate paralysis in insects. Use it sparingly and try to target your pest, because it does affect caterpillars, bees, wasps, flies, and some other insects which are often beneficial.

This product should work on any protein gathering ant (like fire ants). If they are sugar gathering ants, then any bait you can make with baking yeast in it will take care of them. It takes longer but it works. A 50/50 mix of sugar and molasses is the bait. Put a teaspoon full of yeast per cup of bait and dollop that into their trails. They will bring home the yeast which biologically contaminates their food supply. Then they are gone.

No, they aren't fire ants. They usually make a large mound. These are dozens of small ant holes which seem to be destroying the root system of the lawn underneath.

I have had TONS of ants making little ant mounds just like that ALL OVER in the yard ever since we moved in here. I never thought they were bad for the grass though...??

The picture you posted shows no harm to the grass. Do you have other pictures showing where the lawn has been damaged by the ants?

I'm having the same problem and they are not red ants(they are little black ants). I'm finding new mounds every week. Any suggestions on how to control?

Are the ants hurting anything? Anything at all?