I have eradicated nutsedge (aka nutgrass) and other pesky grasses and weeds by “solarizing” the infected area. Though you will have to take the area out of production for several months, this is an effective and environmentally friendly solution for killing and suppressing weeds as well as plant-damaging bacteria, fungi, nematodes and insects.
To solarize soil, first remove weeds, plants and crop debris. Then wet the soil, because moisture will help the heat penetrate the ground. Place clear plastic sheeting tightly over the soil. (The plastic should be clear because black or colored will not heat the soil sufficiently.) Anchor the plastic with bricks or tent stakes, or by burying the edges with soil. Leave the plastic in place for four to six weeks, preferably in the heat of summer, and let the sun do the rest. In the South, this works well in winter, too.
In a few months, you’ll see no further growth under the plastic, and the heat will have effectively sterilized the soil. Before I plant again, I add some good compost and manure to re-establish the natural soil life needed for a healthy garden. Think of this as growing new dirt.
Darlington, South Carolina