Chickens can quickly transform a lush, grassy area into a muddy, foul-smelling mess. As a matter of fact, the technical term for this problem is referred to as fouling the ground. Once the ground is fouled, it's no longer healthy for your birds to stay there, and you will need to relocate the run.
If relocating the run is out of the question, a deep litter system can be used instead. Gravel and/or bark chips can be used for the litter. However, to keep the area fresh, these materials will need to be dug out and replaced about once a year.
One problem with this method is that your chickens may become lazy. After all, the reason they like to scratch around in the grass is to eat vegetation and find bugs. If they don't have a reason to scratch around, then they won't. However, you can encourage them to exercise by mixing pellets and corn in with the gravel or bark used in the deep litter system.
In addition to this, you will want to provide them with a dust bath. This is a shallow box partially filled with dry, powdery dirt where they can stretch their wings. It helps the birds naturally cope with lice and parasites.
Also, keep a small container of grit available for your hens. Grit is naturally available to free range birds, but a supplemental source will need to be provided when raising chickens in a deep litter system run.
photo credit: abooth202