Septic drain field
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You are wise to select shallow rooted plants! Here are a few things to consider when choosing plants, i.e. is the area sunny or shady? Will grass (lawn) work for you? or is the hill too steep to mow? Many groundcovers are not evergreen, i.e. lily of the valley, so think about what you will look at in the winter unless snow-covered.
Select plants that are suitable for dry soils and are low maintenance. The soil over the field is fairly shallow, and you want to minimize traffic on the area to avoid compactions. There is nothing that is completely maintenance free especially until established, but you do want to minimize fertilizing and watering. Expect weeds to grow up around your ground cover until it takes over.
Herbaceous plants, like turfgrasses, are good choices for soil absorption fields. Turfgrasses are durable, resilient, and desirable because of their fibrous root systems that hold soil in place. Once established, these grasses also provide a low maintenance cover.
Suitable evergreen plants are vinca minor (also called myrtle or common periwinkle), which has a pretty little purple flower in the spring; pachysandra terminalis, creeping thymes, or the smaller euonymous varieties. Remember the bigger or woodier the plant, generally the larger the root. Some of the dwarf creeping junipers would also be suitable.
Wild flowers would create a low-maintenance prairie, but they would mostly disappear in the winter and can look weedy. Black-eyed susans (rudbeckia) and purple coneflower (Echinacea) are good choices as they will spread by seeding. The smaller bulbs are another good choice. One that spreads really quickly is Spanish bluebells (Hyacinthoides hispanica) and would look nice coming up around an evergreen cover such as vinca minor. Here is a website from Chicago's Morton Arboretum listing some evergreen options. You will probably need to copy and paste the URL into your browser. Be sure to pay attention to the sun/shade preference.
Good luck with your selection! Thanks again for contacting AaE. Please let us know if you have additional questions or concerns.