ARE THERE ANY GROUND COVER PLANTS THAT WOULD THRIVE IN A HEAVY SHADED AREA (UNDER PINE TREES, FOR EXAMPLE)?
There are perennial ground covers that do well in deep shade. Because you are planting under trees, several conditions should be considered. The lack of direct sun, the most obvious, is compounded by the dry soil conditions found under trees. The soil under pine trees tends to be more acidic as well. With all these conditions you might try Ajuga (Bugleweed), Gallium (Sweet Woodruff), or Pachysandra (Japanese Spurge). Convallaria (Lily of the Valley) and Lamium (Dead Nettle) will also grow under pine trees. If your planting site allows for a little more height, most ferns will also grow in deep shade.
Remember, the dry conditions under trees means you will have to be very consistent in watering your new ground covers until they are established.