Grass paving begins with the same kind of base used for concrete. Then, rather than pouring concrete, the base is covered with a layer of bedding sand, followed by a plastic gridwork. The grid is very strong, capable of supporting firetrucks or other heavy vehivles.
The grids are filled with dirt and planted with grass seed. The roots are protected by the grids, so the grass isn't damaged. Before the dirt, however, I cut out the lines for the labyrinth, removing that portion of the grid. In its place we put pavers. When finished, it looks just like a brick and grass labyrinth, except it is wheelchair accessible (meets ADA standards), it is flat and strong, and it doesn't get soft or mushy. It has the benefit of looking like grass but having the strength of paving.
This labyrinth was done as an Eagle Scout project. I know of numerous Eagle Scout labyrinth projects. We chose the Santa Rosa pattern, a copyrighted design by Lea Goode-Harris, Ph.D. My part was limited to cutting the lines and giving advice. OK, so the advice wasn't always followed, but, it still came out pretty well. To learn more about the Santa Rosa labyrinth, see: www.srlabyrinthfoundation.com.
Cutting the grids with a normal circular saw.
The lowest line in the photo has the pavers added.