What I found over the years is the burlap works into the clay. If you burlap and mulch you reduce the pounds pressure on a given area and you push the burlap into the clay.
As you continue to add burlap and mulch to maintain the trail you keep working organic into the clay and they clay up into the organics. You will at a certain point start to optain structure as critters start to
feed on the organics. What the burlap does is to provide a base to keep the mulch on the tops. The clay will work into the burlap slowly and the burlap will decay over time.
This is similar to using geotextile fabric to hold gravel over a area of clay.
The nice thing about burlap coffee bags is that you can make wood branch stakes and stake the bag into the soil so it stays in place. Most of the time this is only needed on a slope or where there is errosion.
You can solve compaction by adding 30 percent porous material to soil.
I have done tests over a decade proving this.
There have been decades long studies using flyash on trails.
So items like perlite, course biochar, expanded shale, ground brick, etc. You are just looking for material with
alot of pore space to added so the roots can grow.
Another option a friend in Alaska did back in the 80's was to mix cement into the clay on the paths.
He did this with his driveway and believe it or not it did firm it up
enough for him to work with.
In another location they put in a board walk because the amount of traffic was damaging to the ecosystem.
In yet another they put in cedar, loctus, osage orange, etc. boards that had slates. Think of wood that resists decady cut into one inch wide strips. The boards are then bound together with a half inch spacer every foot between the boards. These are created about three foot wide and six to ten feet long. They are then put onto the clay as walkways and plants can growup between the opening.
On another farm they there was alot of large flat rocks along a area that was blasted for a road. They would go to the side of the road and pick up flat rocks to make a path.
I have also seen this done with old
concrete slabs. Look for any recycled brick, cement, concrete, river rock, etc. that can be used for steping stones.
In yet another farm they had alot of wood. So they simply cut four in rounds and planted them in flush with the ground along the trail. They decaded over time and were simply replaced.
Finally alot of people simple lay down a none woven fabric like a geotextile or weed barrier and put some type of gravel or crushed rock on it. This tend to keep the rock in place. It does work best with crushed rock.