[Yorkie]

I have used heavy duty weed suppressant membrane on some of my couch grass / dandelion paths - you do need to create a slit trench with your spade and put the edge of the membrane into the trench, otherwise the couch grass just comes out the sides 

I have other areas where it is not feasible to use membrane, and I use glyphosate on those.

Stacking the 'turves' in my experience just provides an ongoing environment for the perennial weeds to grow.