Let Effective permeability = ue Material permeability = u Total length = le, the total length of the magnetic circuit Gap length = lg, the length of the non magnetic part
Then ue = u * le / (le + lg * (u-1))
For packing fraction of 0.8, you can say le = 1 lg = 0.2 u = 10000 ( say for iron )
ue = 5 approx
See the problem ?