A group of $9$ friction piles are arranged in a square grid maintaining equal spacing in all directions. Each pile is of diameter $300 \mathrm{~mm}$ and length $7 \mathrm{~m} $. Assume that the soil is cohesionless with effective friction angle $\phi^{\prime}=32^{\circ}.$ What is the center-to-center spacing of the piles $\text{(in m)}$ for the pile group efficiency of $ 60 \%$?
- $0.582$
- $0.486$
- $0.391$
- $ 0.677$