Question $3$

A flat$-$lying coal seam $3$ m thick and $75$ m below ground surface has been mined

with $5\mathrm{.}0$ m rooms and $7\mathrm{.}0$ m square pillars, over the lower $2\mathrm{.}2$ m of the seam.

Determine the factor of safety of the pillars, and assess the feasibility of stripping an

extra $0\mathrm{.}6$ m of coal from the roof. The strength of the square pillars, of width $w_p$ and

height $h,$ is given by

$S=7\mathrm{.}5h^{-0\mathrm{.}66}{w}_p^{0\mathrm{.}46}$

where $S$ is in MPa, and $h$ and $w_p$ are in m $.$

The unit weight of the overburden rock is $25k\frac{N}{m^3}.$

Ans: FOS$=1\mathrm{.}98,$ If stripped FOS$=1\mathrm{.}69$

Please use diagrams where needed and add comments. ty