coal mine stooping section is located $120$m below surface. During surface drilling a $5$m

thick dolerite rock was intersected at $70$m below surface.

Goaf angle: $350$

Density of Dolerite: $3$ t$/$m$3$

Density of Host Rock: $2\mathrm{.}5$ t$/$m$3$

Friction angle of dolerite joint: $300.$

Cohesion of Dolerite joint planes: $20$ Kpa

Seam height: $3$m

i$.$ If the miner is obligated to prohibit goafing $($overburden collapse$)$ with a Safety

factor of $1\mathrm{.}5,$ determine the allowable maximum span of the stooping section.