$1\mathrm{.}3.$ Consider a tunnel development end where a new support system is being tested. The development end is supported using Resin bolts $(150$kN peak load$)$ and Steel arches $(120$ kN peak load$).$ The rock density is $2900k\frac{g}{m^3},$ and the thickness of the hanging wall to be supported is $3\mathrm{.}5$ meters.

$1\mathrm{.}3\mathrm{.}1.$ Calculate the support demand for the hanging wall based on the provided rock density and thickness.

$1\mathrm{.}3\mathrm{.}2.$ Calculate the support resistance provided by the support system in the development end, given that there are $5$ resin bolts per meter length of the tunnel and $1$ steel arch every $0\mathrm{.}75$ meters.

$1\mathrm{.}4.$ At $850$ meters below the surface, in rock with a density of $3000k\frac{g}{m^3},$ a system of square pillars is intended for mining. The stoping width will be $2\mathrm{.}4$ meters with $8$ meters wide square pillars and $10$ meters wide bords. The uniaxial compressive strength $($UCS$)$ of the rock was measured in the laboratory to be $140$ MPa $.$

$1\mathrm{.}4\mathrm{.}1.$ Use sketches to illustrate the pillar layout $($i$.$e$.,$ plan view and section view$).$

$1\mathrm{.}4\mathrm{.}2.$ Use the safety factor to evaluate and conclude on the stability of the planned pillar layout system. Write a short recommendation to the Mine Manager based on your judgement.

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