Question #$3$

A mine in limestone is being designed utilizing a pillar method with rectangular pillars.

The clear spacing between the pillars is $8m.$ The pillars are $9m$ square and the

excavation is at a depth of $100m.$ Conditions within the mine are dry. The bedding

planes are smooth with slightly weathered surfaces and no visible aperture. Examination

of the pillars shows that the limestone is horizontally bedded with moderate spacing and

gentle undulations. A point load test of the pillar rock yielded an estimated uniaxial

compressive strength of $120$MPa; Triaxial testing of the pillar rock demonstrated that the

rock failed when the axial stress in the sample was $140$MPa and the confining pressure

was $6$MPa. The unit weight of limestone is $26\mathrm{.}5k\frac{N}{m^3}.$ The ratio of horizontal to

average vertical stress is $0\mathrm{.}09$ at the centre of each pillar. Provide the answers to the

following:

a$.$ Estimate the Rock Mass Rating $($RMR$)$ for the pillars;

b$.$ Determine the Hoek$-$Brown Strength Parameters $m$ and $s$ for the rock mass using

the following equations:

$m=m_i$exp$(\frac{RMR-100}{28})$ and $s=(\frac{RMR-100}{9})$

c$.$ Determine the maximum vertical stress the pillars can sustain at their faces;

d$.$ Determine the maximum vertical stress the pillars can sustain at their centres;

$e.$ Use the tributary area theory in order to estimate the average vertical stress in the

pillar and hence determine the factor of safety of the pillars;

$\frac{{}_1}{{}_c}=\frac{{}_3}{{}_c}+\sqrt[\phantom{2}]{m\frac{{}_3}{{}_c}+s}$