A$.$ A $5$ m span decline tunnel for an underground mine is to be excavated in a hornblende granite rock mass at an average depth of $900$ m below surface with an average overburden density of $2,675$ kg$/$m$^3.$ The principal stress directions are approximately vertical and horizontal with K$0$max of $1\mathrm{.}5$ times the vertical stress and K$0$min of $0\mathrm{.}5$ times sigmav. The rockmass is locally damp but there is no

evidence of flowing water. The exploration adit mapping indicates the following characteristics. There are $3$ dominant joint sets of controlling stability with an occasional random joint set. One of the joint sets will be near perpendicular to the tunnel axis dipping at $25-30$ degrees out of the tunnel face. The adit was damp, but

the decline is expected at depth to have dripping regions. There in an average joint spacing along a of between $0\mathrm{.}1$ to $0\mathrm{.}2$ m with a persistence length of $2-3$ m$.$ Joints are smooth with a typical separation of $0\mathrm{.}5-1\mathrm{.}0$ mm$.$ Any infilling is soft as the joints are moderately weathered. RQD values from core box logging range from $55\%$ to $65\%.$Laboratory tests on core samples of intact rock give an average uniaxial compressive strength $($UCS$)$ of $90$ MPa and mi of $28.$ The decline will be mined via drill and blast method using smooth wall blasting technics where the disturbance factor is assumed to be $0\mathrm{.}8.$

$1.$ RMR

a$.$ Estimate the range of rock mass rating using Bieniawski$$s RMR$89$ method. Show your work on Bieniawski$$s chart.

b$.$ Determine the class of rock mass.

c$.$ Estimate the range of standup times for the decline.

$2.$ Q

a$.$ Estimate the range of rock mass quality using Barton$$s Q system method. Show your work on a chart.

b$.$ Determine the class of rock mass.

$3.$ Estimate the range of GSI values using Various relations with RQD$,$ RMR$,$ Jon, and Q$.$

$4.$ Estimate the range of Mohr$-$Coulomb cohesion and friction representative of the rock mass for these conditions.