Engineering Rock Mechanics

Questions and answers: underground excavation instability mechanisms 349

Af = $($1121 sin8121 + $2151 sin8251 + $5111 ~in0~~1)

= :(; .34.52 - I sin 1371 + e52 36. I sin 1401 + .36.34. I sin 97))

= t(602.9 + 601.6 + 607.4) = 604.0 mm2 24.16 m2

h = ~(112^1 tan 812 + 125 tan 825 + 151 tan 851)

= l(29. tan34 + 24. tan39 + 16. tan50)

= i(19.6 + 19.4 + 19.1) = 19.37 mm E 3.9 m

W = !yAfh = 4 x 22 x 24.16 x 3.9 = 691.0 kN, and

p = 3y h =

3

x 22 x 3.9 = 28.6 kN/m2.

Angles taken from the hemispher-

ical projection:

614 = la1 - a41 = 1058 - 1601 = 102

645 = la4 - a51 = 1160 - 3351 = 175

8551 = la5 -a] I = 1335 - 0581 = 277

814 = 27

845 = 2

851 = 50

Block 145

Scale drawing of block (original scale 5 mm: 1 m):

Af = 5($1Z41 sine141 + &Z5) ~in8~~1 + !$5Z11 sin8511)

= ;(;. 7.78. I sin 1021 + - 78.77. I sin1751 +

= 5(267.0 + 261.7 + 267.5) = 265.4 mm2 E 10.62 m2

-77.7. I sin2271)