Page 605 - Rock Mechanics For Underground Mining

ANSWERS TO PROBLEMS

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(d) p 1 = 20.0 MPa, oriented 030 /30 (dip direction/dip);
p 2 = 10.0 MPa, oriented 135 /24 ;
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p 3 = 8.0 MPa, oriented 257 /50 .
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5 mob = 31.3 (cf. act = 20 ).
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Chapter 7
1 (a) Compressive failure in side wall, tensile failure in crown.
(b) Increase W/H ratio of excavation.
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2 (a) Maximum boundary stress of 55 MPa located 30 below x axis in
right-hand wall, and 30 above horizontal in left-hand wall. Minimum
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boundary stress of 11 MPa, located across diameter perpendicular to that
defining maximum stresses.
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(b) Angular range of boundary failure is ±35.5 about the location of the
maximum stress.
3 Boundary stresses are approximately those for isolated openings.
At A, 1 = 21.31 MPa, 2 = 20 MPa, 3 = 18.69 MPa, and 1 =−54.1 ◦
in problem plane.
4 D 1.2 = 10 m.
5 Maximum and minimum boundary stresses are 112.9 MPa and −2.4 MPa,
both located near the ends of the ellipse.
6 On fault, max = 1.41 MPa.

Chapter 13

1 Initial F of S = 1.1. For F of S = 1.6, w p = 9.2m.
2 For existing layout, F of S = 1.98. If roof coal is stripped, F of S = 1.69.
3 F of S = 5.47.
4 Pillar is stable.

Chapter 15

1 (b) xx = 32.224 MPa, zz = 40.224 MPa, zx = 2.409 MPa.
(c) u z =± 0.080 m.
2 (a) L 0 = 294.1m.
−3
For L = L 0 , W r = 9817.5 MJ per unit length and 33.38 MJ m .
−3
For L L 0 , W r = 85L MJ per unit length and 85 MJ m .
2
−(1 − )p S l
(b) W rp = ln cos
G 2S
l = 100 m, S = 125 m.

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