Rock Mechanics.pdf - Mining and Blasting

ANSWERS TO PROBLEMS
(d) p1 = 20.0 MPa, oriented 030 ◦ /30 ◦ (dip direction/dip);
p2 = 10.0 MPa, oriented 135 ◦ /24 ◦ ;
p3 = 8.0 MPa, oriented 257 ◦ /50 ◦ .
5 mob = 31.3 ◦ (cf. act = 20 ◦ ).
Chapter 7
1 (a) Compressive failure in side wall, tensile failure in crown.
(b) Increase W/H ratio of excavation.
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
boundary stress of 11 MPa, located across diameter perpendicular to that
defining maximum stresses.
(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 D1.2 = 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, wp = 9.2 m.
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) uz =±0.080 m.
2 (a) L0 = 294.1 m.
For L = L0, Wr = 9817.5 MJ per unit length and 33.38 MJ m −3 .
For L ≫ L0, Wr = 85L MJ per unit length and 85 MJ m −3 .
587
(b) Wrp = −(1 − )p2 S
G
l = 100 m, S = 125 m.
ln cos l
2S