Rock Mechanics.pdf - Mining and Blasting

Answers to problems
Chapter 2
1 (a) 200 kN, with clockwise moment.
(b) xx =−15 MPa, yy = 16 MPa, xy = 10 MPa.
(c) ll = 1.41 MPa, mm =−0.41 MPa, lm = 18.42 MPa.
(d) 1 = 8.95 MPa, 2 =−17.95 MPa, = 73.6 ◦ .
(e) = 0 ◦ ; tx = 15 MN m −2 , ty =−10 MN m −2 .
= 60 ◦ ; tx =−1.16 MN m −2 , ty =−18.86 MN m −2 , R = 18.90 MPa
= 90 ◦ ; tx =−10 MN m −2 , ty =−16 MN m −2
2 (a) xx = 7.825, yy = 6.308, zz = 7.866;
xy = 1.422, yz = 0.012, zx =−1.857.
(b) mm = 9.824; nl = 0.079.
(c) I1 = 22.0, I2 = 155.0, I3 = 350.0;.
1 = 10.0 (1 = 43.4 ◦ , 1 = 73.9 ◦ , 1 = 129.05 ◦ );
2 = 7.0 (2 = 108.5 ◦ , 2 = 131.8 ◦ , 2 = 132.4 ◦ );
3 = 5.0 (3 = 51.8 ◦ , 3 = 132.4 ◦ , 3 = 66.2 ◦ ).
4 (a) εxx = 1
2G
− y
.
r 2 + 2x 2y r 4
εyy = 1
(1 − 4)
2G
y 2y3
+
r 2 r 4
,
xy = 1
2(1 − 2)
2G
x 4xy2
+
r 2 r 4
.
(b) xx =−(1 − 2) y
r 2 + 2x 2y r 4
.
yy = (1 − 2) y 2y3
+ ,
r 2 r 4
xy = (1 − 2) x 2xy2
+
r 2 r 4
.
5 (a) 1 = 25.0, 2 = 7.1, 1 = 58 ◦ , 2 = 148 ◦ .
n = 21.0, = 7.2.
(b) ll = 20.9, lm = 7.46.
(c) 1 = 24.94, 2 = 7.10, 1 = 58.3 ◦ , 2 = 148.3 ◦ .
Chapter 3
1 (a) ¯x0A = 0.369 m; ¯x0B = 0.274 m.
(b) ¯x = 0.288 m.
(c) RQD = 95.2.
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