Rock Mechanics.pdf - Mining and Blasting

PRE-MINING STATE OF STRESS
extend infinite distances horizontally from the toe of the 100 m high cliff. The effect
of the ground above the elevation D ′ CD can be treated as a wide surcharge load on a
half-space.
(a) The stress components due to a line load of magnitude P on a half space are
given by
rr =
2P sin
r
= r = 0
where r and are defined in figure (b).
Relative to x, z reference axes, show that the stress components due to the
strip load defined in figure (c) are given by
xx = p
2 [2(2 − 1) + (sin 22 − sin 21)]
zz = p
2 [2(2 − 1) − (sin 22 − sin 21)]
zx = p
2 [cos 21 − cos 22]
(b) If the unit weight of the rock is 27 kN m −3 , calculate the stress components
induced at a point P, 80 m vertically below the toe of the cliff, by the surcharge
load.
(c) If the state of stress at a point Q remote from the toe of the cliff and on the same
elevation as P, is given by xx = 2.16 MPa, zz = 3.24 MPa, zx = 0, estimate
the magnitudes and orientations of the plane principal stresses at P.
2 An element of rock 800 m below ground surface is transgressed by a set of parallel,
smooth continuous joints, dipping as shown in the figure below. The fissures are
water filled below an elevation 100 m below the ground surface. The vertical stress
component pzz is a principal stress, and equal to the depth stress. From the calculated
depth stress, pzz, calculate the range of possible magnitudes of the horizontal stress
component, pxx. The unit weight of the rock mass is 26 kN m −3 , and the unit weight
162