Page 223 - Rock Mechanics For Underground Mining

EFFECT OF PLANES OF WEAKNESS ON ELASTIC STRESS DISTRIBUTION

Figure 7.7 A plane of weakness in-
tersecting a circular opening and ori-
ented parallel to the major principal
stress, showing development of a de-
1
stressed zone for K < .
3
modified by slip. The possibility of separation on the plane of weakness arises if
1
1
tensile stress can develop in the crown of the opening, i.e. if K < .If K ≥ , the
3 3
elastic stress distribution is unaltered by either slip or separation.
1
For the case where K < , separation on the plane of weakness leads to de-stressing
3
of a region in the crown of the opening (and also in the floor, although this is of no
engineering consequence). A reasonable estimate of the extent of the de-stressed
zone, for purposes of support design, for example, can be obtained by considering the
circumscribed ellipse, illustrated in Figure 7.7b. Separation on the plane of weakness
is prevented when B = 0; from equation 6.24, this occurs when
2K

B = p K − 1 + = 0
q
or
2K
q =
1 − K
Since q = W/H = 2a/H, it is readily shown that the height h of the de-stressed
zone above the crown of the opening is given by
1 − 3K

h = a
2K
Case 3. (Figure 7.8) A flat-lying feature whose trace on the excavation boundary is
located at an angle
above the horizontal diameter is shown in Figure 7.8a. Consid-
ering the small element of the boundary, shown in Figure 7.8b, the normal and shear
stress components on the plane of weakness are given by
2
n =

cos
(7.4)
=

sin
cos
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