Page 136 - Rock Mechanics For Underground Mining

ROCK STRENGTH AND DEFORMABILITY

Figure 4.33 Variation of peak prin-
cipal stress difference with the angle
of inclination of the major principal
stress to the plane of weakness, for the
confining pressures indicated for (a) a
phyllite (after Donath, 1972), (b–d) a
slate and two shales (after McLamore
and Gray, 1967).

measured variations in peak principal stress difference with the angle of inclination
of the major principal stress to the plane of weakness.
Jaeger (1960) introduced an instructive analysis of the case in which the rock
contains well-defined, parallel planes of weakness whose normals are inclined at an
angle to the major principal stress direction as shown in Figure 4.34a. Each plane
of weakness has a limiting shear strength defined by Coulomb’s criterion
(4.29)
s = c w + n tan w
Slip on the plane of weakness (ab) will become incipient when the shear stress on
the plane, , becomes equal to, or greater than, the shear strength, s. The stress
Figure 4.34 (a) Transversely iso- transformation equations give the normal and shear stresses on ab as
tropic specimen in triaxial compres-
1
1
sion; (b) variation of peak strength at n = ( 1 + 3 ) + ( 1 − 3 ) cos 2
2 2
constant confining pressure with the
angle of inclination of the normal to and
the plane of weakness to the compres-
1
sion axis ( ). = ( 1 − 3 ) sin 2 (4.30)
2
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