Page 142 - Rock Mechanics For Underground Mining

ROCK STRENGTH AND DEFORMABILITY

surface has a friction angle , so that at limiting equilibrium for the direct shear test
configuration of Figure 4.41a,
S
= tan
N
If the discontinuity surface is inclined at an angle i to the direction of the shear
force, S (Figure 4.41b), then slip will occur when the shear and normal forces on the
∗
∗
discontinuity, S and N , are related by
S ∗
Figure4.40 Peakandresidualeffec- ∗ = tan (4.33)
tive stress shear strength envelopes. N
Resolving S and N in the direction of the discontinuity surface gives
∗
S = S cos i − N sin i
and

N = N cos i + S sin i
∗
Substitution of these values in equation 4.33 and simplification gives the condition
for slip as
S
= tan ( + i) (4.34)
N

Thus the inclined discontinuity surface has an apparent friction angle of ( + i).
Patton extended this model to include the case in which the discontinuity surface
contains a number of ‘teeth’ (Figure 4.41c and d). In a series of model experiments

Figure 4.41 Idealised surface
roughness models illustrating the
roughness angle, i.
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