Physics for Geologists, Second edition

Stress and strain 93
Figure 9.2 Components of weight of a block. The vertical component is a,, that
normal to the sliding surface is a,, and that parallel to the sliding
surface is T. The frictional resistance to sliding is r.
These may be regarded as active stresses. They give rise to reactive stresses,
a normal reaction and frictional resistance (t) that tends to prevent sliding.
As the angle of slope 0 increases, so the shear component of weight increases.
There is some critical value of 0 at which the shear component of weight is
equal to the frictional resistance and the block is just about to slide. The
friction is due to adhesion or cohesion between bodies, or to the roughness
of the surfaces that would be sliding surfaces. The roughness can only be
overcome by deformation or fracture of the protuberances.
The Coulomb or Mohr-Coulomb criterion for simple unlubricated sliding
(see Hubbert 1951: 363) is
where to is the cohesive strength or initial shear strength of the material at
the surface that will become the sliding surface, when the normal stress on is
zero; and tan 4 is the coefficient of sliding friction, 4 being the internal angle
of friction. Sliding will therefore take place when
(pb - pa) gh sin 0 = to + (pb - pa) gh cos 0 tan +.
(from Equations 9.8b, 9 .8~ and 9.9) and
tan 0 =
This equation shows that unlubricated sliding will usually take place on
a slope 0 that is rather greater than 4.
The effect of pore-fluid pressure can be very important, reducing the effec-
tive stress and greatly reducing the angle at which sliding can take place. We
cannot go into this in detail, but the outline is this.
Copyright 2002 by Richard E. Chapman