Physics for Geologists, Second edition

94 Stress and strain
Terzaghi postulated that the total vertical load on sediment is borne partly
by the solid framework, and partly by the pore fluid:
where S(=ybwz) is the total vertical component of overburden pressure, yb,
the mean bulk wet density of the overburden in the vertical thickness z; a
is the effective stress transmitted through the solids, and p is the pore-fluid
pressure (which Terzaghi called the neutral stress). If for any reason the pore
fluids are confined and their pressure increases, then there is a corresponding
decrease in the effective stress - the stress that compacts sediment and sedimentary
rock. Alternatively, if the pore fluid cannot escape, the sedimentary
rock cannot compact because the pore fluid takes most of the load. If (S -p)
is substituted for a, in the Mohr-Coulomb criterion, Equation 9.10, it will
be seen that simple sliding can take place on slopes much less that @ as the
effective stress is reduced. Note that the coefficient of sliding (tan @) is not
changed, but the total effect is.
This was studied extensively by Terzaghi (1936, 1943: 235; 1950) in the
context of soil mechanics and landslides, and by Hubbert and Rubey (1959)
in the broader context of geology. To pursue this topic, it may help to read
Chapman (1979) first.
In any case try this. Place a cold empty can of drink, after chilling in
the fridge, upside down on a glass-topped table - that is, with the opening
downwards. As the warmer external air warms the air in the can, so it
expands and tends to lift the can, and it will slide on a very gentle slope. But
it only slides until it reaches the edge of the glass. As soon as the air pressure
can be reduced to normal, it stops sliding. The same principle is used for
rotating the large radio telescopes. If a can that has a perforation at both
ends is put to the same test, it will not slide when the other does.
Lubricated sliding
Following Kehle (1970), suppose an extensive, relatively thin sheet of a single
liquid is flowing in uniform laminar flow down a gentle slope on a planar
surface (Figure 9.3) and can be regarded as being newtonian (see page 91),
then
Assume that
where H is the total thickness of liquid flowing and H - h is the thickness
contributing to the shear stress at the level of interest. Note that the shear
Copyright 2002 by Richard E. Chapman