Question and answers: permeability 155A9.8 We note that the maximum principal hydraulic conductivity has a
value of 1.596 x lop4 m/s in a sub-horizonal orientation to the northwest.
The intermediate value is 5.927 x lop6 m/s in a sub-horizontal direction
to the northeast, and the minimum value is 3.042 x m/s in a
sub-vertical direction. The maximum value is about 52 times greater
than the minimum value, but the intermediate value is only about twice
the minimum value.
Now consider the geological setting. Dolomitic rock has bedding
planes and often has two sets of joints orthogonal to each other and to the
bedding. The principal hydraulic conductivity values are sub-horizontal
and sub-vertical, indicating that the strata are lying horizontally. Thus,
with no further information, we would predict that there is a hydraul-
ically significant set of vertical fractures striking southeast to northwest
with a less significant vertical set striking northeast to southwest. In fact,
this was the case: the transmissivities of the major northwest fractures
and northeast sheared contacts varied between 0.01 and 0.001 m2/s.
Q9.9 (a) Explain the term ‘effective stress‘.
(b) If a fracture contains water under pressure and the stresses at
the fracture surfaces are being considered, what would be the effect
on the normal stress and on the shear stress in the rock of steadily
increasing the water pressure?
A9.9 (a) The term ’effective stress’, D’, was developed by Terzaghi as
the normal stress component, D, minus the water pressure, u: (T’ = (T - u.
Goodman (1998) explains that, in 1923, Terzaghi “fully understood now
that the addition of an increment of external pressure to a clay resulted
in a temporary increment of water pressure of equal magnitude... when
the water pressure in the soil’s pores had a value u, and the external
pressure had a magnitude p, only the value p - u was effective in causing
force between the grains.”
The water pressure is subtracted only from the normal stress com-
ponents because no shear stresses can be sustained in a fluid. In a
non-particulate intact rock, the validity of the use of effective stresses is
not clear, especially given the long periods of time that water pressures
require for dissipation in intact rock, as we saw in A9.1. The concept
is more likely to be valid in fractured rock masses, where the water
pressure in the fractures can exert a definite overall pressure, as shown
in the sketch below.
*See the biography of K. Terzaghi by Goodman R. E. (1998) The Engineer as Artist.
ASCE Press, Reston, VA, 340pp.