Engineering Rock Mechanics

152 Permeabi/i?,

-Shale-

-Limestone & Dolomite-

-Volcanics

-Metamorphics-

+Salt-

-Granitics-

-Clay

-Sandstone-

Gravel Sands V. fine sands, silts, Homogeneous

glacial tills, stratified clays

clays

-Shale

-FracturedAandstone rn

-Soln.Cavities -Limestone & Dolomite -Unfractured -

-Cavernous/Fractured Basalt - Dense

+Fracturefleathered-Volcanics excl. Basalt-

+Weathered- Metamorphics-

+Bedded Salt-

+Weathered- Granitic Rocks

Conductivity, 10-2 ,o-4 lo-5 10-6 L0-9 lo-10 lo-ll

mls I I I II I I I II

Degree conductivity Of 1 V. high High Moderate Low V.low

Soil type

Figure 9.2 Primary and secondary hydraulic conductivity for rocks and rock masses

(after Isherwood, 1979).

where c is the conductance, given by ge3/12vL and

In the expression for c, e is the aperture between the pair of plates, v is

the kinematic viscosity of the fluid (which for water may be taken as

1.0 x 104m2/s) and L is the length of the plates in the direction of flow.

Figure 9.3 illustrates this equation.

Note that in the formula for the conductance given above, the flow rate

is proportional to the cube of the discontinuity aperture. The flow rate is

thus extremely sensitive to small changes in aperture: a doubling of

aperture results in an eight-fold increase of flow rate. As a consequence,

one very open discontinuity through a rock mass can totally dominate the

water flow conditions.

A natural extension of this formula for conductance is to consider a set

of parallel discontinuities. The hydraulic conductivity parallel to the set is

given by

HL is the head loss between the two end sections.

K=- ke3 (L/T)

12v

where A is the discontinuity frequency.