Engineering Rock Mechanics

Question and answers: permeability 145

the fractures is given by the equation K = 1ge3/12u where 1 is the

fracture frequency, g is gravitational acceleration, e is the fracture

aperture, and u is the kinematic viscosity of the fluid. For a rock mass

with a fracture frequency of one fracture per metre and with fracture

apertures of 0.01 mm, the hydraulic conductivity is 8.3 x 1 O-'O m/s.

(a) What is the hydraulic conductivity of a second rock mass which

has ten fractures per metre and fracture apertures of 1 mm?

(b) What is the main factor contributing to the difference in the

hydraulic conductivity of the two rock masses?

A9.2 (a) We are given K, h and e, so

8.3 x

-- gK - _- - = 8.3 x 16 m/s.

12u he3 1 x (0.01 x 10-3)3

Therefore, the hydraulic conductivity of the second rock mass is

K = he3 x - = 10 x (1 x 10-~)~ x (8.3 x io5) = 8.3 x IO-^ m/s.

( 1;")

which is a ten million fold increase from the value for the first rock mass.

(b) In the second rock mass, the fracture frequency has increased by a

factor of 10 and the aperture by a factor of 100 over the values for the

first rock mass. However, the permeability is linearly proportional to the

fracture frequency but proportional to the cube of the aperture, giving

the ten million fold increase from 10 x 100 x 100 x 100. So it is the fracture

aperture increase that has contributed most to the hydraulic conductivity

increase. This illustrates the significant effect of the fractures and their

properties on governing the flow of water through a fractured rock mass.

Moreover, we noted in Chapter 3 that the process of rock excavation

reduced the normal stress to zero on the excavation surfaces. This en-

ables proximate rock fractures to expand and the hydraulic conductivity

of the disturbed zone around the excavation to increase as a function of

the cube of the fracture aperture increase.

49.3 In question 49.2, the hydraulic aperture was used. For a

fracture with planar and parallel sides, this aperture is the perpen-

dicular distance between the two sides.

(a) Explain the meaning of fracture aperture when the fracture

surfaces are rough.

(b) Do you think that the mechanical aperture and the hydraulic

aperture of a fracture have the same value? If not, which is greater?

A93 (a) When the fracture surfaces are rough, the geometrical aper-

ture will vary all along the fracture. If the aperture geometry were

known, the distribution of geometrical fracture apertures could be gen-

erated, and a mean and standard deviation calculated. However, the

hydraulic aperture will be less than the mean geometrical aperture be-

cause the flow will be controlled by regions of smaller aperture, which

act as bottlenecks to the flow. In 3-D, it is somewhat different because

water flow will occur, along and across the fracture aperture, in the