Engineering Rock Mechanics

Questions and answers: rock masses 125

Note that this result is directly analogous to the result obtained in the

first part of A8.1.

Fractured strata

The total thickness of the rock mass is the sum of the thickness of each

stratum, L = E, ti. This equation should include a term to account for

the thickness of each fracture but, as in 48.1, we assume that this is

negligible compared to the intact rock thickness.

As for the first part of this question, the shear deformation of a single

stratum of intact rock is 6i = ti(t/Gi) and the shear deformation of any

fracture is 8d = t/Gd. For ni fractures in stratum i, the shear deformation ==-- - n

iS &i = ni8d = )Citi(t/Gdi). The total shear deformation is the sum of the YT

shear displacements due to the intact rock and the fractures and is thus

given as 8T = Xi 8i + xi 8di, which, upon substitution of the expressions

for Si and 8di, becomes

~ A2

1

2

3

4

Gdi 1

8T=Xti-+X)Citi-=t t t c"+c-.

i Gi Gdi [. G, 1

8T [F & + 21

Consequently, the total strain is

y=-=

L ti

1

and so the rock mass shear modulus is

c c tl

This equation is directly analogous to the result obtained in A8.1, and

G, shows a similar sensitivity to the fracture frequency and fracture

stiffness values as illustrated in A8.1 for E,. Once again, an assessment

of the fracture stiffness is essential if the behaviour of the rock mass is to

be properly understood.

48.3 When the application of stress is not perpendicular to the

fractures, as in 48.1 and 48.2, it is necessary to transform the

stress components in order to establish rock mass deformation

moduli using the fracture stiff nesses or compliances. This results

in equations for the rock mass modulus, Em, of the type (Wei and

Hudson, 1 986 5,

• 11s: c0s4a + X~~~~cos~asin~a + 12s$,cos2asin2a + 2.2~:~ sin4a
  _--^11
  Em - E

JThis equation is for two orthogonal sets of fractures in 2-D. The method by which

the equations for n sets in 3-D can be developed is given in Wei Z. Q. and Hudson J.

A. (1986) The influence of joints on rock modulus. Proc. Int. Symp. Engineering in Complex

Rock Formations (T. K. Tan, ed.), Pergamon Press, Beijing, pp. 54-62.