Engineering Rock Mechanics

Questions and answers: underground excavation instability mechanisms 361

40

35

a a^30

vi cn^25

0

U

U^3

g 20

8 15

s 10

5

0

-5

80

70

60

E 50

U 40

z

30

20

10

0

R1

vi

c cn

3

1 5 9

1 5

13 17

Node number

9 13 17

Node number

k = 0.3

Boundary

element

results

solution

0 Approximate

21

k = 2.5

Boundary

element

results

0 ADDroximate

soiution

21

419.8 The diagram shows the
relative positions of two paral-
lel horizontal tunnels, each 3 m
in diameter. Prior to excavation,
the principal stresses in the area
werep, = p,, = pz = 11 MPa.
(a) Determine the principal
stresses and their directions at
point A after excavation has

X

been completed. Z

(b) A horizontal fault coincident with the x-axis passes through A.

If the shear strength of the fault is purely frictional with Q = 20°, will

slip on the fault occur at A?

A19.8 Here we will apply the Kirsch solution to each excavation and
superpose the results in order to estimate the state of stress at point A.