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.