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And the traction components become
t
x
= sin
2
(3/2+½cos
) + cos
sin
) +
cos
2
t
z
= sin
cos
(3/2+½cos
In Fig 15.11 a graph is presented of the traction components. Also the results for
K
0
=
0.5 (normally consolidated soil) are presented in the graph. The value of
K
0
makes a difference.
K
0
=0.5
K
0
=4
t
z
t
-1.0
1.0
t
x
x
t
z
/
s
H
t
x
/
s
H
z
Figure 15.11
application 15.3
The lining of a tunnel with radius
R
= 5 m can buckle under local soil and water
pressures. A practical approach for the calculation is by adopting springs on the
lining. These springs represent the ground stiffness. The springs can be determined
using the theory of an elastic half space. The spring constant is then:
k
=
EA
0
/
h
(equation 12.36). At the depth of the tunnel the soil elasticity
E
is 10 MPa. Explain
how you would interpret
A
0
and
h
, and determine the corresponding spring constant
value
k
.
Figure 15.12
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