Geoscience Reference
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i.e. the effects of a cylindrical cavity in a uniform infinite soil and a cavity in a
semi-infinite soil.
C
A CYLINDRICAL CAVITY IN A UNIFORM INFINITE SOIL
Consider a cylindrical cavity with a radius
r
0
and an internal pressure
q
in a 3D
elastic soil (Fig 15.5a). Equilibrium is expressed in terms of effective radial stress
r
'
and effective tangential stress
'
and pore pressure
u
by
r
'
,r
+
(
r
'
'
)
/r = u
,r
(15.1)
'
).
It can be shown that the induced
deformation involves only shear and that no volumetric deformation occurs (no
dilation is assumed)
56
. Hence, no pore pressure are generated, i.e.
u = 0
, and a total
or effective stress approach makes no difference. Consider a zone
r > r
p
where the
soil response is linear-elastic and described by the shear modulus G only. The soil
expands or contracts radially due to a boundary stress
The axial stress is
z
' =
(
r
'
p
at
r = r
p
and the following
stresses and radial displacement
w
comply with this state
r
= q
(
r
p
/r
)
2
= 2Gw/r =
2
Gw
p
r
p
/r
2
and
=
r
and
z
=
0
(15.2a)
w = qr
p
2
/2Gr
and
w
p
= qr
p
/
2
G
(15.2b)
Here,
q
is the cavity pressure. The displacements are relatively small, i.e. |
w| << r
.
z
z
z
at r = r
p
at r = r
p
at r = r
p
at r > r
p
at r > r
p
at r > r
p
at r = r
0
at r = r
0
at r = r
0
w
p
w
p
w
p
elastic zone
elastic zone
elastic zone
w
0
w
0
w
0
plastic zone
plastic zone
plastic zone
r
r
r
r
0
r
0
r
0
r
p
r
p
r
p
r
1
r
1
r
1
r
r
r
c
c
c
q
q
q
(a) cylindrical cavity (b) Mohr circle
Figure 15.5 An expanding cylindrical cavity in cohesive soil
Under higher pressures the soil may behave non-linear in a zone
r
0
< r < r
p
where
r
p
is the radius of the interface between the plastic and elastic region.
Assume a cohesive soil (
= 0
) with no volume change in the plastic zone (also no
56
If no dilation may hold, the pore pressure is not affected. Hence, the dash indicating
effective stresses is omitted for convenience. It may hold for clay. However, in sands
dilation / contraction is not negligible and pore pressures will be involved.
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