Geoscience Reference
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x
d
D
H
s
t
R
z
Figure 15.8 Situation of a tunnel lining in a semi-saturated soil
The stresses around a rigid circular cylindrical cavity with radius R at a depth
D+H can be evaluated in semi-saturated uniform subsoil (Fig 15.8), when adopting
that shear
xz remains zero and no gap exists between soil and structure, thereby
excluding all effects of the boring process and construction. The initial vertical
stress state (without the cavity) at the location of the projected cavity perimeter can
be expressed by
z =
d D +
s ( H
R ) +
s R (1+cos
)
(15.20)
Here, the first term is due to the unsaturated soil weight; the second due to the
weight of the saturated part above the crest of the cavity and the third is the stress
along the perimeter, as a function of
. Incorporating the local hydrostatic pore
pressure p =
w ( H + R cos
) yields for the effective stress
z ' =
d D + (
s
w )( H + R cos
)
(15.21)
The horizontal effective stress, with a constant stress ratio coefficient K 0 ,
becomes
x ' = K 0 (
d D + (
s
w )( H + R cos
))
(15.22)
Adding the pore pressure gives the total horizontal stress
x = K 0
d D + (
w + K 0 (
s
w )( H + R cos
)
(15.23)
When the rigid cavity is installed, Verruijt assumes that horizontal stresses
remain unchanged and vertical stresses change, i.e. the specific weight of the third
term of (1) is changed from
t is the average specific weight of the
cavity (weight per cross-section and length). This gives
s to
t , where
z =
d D +
s ( H
R ) +
t R (1 + cos
)
(15.24)
 
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