Geoscience Reference
In-Depth Information
application 12.2
Consider a fast moving train with velocity
v
on a rail bed on soft soil. The
question is what is the maximum speed, where induced surface vibrations will be
damped, i.e. the critical velocity. The rail bed is composed of a relatively thin
gravel layer on a sand embankment on clay subsoil. The gravel-sand body is
considered to act as a beam with bending stiffness
E
s
I
and mass
A
per metre
length, and the dynamic behaviour of the subsoil is characterised by a spring with
constant
k
. The elasticity modulus is
E
s
=
200
MPa for sand and
E
c
=
60 MPa for
clay. The mass of the sand is
=
2000 kg/m
3
. The sand embankment is 10 m wide
(
B
) and 5 m high (
H
), which gives
A =
50 m
2
and
I = BH
3
/12 = 104 m
4
.
The spring constant is, according to equation (12.36) adopted for two
dimensions,
k = E
c
B/h
, and for
h
the value
B/
2
=
5 m is taken (apex of the dynamic
cone is 90
o
). This yields
k =
30 MN/m. However, the attention is focused on
surface waves, and therefore, instead of
E
c
the shear modulus should be inserted
G
= E/
2(
1+
)
E/3
, thus
k =
15 MN/m applies. Equation (12.49) defines the critical
velocity
2
A
2
B
)
ΒΌ
=
(4x15x10
6
x200x10
6
x104x(2000)
-2
(10x8x10)
-2
)
0.25
v
c
=
(4
kEI/
= 42.5 m/s = 153 km/hr
This result indicates that for a high speed train the structure of a rail bed on soft
soil should be different than standard. Cement-soil mixed piles in the clay or a
(partly buried) concrete bridge founded on piles is a solution in this case.
application 12.3
A circular footing with radius
R
= 5 m is placed on a sandy sea bottom. The soil
has a strength of
c
= 0 kPa and
'
= 9 kN/m
3
.
By using EC7 code determine the bearing capacity
q
when the load inclination is
F
v
/ F
h
= 2. So, what is
F
v,max
?
= 25
o
, and a submerged weight of
application 12.4
Is the result of a pile-loading test a lower or an upper bound value?
application 12.5
A concrete element with a weight of 10 kN falls on the ground; its surface
touching the ground is 1 m
2
. The soil unit weight is 18 kN/m
3
. What is the response
of the soil? Does it vibrate?
application 12.6
Fig 12.8 shows Ehlers' model, which can be applied for dynamic and static soil
response. The apex
is related to active, neutral (shear strength is not mobilised)
or passive soil states. What is the value of
, if a neutral soil state is adopted? For a
passive soil state, does
increase or not, and how much (for a cohesion-less soil)?
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