Civil Engineering Reference
In-Depth Information
1000
N
q
100
10
25
30
35
40
45
o
f
′
Figure 4.3
Variation of
N
q
with
φ
(Berezantzev
et al.
, 1961).
Bolton (1986) suggests restricting equation (4.3) tomean effective stress levels in excess
of 150 kPa, below which the corrected relative density is taken as
I
R
=
5
I
D
−
1.
φ
may then be calculated from
The appropriate value of
φ
=
φ
cv
+
3
I
R
degrees
(4.4)
The average mean effective stress at failure may be taken approximately as the
geometric mean of the end-bearing pressure and the ambient vertical effective
stress, i.e.
N
q
σ
v
p
∼
(4.5)
The end-bearing pressure,
q
b
, may now be calculated, for given values of
φ
cv
,
I
D
,
σ
v
, by iterating between equations (4.3) to (4.5) and the chart for
N
q
shown in
Figure 4.3. As an example, consider the case of
and
30
◦
,
I
D
=
σ
v
=
φ
cv
=
0
.
75 and
l
00 kPa.
Assuming an initial value of
N
q
of 50, equation (4.5) gives
p
=
707 kPa from which
φ
may be calculated as 35
◦
. For this value of
φ
, Figure 4.3 yields a new value of
N
q
of 75. Further iteration yields a final value of
N
q
=
66, and an end-bearing pressure
of
q
b
=
6 MPa.
Figure 4.4 presents charts of end-bearing pressure against ambient vertical effective
stress, for different values of
6
.
φ
cv
and
I
D
The charts are plotted on logarithmic axes,
which obscures the natural variation of q
b
with depth. This variation is non-linear,
showing a gradually reducing rate of increase with depth, similar to that found from
pile load tests. Only at great depths and for dense deposits of sand do end-bearing
pressures exceed 20 MPa. Bolton quotes values
φ
cv
for different types of sand ranging
from 25
◦
for mica up to 40
◦
for feldspar. In practice, presence of silt particles will
φ
cv
for most deposits will rarely lie much above 30
◦
.
mean that
