Environmental Engineering Reference
In-Depth Information
Table 1.16
Statistics of the 10 geotechnical parameters in Clay/10/7490
Parameters n Mean COV Min Max
LL 3822 67.7 0.80 18.1 515
PI 4265 39.7 1.08 1.9 363
LI 3661 1.01 0.78
−
0.75 6.45
σ′
v
/
P
a
3370 1.80 1.47 4.13E-3 38.74
σ′
p
/
P
a
2028 4.37 2.31 0.094 193.30
s
u
/
σ′
v
3538 0.51 1.25 3.68E-3 7.78
S
t
1589 35.0 2.88 1 1467
B
q
1016 0.58 0.35 0.01 1.17
(q
t
-
σ
v
)/
σ′
v
862 8.90 1.17 0.48 95.98
(q
t
-
u
2
)/
σ′
v
668 5.34 1.37 0.61 108.20
OCR 3531 3.85 1.56 1.0 60.23
Source: Ching, J. and Phoon, K.K. 2014b.
Canadian Geotechnical Journal
, 51(6), 686-704, reproduced with permission of the
NRC Research Press.
4. Yln/P
σ
va
5. Yln/P
4
=
(
′
)
Ž
‰
‰
5
=
(
σ
pa
′
)
Stresses and strengths
6.
Yln/
6
=
(
s
uv
σ
′
)
7. Y
7
= ln(
S
t
)
8. Y
8
= B
q
9. Yln
Ž
‰
‰
9
=
[(
q
t
−
σσ
)
/
′
]
CPTU parameters
v
v
10. Yln
=
[(
qu
t
−
)
/
σ
′
]
1
0
2
v
The natural logarithm transform is applied to eight non-negative parameters. For the
parameters that can be potentially negative (LI and B
q
), no transform is needed and Yi
i
sim-
ply denotes the physical parameter itself. There are data points where two or more of these
parameters are simultaneously known. For instance, a disturbed clay sample is extracted
to determine LI, and an undisturbed clay sample is extracted at a nearby borehole at the
same depth to determine
σ
p
. In this study, we describe Y
3
= LI and Yln/
5
=
(
σ
p
P
′
)
as being
′
“simultaneously” known in this sense.
In principle, the construction of a multivariate distribution for (Y
1
, Y
2
, …, Y
10
) will
require multivariate data points. This means a single set of values of (Y
1
, Y
2
, …, Y
10
) is
obtained from the same soil sample or more practically, from soil samples extracted from
adjacent boreholes at comparable depths. The criterion is that a single set of values must be
measured from samples that are strongly correlated in the spatial sense. The database will
be a multivariate database if all 10 tests were conducted in each cited reference. It is evident
that such multivariate data are not available in geotechnical engineering. Nonetheless, it
is not uncommon to have
bivariate
data measured in close spatial proximity, for example,
both Y
3
and Y
5
[LI and ln(
σ
p
P
/ ] are measured in two adjacent boreholes at comparable
depths. One would expect these Y
3
and Y
5
profiles to be correlated. Since there are 10 basic
parameters, it is possible to form
10
C
2
= 45 distinct pairs of parameters. The off-diagonal
numbers in
Table 1.17
show the numbers of data points associated with each pair of param-
eters. The numbers in the leading diagonal of
Table 1.17
show the numbers of data points
associated with a single parameter, which are identical to the numbers shown in the second
column of
Table 1.16
.
′
)
Search WWH ::
Custom Search