Environmental Engineering Reference
In-Depth Information
Table 1.19
Statistics of the estimated
δ
ij
in the form of 90% confidence interval (Median)
X
1
X
2
X
3
X
4
X
5
X
6
X
7
X
8
X
9
X
10
X
1
1.00
0.88~
0.94
(0.91)
0.06~
0.14
(0.10)
0.04~
0.15
(0.09)
0.04~
0.14
(0.09)
0.01~
0.13
(0.07)
−
0.28~
−
0.22
(
−
0.25)
−
0.27~
−
0.21
(
−
0.24)
−
0.35~
−
0.27
(-0.31)
−
0.26~
−
0.15
(
−
0.20)
X
2
1.00
−
0.35~
−
0.29
(
−
0.32)
−
0.24~
−
0.18
(
−
0.21)
−
0.31~
−
0.24
(
−
0.27)
0.01~
0.07
(0.04)
−
0.30~
−
0.19
(
−
0.24)
0.06~
0.16
(0.11)
−
0.04~
0.05
(0.00)
−
0.06~
0.05
(
−
0.01)
X
3
Index properties
1.00
0.55~
0.65
(0.60)
0.00~
0.13
(0.07)
−
0.53~
−
0.45
(
−
0.49)
−
0.64~
−
0.53
(
−
0.58)
−
0.05~
0.03
(
−
0.01)
−
0.11~
0.00
(
−
0.06)
−
0.12~
0.01
(
−
0.05)
X
4
1.00
0.68
-0.76
(0.72)
0.15~
0.25
(0.20)
−
0.59~
−
0.50
(
−
0.54)
−
0.02~
0.09
(0.03)
−
0.43~
−
0.33
(
−
0.38)
−
0.37~
−
0.26
(
−
0.31)
C
=
X
5
1.00
−
0.03
-0.05
(0.01)
0.00~
0.12
(0.06)
−
0.09~
0.02
(
−
0.03)
0.06~
0.18
(0.12)
−
0.03~
0.11
(0.03)
X
6
1.00
0.09
-0.21
(0.15)
−
0.30~
−
0.18
(
−
0.24)
0.65~
0.79
(0.72)
0.55~
0.70
(0.62)
X
7
Stresses and strengths
1.00
0.11
-0.27
(0.19)
0.05~
0.22
(0.14)
-0.17~
0.01
(-0.08)
X
8
1.00
−
0.70~
−
0.56
(
−
0.63)
X
9
Symmetry 1.00 0.67~
0.82
(0.74)
X
10
CPTU parameters 1.00
Source: Ching, J. and Phoon, K.K. 2014b.
Canadian Geotechnical Journal
, 51(6), 686-704, reproduced with permission of the
NRC Research Press.
−
0.51~
−
0.38
(
−
0.44)
1.7.3 Conditioning: bayesian analysis
On the basis of multivariate probability distribution constructed in Section 1.7.2, it is pos-
sible to update the marginal distribution of any one parameter or even the multivariate
distribution of any group of parameters given information from other parameters covered
by the probability distribution. One example of the former is to update the distribution of
Y
6
based on Y
9
measurements. One example of the latter is to update the bivariate distribu-
tion of (Y
5
, Y
6
) based on measurements from (Y
3
, Y
4
, Y
8
, Y
10
). Detailed calculations for this
example are presented below. Ching and Phoon (2014b) covered another example where the
bivariate distribution of (Y
5
, Y
6
) is updated based on measurements from (Y
4
, Y
8
, Y
9
). The
theory has been covered in Section 1.4.5. The estimation of a design property from multiple
data sources is one important practical outcome of a site investigation program. The “con-
ditioning” procedure described in this section can be viewed as a rationalization of simpler
empirical procedures widely adopted in practice such as averaging estimates from different
tests or choosing the most conservative estimate produced by all tests.
Consider an example involving updating the normalized preconsolidation stress (Y
5
) and
the normalized undrained shear strength (Y
6
) at a given depth based on data from other
sources measured at the same depth: LI (Y
3
), the normalized effective vertical stress (Y
4
),
the pore pressure ratio (Y
8
), and the normalized effective cone tip resistance (Y
10
). This
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