Environmental Engineering Reference
In-Depth Information
AB CDEF
GH I
J
KL
MN
O
P
Q
2
3
4
5
Spreadsheet Template for Calibrating a Liquefaction Induced Settlement
Prediction Model
Parameters to be estimated
µ
α
δ
α
6
1.0451
0.3175
Eq. (4.41)
Eqs. (4.37) and (4.39)
Eqs. (4.34) and (4.35)
7
Observed data
σ
p
2
(cm
2
)
Case
No.
Range
?
s
il
(cm)
s
iu
(cm)
µ
p
(cm)
µ
a
(cm)
8
P
(
d
i
|
θ
) n
P
(
d
i
|
θ
)
L
(
θ
|
D
)
δ
p
δ
a
λ
a
ξ
a
9
1
1
.
60
9.60
1.90
0.00
7.00
0.00
0.00
1.10
9.60
0.00
10.70
10
.
70 10.
8
2
10.82
1.31
0.
6
4
0.64
0.29
0.07
11.
3
08
11.308
1.3691
0.0209
7.138
4.379
0.9824
0.6271
11.235
0.0418
0
.
3268
0.3268
0.5356
0.3175
0.3435
0.3449
0.4614
0.5332
0.3227
0.3175
2.375
0.319
0.
1
329
0.1329
0.5281
1
0.3728
0.2786
0.9988
0.3105
1.1954
1
-
2.017874
-26.758609
-
10
2
0
1
.
90
1.
3
1
0.
2
9
0.41
1
.
3691
0
.
5356
0.188
0.502
0.
5
281
-
0.638443
-
Log-likelihood
11
3
1
0
.
00
3
.
40
0.
0
2
0
0.00
.
0209
0
.
3175
-3.92 .31
1
0
3.40
10.70
3.40
3.40
0.02
6.83
4.19
0.94
0
0.73
0.29
0.09
0.06
12
4
1
7
.
00
10
.
70
6.
8
3
0.
7
3
0.13
7.
1
380
.
3435
1.91
0.334
0.
3
728
-
0.986635
-
13
5
1
0
.
00
3
.
40
4.
1
9
0.
2
9
0.13
4.
3
790
.
3449
1.421
0.335
0.
2
786
-
1.278018
-
14
6
1
0
.
00
3
.
40
0.
9
4
0.
0
9
0.32
0
.
98240
.
4614
-0.110.439
0.
9
988
-0.001162
-
15
7
0
.
10
0.
6
.
0
6 .41
.
6271
0
.
5332
-0.59 .5
0.
3
105
-
1.169726
0.6
10.75
0.04
-
16
8
0
9
.
60
10.
7
5
0.
3
5
0.06
11.
2
35
0
.
3227
2.369
0.315
1.
1
954
0.178512
0.35
17
9
1
0
.
00
1
.
60
0.
0
4
0
0.00
.
0418
0
.
3175
-3.22 .31
1
0
1.60
0
18
10
1
.
00
5.00
10.00
10
.
00 10.
4
2
10.42
0.
5
.07
10
.
89
10.89
0
.
3254
0.3254
2.338
0.317
0.
4
453
0.4453
-0.80903
0.5
36
28
1
10
.
00
10.00
20
.
00
22.
5
6
0.
1
6
0.16
0.02
23.
5
77
23.577
0.
3
18
0.318
3.112
0.31
0.
3
493
0.3493
-
1.051828
20.00
22.56
-
37
29
1
15
.
00
15.00
20
.
00
20.00
20.
3
4
20.34
0.
4
7
0.03
21.
2
57
21.257
0
.
3194
0.3194
3.008
0.312
0.
3
163
0.3163
-1.151112
0.47
-
38
30
0
36
.
80
36.80
21.
3
7
21.37
1.
2
.05 2.
3
34
22.334
0.
3
22
0.322
3.057
0.314
0.
2
761
0.2761
-
1.286883
1.2
-
39
31
0
43
.
00
24.
5
9
24.59
1.
3
3
0.05
25.
6
99
25.699
0
.
3213
0.3213
3.197
0.313
0.
2
523
0.2523
-
1.377071
43.00
1.33
-
40
32
0
10
.
00
10.00
13.
9
4
13.94
0.
3
5
0.04
14.
5
69
14.569
0
.
3206
0.3206
2.63
0.313
0.
7
376
0.7376
-0.304418
0.35
-
41
42
43
Notes:
(1) Rows 19 through 35 are skipped to save space.
(2) The setting in Solver is "Maximize the value in Cell P9 by changing the values in Cells I6 and J6".
Figure 4.8
Spreadsheet template for calibrating the model correction factor for predicting liquefaction-
induced settlement.
evaluating the proportion of liquefied soils (
Q
p
) in the real world (population). Nevertheless,
using the same value of
Q
p
consistently when developing liquefaction prediction models can
mitigate the effect of sampling bias and make more comparable those models derived based
on different databases.
It is worth repeating the limitations of the principle of maximum likelihood that were
articulated by Cam (1990). For example, it is not axiomatic that any principle, including the
maximum likelihood principle, can always provide a sensible statistical estimation of model
parameters. It is also important to be suspicious of a statistical estimation if the results change
abruptly through the suppression of a single observation. Finally, it is often helpful to first try
a crude but reliable procedure to locate the general area in which the parameters lie and then
refine that estimate using a more elegant method such as the maximum likelihood principle.
aCknoWleDgMentS
The first author acknowledges the National Science Foundation and U.S. Geological
Survey for their multiple grants that have supported his ongoing studies on soil liquefaction
Search WWH ::
Custom Search