Environmental Engineering Reference
In-Depth Information
Table 2.4
(Continued) Measured shear strength parameters for several typical stratums in the Hangzhou
area of China
Q (10 data)
CQ (10 data)
UU (10 data)
CU (10 data)
Stratum
number
Test
number
c
(kPa)
ϕ
(°)
c
(kPa)
ϕ
(°)
c
(kPa)
ϕ
(°)
c
(kPa)
ϕ
(°)
5
54.1
13.6
68.5
14.5
81.5
8.1
85.7
8.2
6
37.6
15.2
36.3
22.7
53.4
11.4
68.0
12.4
7
29.4
25.1
31.7
28.0
69.2
13.4
73.4
19.0
8
44.1
9.6
57.9
12.9
78.8
7.1
84.9
6.4
9
28.8
21.7
26.6
23.4
62.3
13.8
65.1
17.7
10
49.6
8.4
64.1
9.8
80.8
5.9
92.6
8.3
COV
0.24
0.35
0.32
0.34
0.16
0.32
0.13
0.39
ρ
−
0.720
−
0.723
−
0.485
−
0.765
−
0.584
−
0.644
−
0.378
−
0.467
τ
Source: After Wu CF, Zhu XR, Liu XM.
Chinese Journal of Geotechnical Engineering
2005; 27(1): 94-99 (in Chinese).
Note: Q, Quick direct shear test; CQ, consolidated-quick direct shear test; UU, unconsolidated-undrained triaxial com-
pression test; CU, consolidated-undrained triaxial compression test.
Table 2.5
PDFs and domains of distribution parameters associated with the selected four distribut
if
ons
Range
of p
Range
of q
Distribution
f (x; p, q)
μ
and
σ
2
Trunc
Normal
(
−∞
,
∞
)
(0,
∞
)
p
,
2
q
2
2
µσ
=
=
1
2
1
2
xp
q
−
p
q
π
exp
−
1
−−
Φ
q
Log
normal
(
−∞
,
∞
)
(0,
∞
)
exp(
p
05
.
q
2
),
2
µ
=
+
1
1
2
ln
xp
q
−
π
exp
−
2
[exp(
q
2
) exp(
1
2
p
q
2
)
qx
2
σ
=
−
+
Trunc
Gumbel
(
−∞
,
∞
)
(0,
∞
)
q
exp{
−−−−−
−−
q xp
(
)
exp[
qx p
(
)]}
p
0 5772
.
q
,
2
2
(
6
q
2
)
µ
=+
σ
=
π
{ xp[
1
exp(
pq
)]}
Weibull
(0,
∞
)
(0,
∞
)
p
(
11
),
[(
q
q
−
1
q
µ
=+
=
Γ
q
p
x
p
x
p
−
exp
2
p
2
12
q
)
2
(
11
q
)]
σ
Γ
+ −+
Γ
Note:
Φ
denotes the standard normal distribution function;
Γ
is the gamma function.
Table 2.6
AIC and BIC values for the TruncNormal, Lognormal, TruncGumbel, and Weibull distributions
TruncNormal
[AIC, BIC]
Lognormal
[AIC, BIC]
TruncGumbel
[AIC, BIC]
Dataset
Parameter
Weibull [AIC, BIC]
CD
c
569.36, 573.65
599.31, 603.60
599.53, 603.81
569.12, 573.41
300.88, 305.17
300.26, 304.55
314.60, 318.89
315.93, 320.21
ϕ
CU
c
613.31, 617.63
678.29, 682.61
632.61, 636.93
617.04, 621.35
340.35, 344.67
342.19, 346.50
357.50, 361.82
345.03, 349.35
ϕ
UU
c
667.96, 672.18
677.13, 681.35
680.20, 684.43
667.49, 671.71
345.39, 349.62
339.06, 343.29
339.17, 343.39
344.46, 348.68
ϕ
Note: The AIC and BIC values are bold if the corresponding distribution is preferred.
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