Environmental Engineering Reference
In-Depth Information
F
2
(ϕ)
Marginal CDF of ϕ
f
i
(.)
Marginal PDF of
X
i
f
1
(
c
)
Marginal PDF of
c
f
2
(ϕ)
Marginal PDF of ϕ
f
(
x
;
p
,
q
)
Marginal PDF of
X
with distribution parameters
p
and
q
F
i
−1
(.
Inverse CDF of
X
i
g
(.)
Performance function
k
1
Number of distribution parameters
k
2
Number of copula parameters
K
a
Coefficient of active earth pressure
m
Sample size of simulated data
M
resisting
Resisting moments
M
overturning
Overturning moments
M
(
u
1
,
u
2
; θ)
First derivative of
C
(
u
1
,
u
2
; θ) with respect to
u
2
n
Dimension of
X
N
Sample size of measured data
PDF
Probability density function
P
(.)
Probability
P
a
Active earth thrust
p
f
Probability of failure
p
,
q
Marginal distribution parameters
p
f
Gaussian
Probability of failure produced by Gaussian copula
Q
Quick direct shear test
Q
Upper triangular Cholesky factor of
r
matrix
r
Correlation matrix underlying the Gaussian copula
sign(.)
Indicator function
UU
Unconsolidated-undrained triaxial compression test
u
Correlated standard uniform vector [
U
1
,
U
2
, …,
U
n
]
U
i
i
ith component in
u
= [
U
1
,
U
2
, …,
U
n
]
U
Standard uniform variable
v
Uncorrelated standard uniform vector [
V
1
,
V
2
, …,
V
n
]
W
1
,
W
2
Component weights of the retaining wall
Sample means of
X
1
and
X
2
x
12
,
X
Random vector of [
X
1
,
X
2
, …,
X
n
]
X
i
ith component in
X
= [
X
1
,
X
2
, …,
X
n
]
X
Uncertain soil parameter
y
Correlated standard normal vector [
Y
1
,
Y
2
, …,
Y
n
]
Z
Uncorrelated standard normal vector [
Z
1
,
Z
2
, …,
Z
n
]
reFerenCeS
Abd Alghaffar MA, Dymiotis-Wellington C. Time-variant reliability of retaining walls and calibration
of partial factors.
Structure and Infrastructure Engineering
2007; 3(3): 187-198.
Akaike H. A new look at the statistical model identification.
IEEE Transactions on Automatic Control
1974; 19(6): 716-723.
Ang AH-S, Tang WH.
Probability Concepts in Engineering Planning and Design, Vol. II: Decision,
Risk, and Reliability
. John Wiley and Sons: New York, 1984.
Baecher GB, Christian JT.
Reliability and Statistics in Geotechnical Engineering
. John Wiley and Sons:
New York, 2003.
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