Environmental Engineering Reference
In-Depth Information
m
i
Sample mean of Xi
i
or Y
i
N(μ, σ
2
)
Normal distribution with mean = μ and variance = σ
2
n
Sample size
N
SPT-N value
n
ij
Number of the bivariate (Xi,
i
, X
j
) data points
N
kE
Cone factor = (
q
t
-
u
2
)/
s
u
N
kT
Cone factor = (
q
t
- σ
v
)/
s
u
OCR
Overconsolidation ratio
P(⋅)
Probability
p
p
-Value in hypothesis testing
P
a
One atmosphere pressure (=101.3 kPa)
PDF
Probability density function
PI
Plasticity index
Q
d
Mahalanobis distance
q
t
Corrected cone tip resistance
s
Sample standard deviation
s
i
Sample standard deviation of Xi
i
or Y
i
SPT
Standard penetration test
S
t
Sensitivity
s
u
(mob)
In situ
undrained shear strength mobilized in embankment and slope
SU, SB, SL
Three members for the Johnson distribution
s
u
Undrained shear strength
s
re
Remolded undrained shear strength
t
η
η-Percentile of Student's
t
-distribution
U
Uniform [0, 1] random variable
u
Upper triangle Cholesky factor of
C
matrix
u
0
Hydrostatic pore pressure
u
2
Pore pressure behind the cone
x
η
η-Percentile of standard normal distribution
X
(
k
)
kth sample of X
X
(Correlated) standard normal vector (X
1
, X
2
, …, X
d
)
T
X
(Standard) normal random variable
X
[
i
]
ith partition vector of
X
X
i
ith component in
X
= (X
1
, X
2
, …, X
d
)
T
X
n
Normalized X [=(X -
b
X
)/
a
X
]
X
r
Rank of X
y
η
η-Percentile of Y
Y
(
k
)
kth sample of Y
y
Random vector of (Y
1
, Y
2
, …, Y
d
)
T
Y
Uncertain soil parameter
Y
i
ith component in
y
= (Y
1
, Y
2
, …, Y
d
)
T
Y
n
Normalized Y [=(Y -
b
Y
)/a
Y
]
Z
Uncorrelated standard normal vector (Z
1
, Z
2
, …, Z
d
)
T
σ
v
Total vertical stress
reFerenCeS
Arslan, O. 2004. Family of multivariate generalized t distributions.
Journal of Multivariate Analysis
,
89(2), 329-333.
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