Environmental Engineering Reference
In-Depth Information
ϕ
Friction angle
μ
Mean value
λ
Mean value of ln(Y)
μ
Mean vector (μ
1
, μ
2
, …, μ
d
)
T
δ
Pearson product-moment correlation coefficient
α
Significance level of the test
ρ
Spearman rank correlation coefficient
σ
Standard deviation
ξ
Standard deviation of ln(Y)
κ
The transformation between X and Y for the Johnson distribution
σ
v
Vertical effective stress
′
Φ
−1
(.)
Inverse cumulative distribution function for standard normal
χ
2
η-Percentile of χ-squared distribution
σ
2
Variance
μ
i
Mean value of Xi
i
or Y
i
σ
i
Standard deviation of Xi
i
or Y
i
δ
ij
Pearson product-moment correlation coefficient between Xi
i
and X
j
ρ
ij
Spearman rank correlation coefficient between Xi
i
and X
j
μ
MLE
Maximum likelihood estimate for μ
σ
MLE
Maximum likelihood estimate for σ
δ
MLE
Maximum likelihood estimate for δ
σ
p
Preconsolidation stress
′
(
)
qu
t
-
/
σ
Effective cone tip resistance
2
v
(
q
t
- σσ
)
/
′
Normalized cone tip resistance normalized
v
v
′σ
Normalized excess pore pressure
(
uu
v
2
−
)
/
0
μ
update
Updated (conditional) mean vector
|
C
|
Determinant of
C
matrix
Parameters for the Johnson distribution
a
bbab
XX XYY
,
,
*
,
,
B
Bootstrap sample size
B
q
Pore pressure ratio = (
u
2
-
u
0
)/(
q
t
- σ
v
)
C
Correlation matrix (or covariance matrix)
C
[
ij
]
(
i
,
j
) Partition of
C
matrix
C
−1
Inverse of
C
matrix
CDF
Cumulative distribution function
COV(.,.)
Covariance
COV
Coefficient of variation
CPTU
Piezocone penetration test
C
update
Updated (conditional) covariance matrix
d
Dimension of X (or dimension of Y)
E
u
Undrained modulus
F(.)
Cumulative distribution function (CDF)
f
(.)
Probability density function (PDF)
F
χ
2
CDF of the χ-square distribution with d degrees of freedom
F
n
(⋅)
Empirical cumulative distribution function
H
0
Null hypothesis
H
1
Alternative hypothesis
I(⋅)
Indicator function
iid
Independent identically distributed
LL
Liquid limit
m
Sample mean
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