Maximum likelihood principle and its application in soil liquefaction assessment - Risk and Reliability in Geotechnical Engineering - page 214

SPT = standard penetration test
T = n × n correlation matrix with element in the i th row and j ith column denoted by T ij
T ij = correlation coefficient between ln( c u ) at location i and location j
w L = weighting factor to apply to liquefied cases in the weighted likelihood function
w NL = weighting factor to apply to non-liquefied cases in the weighted likelihood function
α = model correction factor
β a = actual reliability index
β c = calculated reliability index
δ a = COV of S a
δ α = COV of α
Δ = distance between two points in a random field
Δ z i = thickness of the i ith layer
ε β = correction factor for reliability index
ε vi = volumetric strain of the i ith layer
θ = vector denoting uncertain parameters to be estimated
θ * = value of θ where the likelihood function is maximized
λ = mean of the logarithm of a lognormal random variable
Λ = n-dimensional column vector with all elements being λ
μ = mean of a random variable
μ a = mean of S a
μ p = mean of S p
μ α = mean of α
ξ = standard deviation of the logarithm of a lognormal random variable
ρ = correlation coefficient
ρ(Δ) = correlation function
σ = standard deviation of a random variable
σ a = standard deviation of S a
σ p = standard deviation of S p
σ α = standard deviation of α
σσ
vo

, ′ = vertical total and effective overburden stresses, respectively
φ = friction angle
Ω = correlation distance

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