Maximum likelihood principle and its application in soil liquefaction assessment - Risk and Reliability in Geotechnical Engineering - page 212

since 1997. The third author thanks the National 973 Basic Research Program of China
(2011CB013800, 2014CB049100) for the support of his research detailed in this chapter.
Much material presented in this chapter was the results of re-analysis of the first author's
prior work and the collaborative work by the first author and his collaborators, Dr. Jianye
Ching and Dr. Chieh-Sheng Ku. The authors thank Dr. Ching and Dr. Ku for their contribu-
tions, Mr. Wenping Gong, Dr. Zhe Luo and Dr. Lei Wang for reviewing the manuscript, and
Mr. Godfrey Kimball for providing the requisite editorial assistance.

aPPenDIX 4a: MoDel oF robertSon anD
WrIDe (1998) anD robertSon (2009)

CSR is the adjusted cyclic stress ratio defined as

σ
σ

a 1 1

vo
vo

max

CSR = 065 . () MSF r

d

′ g K

σ

where
σ vo , σ vo are the vertical total and effective overburden stresses, respectively

g the acceleration of gravity
a max the peak ground surface acceleration (unit: g)
r d the depth-dependent shear stress reduction factor
MSF the magnitude scaling factor
K σ the overburden correction factor for CSR ( K σ = 1 for

′

σ vo ′ < 1 atm)

The terms r d , MSF, and K σ follow the definitions provided in Youd et al. (2001). For MSF,
the lower-bound equation is used

MSF = 10 224

. .

M w

2 56

where M w = moment magnitude.
Though CSR as defined above is often denoted as CSR 7. 5 , for simplicity, CSR is used in
this study. In a deterministic model, as in the Robertson and Wride method, CRR is evalu-
ated and compared with CSR to obtain a measure of the liquefaction potential.
Let q c denote the raw cone resistance, which is generally in MPa, but may require con-
version into kPa when used with other parameters to derive the dimensionless parameters
such as Q t and q t1N . Let u 2 denote the penetration pore pressure (kPa). Let q t = q c + (1 − a ) u 2
denote the corrected cone resistance, where a is the area ratio of the cone used (in this study,
a = 0.85). In the Robertson and Wride model, CRR is computed as

‡
ˆ
Š

0 833 . [( q ) / 1000 ] + 005 . q ≤ 50

t1N,cs t1N,cs

CRR =

93 [( q ) / 1000 ]

3

+ 008 0 . ≤ q t1N,cs < 160

t1N,cs

where

q = K q

t1N,cs c t1N