Maximum likelihood principle and its application in soil liquefaction assessment - Risk and Reliability in Geotechnical Engineering - page 178

Maximum likelihood principle
and its application in soil
liquefaction assessment
Charng Hsein Juang, Sara Khoshnevisan, and Jie Zhang
4.1 IntroDuCtIon
The occurrence of soil liquefaction and ground failure during great earthquakes is one of
the most crucial factors in the subsequent economic devastation and loss of lives that can
result from such catastrophic events. Due to the difficulty and expense of securing and
testing high-quality undisturbed samples of soils, empirical methods based on in situ tests
such as the standard penetration test (SPT) or the cone penetration test (CPT) remain the
dominant approaches in engineering practice for evaluating the liquefaction potential and
its effect. Indeed, the simplified procedure pioneered by Seed and Idriss (1971) is perhaps
the method most widely used over the last 40 years for evaluating liquefaction potential.
In this procedure, developed from field observations and field and laboratory tests with a
strong theoretical basis, the liquefaction potential of a soil is most often expressed as a fac-
tor of safety ( F S ), which is defined as the ratio of cyclic resistance ratio ( CRR ) over cyclic
stress ratio ( CSR ). In the context of liquefaction assessment, CSR represents a dimensionless
measure of the cyclic shear stress applied to a soil through seismic loading, and CRR repre-
sents the corresponding measure of the cyclic shear resistance of the soil. In a deterministic
assessment of the liquefaction potential, liquefaction occurs if F S ≤ 1 and does not occur if
F S > 1. In many situations, it is desirable to express the liquefaction potential in terms of
probability of liquefaction ( P L ) rather than with a factor of safety ( F S ). Examples of how this
expression of liquefaction potential may be used can involve: (1) mapping the liquefaction
potential in a district where it is easier to interpret the liquefaction potential in terms of
probability rather than factor of safety; (2) post-event investigations where the conservative
bias that was typically built into existing deterministic models becomes undesirable, as it
may mislead the assessment; and (3) performance-based earthquake engineering, where the
unbiased probability at the component level is required. Thus, there is definitely a need for
estimating the probability of liquefaction.
Many approaches have been taken to develop simplified probabilistic models for liquefac-
tion potential evaluation; for example, discriminant analysis (Christian and Swiger 1975),
logistic regression (Liao et al. 1988; Lai et al. 2006), Bayesian mapping (Juang et al. 1999,
2000, 2002), and the Bayesian regression approach (Cetin et al. 2002; Moss et al. 2006;
Boulanger and Idriss 2012). Underlying many of these approaches is the maximum likeli-
hood principle (Edwards 1974; Aldrich 1997; Stigler 2007), which is widely used in sta-
tistical estimation. The ability to consistently consider multiple types of data for model
calibration makes the maximum likelihood method particularly suitable for developing liq-
uefaction probability models. While the maximum likelihood method is increasingly used
by researchers in liquefaction analysis and other fields in geotechnical engineering, there is
no easy-to-access publication to elucidate how this method works and how it can be used
efficiently. This missing element hinders the wider use of the maximum likelihood method
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